A review presentation about the research and experiments done at HERA related to Deep Inelastic Scattering, High Energy Physics and Quantum Chromodynamics

1. “DEEP INELASTIC SCATTERING AT HERA: A
REVIEW OF EXPERIMENTAL RESULTS IN THE
LIGHT OF QUANTUM CHROMODYNAMICS”
SUBMITTED BY:
SUBHAM CHAKRABORTY;
MS/19/PH/010;
419/137.
SUPERVISOR: COORDINATOR:
DR. AKBARI JAHAN; DR. TADO KARLO;
ASSISTANT PROFESSOR; HEAD OF THE DEPARTMENT;
DEPARTMENT OF PHYSICS. DEPARTMENT OF PHYSICS.
NORTH EASTERN REGIONAL INSTITUTE OF SCIENCE AND TECHNOLOGY.
A PRESENTATION SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENT FOR PAPER 8299

2. CONTENTS:
 INTRODUCTION
 HERA COLLIDER: H1 AND ZEUS EXPERIMENTS
 BRIEF INTRODUCTION TO DEEP INELASTIC SCATTERING
 EXCLUSIVE MEASUREMENTS AT HERA
 SEARCHES FOR NEW PHYSICS IN ep COLLISION
 SUMMARY AND CONCLUSION
 REFERENCES

3. INTRODUCTION

4.  The proton is quite an amazing particle.
If free, it does not decay on any timescale
people have been able to explore. It takes
an energetic missile to destroy it by deep-
inelastic scattering (DIS).
 What is really known about the proton is
actually quite limited. The proton’s
charge has been determined to be +1, its
mass has been measured to be 1.6×10-27
kg, and its spin is 1/2. And it has
structure, which is mostly explored in
momentum space, and is the main subject
of this review.
 The tool of choice to investigate the
proton structure is generally DIS
(1). The probes are generally
leptons. The data discussed in this
review come from HERA, the first
and so far, only electron proton (ep)
collider, which operated at DESY
from 1992 to 2007. HERA had four
interaction zones, but only two of
them were occupied by the two ep
collider experiments, ZEUS and H1.

5.  A varied program of physics has developed at HERA, for instance in the physics of
quasi-real photon interactions. This presentation will however concentrate on the results
achieved at HERA by the H1 and ZEUS experiments in the area of deep inelastic
scattering. These have had a major impact in several areas: the structure of the proton, the
investigation of the mechanism of diffractive scattering, and the properties of the strong
and electroweak interactions.

6. HERA COLLIDER: H1 AND
ZEUS EXPERIMENTS

7.  HERA is 6.3 km in circumference and collides electrons or positrons of up to 30 GeV
with protons of up to 820 GeV at four interaction points around the ring. The bunches of
electrons and protons cross at each interaction point every 96 ns. The design luminosity
in 1.5×1031 cm-2s-1.
 The electron storage ring is based on conventional magnets but the high energy of the
protons requires superconducting magnets providing a bending field of approximately
4.7 T.
 HERA began operation in 1992 and has run with electrons and positrons of up to 27.7
GeV and protons of 820 GeV.
 The maximum luminosity achieved by HERA up to spring 1997 was ∼0.9×1031 cm-2s-1.

8. Fig. 1: - An aerial view of the DESY
laboratory showing the location of the
underground HERA ring. The other track
shown called PETRA is a particle storage
ring.
Fig. 2: - This is a picture of part of the
HERA accelerator inside the tunnel about
25 meters under the ground. The beam pipes
must be evacuated and huge magnetic fields
must be applied all around the accelerator to
contain and focus the particle beams.

9. Fig. 3: - The luminosity delivered by
HERA between 1992 and mid-1997 as
a function of day of the run.

10. Fig. 4: - The HERA collider with the four experiments H1, ZEUS, HERMES and
HERA-B on the left and its pre-accelerators on the right.

11. Fig. 5: - Picture of the inside of the HERA tunnel, showing the superconducting
dipoles on top for the proton ring, and the positron (or electron) ring below.

12. H1 DETECTOR
 The main component of the H1 detector was the finely segmented liquid argon
calorimeter (LAr) with resolutions, as measured with test beams, of 0.11√(E/GeV) and
0.50√(E/GeV) for electromagnetic and hadronic particles, respectively.
 The LAr was surrounded by a superconducting coil, which provided a solenoidal
magnetic field of 1.16 T and an instrumented iron structure acting as both a shower tail
catcher and a muon detector.
 In 1996 an upgrade was performed, during which the backward detectors were replaced
by a backward drift chamber attached to a new lead fiber calorimeter with a high-
resolution (0.07 √(E/GeV)) electromagnetic section (EMC) followed by a hadronic
section. In the upgraded configuration, the innermost central tracking detector of H1 also
contained the central and backward silicon trackers.

13. Fig. 6: - Schematic view of H1 detector.

14. Fig. 7: - Schematic view of H1 detector.

15. ZEUS DETECTOR
 The main component of the ZEUS detector was the uranium–scintillator calorimeter. It
was segmented into one EMC and either one or two hadronic sections.
 Under test-beam conditions, the energy resolutions were 0.18√(E/GeV) and
0.35√(E/GeV) for the EMC and hadronic sections, respectively. The timing resolution of
the calorimeter was 1 ns for energy deposits greater than 4.5 GeV.
 Scintillator-tile presampler detectors were mounted in front of the calorimeter. Charged
particles were tracked in the central tracking detector, which operated in a magnetic field
of 1.4 T provided by a thin superconducting solenoid that was positioned inside the
calorimeter.
 Planar drift chambers provided additional tracking in the forward and rear directions.

16. Fig. 8: - Schematic view of ZEUS detector.

17. DEEP INELASTIC
SCATTERING

18.  DIS has been the tool of choice to reveal the structure of the proton within the
framework of pQCD, which itself is tested in the process. The scattering process itself
is connected to the electroweak interaction, namely the exchange of photons and Z
bosons for neutral-current (NC) interactions and W+ and W- bosons for charged-current
(CC) interactions.

19.  Basic idea: smash a well known probe
on a nucleon or nucleus in order to try
to figure out what is inside.
 Photons are well suited for that purpose
because their interactions are well
understood.
 Deep inelastic scattering: collision
between an electron and a nucleon or
nucleus by exchange of a virtual
photon.

20. KINEMATICS AND STRUCTURE
FUNCTIONS

21. s = (k+p)2 = 4EeEp; Centre-of-mass energy squared
Q2 = -q2 = (k-k’)2 = 2EeE’e(1-cosθ’e); Negative squared four momentum
transfer
ν = q.p/Mp; Energy transfer in proton rest frame
νmax = s/(2Mp); Maximum energy transfer
y = (q.p)/(k.p) = ν/νmax; Fraction of energy transfer
x = Q2/(2q.p); Bjorken scaling variable
W2 = (p + q)2; Invariant mass of total hadronic
system

22. These variables are not all independent. For instance, we have the following relations:
𝑊𝑊2
= 𝑄𝑄2
1 − 𝑥𝑥
𝑥𝑥
+ 𝑚𝑚𝑝𝑝
2
Q2 = xys
where mp is the mass of the proton and s is the center of mass energy squared of the
lepton-proton interaction.
At the Born level, i.e., ignoring higher order electroweak processes, the double
differential cross sections for charged lepton proton neutral current scattering are given
by:
𝑑𝑑2
𝜎𝜎𝑁𝑁𝑁𝑁
𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵
(𝑙𝑙±
𝑝𝑝)
𝑑𝑑𝑑𝑑𝑑𝑑𝑄𝑄2
=
2𝜋𝜋𝛼𝛼2
𝑥𝑥𝑄𝑄4
[𝑦𝑦2
2𝑥𝑥𝐹𝐹1 𝑥𝑥, 𝑄𝑄2
+ 2 1 − 𝑦𝑦 𝐹𝐹2 𝑥𝑥, 𝑄𝑄2
∓ 2𝑦𝑦 − 𝑦𝑦2
𝑥𝑥𝐹𝐹3 𝑥𝑥, 𝑄𝑄2
]

23. In terms of F2, FL, and xF3
𝑑𝑑2
𝜎𝜎𝑁𝑁𝑁𝑁
𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵
(𝑙𝑙±
𝑝𝑝)
𝑑𝑑𝑑𝑑𝑑𝑑𝑄𝑄2
=
2𝜋𝜋𝛼𝛼2
𝑥𝑥𝑄𝑄4
[ 1 + 1 − 𝑦𝑦2
𝐹𝐹2 𝑥𝑥, 𝑄𝑄2
− 𝑦𝑦2
𝐹𝐹𝐿𝐿 𝑥𝑥, 𝑄𝑄2
∓ 1 + 1 − 𝑦𝑦2
𝑥𝑥𝐹𝐹3 𝑥𝑥, 𝑄𝑄2
}]
In lowest order QCD and when massless partons are considered FL = 0
𝐹𝐹2 𝑥𝑥, 𝑄𝑄2
= �
𝑞𝑞
𝐴𝐴𝑞𝑞 𝑄𝑄2
𝑥𝑥𝑥𝑥 𝑥𝑥 + 𝑥𝑥�
𝑞𝑞 𝑥𝑥
𝑥𝑥𝐹𝐹3 𝑥𝑥, 𝑄𝑄2
= �
𝑞𝑞
𝐵𝐵𝑞𝑞 𝑄𝑄2
𝑥𝑥𝑥𝑥 𝑥𝑥 − 𝑥𝑥�
𝑞𝑞 𝑥𝑥
Where the functions q(x) and �
𝑞𝑞 𝑥𝑥 are the quark and anti-quark densities in the proton
respectively.

24. 𝐴𝐴𝑞𝑞 𝑄𝑄2
= 𝑒𝑒𝑙𝑙
2
𝑒𝑒𝑞𝑞
2
+ 2 𝑒𝑒𝑙𝑙 𝑒𝑒𝑞𝑞 𝑣𝑣𝑒𝑒𝑣𝑣𝑞𝑞
1
4 𝑠𝑠𝑠𝑠𝑠𝑠2 𝜃𝜃𝑤𝑤𝑐𝑐𝑐𝑐𝑐𝑐2 𝜃𝜃𝑤𝑤
𝑄𝑄2
𝑄𝑄2 + 𝑀𝑀𝑍𝑍
2 +
𝑣𝑣𝑙𝑙
2
+ 𝑎𝑎𝑙𝑙
2
𝑣𝑣𝑞𝑞
2
+ 𝑎𝑎𝑞𝑞
2
1
4 𝑠𝑠𝑠𝑠𝑠𝑠2 𝜃𝜃𝑤𝑤𝑐𝑐𝑐𝑐𝑐𝑐2 𝜃𝜃𝑤𝑤
2
𝑄𝑄4
(𝑄𝑄2+𝑀𝑀𝑍𝑍
2
)2
𝐵𝐵𝑞𝑞 𝑄𝑄2
= 2 𝑒𝑒𝑙𝑙 𝑒𝑒𝑞𝑞 𝑎𝑎𝑙𝑙𝑎𝑎𝑞𝑞
1
4 𝑠𝑠𝑠𝑠𝑠𝑠2 𝜃𝜃𝑤𝑤𝑐𝑐𝑐𝑐𝑐𝑐2 𝜃𝜃𝑤𝑤
𝑄𝑄2
𝑄𝑄2 + 𝑀𝑀𝑍𝑍
2 +
𝑣𝑣𝑙𝑙𝑎𝑎𝑙𝑙𝑣𝑣𝑞𝑞𝑎𝑎𝑞𝑞
1
4 𝑠𝑠𝑠𝑠𝑠𝑠2 𝜃𝜃𝑤𝑤𝑐𝑐𝑐𝑐𝑐𝑐2 𝜃𝜃𝑤𝑤
2
𝑄𝑄4
(𝑄𝑄2+𝑀𝑀𝑍𝑍
2
)2
The differential cross section for charged current lepton-proton interactions is given
by:
𝑑𝑑2
𝜎𝜎𝐶𝐶𝐶𝐶
𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵
(𝑙𝑙±
𝑝𝑝)
𝑑𝑑𝑑𝑑𝑑𝑑𝑄𝑄2
=
𝜋𝜋𝛼𝛼2
8𝑠𝑠𝑠𝑠𝑠𝑠4𝜃𝜃𝑤𝑤
1
(𝑄𝑄2+𝑀𝑀𝑊𝑊
2
)2
[ 1 + 1 − 𝑦𝑦2
𝑊𝑊
2
±
∓ 1 − 1 − 𝑦𝑦2
𝑊𝑊
3
±
]

25. 𝑊𝑊2
+
= 𝑥𝑥 �
𝑖𝑖
𝑑𝑑𝑖𝑖 𝑥𝑥 + �
𝑢𝑢𝑖𝑖 𝑥𝑥
𝑊𝑊2
−
= 𝑥𝑥 �
𝑖𝑖
𝑢𝑢𝑖𝑖 𝑥𝑥 + ̅
𝑑𝑑𝑖𝑖 𝑥𝑥
𝑊𝑊3
+
= 𝑥𝑥 �
𝑖𝑖
𝑑𝑑𝑖𝑖 𝑥𝑥 − �
𝑢𝑢𝑖𝑖 𝑥𝑥
𝑊𝑊3
−
= 𝑥𝑥 �
𝑖𝑖
𝑢𝑢𝑖𝑖 𝑥𝑥 − ̅
𝑑𝑑𝑖𝑖 𝑥𝑥
where we define W2 (W3) as x times the
sum (difference) of the quark and
antiquark densities. Only those quarks and
anti-quarks, which are allowed by charge
conservation at the quark vertex are taken
into consideration.
According to DGLAP equations:
𝑑𝑑𝑞𝑞𝑓𝑓(𝑥𝑥, 𝑄𝑄2
)
𝑑𝑑 log 𝑄𝑄2
=
𝛼𝛼𝑠𝑠(𝑄𝑄2
)
2𝜋𝜋
�
𝑥𝑥
1
[𝑞𝑞𝑓𝑓 𝑧𝑧, 𝑄𝑄2
𝑃𝑃𝑞𝑞𝑞𝑞
𝑥𝑥
𝑧𝑧
+ 𝐺𝐺 𝑧𝑧, 𝑄𝑄2
𝑃𝑃𝑞𝑞𝑞𝑞
𝑥𝑥
𝑧𝑧
]
𝑑𝑑𝑑𝑑
𝑧𝑧

26. 𝑑𝑑𝑑𝑑 𝑥𝑥, 𝑄𝑄2
𝑑𝑑 log 𝑄𝑄2
=
𝛼𝛼𝑠𝑠 𝑄𝑄2
2𝜋𝜋
�
𝑥𝑥
1
[𝐺𝐺 𝑧𝑧, 𝑄𝑄2
𝑃𝑃
𝑔𝑔𝑔𝑔
𝑥𝑥
𝑧𝑧
+ �
𝑓𝑓
[𝑞𝑞𝑓𝑓 𝑧𝑧, 𝑄𝑄2
+ �
𝑞𝑞𝑓𝑓 𝑧𝑧, 𝑄𝑄2
]𝑃𝑃
𝑔𝑔𝑔𝑔(
𝑥𝑥
𝑧𝑧
)]
𝑑𝑑𝑑𝑑
𝑧𝑧
Where G(x,Q2) is the gluon density in the proton and the splitting functions Pij(y)
define the probability of obtaining a parton i from the splitting of parton j, where parton
i has a fraction y of the x value of parton j.
The measurements of the scaling violations at small x thus give an indirect
measurement of the gluon density, whereas the scaling violations at large x, where the
contribution from gluon splitting is negligible, allow a determination of the strong
coupling constant αs.

27. At O(αs) QCD the structure function FL becomes non-zero:
𝐹𝐹𝐿𝐿 =
𝛼𝛼𝑠𝑠(𝑄𝑄2
)
𝜋𝜋
�
𝑥𝑥
1
𝑑𝑑𝑑𝑑
𝑦𝑦
𝑥𝑥
𝑦𝑦
2
4
3
𝐹𝐹2 𝑦𝑦, 𝑄𝑄2
+ 2 1 −
𝑥𝑥
𝑦𝑦
𝑦𝑦𝑦𝑦 𝑦𝑦, 𝑄𝑄2

28. EXCLUSIVE
MEASUREMENTS AT HERA

29. JET PRODUCTION AND STRONG
COUPLING MEASUREMENT
 Due to the asymptotic freedom property of the strong interaction, the quarks or gluons
produced with high energy during the scattering cannot exist as free particles and must
form hadrons. The hadronisation process leads to “jets” of quasi-stable particles that are
measured in the detectors.
 The DIS events contain most of the time a single jet corresponding to the scattered parton.
In the so-called Breit frame of reference (the virtual photon rest frame) this scattered quark
acquire no transverse momentum w.r.t the virtual photon direction.
 The jet production rate in the Breit frame is sensitive to the strong coupling αs.

30.  The full acceptance and high granularity of the H1 and ZEUS detectors at HERA allow a
precise reconstruction of the hadronic final state and consequently the measurement of jet
production.
 The decrease of the strong coupling with increasing scale (decreasing distance) is
observed, confirming the hypothesis of asymptotic freedom of QCD and the prediction as
formulated by the equation,
𝛼𝛼𝑆𝑆 𝑄𝑄2
=
𝛼𝛼𝑆𝑆 𝜇𝜇2
1 + 𝛽𝛽 𝛼𝛼𝑆𝑆 𝜇𝜇2 log �
𝑄𝑄2
𝜇𝜇2
where µ is an arbitrary scale at which the reference coupling is defined, while Q2 is here
the scale at which the strong interaction takes place and β is a negative coefficient.

31. Fig. 9: - The mechanism of jet production in the Breit frame (left) and the
measurements of the strong coupling as a function of the transverse jet moments (right).

32. THE HEAVY FLAVOUR CONTENT
OF THE PROTON
 An interesting feature of deep inelastic scattering is the production of heavy quarks,
namely charm c or beauty b. The production can be seen as the interaction between the
electron and a heavy quark produced in a short time fluctuation of a gluon.
 The measurement of DIS processes with a heavy quark in the final state requires special
experimental techniques to identify beauty or charm hadrons. Indeed, the heavy quarks
“hadronise” into heavy mesons or baryons which subsequently decay into lighter hadrons.
They are identified in the hadronic final state of DIS events as resonances with known
masses. For instance, D* mesons are identified in the golden decay
mode 𝐷𝐷∗
→ 𝐷𝐷𝐷𝐷 → 𝐾𝐾𝜋𝜋+
𝜋𝜋−
.

33.  An alternative experimental technique makes use of the long lifetime of heavy hadrons,
which give rise to displaced decay vertices in the event. These vertices can be
reconstructed using silicon detectors. These detectors provide very precise measurements
and allow for the reconstruction of the decay vertices with a precision of a few hundred
microns, enough to identify for instance beauty hadrons which fly typically 2 mm before
their decay into stable particles. The reconstruction of displaced (secondary) vertices “tag”
therefore heavy quarks in DIS events.
 The reduced cross section of DIS processes with a heavy quark (c or b) in the final state
can be parameterised in terms of charm or beauty structure functions:
𝜎𝜎𝑟𝑟
⁄
𝑐𝑐 ̅
𝑐𝑐 𝑏𝑏�
𝑏𝑏
= 𝐹𝐹2
⁄
𝑐𝑐 ̅
𝑐𝑐 𝑏𝑏�
𝑏𝑏
−
𝑦𝑦2
𝑌𝑌+
𝐹𝐹𝐿𝐿
⁄
𝑐𝑐 ̅
𝑐𝑐 𝑏𝑏�
𝑏𝑏

34.  The measurement of heavy quark production in DIS allows to extract the “heavy” structure
functions and therefore the charm or the beauty content of the proton. This content can be
compared with the nominal content in light quarks.
Fig. 10: - The contributions to the total
cross sections 𝑓𝑓𝑐𝑐 ̅
𝑐𝑐
and 𝑓𝑓𝑏𝑏�
𝑏𝑏
shown as a
function of x for two different Q2
values. The inner error bars show the
statistical error, the outer error bars
represent the statistical and systematic
errors added in quadrature. The 𝑓𝑓𝑐𝑐 ̅
𝑐𝑐
from ZEUS obtained from
measurements of D* mesons and the
predictions of the H1 NLO QCD fit are
also shown.

35. THE SEARCH FOR EXOTIC
RESONANCES
 The known hadrons are composed of two or three quarks. Hadrons containing more than
three quarks are not forbidden within the present theory of strong interactions.
 The search for resonances decaying to K+n in the fixed-target experiments data revealed
an evidence for the existence of a narrow baryon resonance with a mass of around 1530
MeV and positive strangeness.
 This hadron may be explained as a bound state of five quarks, i.e., as a pentaquark, Θ+ =
uudd ̅
𝑠𝑠. The quantum numbers of this state also allow decays to 𝐾𝐾𝑆𝑆
0
𝑝𝑝.
 A strange pentaquark decay mode 𝐾𝐾𝑆𝑆
0
𝑝𝑝 has been searched by ZEUS collaboration.

36.  The results support the existence of such state, with a mass of 1521.5 ± 1.5 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠. +
2.8 − 1.7 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠. MeV and a Gaussian width consistent with the experimental resolution
of 2 MeV. The observation is not confirmed by a similar analysis performed by H1.
 Searches for other types of pentaquarks were also performed. A candidate for an anti-
charmed pentaquark Θc = uudd ̅
𝑐𝑐 was reported by the H1 collaboration.
 The decays Θ𝑐𝑐→𝐷𝐷∗
𝑝𝑝 were searched for in the ep data collected at HERA I. The obtained
invariant mass spectrum, indicate a resonance with a mass of 3099 ± 3(𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠) ± 5(𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠)
MeV and a measured Gaussian width of 12 ± 3 MeV, compatible with the experimental
resolution. This signal was however not confirmed by the ZEUS experiment.

37. Fig. 11: - Example of a signal attributed to an exotic resonance which can be assimilated
to a pentaquark state Θ+ = uudd ̅
𝑠𝑠 with a mass of approximately 1530 MeV.

38. DIFFRACTION
 The electron-proton interactions can also proceed not via direct electron proton scattering
but via a colour-less object, evaporated from the proton. This sort of interactions, called
also “diffractive”, occur in about 10% of DIS processes.
 Such “soft” interactions involve slow gluon exchanges and long distances and cannot be
calculated in the perturbative QCD. They are commonly discussed in terms of exchanges
with net vacuum quantum numbers, though the exact nature of these exchanges is not well
known.
 The presence of processes of the type ep → eXP in deep-inelastic scattering (DIS) at low
Bjorken-x at the HERA collider offers a uniquely well controlled environment in which to
study the QCD properties and structure of diffraction. Several measurements of the semi-
inclusive cross section for this ‘diffractive DIS’ process have been made by the H1 and
ZEUS collaborations.

39. Fig. 12: - A scheme of the diffractive interaction in ep collisions and the
definition of the associated variables.

40. Fig. 13: - An example of
reduced differential
diffractive cross section
measurement for xIP =
0.03: (left) as a function
of the fraction of
momentum carried by
the struck parton β at
various Q2 values and
(right) as a function of
Q2 in various β – x bins.

41. SEARCHES FOR NEW
PHYSICS IN ep COLLISION

42. The three highest energy
colliders providing data are LEP (e+e-),
HERA (e±p) and Tevatron (p ̅
𝑝𝑝).In total,
LEP experiments accumulated
approximately 3.5 fb-1 for centre-of-
mass energy ranging from 89 to 209
GeV. HERA and Tevatron experiments
will collect a similar amount of
luminosity at the end of their respective
data taking periods.

44.  The LEP and the Tevatron are “annihilation”
colliders, which can produce any fermion-
antifermion pair which couples to a boson
produced in the s -channel. Therefore, new
particles which do not couple directly to the SM
fermions can be produced.
 In contrast, HERA is a “scattering” collider, where
the exchanged SM boson is in the t-channel. Only
new bosons that couple both to leptons and quarks
could be produced in the s-channel of eq
collisions and the rate would depend on the non-
SM e-q-boson coupling.
Fig. 13: - Differential partonic
luminosities ⁄
(𝑑𝑑𝑑𝑑 𝑑𝑑𝑀𝑀2
) at
LEP, HERA and Tevatron as a
function of the centre-of-mass
energy of the parton parton
collision.

45. A few searches for new physics at HERA are briefly described below.
SUSY
 A popular extension the Standard Model is supersymmetry (SUSY). SUSY unifies internal
symmetries with Lorentz invariance and associates supersymmetric partners (s particles) to
the known SM particles.
 Supersymmetric models provide solutions to many problems of the SM (hierarchy, fine-
tuning, unification) and predict spectacular final states in high-energy particle collisions.
Despite extensive studies at colliders and elsewhere, no trace of SUSY has yet been
detected.
 The production of single s particles is possible if the conservation of the multiplicative
quantum number RP is violated (R–parity is RP = (–1)3B + L +2S where B, L, and S denote the
particle’s baryon number, lepton number, and spin respectively).

46.  In R–parity violating models, s–channel squark production at HERA via the electron-
quark-squark Yukawa coupling (λ) is possible. A special case is the stop ( ̃
𝑡𝑡) which in
many SUSY scenarios is the lightest s quark.
Fig. 14: - Exclusion domain of
the RP – violating coupling as a
function of the squark mass
(left). The interpretation of
these limits in a constrained
model based on the grand
unification theory as an
exclusion domain in the plane
𝑚𝑚0 − 𝑚𝑚 ⁄
1 2,where 𝑚𝑚0(𝑚𝑚 ⁄
1 2) is
the scaler (fermionic) mass
parameter at the unification
scale.

47. LEPTOQUARKS
 Leptoquarks are hypothetical bosons which couple to a lepton and a quark via a Yukawa
coupling (denoted λ).
 In the Standard model, both quarks and leptons occur in left-handed SU(2) doublets and
right-handed SU(2) singlets. The symmetry between quarks and leptons leads to the
cancellation of triangle anomalies which make the SM renormalizable.
 Leptoquarks appear in theories in which this symmetry is more fundamental.
 Leptoquarks (LQs) are colour triplets, which would be pair produced in either q�
𝑞𝑞 or gg
interactions at p ̅
𝑝𝑝 or pp colliders. Because they carry electroweak charge, they would also
be pair produced in 𝑒𝑒+
𝑒𝑒−
collisions.

48.  The experimental signature of the leptoquarks is a narrow peak in the electron–jet or
neutrino–jet mass spectra. In the absence of such observation, exclusion limits on the
model parameters are calculated. For a coupling of electroweak strength λ = 0.3,
leptoquarks lighter than ~ 290 GeV are excluded by both ZEUS and H1.
Fig. 15: - The excluded domain in the
plane coupling-mass for leptoquark
searches at HERA, compared with
searches at LEP and Tevatron.

49. SEARCHES FOR EXCITED
FERMIONS
 In the Standard Model, the fermion masses span more than 6 orders of magnitude, from
neutrinos with masses of the order of 1 eV to the top quark, the heaviest known fermion
with a mass of 174 GeV. This fermion mass hierarchy is one of the greatest puzzles of
the Standard Model (SM).
 It can naturally be explained if the SM fermions are composite, so that various fermion
masses can be built from different ground states of the composing particles. In this case
excited states of the known fermion may also exist and be produced at colliders.

50.  Excited neutrinos can be produced in electron–proton collisions at HERA via the t–
channel charged current (CC) reaction 𝑒𝑒±
𝑝𝑝 → 𝑣𝑣∗
𝑋𝑋. The cross section is much larger in e-
p collisions than in e+p collisions due to the helicity enhancement, specific to CC-like
processes. The most recent analysis uses a data sample corresponding to an integrated
luminosity of 114 pb-1 data sample collected by the H1 collaboration.
 The excited neutrinos are searched for in the following decay channels: 𝜈𝜈∗
→ 𝜈𝜈𝜈𝜈, 𝜈𝜈𝜈𝜈, 𝑒𝑒𝑒𝑒.
The W and Z bosons are reconstructed in the hadronic channel W, Z → jets. The analysis
covers 80% (70%) of the total branching ratio for f = - f / (f = f /).
 For the events selected in the νγ and νZ channels, the neutrino is assumed to be the only
non-detected particle in the event and its kinematics is reconstructed assuming the balance
of the transverse momenta and the conservation ∑ 𝐸𝐸 − 𝑃𝑃𝑧𝑧 = 2𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
𝑒𝑒
= 55.2 𝐺𝐺𝐺𝐺𝐺𝐺.

51. Fig. 16: – The invariant mass of the excited neutrino candidates reconstructed in the three
decay channels.
The present results greatly extend previous searched domains at HERA and confirm the
HERA unique sensitivity for excited neutrinos with masses beyond LEP reach.

52. THE MODEL INDEPENDENT
NEW PHYSICS SEARCH
 The data can also be investigated in a model independent approach in order to search for
deviations from the Standard Model predictions. The idea is to define a common phase
space for all types of final state identified particles.
 The events are then classified according to the particle content. Kinematical quantities are
defined, like the mass and the scalar transverse momentum, and a non-biased search
algorithm is applied in order to look for local deviations that may appear due to for
instance to a hypothetical multi–channel decay of a heavy particle.

53.  The analysis has also been performed by the H1 collaboration. “Objects” are defined from
particle identification: electron (e), muon (µ), photon (γ), jet (j) and neutrino (ν) (or non-
interacting particles). All final states are analysed having at least two objects with a
transverse momentum (PT) above 20 GeV and in the polar angle range 100 < θ < 1400.
 All selected events are then classified into exclusive event classes (e.g. ej, jj, jν) according
to the number and types of objects detected in the final state.
 The general search at high PT gives a global view of the physics rates as a function of the
final state topology and require a good understanding of the Standard Model and of the
detector. This type of analysis is necessary for the searches program at present and future
colliders, as it provides an extra security belt against the unexpected phenomena that may
occur in a new pattern, different from what is predicted from the existing models.

54. Fig. 17: - The result of the H1 general search. The data (points) and Standard Model
expectation (histogram) for all event classes with a SM expectation greater than 0.1 events
are shown.

55. SUMMARY AND
CONCLUSION

56.  The H1 and ZEUS Collaborations published the final combined cross section for
inclusive deep-inelastic ep scattering at HERA. This is one of HERA’s legacies.
 The knowledge of the structure of baryonic matter, dominating the visible universe, has
made huge progress in the last decades, thanks to an impressive effort to unravel the
nucleon structure in fixed target experiments and at the HERA ep collider.
 With the advent of the new “Large Hadron Collider”, which will begin proton–proton
collisions at a centre-of-mass energy of 14 TeV in 2008, or by enabling even more
ambitious DIS experiments beyond HERA, the question of the next matter substructure
may be answered.

57.  The study of exclusive vector meson production in DIS and the first observation of charm
production in DIS has also opened up the possibility of further tying down the gluon
distribution.
 A whole new field of study of the deep inelastic structure of diffraction has been opened
up by HERA. This study has already produced much of interest and has the promise of
truly revolutionising our understanding of the mechanism of diffraction.
 Finally, the data at high Q2 and x are allowing detailed tests of the charged and neutral
weak current, and at the edge of the kinematic region currently accessible there are
indications of an excess of events which could indicate new physics.

58. REFERENCES

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Int. J. Mod. Phys., A 1543 (1998) [arXiv:hep-ex/9712030].
3. R. Hofstadter, R. W. McAllister, Phys. Rev., A 13, 217 (1955).
4. C. G. Callan, D. J. Gross, High-energy electroproduction and the constitution of the electric,
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5. A. Bodek et al., Phys. Rev. D, 20, 1471 (1979).
6. Quarks and Leptons by Halzen and Martin.
7. J. Friedman, H. Kendall, and R. Taylor, 1990 Nobel lectures.
8. Introduction to Elementary particles by David J. Griffiths.

60. THANK YOU.