1. MSci Project Report: Looking for New Physics at the LHC Using
Tau Leptons
Sophie Middleton
Supervised by Dr David Colling
Assessed by Dr Morgan Wascko
April 30, 2012
2. Abstract
The following report presents a search for the standard model Higgs boson in real CMS data taken during
the 2011A run with an integrated luminosity of 2094 pb 1
. The search aims to look for the di-tau decay of
a neutral Higgs boson prodcued via vector boson fusion using the e⌧had and µ⌧had tau decay channels.
Initially, work is done to establish accurate estimates of backgrounds to this process including the Z ! ⌧⌧
decay, W+Jets and QCD backgrounds. Estimates of the Z ! ⌧⌧ are derived from the Z ! ee, µµ data;
cross-sections are derived from data for all three processes and are shown to be consistant with each other
and theoretical predictions.
No excess is found in the observed tau-pair invarient mass for either tau decay channel. This results in
upper limits being placed on Higgs boson production cross section at a 95 % confidence level for Higgs
masses in the range 115-140 GeV/C2
.
3. Declaration
The majority of the work within this report is my own, however, specific credit must go to my fellow MSci
students: David Kirkpatrick and Edward Evans who helped with calculations of the Z ! µµ and ee cross-
sections which were used in the final analysis. Everything else unless explicitly referenced is my own work
and interpretation of the results provided.
The data used is 2011A CMS data which was taken at CERN during the first half of 2011 and the ntu-
ple ROOT trees used for the analysis as well as the Monte Carlo simulations were provided by Mike Cutajar
who I must acknowledge for his assistance in the statistical analysis as well as for providing sections of
example code.
Sophie Middleton
I
4. Acknowledgments
First of all I would like to thank my supervisor, Dr David Colling, for giving me the opportunity to work on
one of the most revolutionary experiments every built and for his guidance throughout; work on my MSci
project has given me a great insight into the world of particle physics research at its most sophisticated level
and has inspired me to pursue further study in this field.
I must also thank Mike Cutajar for his assistance and expertise in the use of LandS which was used to
establish limits on the Higgs cross-section.
II
7. Chapter 1
Introduction: Standard Model and
Higgs Phenomenology
1.1 Introduction
The project is focused on the use of the Compact Muon Solenoid (CMS) detector, based at the LHC in
CERN, for detecting charged leptons, particularly, tau leptons and their use in the search for the standard
model Higgs boson. The di-tau decay channel of the standard model Higgs has a moderate branching fraction
of ⇡10% in the low mass region this along with the low levels of background when compared to heavy quark
processes make it a good channel for discovery.
From the latter part of the twentieth century research into particle physics has taken place using high
energy accelerators, these allow subatomic particle to be collided at high energy e↵ectively ‘recreating the
conditions shortly after the Big Bang.’ This allows analysis of the particles and forces that have shaped the
universe since. The LHC is currently the highest energy collider every built, with a design centre-of-mass
energy of 14TeV, making it incredibly useful, not just in Higgs searches but for SUSY searches as well as
analysis of CP violation and searches for even more exotic physics.
CMS is one of two general purpose detectors (the second being ATLAS) which is primarily focused on
Higgs searches. This builds on decades of previous research at CERN, with experiments such as LEP in the
1990’s, as well as the Tevatron experiments. These experiments combined have already made huge steps in
excluding, at a 95 % confidence level, Higgs masses below 114GeV/c2
and above 200GeV/c2
as well as a
region around 150 160GeV/c2
.The CMS and ATLAS experiments have already provided huge amounts of
data leading to further mass regions been excluded at a 95 % confidence level.
The Higgs Boson is a result of the Higgs Mechanism which was hypothesized to introduce spontaneous
symmetry breaking to account for the fact that the weak force bosons (W±
, Z0
) posses mass while the
strong and electromagnetic force carriers do not. Finding (or excluding) the standard model Higgs boson is,
therefore, of extreme importance to our understanding of the universe.
1.2 Aims
• To familiarize oneself with the ROOT Framework and C++ as a language for interpreting data from
high energy physics experiments in a LINUX environment
• To Understand the mathematical derivation of concepts within the standard model formulation includ-
ing: QED, QCD, Electroweak theory and the Higgs Mechanism
• To apply e↵ective analytical techniques to real and simulated data
• To compare and inspect results from detector data and Monte Carlo to estimate signal and background
yields
• To carry out statistical analysis using LandS to put limits on the probability of there being a Higgs
particle in the 2011A CMS data
1
8. Project Report Introduction: The Higgs Boson 2
1.3 The Standard Model
The standard model of particle physics brings together two major extant theories: electroweak theory, which
proposes that the electromagnetic and weak forces are manifestations of the same fundamental process , and
quantum chromo-dynamics (QCD), the theory of strong interactions. The standard model proposes that
these forces are a result of the exchange of force mediating gauge bosons (s=1). Strong interactions are
mediated by gluons, electromagnetic interactions by the photon and the weak force by the W±
and Z bosons.
The standard model is a quantum field theory formulated on the SU(2)c ⇥ SU(2)L ⇥ U(1)Y gauge group,
where SU(3)c represents QCD and SU(2)L ⇥ SU(3)Y represents the electroweak theory. C defines colour,
the strong equivalent of charge, L defines a left-handed current and Y defines weak hyper-charge involved in
electroweak interactions.[1][2]
Photons and gluons are massless, however, the weak gauge bosons must posses mass otherwise the cross
section of the weak interaction would diverge to infinity. This presented somewhat of a problem in the
course of electroweak unification and to account for weak boson mass spontaneous symmetry breaking was
introduced and proposes that all massive particles acquire their mass via the Higgs Mechanism (section 1.5).
The table below summarizes the fundamental particles in the standard model:
Fermion/Boson Type Particles Spin Charge Interactions
Fermion Lepton ⌫e, ⌫µ, ⌫⌧ 1/2 0 weak
e, µ, ⌧ 1/2 -1 weak, EM
Fermions Quarks u,c,t 1/2 +2/3 EM, weak, strong
d,s,b 1/2 -1/3 EM, weak, strong
Fermion/Boson Interaction Particles Spin Charge Mass(GeV/c2
)
Boson EM 1 0 0
Boson Strong 8 gluons 1 0 0
Boson Weak W+
1 +1 80.4
W 1 -1 80.4
Z0
1 0 91.2
Boson Higgs 0 0 ???
In the standard model there are two types of fundamental half-integer spin fermions: leptons, quarks
as well as the described spin-1 force mediating bosons. Quarks may be distinguished from leptons by there
strong interactions; each quark must posses a “strong charge” named after one of three colours: red, blue
or green. In total the SM predicts 61 elementary particles: 36 quarks, 12 leptons, 12 force mediator and 1
Higgs.
Although, to date, the SM has proven successful in terms of experimental proof it is, however, not a fully
unified theory in that it is not built around a single representation with one coupling constant as well as
being unable to fully account for neutrinos masses and the extent of CP-violation in the universe as well as
not providing a viable dark matter candidate or accounting for the Higgs heirarchy problem. [3][4]
1.4 Quantum Field Theories
Quantum Field Theory, or QFT, was initially proposed by Paul Dirac in the late 1920’s; QFT builds quan-
tum mechanics into a theory of canonically quantized fields operating on a vacuum thus correcting several
limitations to quantum mechanics such as the possibility of particle creation/annihilation and the negative
probabilities which arise when special relativity is incorporated [3]. The standard model formulation relies on
quantum field theories constructed upon gauge invariant Lagrangian. In field theory the Euler-Lagrangian
equations of motion is expressed as:
@µ(
@L
@(@µ )
)
@L
@
= 0 (1.1)
where @µ is the space-time four vector and the field is a function of xµ. The Lagrangian density L for
boson fields is given by the Klein-Gordon Lagrangian:
LKG =
1
2
(@µ )(@µ
)
1
2
m2 2
= 0 (1.2)
Applying the Euler-Lagrange eqn. gives:
@µ@µ
+ m2
= 0 (1.3)
9. Project Report Introduction: The Higgs Boson 3
This is the expected Lorenz covariant Klein-Gordon eqn.
Similarly, one can derive the Lagrangian density for a free fermion field which is given by the Dirac
Lagrangian:
LDirac = ¯(i µ
@µ m) (1.4)
At the heart of the standard model is the principle of local gauge invariance: the idea that the laws
of physics are invariant under certain local phase transformations. Imposing local gauge invariance on
the Lagrangian gives the interaction between particles and introduces gauge fields as mediators of these
interactions. This will be shown in the next section for QED, QCD and the Electroweak cases.[1]
1.4.1 QED:Quantum Electro-Dynamics
Quantum Electro-Dynamics (QED) was developed to explain electromagnetic interactions in terms of boson
exchange. This was the first successful gauge theory and is based on the U(1) gauge group. The Lagrangian
density for the Dirac equation describing spin-1/2 fermions may be written as:
LD = i ¯ µ
@µ m ¯ (1.5)
which comprises of a kinetic term and a mass term, where and ¯ are the spinor and its adjoint fields
and µ are the Dirac gamma matrices. This Lagrangian is invariant under global U(1) gauge transformation,
however, it is not invarient under local gauge transformation, which may be written as:
! 0
= eiq✓(x)
(1.6)
where ✓ is a space-time dependent function with constant coupling factor q. Local gauge invariance can
be restored by introducing the covariant derivative:
Dµ = @µ + iqAµ (1.7)
where q is the electromagnetic coupling constant and Aµ is commonly known as the gauge field, a
compensating vector field necessary to balance the gauge freedom of [1]. Aµ has gauge freedom such that
it transforms as:
Aµ ! Aµ + @µ✓(x) (1.8)
Therefore, by enforcing that QED is invariant under local gauge (U(1)) transformation we have introduced
a new field , Aµ, which mediates the EM force.Aµ may be interpreted as the electromagnetic vector potential
meaning EM interactions can be understood in terms of photon exchange.
The Dirac Lagrangian (1.5) may now be written in the form of a new ’gauged’ Lagrangian:
LD = i ¯ µ
Dµ m ¯ = i ¯ µ
@µ q ¯ µ
Aµ m ¯ (1.9)
which is invariant under the local gauge transformation.
The gauge invariant kinetic term for the field Aµ can be introduced using a field tensor:
Fµ⌫ = @µA⌫ @µAµ (1.10)
meaning the complete QED Lagrangian may be written as:
LQED = i ¯ µ
@µ q ¯ µ
Aµ m ¯ 1
4
Fµ⌫Fµ⌫
(1.11)
where the third term describes the photon field interacting with fermions with strength q which is equiv-
alent to the electric charge of the fermion.
1.4.2 QCD: Quantum Chromo-Dynamics
QCD is the strong force equivalent of QED and can be formulated in an analogous way by requiring gauge
invariance. Beginning with a free Lagrangian denoted by:
L0 = i ¯j
µ
@µ j m ¯j j (1.12)
where j describes the quark field with color index j=1,2,3 (from now onward the j is dropped). However,
we are no longer looking at the U(1) gauge group, strong force is instead formulated on the non-abelian
SU(3)c group so the local transformation is given by:
10. Project Report Introduction: The Higgs Boson 4
! 0
= ei✓a(x)Ta
(1.13)
where ✓a(x) is the space-time dependent phase and Ta are the eight Gell-Mann matrices. A covariant
derivative which maintains the invariance of the theory can be constructed to compensate the local phase
transformation of :
Dµ = @µ + igstrongTaGa
µ (1.14)
where Ga
µ corresponds to 8 new gauge fields which mediate the strong interaction via gluon exchange.
Due to SU(3)c been an non-abelian group the gauge field now transforms as:
Ga0
µ = Ga
µ =
1
@µ✓a fabc✓bGc
µ (1.15)
where fabc are the structure constants of the group defined by the commutation relation of SU(3) gener-
ators:
[Ta, Tb] = fabcTc (1.16)
The complete Lagrangian density for QCD may be written as:
LQCD = i ¯j
µ
@µ j m ¯j j gs
¯ µ
TaGa
µ
1
4
Ga
µ⌫Gµ⌫
a (1.17)
where the tensor field is given by:
Ga
µ⌫ = @µGa
⌫ @⌫Ga
µ gstrongfabcGb
µGc
⌫ (1.18)
The last term does not appear in QED and arises from the non-abelian structure of the SU(3)c group
where the generators are matrices which do not commute. The third term of the QCD Lagrangian is
interpreted as gluon field Ga
µ interacting with the quarks. The quadratic term GµG⌫ describes how gluons
self-interact. Such self-interaction accounts for the divergent nature of the strong force which results in only
confined states of quarks being visible in nature.
1.4.3 Unifying the EM and Weak Forces: Electroweak Theory
Electroweak theory was originally formulated by Glashow, Weinberg and Salam in the 1960s and unifies
the electromagnetic and weak interactions. Electroweak theory is formulated under SU(2)c ⇥ U(1)Y gauge
invariance where Y describes the weak hyper-charge and is related to EM charge(Q) and weak Isospin (I3)
by the following relation:
Q = I3 +
Y
2
(1.19)
The covariant derivative which makes the Lagrangian invariant under SU(2)c ⇥U(1)Y gauge transforma-
tion takes the form:
Dµ = @µ + ig
⌧
2
Wµ + i
1
2
g0
Y Bµ (1.20)
This achieves the required local invariance when ⌧§
are the generators of SU(2) and Wµ and Bµ are the
gauge fields associated with SU(2) i.e fields associated with the weak and electromagnetic forces respectively.
The electro-weak field tensors are given by:
Wa
µ⌫ = @µ Wa
⌫ @⌫ Wµ g✏abc
Wb
µ Wc
⌫ (1.21)
Bµ⌫ = @µB⌫ @⌫Bµ (1.22)
This leads to an Electroweak Lagrangian density of the form:
LEW = iL¯µ
(@µ + ig
⌧
2
Wµ + i
1
2
g0
Y Bµ)L + iR¯µ
(@µ + i
1
2
g0
Y Bµ)R
1
4
Wµ⌫ W⌫µ 1
4
Bµ⌫Bµ⌫
(1.23)
where L and R describe left handed doublets and right handed singlets of fermionic fields.
The use of left handed doublets and right handed singlets accounts for the fact that the weak force
violating parity meaning only left-handed chirality fermion states interact with the SU(2) gauge field.
11. Project Report Introduction: The Higgs Boson 5
Wµ = (W1
µ, W2
µ, W3
µ) is a three component vector field. The physical electroweak fields associated with
the W±
, Z0
and are therefore defined as a combination of these four EM and weak gauge fields:
W±
=
r
1
2
(W1
µ ⌥ iW2
µ) (1.24)
Zµ = Bµsin✓w W3
µcos✓w (1.25)
Aµ = Bµcos✓w + W3
µsin✓w (1.26)
where ✓w describes the Weinberg angle, defined as tan 1
(g0
g ).
1.5 Spontaneous Symmetry Breaking and The Higgs Mechanism
In the previous formulation all gauge bosons appear massless since a mass term of the form an integer-spin
field of the form m2
AµAµ
is not invariant under the SU(2)L ⇥ U(1)Y gauge transformation. However, It has
been experimentally observed that the weak gauge bosons posses mass, therefore, to allow a massless photon
the symmetry of the electroweak theory needs to be broken. The Higgs Mechanism finds away to introduce
spontaneous symmetry breaking without destroying the gauge invariance of the electroweak theory and thus
provides a way for bosons to acquire mass by requiring that the symmetry of a system be spontaneously
broken when the vacuum state of the system is not invariant under local gauge transformation but the
Lagrangian density is.[1]
This may be accomplished by introducing a scalar field, ‘The Higgs field’, defined as a SU(2) doublet with
two complex scalar terms:
=
✓ +
0
◆
=
✓
1 + i 2
3 + i 4
◆
(1.27)
The Lagrangian density for this field is given as:
LHiggs = (Dµ )†
(Dµ
) VHiggs( †
) (1.28)
where Dµ is the electroweak covariant derivative described in equation 1.20 and V is the vacuum potential
which we assume has the form:
VHiggs = µ2 †
+ ( †
)2
(1.29)
By requiring that µ2
< 0 and > 0 the symmetry is no longer unique but takes the form of a continuous
ring in the complex plane.The vacuum expectation value for will occur at a potential minimum i.e. when
@V
@ † = 0 and is given by:
vacuum =
1
p
2
✓
0
v + h(x)
◆
, v =
r
µ2
(1.30)
where v is the vacuum expectation value(vev) and h(x)is the Higgs field expressed as a quantum fluctuation
about this vev. This is zero for the charged component and therefore preserves EM symmetry but non-zero
for the neutral component and therefore breaks electroweak gauge invariance this may be referred to as
spontaneous symmetry breaking.
If the expressions in 1.20,1.29 and 1.30 are substituted into the Higgs Lagrangian density and the covariant
derivative expanded the Higgs Lagrangian density after symmetry breaking is obtained:
@µh@µ
h +
1
8
(v + h)2
g2
(W1
µ + iW2
µ)(W1µ
iW2µ
) +
1
8
(v + h)2
(g0
Bµ gW3
µ gW3µ
) (1.31)
= @µh@µ
h 2µ2
h2
+h.o.t+
g2
µ2
4
W+µ
Wµ
g2
µ
2
p hW+µ
Wµ +
g2
µ2
8 cos✓2
w
Z0µ
Z0
µ
g2
µ
4
p
cos✓2
w
hZ0µ
Z0
µ+
g2
8cos✓2
w
h2
Z0µ
Z0
µ
(1.32)
Here, the first term describes the free Higgs boson field, the 2µ2
h2
, g2
µ2
4 W+µ
Wµ and g2
µ2
8 cos✓2
w
Z0µ
Z0
µ
terms describe the masses of the H0
, W±
and Z0
fields respectively. The higher order terms (h.o.t) predict 3
and 4 point Higgs boson self-interactions and the remaining terms describe the interaction between the Higgs
and weak bosons. Since there is no photon mass term in the Lagrangian this allows the photon to remain
massless while the weak bosons now have mass.
12. Project Report Introduction: The Higgs Boson 6
A consequence of the Higgs mechanism and the Higgs field is the manifestation of Higgs quanta, this
excitation is known as the Higgs boson and is the final missing particle of standard model.
The Higgs mass is an unknown, it must be less than 1TeV due to measurements of the WW scattering
cross section. To cancel a mass of 1TeV the bare Higgs mass would have to be 1019
GeV/c2
, which is known
as the fine tuning problem. To solve this various SUSY theories have been derived in which each boson has
a corresponding fermion of equal mass and quantum numbers (except spin), but no such superpartners have
yet been found.
1.6 Higgs Production at the LHC
This project aims to analyze the Z! ⌧⌧ channel using 2011A CMS data looking for an excess of events
which could suggest the presence of a Higgs particle produced via Vector Boson Fusion VBF(qq!Hqq). As
can be seen in the Feynmann diagram in figure 1.3 vector boson fusion is so called as vector bosons form
from the partons of the protons in the LHC beam; these then fuse to form the Higgs. The remnants of the
quarks hadronize into two jets in the forward part of the detector - these jets can be used as indicators that
a VBF event has occurred. VBF production, despite having a cross section at least an order of magnitude
lower than gluon fusion in the low Higgs mass range i.e. below mH = 2mw (see Figure 1.1), is a promising
channel for Higgs discovery due the two outgoing jets which provide a characteristic signature for Higgs
production. VBF jets are mainly in the forward direction with hadronic activity being heavily suppressed in
the central region due to the lack of colour exchange between the leading quark jets. Therefore, VBF can
be distinguished from background QCD by looking for a large rapidity gap between jets along with use of a
‘central jet veto’.
Figure 1.1: Relative cross sections for Higgs production
as functions of Higgs mass [1]
Figure 1.2: Relative Branching Ratios of the Higgs as
functions of Higgs mass [1]
This Higgs particle can only be detected at CMS by identifying its decay products, figure 1.2 shows the
relative branching ratios for Higgs decays. In the low mass range, the decay width of any fermionic decay
of the Higgs is proportional to the fermions mass squared; therefore, the heaviest fermions have the largest
branching fraction. The H !bb channel has the highest branching ratio in this range, however, this channel
su↵ers from large amounts of QCD background and therefore is not the best channel for Higgs discovery. The
H! ⌧⌧ along with the described VBF conditions will allow background from lepton+jet processes arising
from W/Z production via QCD to be removed, therefore allowing a relatively clean signature of the Higgs.
Figure 1.3: Feynmann Diagrams of main source of higgs production in the LHC a)gluon fusion b)VBF c)tt
fusion d)W/Z associated production [1]
13. Chapter 2
The CMS Detector Design
2.1 The Large Hadron Collider ( LHC)
The Large Hadron Collider is a 27km circumference proton-proton collider based at CERN, the LHC is cur-
rently running at
p
s =7 TeV but will eventually run at
p
s=14TeV making it the highest energy accelerator
on Earth. The Compact Muon Solenoid (CMS) is one of 2 general purpose detectors at the LHC and its
primary aim is detection of the Standard Mode Higgs boson.
2.2 CMS Detector
The distinguishing feature of the CMS detector is a 3.8T superconducting solenoid, 6m in internal diameter.
Within the volume of this field are a series of sub-detectors, starting nearest to the beam interaction point,
these are: the silicon pixel tracker, the silicon strip tracker, the Electromagnetic Calorimeter(ECAL) and
the Hadronic Calorimeter(HCAL). Muon production is detected in gas-ionization detectors embedded in the
steel return yoke, these components will be described in detail later in the chapter.
CMS uses a right-handed co-ordinate system in which the origin is at the nominal interaction point. The
x axis points to the centre of the LHC while the y axis points perpendicular to the LHC plane and the z
axis points along the counterclockwise beam direction. The polar angle is measured from the positive z axis
and the azimuthal angle is measured in the xy plane. Pseudo-rapidity is defined as: ⌘ = ln[tan(✓/2)] and
pT =
q
(p2
x + p2
y) where |⌘| is used instead of theta as it is Lorentz invariant.[5]
Figure 2.1: An Overview of the CMS detector at
CERN [1])
Figure 2.2: Di↵erent types of particles detected in dif-
ferent parts [1]
2.2.1 The Tracker
Within a magnetic field of known strength (3.8T) the momentum of a charged particle may be reconstructed
from measurements of the radius of its track through this field. The CMS tracking system makes use of
this to achieve precise measurements of the trajectories and therefore the momentum of charged particles
7
14. Project Report The CMS Detector Design 8
allowing precise reconstruction of vertices hence the need for high granularity and fast response time. The
inner tracker measures charged particle tracks within the range |⌘| < 2.5.
The tracking system comprises of two trackers: the pixel detector and the silicon strip detector. The
pixel detector is the first detection layer surrounding the beam pipe and consists of 3 concentric cylindrical
layers of silicon pixel sensors as well as a pixel end-cap disk placed on each end. A total of 66⇥106
pixels are
used across the whole subsystem, this provides high 3D resolution that is ideal for identification of primary
vertices and track seeding. Surrounding this is the silicon strip detector made of silicon micro-strip sensors
positioned in 10 layers of cylindrical barrels and 12 layers in the endcap disks. The barrel modules have
di↵erent sizes and contain di↵erent numbers of strips but the separation is kept at 100 200µm to ensure
good hit position resolution. When a charged particle passes through the strip detector electron-hole pairs
are created, the silicon is doped with impurities and a p-n diode junction is created which is held with a
reverse bias so as to e ciently collect the charge liberated. The electron/hole pairs are read out from the
strip.
The CMS tracker consists of 1440 silicon pixel and 15148 silicon strip detector modules and provides
an impact parameter resolution of approximately 15µm and a transverse momentum resolution of about
1.5 % for 100 GeV particles [4]. The pixel detector is required close to beam pipe for higher resolution as
here it experiences a high particle flux, further out the occupancy drops meaning the micro-strip detector is
su cient. The performance of the combined system give >95 % reconstruction e ciency as well as a radial
vertex resolution of 20 µm and longitudinal vertex resolution of 100µm for particles of 10 < E < 100GeV
[4].
Figure 2.3: Resolution of track parameters for single muons with transverse momenta of 1,10,100GeV: trans-
verse momentum resolution (left) and global track reconstruction e ciency (all tracks) (right) [4]
(right).
Figure 2.1 shows the reconstruction e ciency as a function of ⌘, the e ciency is about 99 % up to
|⌘| = 1.6. This e ciency drop is mainly due to the reduced coverage by the pixel forward disks. The tracker
provides coverage up to |⌘| = 2.5. Momentum resolution may be parameterized by:
pT
pT
= apT + 0.5% (2.1)
where a=15 for ⌘ <1.6 and 60 for ⌘ between 1.6 and 2.5. This change in a is due to change in the the
radiation length(X0) of material inside the active volume of the tracker which increases from approx. 0.4X0
at |⌘| = 0 to 1X0 at |⌘| = 1.6, before decreasing to⇡ 0.6X0 at |⌘| = 2.5 . At a transverse momentum
of 100GeV multiple scattering in the tracker material accounts for 20-30 % of the transverse momentum
resolution while at lower momentum it is dominated by multiple scattering [4].
2.2.2 The ECAL
Electromagnetic showers occur when there is an exponential increase in particles at high energies. Initially,
a high energy photon undergoes pair production, producing an electron-positron pair which in turn radiate
a high energy photon. This ‘chain’ will continue over a length scale of X0 which is defined above. The
electromagnetic calorimeter detects such a shower by placing ionization detectors between sheets of dense
material (lead-tungstate) which will initiate this shower.
The electromagnetic calorimeter is crucial in the reconstruction of photons and electrons from ⌧ decay, in
order to do this accurately the ECAL is required to have both excellent energy resolution and high granularity.
CMS has chosen Lead Tungstate as a scintillation material and the ECAL is constructed in two regions: the
barrel at |⌘| < 1.479 and the endcap at 1.479 < |⌘| < 3, there is however, a transition region between 1.444
and 1.567. The barrel region comprises crystals of 25.8 X0 and a granularity of ⇥ ⌘= 0.00174⇥0.00174.
The endcap region is instrumented with a lead-silicon preshower detector which consists 2 orthogonal strip
detectors with a strip pitch of 1.9mm. On the whole, the ECAL has an energy resolution of > 0.5 % for
15. Project Report The CMS Detector Design 9
unconverted photons of energy greater than 100GeV. The energy resolution is greater than 3 % for the range
of electron used in this report.[4][5]
The Lead tungstate scintillation material has the required high density and small Moliere radius to provide
small lateral spread in the electromagnetic shower this is crucial in order to distinguish energy deposits from
di↵erent sources and achieve high position resolution. On average, 90 % of the shower created from a single
photon can be contained within one crystal. The amount of energy deposited in the ECAL is interpreted
through scintillation of light which is detected via photo-detectors and read out from the back.
2.2.3 The HCAL
Hadronic showers produce much larger numbers of particles and therefore have a much larger lateral spread
so the hadronic calorimeter(HCAL) does not require the same level of granularity as the ECAL. Hadronic
showers take place over a characteristic length denoted by (the absorption length) which is significantly
larger than the X0 meaning much more material is required to contain the hadronic shower.
The HCAL comprises of three regions: the hadronic barrel(HB), endcap (HE) and forward(HF) which
provides coverage up to |⌘|=5.3, this gives a combined depth of 11 absorption lengths. The HB and HE
consist of brass absorber plates interleaved a plastic scintillator. The energy of the shower is measured via
Cerenkov light emission from particle interactions with radiation-resistant quartz fibres which are inserted
into the brass plates.
The HCAL provides an energy resolution of 10 % for particles of energy greater than 100GeV [4].
2.2.4 The Muon System
The muon system is placed furthest from the beam as only muons and neutrinos travel to these distances
without depositing large amounts of energy. The muon barrel region is covered by drift tubes and the endcap
regions by cathode strip chambers. In both regions resistive plate chambers provide additional coordinate
and timing information, with a time resolution of 2ns allowing fast trigger decisions to be made. Muons can
be reconstructed in the range |⌘| <2.4, with a typical pT resolution, for the combined tracker and muon
system, of 1 % for particles of E=100GeV as well as a detector e ciency of >95%.[4]
2.2.5 Tau Triggers and Reconstruction
The aim of the trigger system is to reduce the data rate from 100TB/s to a more manageable 100-200MB/s
by identifying events of interest; the trigger system, consists of the level-1 and High-level triggers, the former
reduces the event rate from 40MHz to 100kHz and the latter reduces this to 100Hz. The e ciency of the
trigger is > 95%.
Taus have a lifetime of approx 10 13
s and therefore are not detected directly in the detector. However,
they decay either leptonically or hadronically to known decay products which may be detected. Electrons and
muons from tau decays are expected to be isolated in the detector; muons are reconstructed from information
in the tracker and muon system. On the other hand, electrons are reconstructed by a combination of tracks
produced by the Gaussian Sum Filter algorithm with ECAL clusters [5]. Specific requirements are enforced
to distinguish the electrons from pions which may produce ‘fake electrons’ as well as electrons from other
sources such as photon conversions. Particle flow algorithims are used to reconstruct composite objects such
as jets and to measure missing energy.
Hadronic decays of tau leptons lead to hadronic jets, these may be either 1 or 3 prong decays and are
therefore relatively collimated when compared to background QCD, which may contain tens of charged
particles. At high transverse momentum events the tau lepton is not massive enough to pull decay products
apart hence a relatively narrow shower forms in the HCAL this allows trigger decisions to be made. Also, Tau-
jets are usually colour-isolated from the underlying event as a result of the secondary vertex been su ciently
displaced, this results in a more confined and therefore isolated jet.
Background may also appear due to electrons or muons ‘faking’ a tau signature. In such cases elec-
trons/muons appear as the extreme case of a tau with a single charged hadron which can be reduced by
looking at the E/HCAL signatures in the electron case or HCAL and muon tracking signatures in the muon
case.
One way to search for Tau-jets uses 3x3 calorimeter regions in the L1, each of which has a 4x4 of combined
ECAL+HCAL towers. Each region is equipped with a ‘tau-veto-bit’ which is turned ‘on’ if the region has
two or more active ECAL or HCAL towers, if no bit is set ‘on’ in the nine regions within the window then
the jet is considered to originate from a tau decay. This takes advantage of the fact that tau hadronic jets
are more collimated than QCD jets.
Tau-jet reconstruction at the HLT uses Particle Flow(PF) techniques. The PF techniques first identifies
electrons and muons and removes their tracks and calorimetric signatures. PF charged hadrons are then
16. Project Report The CMS Detector Design 10
Figure 2.4: A) ID of electrons and Photons and B) ID
of Tau jets in L1 trigger [2] Figure 2.5: Reconstruction of tau-jet at HLT [1]
reconstructed by linking the remaining tracks to their corresponding HCAL deposits. First, a leading track
is found within a matching cone around the jet axis with pt > pT m, there must be 1 or 3 tracks which
originate from the same vertex and lie within a signal cone around this track. There should be no additional
tracks within an isolation cone around the jet axis.
2.3 Isolation
In order to eliminate leptons with significant numbers of charged hadrons along their track a relative isolation
parameter is defined, this help discriminate against the already discussed QCD background. In the following
a analysis particle flow algorithms are used to reconstruct events. The relative isolation parameter may be
calculated from the following equation:
Irel =
⌃(Pcharged
T + ET + Eneutral
T )
Pl
T
(2.2)
An extra factor of was introduced in the 2011A run to account for excess pile-up when compared to
previous runs.It is assumed that the ratio of charged to neutral particles is 2:1 and this is used to predict the
neutral particle deposits based on PU particle deposits. The above expression now becomes:
Irel =
⌃(Pcharged
T + max(ET + Eneutral
T 0.5EP U
T , 0.0))
Pl
T
(2.3)
2.4 Current Limits and Previous Work
Prior to CMS and ATLAS work to find experimental proof for the existence of the Higgs had been undertaken
by LEP as well as the two experiments at the Tevatron: DØ and CDF. LEP was an electron-positron
collider based at CERN in the 1990s; which produced aimed to produce Higgs bosons via quark-anti-quark
annihilation in association with a Z boson with a centre-of-mass energy of 205GeV. Higgs masses below
114.5GeV/c2
were excluded by these experiments within a 95 % confidence level meaning that the Standard
Model Higgs boson with that mass would yield more evidence than that observed in our data in at least
95% of the a set of toy data models. Further information can be found from precision measurements of the
W and Z masses which have excluded a mass region above 200GeV/c2
. The Tevatron aimed to produce
Higgs particles through gluon fusion as well as a smaller number by W,Z Bremsstrahlung (Section 1.6) and
has excluded a region around 150 160GeV/c2
at a 95 % confidence level. Figure 2.5 shows the latest
combined results from CMS for all channels under analysis as of 13/12/2011. As can be seen the Higgs has
been excluded from 127 to 600 GeV at 95 % confidence level, and 128 to 525 GeV at 99 % confidence level.
However, SM Higgs bosons with a mass between 115 GeV and 127 GeV are still possible, this is within the
region been searched for the this particular analysis. There is an excess of events when compared to the SM
prediction in this mass region this appears, quite consistently, in five independent channels. This is visible as
a small peak over the 2 sigma band in the figure below. This excess is not enough, at this point, to warrant
a‘discovery’. This excess of events could be a statistical fluctuation in known background processes. The
larger data samples to be collected in 2012 will reduce the statistical uncertainties, enabling CMS to make a
clearer conclusion on the possibility of the existence of a standard model Higgs boson in this mass region. [7]
17. Project Report The CMS Detector Design 11
Figure 2.6: Combined Results from LEP, Tevatron and
CMS (as of end of 2011)
Figure 2.7: Combined 2011 and 2010 results for low
mass region
18. Chapter 3
Software
Once the pre-selection of events and reduction of the data volume is carried out by the online trigger and
Data Acquisition System (TDAQ) events must be reconstructed and o✏ine analysis must take place. Below
is an outline of the computing techniques used to analyse the data in the following analysis. [8]
3.1 The ROOT Framework
The following analysis of the CMS 2011A data makes use of the data analysis framework ROOT. ROOT
was developed at CERN by Rene Brun and Fons Rademaker in the mid-1990’s to allow for the analysis of
the huge amounts of data expected from experiments such as the NA49 and later the Large Hadron Collider
experiments. ROOT is a C++ based object orientated analysis framework which is highly specialiesd for use
in High Energy Physics. Thus, since its development ROOT has become an integral part of experimental
particle physics and the physics community who have built in and added to the original software to create
a specific, highly skilled and powerful analysis tool. The ROOT framework provides a set of common tools
for all CMS analysis . The analysis given in the following chapter was undertaken using ready-collated
ntuples but the analysis and plots where created by myself throughout the project using the ROOT libraries.
Numbers extracted from ROOT plots will of course have some influence from counting/rounding errors,
however, the main source of error will be statistical error in the number of estimated events and will be
accounted for using Poisson statistics. When numbers are used directly from ROOT the quoted error will be
Poisson error.
3.2 RooFit
RooFit is a template fitting package used in the following analysis to extrapolate fit statistics and for back-
ground analysis. In RooFit the errors provided are statistical only and do not take into account any systemic
bias which may be present within the results. Roofit also does not take into account any statistical errors
already present in the data and may therefore give a systemic under-estimate on a fit.[9]
3.3 LandS
For the final statistical analysis the LandS statistics package is used to extract a cross section the numbers
output by the package are, of course, subject to statistical error, however, systemic error can be added into
the datacard and is parameterized as nusicence parameters in the underlying algorithms used to calculate
the cross-sectional limits. The final quoted error is a combination of LandS calculation of the statistical error
as well as that resulting from the specified systemic errors.
3.4 Event Generators
In order to provide simulation of possible background e↵ects in the data a number of Monte Carlo simulations
will be used to model: Z+jets, W+jets and t¯t events*. These are studied under the same ROOT framework
as the reconstructed CMS data events; such Monte Carlo is often referred to as ‘truth data’ as it avoids
any detector e↵ects and therefore allows e ciencies etc. of the detector to be calculated. In this analysis
MadGraph [10] was used to generate the background models, these were ready provided for the analysis.
*These were provided by Mike Cutajar and are listed in Appendix 1.
12
19. Chapter 4
Results and Analysis
The following analysis begins by looking for the 3 di-lepton decays of the Z boson in the CMS 2011 A data.
The reasoning behind this large emphasis on the Z boson decays is to put a very accurate estimate of final
events resulting from Z ! ⌧⌧, the predominant source of background in the Higgs di-tau decay channel. This
estimate will eventually be derived from the Z! ee and µµ data, where lepton universality, and therefore
identical coupling by each lepton to the gauge boson, results in equal numbers of decays to each of the 3
leptons. As the data from all processes in the same CMS run (2011A) is subject to the same conditions it is
from the data, and not an MC, that this ‘expected’ Z ! ⌧⌧ is taken for the final statistical analysis which
aims to put an upper limit at a 95 % confidence level on (pp ! H ! ⌧⌧)/ SM .
4.1 Z ! µ+
µ analysis
The first part of the data analysis process is to identify the di-lepton decays of the Z boson, this is done by
finding two oppositely charged, same type leptons within the data and combining their Lorentz vectors; the
invariant mass of the resulting vector is then found and plotted against number of events.
4.1.1 Z Production, Initial and Final State Radiation
Z bosons in CMS are produced by Drell-Yan processes where a quark and anti-quark interact to produce
the Z boson. The above method may run into di culty due to initial and final state radiation. Initial
state radiation, in the form of photon or gluon emission, occurs in any process which involves either charged
or colored particles in the initial state, in the process shown in figure 4.1 this occurs when the incoming
quark/anti-quark pair emit a photon/gluon before producing the Z boson. Final state radiation occurs when
the resulting 2 oppositely charged muons emit radiation, this process will ‘remove’ energy from the scene
and will reduce the calculated Z reconstructed mass resulting in asymmetry in the observed resonance peak.
The Feynman diagram in figure 4.1 shows both these processes occurring.
Figure 4.1: Feynmann Diagram of ISR and ISR for Z from quark interactions which decays into 2 muons
These two processes are quantum mechanically very di↵erent, and may be distinguished experimentally.
ISR processes result in an invariant mass being found which is larger than the quoted Z mass whereas the
FSR processes give a lower than expected invariant mass. The e↵ect of FSR is increased further in the
di-electron channel due to the its inverse dependence on mass, this is discussed in more detail in section 4.3.
4.1.2 Muon Quality Cuts
In order to exclude background processes such as QCD or meson decay a number of kinematic and isolation
cuts must be applied to the data and MC, these are summarized in the table below:
13
20. Project Report Results and Analysis 14
Cut Value Cutflow % reduction
Before Any Cuts 1565188 N/A
Pseudorapidity of muon <2.1 1465961 6.34 %
Transverse Muon Mommentum >20 GeV/c2
969508 31.72 %
|dxy| < 0.045cm 932173 2.39 %
|dz| < 0.2 cm 919417 0.81 %
Chi Squared < 10 867347 3.33%
Muon Matched Stations > 1 780988 5.33%
Muon Hits > 0 0 0
Muon Track Hits > 10 749039 2.04 %
Muon Pixel Hits >0 724966 1.54 %
Muon Isolation Parameter <0.1 142373 9.12%
ALL 582593 37.22% remains
Where |dxy| and |dz| refer to the impact parameters in the transverse and longitudinal directions respec-
tively. When these cuts are all enforced the total number of muon events selected is reduced from 1565188
events to 582593 events, the majority of the events removed are from the low mass region including resonance
peaks from other particles as well as background resulting from QCD processes and other Z+jets.
To suppress background from decays of other neutral particles muon detected at the outer muon system
should have a matching track in the inner detector; this inner detector track should have created at least
10 track hits because the short lifetime of the Z boson leads to a decay close to the primary vertex and the
outgoing tracks pass the entire track detector. The more the muon interacts with the inner tracker, as well
as the outer muon system, the more precise the track measurement will be. To reject poorly reconstructed
candidates every track should have at least 1 hit in the muon system and more than ten hits in the inner
tracker. These cuts can be seen to reduce particle number by 2.54 %.
As the track of a muon is determined from a fit to the hits in the inner tracking detector and the muon
chambers, the Chi-squared of this fit can also be used to judge the reconstruction quality of the muon track
and should not exceed 10. Figure 4.2 shows how the mass reconstruction looks with this cut applied. There
is no overall shape change, a small reduction in the 10 GeV/c2
peak is visible as well as an even smaller
percentage change in the 3GeV/c2
peak.
Figure 4.2: Overall shape of the di-muon data plot
when only muons with Chi squared >10 are plotted
Figure 4.3: Overall shape of data when just Pseudo-
rapidity of muon < 2.1 applied-little change in shape
seen
Muons with pseudorapidity >2.1 (tracker acceptance) are disregarded; this is because, as seen in figure
2.2 the reconstruction e ciency significantly decreases outside this range, this cut therefore ensures a good
quality Z peak can be seen. This cut reduces total number but there is little change to the overall shape of
the distribution. A plot for this cut alone is shown in figure 4.3.
The muons are required to have a relative isolation (Section 2.3) < 0.1; this improves the reconstruction
quality by decreasing QCD background and shows one of the greatest individual decrease in number of
particles. Figure 4.4 shows the data when the isolation parameter alone in applied. It is clear that the large
bump at low mass has almost disappeared, meaning, as expected, the majority of hits here came from QCD
background.
The most important kinematic cut is the muon momentum cut, muons resulting from Z decay will have
relatively high energies and to reduce low energy muon background it is required that selected muons have
transverse momentum > 20GeV/c2
. The results for this cut alone are shown in figure 4.5. It is clear that
there is a large reduction in total particle number as well as overall shape. The smaller resonance peaks at
21. Project Report Results and Analysis 15
0-1.5, 3 and 10 GeV/c2
have been reduced significantly as well as the larger spread of background resulting
from QCD processes. In total a reduction of around 32 % is observed by applying this momentum cut.
Figure 4.4: Overall shape of data when just Isolation
<0.1 cut applied-QCD removed
Figure 4.5: Overall shape of the di-muon data plot
when only muons with > 20GeV/c2
plotted
Figure 4.6 shows both the real and generated data with all kinematic cuts and isolation applied. Here an
energy shift of 0.16% has been applied to the MC, this alters the shape and ensures consistency.
A clear resonance peak is now observed with a mean of 90.839 ± 0.41GeV/c2
which is slightly lower than
the PDG quoted value of 91.1876 ± 0.0021GeV/c2
. This lowering may be a result of missing final state
radiation. The Z resonance peak may be parameterised by a Breit-Wigner function (Figure 4.7) defined by:
f(E) =
k
(E2 M2) + M2 2
(4.1)
where E=energy, M=mean mass value and =decay width and k = 2
p
2M
⇡
p
M2+
with =
p
M2(M2 + 2
The reconstructed resonance peak has a relatively large width, quoted as 3.9 ± 0.008 GeV by ROOT.
Both stable and unstable (including the Z resonance) particles can be characterized by their spin-parity and
centre-of-mass energy s. In the case of a stable particle this value is real,s =m2
0, in the case of quasi-stable
particles and resonances such as that for the Z boson s has complex values which may be parameterized by
the two real values “mass” ,m, (the mean of the resonance peak) and “width” (the width of the resonance
peak), these may be combined in the form s = (m i
2 )2
among other ways. [12]
A ratio of these resonance characterization parameters can be defined as ( /m), this spans a wide range
of values for di↵erent decaying particles, for the experimental data above this parameter is found to be
0.0430 ± 0.0001. from the Breit-Wigner fit below, this is relatively large compared with much smaller values
for other electroweakly decaying particles e.g. ( /m)⇡0 ⇠ 10 7
, ( /m)⇡± ⇠ 10 15
and ( /m)K0 ⇠ 10 14
[12].
Figure 4.6: Inclusive events in the Z to di-muon decay
channel along with Monte Carlo generated events
Figure 4.7: Breit-Wigner fit to the final data for
di-muon mass. Mean:90.839+/-0.004 Sigma:3.908+/-
0.008
4.1.3 Background and Other Particles
It is clear from figure 4.2-4.5 that as well as having large amounts of QCD background there are 3 other
regions which show significant resonance peaks, although much lower in amplitude than the main Z peak,
22. Project Report Results and Analysis 16
it is believed that these are other particles and must be removed from the final sample. The smaller peak
at 9.450 ± 0.002GeV/c2
makes up around 0.53 % of the background (i.e. that removed by above cuts) and
corresponds to the di-muon decay of the Upsilon Meson, the bound state of a bottom/anti-bottom quark,
which has a quoted mass of 9.46GeV/c2
. This particular meson decay has been previously analyzed at the
CMS detector and is made up of three resonance peaks for the 1s, 2s, and 3s states, the first being the
strongest and resembling that shown in figure 4.8, much smaller peaks should be observed for the 2s and 3s
states but in the data these are clouded by other background e↵ects and are therefore not visible.
Figure 4.8: Upsilon particle reconstructed from data
with mean around 9.448+/-0.002 (RooFit)
Figure 4.9: J/psi particle reconstructed from data with
mean around 3.0890 +/-0.0006 (RooFit)
The J/Psi meson, with quoted mass of 3.096GeV/c2
, is responsible for the strong resonance centered on
3.090 ± 0.0006GeV/c2
which spans 3.02 -3.15GeV/c2
; this is shown in figure 4.9 and makes up 3.63 % of the
removed background.
The 3rd region, at relatively low mass, is due to 3 specific di-muon decays namely that from the: ⇢ meson
(rest mass 0.775GeV/c2
2), ! meson (rest mass 0.782GeV/c2
) and meson (rest mass 1.018GeV/c2
). The
first two can be seen by the distribution in figure 4.10 with a mean of 0.7795 ± 0.002GeV/c2
and the latter
in figure 4.11 where the data peaks at 1.023 ± 0.003GeV/c2
.
Figure 4.10: rho/omega particles reconstructed from
data with mean around 0.7795 ± 0.002 (RooFit)
Figure 4.11: phi particle reconstructed from data with
mean around 1.023 ±0.003 (RooFit)
In total only 4.86 % of the background in the di-muon channel is believed to come from other particles.
The majority of these particles are removed by the transverse momentum cut but a small fraction will remain
within the allowed parameters and remain, helping lower the experimental mean of the final data.
4.2 Jets
As described in the introduction, the aim of this analysis is to search for a VBF Higgs. In order to do this
the number of VBF events in each channel must be found. VBF processes have the characteristics of having
two outgoing jets at high rapidity gap and without a central jet. This will be used in the following analysis
to find the number of dimuon, dielectron and di-tau VBF events within the data.
4.2.1 Jets Selection and VBF Criteria
In order to suppress background from ‘fake-jet’ candidates which may result from other processes within
the detector a number of cuts are placed on the jet candidates within all three di-lepton channels, these are
23. Project Report Results and Analysis 17
summarized below. Such ‘fake-jets’ may originate, primarily, from the promotion of low ET jets, coming
from hard parton interactions, to higher energy or through the close impact of either a particle or low ET
jet from pileup interactions. Fake jets can also be formed in the calorimeter when particles from di↵erent
interactions impact in close proximity. Electron can also form fake jets [14]. There is no generic solution for
identifying whether a jet is fake or not, but usually fake jets have low transverse momentum, are found near
the HE/HF boundary and have a broader transverse profile than expected.
Cut Value
mµµ > 50GeV/c2
Pseudo-rapidity of jet <4.5
Transverse Jet Momentum >30 GeV/c2
Jet Beta -
JetMuDeltaR( R1 and 2) >0.5
Mass of Dijet >400
Delta|⌘| jj >4
Opposite Hemispheres True
Central Jet Veto True
The Beta cut is ignored here to allow us to see both forward and backward jets. The central jet veto
requirement ensures there is no jets between the two selected jets. The last four cuts here help identify VBF
jets and will be discussed later.
Two overlap parameters R1 and R2 are created, these are defined as the square root of the sum of the
squares of the di↵erences in muon and jet pseudo-rapidity and ; it is required that R 1 and 2 >0.5. Only
jets which have transverse momentum > 30 GeV/c2
are selected, this is essential for pile-up suppression and
the removal of electronic noise as well as other sources of fake jets. This momentum cut is very e↵ective at
removing low momentum ‘fake-jets’ reducing the number of selected jets by 39%. In addition, jets must have
|⌘| < 4.5 as well as |⌘| > 2.4, corresponding to HCAL coverage . It is also necessary to ensure the jets are
not co-linear with the muons.
Figure 4.12: Di↵erence in pseudorapidity of the two
outgoing jets pre-VBF
Figure 4.13: Dijet Invariant Mass in Muon Channel
pre-VBf selection
Figure 4.13 shows the distribution of reconstructed dijet mass for jets in the muon channel prior to
VBF selection, it is clear that the mass of the jets reaches much higher than the Z mass ranging as far as
1500GeV/c2
but with maximum number of jets around 95GeV/c2
. Figures 4.12 and 4.13 show the spread of
jets in terms of mass and ⌘, in both cases good agreement with MC is seen. It is visible that the majority
of jets occur at low mass and separation-these are tagged as fakes and are removed.
4.2.2 VBF cutflow
As with the muon discussion it is helpful to look at each cut separately to see how the VBF selection criteria
a↵ect the momentum and rapidity distributions of the reconstructed Z boson. First we apply mµµ >50 with
2 jets of pt > 30, figures 4.14 and 4.18 are produced in this case. Next we add the VBF criteria that the
separation ⌘jj > 4 this gives figures 4.15 and 4.19, the central jet veto cut is then added producing figures
4.16 and 4.20. Finally the condition that mjj > 400GeV/c2
is added producing figures 4.17 and 4.21. As
can be see the shape of the momentum and rapidity distribution gets more and more disrupted as more and
more events are cut out. In the first instance the MC and data are reasonably well aligned,however, in the
final VBF selection these appear much less correlated. However, in the majority of cases the data is within
errors of the MC. This di↵erence in shape is due to di↵erences in number of events. The MC has been scaled
24. Project Report Results and Analysis 18
by a numerical factor of 0.1855 which is equivalent to the data luminosity/luminosity of the MC. The MC
therefore has the scaled down shape which would be produced if there where 5 x more events than in the
data. As the data has so few events statistical uncertainties result in the types of fluctuations seen in the
final VBF plots for the data. As the luminosity of the LHC increases the shape of the data should match
that of the MC much better but for now this matching in errors is su cient.
Figure 4.14: Pt of the reconstructed Z particle when
mµµ >50 and 2 jet cuts are applied.
Figure 4.15: Pt of reconstructed Z particle when
mµµ >50, 2 jets and delta eta >4 cuts are enforced
Figure 4.16: Pt of the reconstructed Z particle when
mµµ >50, 2 jet, delta eta and central jet veto cuts
enforced
Figure 4.17: Pt of the reconstructed Z particle when
mµµ >50, 2 jet, delta eta, central jet veto and jet mass
cuts enforced
Figure 4.18: Eta of the reconstructed Z particle when
mµµ >50 and 2 jet cuts are applied.
Figure 4.19: Eta of reconstructed Z particle when
mµµ >50, 2 jets and delta eta >4 cuts are enforced
After all cuts are applied only 382 ± 19.5 (stat.) ± 11.5 (sys.) ±15.3 (lumi) data events remain and
431.44 ± 21 (stat) ± 0.69 (momentum shift) ± 12.9 (sys.) ± 17 (lumi) MC events. The statistical error is
calculated from Poisson statistics and the systemic errors are a combination of errors in separation of pile up
(0.5%) , trigger errors (2 %) and background e↵ects (0.5%) . Systemic and luminosity (4 %) uncertainties
account for a total systemic uncertainty of 7 % these are discussed in sections 4.3.1 and 4.3.2 . The quoted
momentum shift accounts for 0.16 % and is applied as a correction to the MC to account for a bias which
was placed on the MC. This ensures that the shapes of the data and MC align. A 3% trigger shift is also
applied to the MC and is discussed in Section 4.3.1.
25. Project Report Results and Analysis 19
Figure 4.20: Eta of the reconstructed Z particle when
mµµ >50, 2 jet, delta eta and central jet veto cuts
enforced
Figure 4.21: Eta of the reconstructed Z particle when
mµµ >50, 2 jet, delta eta, central jet veto and jet mass
cuts enforced
The table below gives a break-down of the number of events remaining after each VBF cut.
Cut Data Events remaining (stat.)(sys)(lumi) MC Events remaining (stat)(sys)(mom)(lumi)
Muon Selection 582593 ± 800 ± 17468 ± 23424 563293 ± 751 ±16898± 901 ± 22532
Jet Selection 22200 ± 150 ±666 ± 888 22910.7± 15.1 ± 687 ± 36.7±916
Delta Eta>4 796 ± 28 ± 424 ± 32 750±25.6 ±22.5 ±1.2 ±30
CJV 689 ± 30 ± 21 ± 28 722.812±26.9 ± 21.7 ± 1.16±28.9
mjj > 400GeV 385 ± 19.5± 11.5 ±15 .3 431.44± 21 ± 12.9 ± 0.69 ±17
Figure 4.22: VBF events in the Z to di-muon decay channel along with Monte Carlo generated events
4.3 Z ! e+
e analysis
Similar analysis may be done for the Z! ee decay, this occurs in a similar way to that for the di-muon decay
and results in the distribution of invariant masses as shown in figure 4.23. This is with isolation or kinematic
cuts enforced on the data as given in the table below but without VBF cuts.
Cut Value
Transverse Momentum > 20
Pseudorapidity < 2.1
|dxy| <0.045cm
|dz| < 0.2cm
Isolation (barrel) iso < 0.1
Isolation (endcap) iso < 0.3
Nhits <1
Delta R <0.1
Not in ECAL gap |⌘| <1.46 and |⌘| >1.558
Electrons are reconstructed by combining tracks produced by the Gaussian Sum Filter algorithm with
ECAL superclusters. It is necessary to apply cuts to distinguish prompt electrons from charged pions faking
26. Project Report Results and Analysis 20
electrons and electrons produced by photon conversions. The main parameters used to reduce the fake
electron rate are:
• The angular di↵erence (di↵erence in acoplanarity) between the track and the supercluster ( )
• The ratio of hadronic calorimeter (HCAL) to ECAL energy associated with the supercluster (H/E),
this must be small as electron would deposit much more energy in the ECAL
• The ECAL shower shape described by the RMS of the energy in the direction within the supercluster
( i⌘i⌘),
In this analysis W985 electron selection is used which splits electrons found in barrel and endcap:
Barrel/Endcap Cut
Barrel H/E <0.04
<0.06
⌘ < 0.004
i⌘i⌘ < 0.01
Endcap H/E <0.025
<0.03
⌘ < 0.006
i⌘i⌘ < 0.03
In both regions it is required that ‘Conv’<0.5 this rejects electrons from photon conversion.
The resonance peak is fitted with a Breit-Wigner and has a mean of 90. 575 ± 0.006 and sigma 5.25 ±
0.013, this is larger than the quoted di-muon sigma of 3.89 ±0.01, this may be as a result of Bremsstrahlung
or increased FSR. Bremsstrahlung radiation is produced when a high energy charged electron decelerates
and is deflected by the electric field from the charged atomic nucleus, this is represented in figure 4.26. As
in the discussion of FSR, this means that the electrons lose energy, as this is then used for determining the
invariant mass of the decaying Z it may result in a slightly lower mass being calculated this will result in a
broadened peak in the direction of lower mass. This has greater e↵ect in the electron channel due to a 1
m4
dependence.
Figure 4.23: Inclusive events in the Z to di-electron de-
cay channel along with Monte Carlo generated events
Figure 4.24: VBF events in the Z to di-electron decay
channel along with Monte Carlo generated events
In total 462723 ± 680(stat.) ± 27763 (sys) ± 18509 (lumi) inclusive data events and 450120 ± 671 (stat)
± 27007 (sys) ± 18005 (lumi) MC inclusive events are observed. These numbers appear to suggest that the
di-electron data is consistant, within errors, with expectation (MC).
The final number of VBF Z ! ee events is found to be 307 ± 17.5(stat.) ± 18.4(sys) ± 12.3 (lumi). For
the MC the value is found to be 367 ± 19.2 (stat) ± 22 (sys.) ± 0.59 (mom. shift) ±14.7 (lumi.) . The
systemic calculations are discussed in the following two sections they include pile up e↵ects (1.5 %), trigger
e↵ects (4%), background e↵ects (0.5 %) and luminosity uncertainties (4 %). These two values are consistent
within errors and the final VBF distribution, shown in figure 4.24 shows reasonable shape consistency with
the discrepancies being due to the systemic uncertainties (error bars are purely stat.).
4.3.1 Correction Factors
In order to compare the selected events from both MC and data a number of correction factors where applied:
27. Project Report Results and Analysis 21
Figure 4.25: Di-electron results fitted to a Breit-
Wigner function with mean 90. 575 ± 0.006
Figure 4.26: Diagram representation of bremstrahlung
radiation [15]
• Momentum Shift-Applied to muon MC to correct a bias which introduced calibration problems in the
relative MC and data shapes. This was accounted for within the code for the inclusive result and is
quoted as an error for the VBF case. The shift is small and is estimated to be - 0.16 %
• PU corrections-As the Monte Carlo samples contain a flat PU distribution an additional weight is ap-
plied to fit the distribution observed in data [16]. This re-weighting is done by producing a distribution
of the number of reconstructed vertices for both the data and MC. Both histograms are then normalized
to unity and an event weight is found to be the ratio of data/MC for each bin.
• Trigger Shift-In the above section the MC is scaled by 3% relative to the data to account di↵erences
in the trigger e ciencies which were measured for leptons that are spatially matched to the trigger
objects. However, in the data used the leptons were accepted even if they are in a di↵erent part of the
detector to the lepton reconstructed at trigger level.
4.3.2 Calculation of E ciency and Acceptances for the di-electron and di-muon
cases
The data detection will not be 100 % e cient at identifying, isolating, reconstructing and even triggering
and therefore all the data in the above discussion is open to systemic error from such sources. Appendix A.3
lists the e ciencies and correction factors used for ID and trigger. A selection e ciency can be calculated
by finding the ratio:
NMC
selected
NMC
T otal
. An acceptance may also be calculated by finding the the fraction of Z events
falling within the pt and eta cuts, this gives a total e ciency( acceptance x sel. e↵.) of 0.187 in the di-electron
case and 0.263 for the di- muon case. These are used in the following cross-section calculations.
4.3.3 Observed di-electron and di-muon Cross-sections
The cross-section is found by dividing the number of observed events (factoring in the e ciency and ac-
ceptance) by the integrated luminosity which is quoted as 2094 pb 1
. For the di-muon case an inclusive
cross-section of 1055 ± 32 (stat) ± 32 (sys.) ± 42 (lumi) pb and for the di-electron case an inclusive cross-
section of 1022 ± 32 (stat.) ± 61 (sys.) ± 41 (lumi.)is found. These are found to be within 1 of each other
i.e. they are consistent within their respective errors as expected by lepton universality. In the VBF case
307 ± 17.5(stat.) ± 18.4(sys) ± 12.3 (lumi) di-electron and 382 ± 19.5 (stat.) ± 11.5 (sys.) ±15.3 (lumi)
di-muon events are found. These are numerically consistent when there respective e ciencies are taken into
account, again as to be expected. The errors quoted here are Poisson statistical error and systemic error
which results from luminosity (4%) as well as trigger (2% for di muon case and 4% in the di-electron case),
pile-up e↵ects (0.5% in di-muon case and 1.5% in the electron case) these are all justified in [17]. In addition,
an uncertainty due background contributions is calculated to be 0.5% in both cases. This results in a total
systemic uncertainty in the di-muon case of 7% and in the di-electron case 10%.
4.4 Z ! ⌧+
⌧ analysis
The case for Z ! ⌧+
⌧ is much more complicated as due to the short lifetime of the ⌧ only the decay
products are visible in the detector. Therefore, before finding the invariant mass of the Z boson the individual
⌧ decays must be reconstructed. The tau lepton decays both leptonically i.e. to e or µ particles and there
28. Project Report Results and Analysis 22
corresponding neutrinos or hadronically i.e. to mesons which appear as jets of quarks and gluons; the table
below summarizes these decays:
Decay Mode Branching Fraction (%) Leptonic, Hadronic or Semi?
⌧ ! µ ⌫µ ¯⌫⌧ 17.4 Purely Leptonic
⌧ ! e ¯⌫e⌫⌧ 17.9 Purely Leptonic
⌧ ! ⇡ ⌫⌧ 10.9 Hadronic (1-prong)
⌧ ! ⇡ ⌫⌧ ⇡0
25.5 Hadronic (1- prong)
⌧ ! ⇡ ⌫⌧ ⇡0
⇡0
9.3 Hadronic (1-prong)
⌧ ! ⇡ ⌫⌧ ⇡0
⇡0
⇡0
1.1 Hadronic (1-prong)
⌧ ! K ⌫⌧ 0.7 Hadronic (1-prong)
⌧ ! K ⇡0
⌫⌧ 0.5 Hadronic (1-prong)
⌧ ! ⇡ ⇡+
⇡ ⌫⌧ 9.3 Hadronic (3-prong)
⌧ ! ⇡ ⇡+
⇡ ⌫⌧ ⇡0
4.8 Hadronic (3-prong)
other 1.4 -
With corresponding expressions for ⌧+
. This results in decays of the Z ! ⌧+
⌧ ! ⌧hadµ, ⌧hade, ⌧had
⌧had ,ee,µµ or eµ, with neutrinos left out. The overall branching fraction to hadronic events is ⇡ 65% (3
times that to leptons) due to there being 3 colours of each quark. Hadronic decays may be 1 prong or
3 prong, both create very collimated jets in comparison to background QCD jets. This helps the trigger
system make accurate conclusions over which jets come from hadronic tau decays. The following analysis
concentrates on the use of the semi-leptonic decays namely: ⌧hadµ and ⌧hade as despite having the largest
individual branching fraction the hadronic decay has large QCD background and su↵ers twice as much from
ine ciencies in separating this from the tau signal.
Figure 4.27: Feynmann Diagrams for e⌧had and µ⌧had decays [6]
4.4.1 Kinematic Selection and Hadronic Tau Ideintification
The µ⌧had and e⌧had channels will have similar kinematic selection criteria. The basic kinematic requirement
is that an event contains only one lepton with pT > 15 GeV which is, in the electron case, located in the
ECAL or in the muon case, in the muon system. In addition, each event must have one PF tau candidate
with pT > 20GeV, |⌘| < 2.3 and |dz| < 0.2cm. It is also required that the taus do not fall in the ECAL gap
defined as 1.442 < |⌘| < 1.566. Electron must also pass the WP80 as well as ID and conversion rejection cuts
(Section 4.3), such cuts are not enforced on the muons as global and track quality cuts have already been
passed. All the cuts documented in sections (Section 4.1.2) and (Section 4.3) still apply. [6]
For Tau identification it is required that a valid decay mode is found by the particle flow algorithm and
discrimination is performed against muons and electrons as discussed in Section 2.2.5 (this is done prior
to the analysis). In addition lepton-rejection is enhanced by ensuring that E+H
plead
> 0.2 which rejects both
electrons and muons faking a tau signal. Di-candidates are made with a minimum overlap ( R) of 0.2.
Further muon and electron rejection ensures that no muons and electrons are included within the isolation
cone.
Loose Tau Isolation ensures that no neutral hadrons or photons of ET >1GeV or charged hadrons with
ET > 1.5GeV are present:
IT auP F
rel =
⌃pT >1GeV
h0 + ⌃pT >1GeV
+ ⌃pT >1.5GeV
h±
plepton
T
< 0.5 (4.2)
Further QCD discrimination is performed by ensuring that pleading >5GeV, this is done prior to the
analysis.
29. Project Report Results and Analysis 23
The remaining fraction of events will still have large amounts of Z ! ll background. To reduce this a
“loose” lepton criteria is created which requires a candidate to have pT > 10GeV and |⌘| < 2.4 and in the
electron case passing WP95 ID . Events containing two oppositely signed ‘loose’ leptons are rejected.
All oppositely charged lepton-tau pairs passing these criteria are then constructed. To discriminate against
background from W decays it is required that MT (l, Emissing
T ) < 40GeV/c2
and P⇣ = Pmis
⇣ -1.5Pvis
⇣ > 20,
these are discussed in detail below.
4.4.2 ⌧had + µ Event Reconstruction and Background analysis
Figure 4.30 shows the invariant mass for reconstructed ⌧µ for both real data and generated data for back-
ground processes namely:QCD, Wjets (W ! l⌫l, W! ⌧⌫⌧ +jets) and t¯t events. The table below documents
the cut-flow as each kinematic and isolation cuts is applied to the data and MC backgrounds.
Cut Data W+jets t¯tjets
Kinematic Cuts (as given above) 85612 15705 1750
Relative Isolation < 0.1 46610 27387 1767
R(mu, tau)<0.2 46580 27344 1784
Oppositely charged 35429 20948 1476
Pzeta - 1.5*Pzetavis > 20 22356 3395 678
Transverse Mass (mu,MET) < 40GeV/c2
17994 2679 170
VBF cuts (as given above) 23 4.11 1.88
The relative isolation cut is used to reduce the QCD background, this will be discussed in more detail
later. The transverse mass is calculated as
q
E2
t (mu, MET) (P2
x (mu, MET) + P2
y (mu, MET)) where
MET describes missing transverse energy i.e. that taken by the neutrinos. This cut, as will be shown in
the control plots below, is used to remove large amounts of W+jet background, but as the table suggests,
not all of it. As can be seen in figure 4.28 in real tau decays the outgoing neutrinos tend to be collinear to
outgoing tau products, this is not the case in t¯t and W+jet processes. In the case of the µ⌧had channel W+jet
background, W ! l⌫l, can fake the Z decay where the isolated muon reconstructed in the event originates
from a genuine muon produced in the decay of the W boson, the tau jet on the other hand is termed a
‘fake-jet’ and is due to either a quark or gluon jet faking the signature of a hadronic tau decay.
The P⇣ variable was introduced by CDF where the ⇣ axis defines a bisector between the two decay
products, a Pvisible
⇣ factor is first found as the projection of the muon and tau-jet momenta onto this axis.
A second variable Pmissing
⇣ is defined as the projection of the MET momenta onto this axis. If the products
are from a real decay then these will be collinear whereas in W+jet they will not be. The factor P⇣ in the
table above is the total momenta (MET, mu,tau) projected on this axis. Ensuring that Pmis
⇣ -1.5Pvis
⇣ > 20
ensures that the these two vectors are in a similar direction and will therefore reduce the number of W+Jet
fakes in the final sample.
Figure 4.28: Relative directions of MET and tau variables for real and W+jets processes [18]
This analysis aims to calculate background contributions to the data from reducible background processes
specifically QCD, W+jet and t¯t. These will have relatively big cross sections at the LHC and will therefore
give significant background in the data. The following control plots (figures 4.29-4.32) can be used to look at
accurate ways to extrapolate the relative numbers of these background process, these are unstacked to allow
specific shape analysis.
The signal (i.e. the actual Z decay) is only present in the opposite sign region and therefore the same
sign region is purely background events. The background in the SS region is mainly W+jets and QCD, an
estimate of which will be discussed in the following section. The opposite sign region has several contributions
from QCD, Z ! µµ and W ! µ⌫ as well as the signal. It is clear that at this point there are many more
events in the data than is expected for pure Z ! ⌧⌧ in both OS and SS regions. From figure 4.30 we can
see that in the opposite sign case, below a transverse mass of 40 GeV/c2
the data follows a similar shaped
fall of to the Z+Jets MC but is broadened due to increasing W+Jet contributions as well as QCD e↵ects.
After MT =40 the data begins to become more consistent with the MC for W+Jet. A side-band region may
30. Project Report Results and Analysis 24
Figure 4.29: Transverse Mass distribution in theµ⌧had
channel Figure 4.30: PZeta Distribution in µ⌧had channel
Figure 4.31: Transverse Mass distribution in the µ⌧had
channel for same sign region
Figure 4.32: Invariant Mass plot in W+Jet control re-
gion for SS:OS (3:1)(from data)
be defined as MT > 80GeV/c2
where it is assumed that W+Jet background dominates. A similar conclusion
can be made from figure 4.31, before P⇣ < 20 the data has reasonable consistency with the Z! ⌧⌧ MC,
with slight di↵erences due to the described backgrounds. After this point the data becomes consistent with
the W+Jet MC and it can be assumed by P⇣ < 40 that anything remaining is W+Jet background. This
region is defined as the W+jet control region. One can also define a Z ! ll control region in the 80-110 GeV
mass window. This will be estimated numerically for the µ⌧ case and has much smaller e↵ect.
4.4.3 Method of Background Estimation
For all of the stated backgrounds the background is not taken directly from the MC but is extrapolated
from the data using defind control regions to calculate an e ciency factor (✏ = NselectedMC
/NcontrolMC
)
and using Ndata = ✏Ndatacontrol to get an estimate of background contribution to data. Background is not
taken directly from MC as although these are good first order approximations they are unsatisfactory due
to uncertainties in the PDF as well as radiation simulation and detector response.[6]
4.4.4 W+jets background in µ⌧had Channel
As described in the above section, it is expected that a large majority of W+jet events will be removed by
the requirement that transverse mass < 40GeV/c2
along with the P⇣ cut, however, not all are removed. In
order for W + jets events to pass the transverse mass cut either the transverse momentum of the tau-jet
candidate, the missing transverse momentum or the angle between the missing momentum and muon must
be small. In the latter scenario, the angle between the tau-jet and muon must be large.
Using a template derived from the Monte Carlo for the transverse mass distribution of W events the
number of W events in the data region can be predicted by counting the number of data events in the
sideband, the region dominated by W events. This method is described in [19]. From the previous discussion
it is clear that the majority of the W+jets occur at high values of transverse mass i.e.MT > 40GeV/c2
and
after MT > 80GeV/c2
there is little contribution from any other background process. An e ciency factor f
can be defined:
31. Project Report Results and Analysis 25
f =
R 40
0
PW (MT ) dMT
R 1
80
PW (MT ) dMT
, Ndata
MT <40 = (Ndata
MT >80 Nt¯t
MT >80)f (4.3)
where Pw describes a PDF,which is chosen to be a log-normal function, fitted to the Monte Carlo for the
W+jet when no cut is applied. This ratio is found to be 0.7 ± 0.037 where the error is found by varying the
plot by its respective errors and recalculating the integral. In addition error is induced due to the fact the
fit in figure 4.33 is not exact specifically, an underestimate in the < 40 range is clearly visible. Errors due to
RooFit in this region are found to change ±174 events out of at total of 2679 events. An error of ± 200 in
the region > 80 is estimated by varying fit by horizontal error bars for mass between 80-85. The quoted error
in f is calculated through propagation of errors from the described sources. Further error may be induced in
the calculation from RooFit which does not take into account the statistical uncertainties on the template
histograms. This means that shapes with larger statistical fluctuations get penalized by the fit resulting in
an underestimate; this is systemic. [9]
Figure 4.33: Fit template to the transverse mass for
W+jet Monte Carlo. Vertical error bars: Poisson
statistics and horizontal: bin width
Figure 4.34: Invariant mass plots for data regions B,C
and D. C and D are considered 100 % pure and C is
considered 82 % pure
The number of W+jets expected within the data is extrapolated by multiplying the above e ciency by
the number of data events in the sideband region (after subtracting the expected t¯t contribution). The value
is found to be 2580±220 for opposite sign events. The errors in these values are due to propagation of Poisson
statistical errors in the values of N as well as that in the factor defined above. The numbers quoted above
are for inclusive searches, for VBF the number of W+jet events expected in the data is just 4.11 ± 2.03. In
addition, 741 ± 76 W+Jets are found in the inclusive SS region, a ratio of OS:SS of 3.5:1 as expected.
4.4.5 QCD Background in the µ⌧had Channel
QCD multi-jet processes contain real muon and electrons as well as a ‘fake’ hadronic jet, this has a low
e ciency but will contribute due to its large cross-section (1000 x Z ! ⌧⌧). QCD will have a considerable
contribution and may be numerically estimated using the ABCD technique described in detail in [20]. In
this technique the data events are split into 4 regions: A,opposite sign isolated events (those which remain
in signal), B, opposite sign non-isolated region, C, same-sign isolated events and D, same sign non-isolated
region; where the relative isolation is required to be less than 0.1 meaning that B and D are assumed to be
pure QCD regions. It is assumed that the ratio of isolated to non-isolated events in opposite and same sign
regions are equivalent meaning number of QCD events in the final data selection may be calculated from:
n(A) =
n(C)n(B)
n(D)
.f(C) (4.4)
where f(C) describes the purity of region C as is found to be 0.82:
f(C) =
N(C)SS
iso N(W + jets)SS
iso N(otherbackground)SS
iso
N(C)SS
iso
(4.5)
Where N(W + jets)SS
is taken as 741 and the other backgrounds is mainly t¯t in the µ⌧had case (80
events) but will include + jets in the e⌧had case. This gives 3580 ± 324 QCD events in the signal region.
A similar analysis can be done for the VBF case which has much fewer data events, 5.32 ± 3.3 (stat)
events are found in that case out of 23 ± 4.8(stat) total data events.
In figures 4.35 and 4.36 the QCD distribution is modelled on the SS data shape but has been normalised
to have the number of events as calculated here.
32. Project Report Results and Analysis 26
4.4.6 t¯t, Di-boson and Z ! l+
l background in the µ⌧had channel
There will also be contributions from other sources such as t¯t which can fake tau-jets in both the µ⌧had and
e⌧had channels but this background is very small in the µ⌧had channel making up around 1 % of the data in
both the OS, where 140 events are found, and SS regions,where 80 events are found. This small contribution
is expected as the cross-section is limited by the large top quark mass. This is extrapolated from fits to the
MC for this process. In the VBF analysis only 1.88 ± 1.37 OS t¯t events and 0 SS events are found. Di-boson
backgrounds (WW and ZZ decays) are very small (expected 33 from MC in OS and SS pre-vbf and 0 in vbf
selection) and are combined with the W+Jet MC in the final figures.
There may also be background from other Z+jets processes this provides background from two sources:
• A second Drell-Yan muon faking a hadronic tau, these are OS .
• A recoiling jet faking a tau-jet
This is estimated using the control region around the Z resonance peak (80-110 GeV/c2
) when any second-
lepton veto is ignored and the number of events in this region is multiplied by a selection e ciency calculated
from ee and µµ data. 1618 events are found in this region of the data, multiplying this by the average
di-lepton selection e ciency, 0.225, calculated in section 4.3.2 gives 364 events. This is seen to make up just
2 % of the total number of post-selection events.
Non-VBF(stat.) VBF (stat.)
Diboson 33±5.7 0
t¯t 140 ± 12 1.88 ±1.37
Z (other jets/dileptons) 364 ± 19 0
W+Jets 2580 ± 220 4.11 ± 2.03
QCD 3580 ± 324 5.32 ±3.3
Z ! ⌧⌧ 11025 ± 105 12.99 ±3.60
Total Backgrounds 6964 ±392 11.3 ± 4.12
Total MC 17991 ± 406 24.30 ±5.46
Data 17994 ± 134 23 ±4.80
Expected S/B 61.3 % 53.5%
Expected S/
p
B 132 3.86
The errors quoted in the above table are statistical and in most cases are from Poisson statistics, however,
in the case of QCD and W+jets statistical errors from various discussed sources are added in quadrature.
This is also the case in the background and MC summation rows. The signal to background ratio given here
describes the ratio between the expected Z ! ⌧⌧ yield and the number of MC events. In the inclusive case 61
% of selected events are expected to be signal whereas in the VBF case this is reduced to 53% of events. This
reduction is not large and the yield of total data and expected S+B events is very close. The final Z ! ⌧⌧
inclusive and vbf signals are shown in figures 4.35 and 4.36. It is clear that both shape-wise and numerically
(within errors) the MC, when all backgrounds are accounted for, and data are reasonably consistent this
suggests that there is no huge excess indicating other particles are present and the background estimation is
accurate, however, statistical analysis is still needed to put a limit on this conclusion. For the VBF results the
total number of events is much smaller (23) but the shape remains similar, with the characteristic maximum
around 60. Statistical fluctuations are relatively large due to the small number of events now present. There
is still a very large fraction of QCD events remaining in this sample, this large fraction can now only be
reduced by improving the e ciency of the tau-jet trigger.
4.4.7 ⌧had+e Event Reconstruction and Background analysis
The W+jet and QCD background in e⌧had channel are estimated as described above and are found to be
1254 ± 35.41 and 2438 ± 234 respectively where the errors are derived in a similar way as those for the µ⌧had
case. In the QCD B and D are defined as having isolation >0.3 which is the isolation required for electrons
in the endcap where A and C are still defined as having isolation <0.1 as required for electrons in the barrel.
As well as the above described cuts a di-electron veto was added this helped reduce the background from
Z ! ee; there is a larger contribution from this process which is clearly visible around the Z resonance region
in both the data and MC. This is a result of the fact that electrons which have lost some energy due to
Bremsstrahlung/FSR can fake a tau signature (Section 4.3). As a result shape analysis is used to estimate
the number of Z ! l+
l events may by fitting the peak in the data which is visible around 90GeV/c2
with
the characteristic Breit-Wigner as seen in figure 4.40.
33. Project Report Results and Analysis 27
Figure 4.35: MC for Z ! ⌧⌧ along with other back-
ground, these are numerically consistent with small de-
viations in shape
Figure 4.36: MC for Z+Jet and W+jet and data which
will include background sources for µ⌧ VBF events
Figure 4.37: pre-VBF invarient mass plot-clear devia-
tion from MC -due to large amounts of background
Figure 4.38: VBF invarient mass plot for both data
and MC for Z+jets and other backgrounds
Figure 4.39: Signal for Z ! ⌧⌧ is parameterized as log
normal with statistical errors
Figure 4.40: Fit template to the Z resonance parame-
terized by Breit-Wigner with statistical errors
The number of events in the complete Breit-Wigner is found to be 2880 ± 265 by integrating the fit . The
characteristic tau-decay is then fitted to a log-normal function using RooFit, this is modeled on the µ⌧had
case where it was shown that there was little shape contribution from other di-leptons, the number of events
in the Z resonance region when the log-normal shape is found by integrating the fit in this region. This gives
1320 ± 134 events. The di↵erence BW-LogN is the found to be 1560 ±297; this suggests a total of 1560 ±
134 Z events which are faking that e+tau signature.
A prominent resonance is clearly visible in the MC too; the number of Z ! ll events there is found in
the same way to be 1382 ± 176 and 354 ±78 QCD events are found in this region.
4.4.8 +jets Background in the e⌧had Channel
This background contributes to the e⌧had channel only is a result of a photon faking a Z signature. An
estimate of its contribution can be found by defining a control region in which the di↵erence in between
the electron and tau is > 2.5 and where any di-electron cuts are ignored. The control region for this process
34. Project Report Results and Analysis 28
must also have |cot(✓e ✓track)| < 0.05.
Figure 4.41: for data and MC backgrounds ( con-
trol region)
Figure 4.42: Invarient Mass in the + jets control
region
The number of estimated photon+jet events is then:
NSignal = Ncontrol✏ (4.6)
where ✏ described an MC -measured e ciency for the OS region. This is found to be the ratio of MC +
QCD background events in signal region to MC+ QCD background events in control region. ✏OS is found to
be 0.17 ± 0.012 and ✏SS is found to be 0.44 ±0.01, where the error is statistical and found by propagating
statistical errors. Which results in 3690 ± 262 expected + jet events expected in the opposite sign data
and 775 ± 128 same sign data events. These are added to the QCD plot in figure 4.37.
The table below summarizes the numbers of events in the e⌧had channel for both VBF and non-VBF
processes.
Non-VBF (stat.) VBF (stat.)
Di-boson 28±5.29 0
t¯t 79 ± 8.89 0
Z (other jets/dileptons) 1560 ±134 0
+ jets 3065 ± 262 0
W+Jets 1254 ±35.41 1.42 ±1
QCD 2438± 234 4.08 ± 2.02
Z ! ⌧⌧ + Z resonance peak 8216 ± 90.64 -
Expected ! ⌧⌧ 6834 ± 198 5.22 ± 2.28
Total Backgrounds 8396 ± 378 5.5 ±2.51
Total MC 15258 ± 426 10.72±3.38
Data 15125 ±123 10 ±3.16
Expected S/B 45% 48%
Expected S/
p
B 55.3 1.59
There is a slight excess in the MC, this is possibly due to an over-estimate in the background calculations,
however, numerically the data and MC are consistent within errors when all backgrounds are considered. In
these results S/B’s of 45-48 % are found, this means that this percentage of total events originate from the
target Z decay, the cuts enforced on the selected events act to maximize this fraction but, o↵ course, much
better background exclusion is needed to get a pure signal. Figures 4.37 and 4.38 show the relative shapes of
the backgrounds and data for both inclusive and vbf results. In both cases the data is relatively consistent
with the sum of the MC processes suggesting no huge excess resulting from incorrect background analysis or
unaccounted for processes. Bin for bin there are some deviations, this could be a result of QCD and + jets
estimate where the histogram is modeled on the same-sign data (region C) and scaled. In order to get a
better estimate of shape an MC of the opposite sign QCD and + jets regions should be used. There is also
a larger tail in the VBF case which extends much further for MC than the observed data. This is probably
a result of the low luminosity of these reuslts and the fact that such small numbers ( < 1) are expected in
these regions for this luminosity. At increased luminosity the shape should match that of the inclusive results
with slight alterations due to reduced contributions from QCD.
35. Project Report Results and Analysis 29
4.4.9 Systemic, Statistical and Theoretical Uncertainty
All the errors quoted above are statistical and were either obtained from assuming Poisson statistics or via
ROOT, however, this does not take into account possible systemic errors which a↵ect the system as a whole.
Below is a list of systemic uncertainties:
• Trigger e ciencies:-The trigger and ID used to correct the MC are listed in appendix 3 and were
obtained from “tag-and-probe” [21]they have small dependence on transverse momentum and rapidity
corresponding to various detectors in CMS.
• Lepton ID e ciencies:-Ine ciencies in detection of electron and muon are small (<1%). These are
found using tag-and-probe techniques [29].
• Hadronic tau ID e ciencies:- These are taken from [21] where data samples are selected using only
the kinematic cuts as described in the present analysis and background is suppressed. The e ciency is
taken to be a ratio between the number of events that pass the tau ID requirement and the number of
preselected events. The uncertainty here is 23 %, in terms of number of events this introduces ±5.29
into the final µ⌧had VBF data and ±2.3 into the e⌧had final VBF data.
• Lepton Energy Scaling Uncertainties:-The e↵ect of energy scaling uncertainties on the acceptance was
calculated in [21] to be around 1 % based on ECAL resolution in the case of electrons and muon system
resolution in the case of muons.[6]
• Tau energy Scaling Uncertainties:- Found to be 3.2% [21] by taking into account the energies of the
reconstructed taus and varying these within their respective uncertainty. After each independent shift,
the missing transverse energy is recalculated and the event selection is repeated. The event yield is
compared to the nominal value and the relative di↵erence is quoted as the systematic uncertainty. This
accounts for a di↵erence of ±0.81 events in the µ⌧had VBF data and ± 0.35 in the e⌧had VBF data.
• Luminosity Uncertainty:- quoted as 4 % throughout the 2011A run giving di↵erences of ± 0.92 in the
µ⌧had VBF data and ± 0.4 in the e⌧had VBF data.
• Theoretical Uncertainty:- induced from the use of MC for background simulations and for Higgs decay
simulations as well as uncertainties due to the inaccuracy of the reconstruction methods used. This
arises from the uncertainty in the theoretical calculations of cross-sections and simulation of the physics.
It is estimated that the error in the VBF Higgs MC will be just 2 % [1] with similar results expected
for the SM MCs, in the ggH case this becomes 12%. These errors where found by comparing results
from di↵erent generators.
Uncertainty e⌧ µ⌧
Trigger 1 % 0.2%
Electron ID 1.3% -
Muon ID - 0.9 %
Tau ID 23% 23%
Electron Energy Scale 1.1% -
Muon Energy Scale - 1.1%
Tau Energy Scale 3.2% 3.2%
Luminosity 4% 4%
All the above uncertainties are taken into account within the LandS routine that is used to gain the final
cross-section value in the following analysis and are modeled as either log-normal or gamma functions.
4.4.10 Signal Events and Z ! ⌧⌧ cross section
The number of signal events is found by subtracting background from data.
The cross section may be extracted from the data by the following equation:
(pp ! Z ! ⌧⌧) =
N
✏ABrL
(4.7)
where N is the number of signal events extracted, A is the acceptance, ✏ is the selection e ciency, Br
is the decay branching ratio (0.224 for µ⌧had and 0.23 for e⌧had) and L is the integrated luminosity of the
2011A run which is quoted as 2.094fb 1
. These are summarized in the table below for both µ⌧had and e⌧had.
