Particle Physics in a nutshell

Particle Physics in a Nutshell
(or “the things we do at CERN”)
Raquel G´omez Ambrosio
Universit`a & INFN @Torino & CMS @CERN
Introduction at Maplesoft
June 13, 2016
Raquel Gomez Ambrosio Particle Physics in a Nutshell June 13, 2016 1 / 53

HiggsTools
HiggsTools is one of the many training networks from the Marie Sklodowska-Curie Actions.
13 European Universities
4 Research Institutes (DESY, MPI, PSI, CERN)
3 Private Partners (Maplesoft, Wolfram, Shell)



20 students & several senior physicists

higgstoolsAosta Valley, Italy. July 2015

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Aosta Valley, Italy. July 2015

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Where I work

My supervisors
Chiara Mariotti (CMS)
Giampiero Passarino (Univ. of Turin)

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Main Experiements at LHC
ATLAS, CMS, LHCb, ALICE

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Disclaimer
Summarized and incomplete history of the
Standard Model

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Historical Introduction: The Greek
Until the XIX century, humans didn’t think too much about the constituents of matter, but rather
about their properties. Studying them through alchemy and chemistry.
In the IV century B.C. some greek thinkers (Δημόκριτος, Επίκουρος) proposed the idea of the
atom as the smallest component of matter.
But the idea was thrown down by ᾿Αριστοτέλης and his school, alleging that if matter would
be discrete instead of continuous, that would imply some kind of vacuum inside it, which is an
uncomfortable concept.
Philosophy and Physics have always been closely related.

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Historical Introduction: The 19th Century
In the XIX century scientists became more interested in the nature of matter: Dalton confirmed
Laviosier’s law for conservation of matter and Avogrado postulated his law for the number of
particles in a gas. Defying the previously accepted interpretation.
This was finally confirmed with Mendeleev and the periodic table in 1869.

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The 20th century: The Golden Years for particle physics
By the beginning of the XX century everyone had their own atomic model: Thomson, Rutherford,
Bohr, Sommerfeld, Schr¨odinger, Dirac . . .
And the foundations of particle physics where established:
1897: Discovery of the electron (J.J. Thomson)
1911: Discovery of the proton (Rutherford)
1932: Discovery of the neutron (Chadwick)

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The 20th Century: The Golden Years for particle physics
Things seemed to ﬁnally make sense, but that wouldn’t last long. In the following years, particle-
detecting techniques (and technologies) improved and dozens of new particles were found.

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Some had been predicted by the theorists: pions (π0, π+, π−), positron (e+), neutrinos (ν) . . .

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Some had been predicted by the theorists: pions (π0, π+, π−), positron (e+), neutrinos (ν) . . .
But other were completely gratuitous: µ, K0, K+, K−, Λ, Ξ−, Ξ0, Ω0 , . . .
The lightest of these particles were called leptons, the intermediate ones were called mesons, and
the heaviest were called baryons

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Murray Gell-Mann: The Eightfold way
Murray Gell-Mann decided to sort the mesons and baryons in octets, according to their properties

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Some group theory: SU(N)
Group thery was already a tool used in particle physics: At that time, SU(2) was known to be the
group characterizing “spin”, the 3 generators of SU(2) are called ”Pauli Matrices” by physicists.
For the case of mesons and baryons, SU(3) seemed to be more appropriate: SU(3) acts on 3
elements and has rank 2 (i.e. 2 Casimir operators). Casimir operators are very important in
physics, we use them to characterize objects. In the case of the eightfold way: Q and S.
Look at the fundamental representation:
3 ⊗ ¯3 = 8 ⊕ 1
3 ⊗ 3 ⊗ 3 = 10 ⊕ 8 ⊕ 8 ⊕ 1
The elements of the vector space where this group acts where called “Quarks”. In particular: Up,
Down, and Strange (u,d,s).

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Murray Gell-Mann: The Quarks
This is how the “Quark model” was established. Murray Gell-Mann won the nobel prize in 1969.
And he deserves to be called The Mendeleev of physics
and, yes, we do call the generators of SU(3) “Gell-Mann matrices” . . .

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J/Ψ
In 1974 something dramatic happened: a heavy meson with a very long mean life was discovered.
“It’s as though someone came upon an isolated village in Peru or the Caucasus where people
live to be 70,000 years old.” D.Griﬀths

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J/Ψ
After some months of debate the riddle was solved: If we have 4 fundamental leptons (e, νe , µ, νµ)
why not have 4 fundamental quarks too?
Gell-Mann’s ﬂavor symmetry was promoted, SU(3) → SU(4) and the Quark model survived. The
fourth Quark was called “Charm” (as well as the new casimir operator).

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The Standard Model
More leptons and quarks were discovered until we arrived to the current picture: These are the
fundamental particles that constitute all matter that we know.

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Interlude: Quantum Mechanics, the change of paradigm
Recall, in the early XX century we lived the Quantum revolution. Planck, Born, DeBroglie, Einstein,
Heisenberg, Schr¨odinger, . . . had established a very successful framework in which particles were
neither waves nor matter. But both at the same time.

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Interlude: Quantum Mechanics, the change of paradigm
Quantum Coﬀee, Toronto

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The Standard Model: Tomonaga, Feynman, Schwinger (& Dyson)
Particles can not be described as tiny static spheres. We understand particles to be perturbations
in a ﬁeld, and as such they are described by a wave function.
The wave function, tells us the probability of ﬁnding the particle in a certain point at a certain
time. For instance, for an electron:
LDirac = ¯ψ(i cγµ
∂µ − mc2
)ψ, ψ → ψeiθ
Global U(1) symmetry
The γ matrices are the 4-dim representation of SU(2),
however we like to call them “Dirac Matrices”

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∂µ − mc2
)ψ, ψ → ψeiθ
What happens if we promote the global symmetry to a local one: θ → θ(x)?
The Lagrangian will be symmetric under a local U(1) as long as . . .
Aµ → Aµ −
1
qe
∂µθ(x), ∂µ → Dµ = ∂µ + iqe Aµ
L = LDirac −
1
4
Fµν
Fµν , Fµν = ∂µAν − ∂ν Aµ

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∂µ − mc2
)ψ, ψ → ψeiθ
What happens if we promote the global symmetry to a local one: θ → θ(x)?
The Lagrangian will be symmetric under a local U(1) as long as . . .
Aµ → Aµ −
1
qe
∂µθ(x), ∂µ → Dµ = ∂µ + iqe Aµ
L = LDirac −
1
4
Fµν
Fµν , Fµν = ∂µAν − ∂ν Aµ
The new ﬁeld Aµ is the photon! It appeared naturally by making our global symmetry local.

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Yang-Mills theories
In 1954, C.N. Yang and R. Mills decided to extend this technique to other Lagrangians, with
non-abelian symmetry groups. And they found that it worked pretty well.
Strong force → SU(3): 8 new ﬁelds (dimension of SU(3)), called Gluons: Gµν
Weak Force → SU(2): 3 new ﬁelds: Z0, W +, W −
The Gauge Bosons Z0, W +, W − were observed at CERN in 1983. Thanks to some experiments
designed by Carlo Rubbia and Simon Van der Meer.
They also got their Nobel Prize . . . those were great years for particle physics.

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The Standard Model: Electromagnetic, Electroweak and Strong Force
Particle Fever

The Standard Model: Electromagnetic, Electroweak and Strong Force

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Unfortunately it is not so easy . . .
On one hand, the weak force is entangled with the electromagnetic one → SU(2) ⊗ U(1)
On the other hand, the ﬁelds of SU(2) are not really Z0, W +, W −, but a mixture of them.
Such a “mixture”, i.e. the breaking of a symmetry, must imply the appearance of new
particles (one per broken symmetry, Goldstone’s theorem )
And this new particle appearing is . . .

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The Higgs Mechanism
The Higgs boson can not be classified as “matter” (like leptons and quarks) nor as a gauge
field (like photons, gluons . . . )
In 1964, Brout, Englert and Higgs came up with an interpretation of the Higgs as a “sea of
particles where all other particles float”
Englert and Higgs won the Nobel Prize for this in 2013

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Long Story Short:
The Higgs boson messes up everything

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The “true” Standard Model Lagrangian

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Higgs Boson searches
Finally, you are ready to hear about my work . . .

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The Higgs boson
On July 4th 2012, the Higgs boson discovery was oﬃcially announced at CERN.

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Higgs Boson Production at LHC. For a theorist: Feynman Diagrams
Gluon-Gluon Fusion: Main production channel
Vector Boson Fusion: Second most important channel
If you want more . . . click here:
http://www.scholarpedia.org/article/The_Higgs_Boson_discovery

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Higgs Boson Production at LHC. For an experimentalist: Events

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CMS Detector, the Compact Muon Solenoid

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CMS Detector, the Compact Muon Solenoid: Pileup

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The interface between theorists and experimentalists: The analysis
A big part of our work is to ﬁnd a common framework for
theorists and experimentalists to work together

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The analysis
This is the main process that we study in Turin: Vector Boson Fusion
p
p
Tagged jet 1
Tagged jet 2
Underlying Events
Underlying Events

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The Higgs decays before it can be detected
H
Z
Z
e−
e+
µ+
µ−
H
W −
W +
e−
¯νe
µ+
νµ
Given any of this processes, and the initial conditions, it is relatively easy for a theorist to
provide a prediction for it (i.e, a numerical value for the probability of it to happen)
But . . . we don’t really know the initial conditions!
Also, processes in the detector interfere with each other, they are not isolated.

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The Monte Carlo generators
One dimensional Monte Carlo generator:
One of the challenges for the next years is to develop the technology to calculate the biggest
possible amount of Monte Carlo events, with the maximum precision and the minimum amount of
entropy (i.e. computer memory and time)

The analysis
A theoretical prediction looks more like this:

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How do you compare observations with predictions, then?
Monte Carlo generators + Experimental data
These are called “The Nobel plots”

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New physics?
Since this is a historical talk, I have to tell you about a
might-be historical event

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December 2015 . . . it happened again

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It could be just an statistical artifact
The ﬂuctuation is inside the “margin of error”

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However, no one seems to care:
Number of submissions related to the new resonance, by date: Until today, 445
(Credits: Dr.Andr´e David, http://jsfiddle.net/adavid/bk2tmc2m/show/)

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Are we in front of new physics?
We live for sure exciting times for particle physics
However we will only get conﬁrmation about this discovery in August at ICHEP conference
in Chicago. Feel free to ask me about it then!
Even if this new particle gets ruled out, we have plenty of work to do . . .

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Open questions in particle physics
Main question now is: How can we incorporate gravity to the SM
In principle it is possible to formulate gravity as a Yang-Mills theory, with symmetry group SO(3,1),
or “Lorenz group” for physicists.
SO(3,1) is isomorphic to SU(2)⊗SU(2) and would correspond to a gauge boson with Spin 2.
However, after doing this one encounters fundamental problems, mainly:
How to quantize this theory (i.e., make it compatible with quantum physics)
How to renormalize this theory (i.e., make it convergent at very high energies)
Is the 750 particle “the” Graviton?

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Recommended reading:
“Introduction to Elementary Particles ”, D. Griﬃths (very easy)
“Diagrammatica: The Path to Feynman Diagrams”, M. Veltman (advanced)
“Simple Introduction to Particle Physics” (mathematical)
( click here: http://arxiv.org/pdf/0810.3328v1.pdf)

Particle Physics in a nutshell

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