Download Physics of the Large Hadron Collider Lecture 1: Fundamentals of the

Physics of the Large Hadron Collider
Lecture 1: Fundamentals of the LHC
Johan Alwall, SLAC
Michelson lectures at Case Western Reserve
April 13-16, 2009
Outline
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Introduction: What is the LHC?
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Fundamentals of QCD
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Fundamentals of Electroweak Physics
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The Standard Model and the Higgs
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What is the LHC
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What is the LHC
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What is the LHC
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14 TeV proton-proton collider
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27 km (17 miles) in circumference
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Luminosity: Initial: 1033 /cm2s (10 fb-1/year)
Nominal: 1034 /cm2s (100 fb-1/year)
4 detectors:
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ATLAS, CMS: general-purpose detectors
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ALICE: Specialized for heavy-ion collisions
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LHC-B: One-arm large- detector for bottom-quark
physics
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What is the LHC
The CMS (Compact Muon Solenoid) detector
cms.cern.ch
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What is the LHC
The ATLAS detector
atlas.ch
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What is the LHC
Real ATLAS events (from startup run)
Images from atlas.ch
“Splash” event, when the LHC beam
was steered into a magnet upstream
Cosmic ray muon event
from the detector
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What is the LHC
Simulated ATLAS events
Images from atlas.ch
Supersymmetry event with jets
and muons
Higgs boson event with H→ZZ
recoiling agains jet
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Fundamentals of QCD
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The theory of strong interactions; describes
interactions between quarks and gluons
Represented by a gauge theory with the gauge
group SU(3)C (for color)
Non-abelian field theory
→ gluon carries color charge (self-interacting)
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Fundamentals of QCD
Running of QCD coupling due to quantum
loops leads to “asymptotic freedom”:
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Fundamentals of QCD
Can be understood in terms of screening and
anti-screening by vacuum bubbles:
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Fundamentals of QCD
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At low energy (~1 GeV) QCD is confining
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No free color charges
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Quarks/gluons always confined in hadrons
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Different degrees of freedom at large and small
energies (quarks, gluons vs. hadrons, pions)
–
No analytic proof, but strong evidence from lattice
simulations that SU(3) is confining Millennium $1M Prize!
Coupling constant s 10 x stronger than
electromagnetic coupling EM (at Z mass)
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Parton distribution functions
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Probability for finding a quark or gluon in a
hadron
Function of x (momentum fraction of parton)
and 2 (momentum transfer in process)
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Parton distribution functions
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Probability for finding a quark or gluon in a
hadron
Function of x (momentum fraction of parton)
and 2 (momentum transfer in process)
Increases as power-law for small x and
logarithmically for large Q2
Behaviour governed by DGLAP equation
(Dokshitzer-Gribov-Lipatov-Altarelli-Parisi)
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Parton distribution functions
●
●
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Probability for finding a quark or gluon in a
hadron
Function of x (momentum fraction of parton)
and 2 (momentum transfer in process)
Increases as power-law for small x and
logarithmically for large Q2
Behaviour governed by DGLAP equation
(Dokshitzer-Gribov-Lipatov-Altarelli-Parisi)
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Splitting functions and DGLAP
QCD bremsstrahlung – logarithmic divergences
as energy fraction z → 0 and virtuality k2 → 0
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Leading contribution from the soft and collinear regions of
phase space
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Subsequent emissions factorize (no interference in
soft/collinear regions) → Allows log resummation to all orders
–
Integration over multiple emissions gives evolution from
interaction scale 2 to hadronic scale ~ 1 GeV
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Parton showering
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Can describe QCD radiation in the soft and
collinear limit as subsequent independent
emissions, called “parton shower”.
Every hard interaction always associated with
extra QCD radiation
Initial high-energy
parton gives showerlike “jet”
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Parton showering
At end of shower, need hadronization ansatz to
pass from partons to color neutral hadrons
–
Phenomenological models, based on general
behaviour of QCD, e.g. the Lund string model or
Herwig cluster model
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Simulation of LHC collision
Hadronization,
hadron decay
Hard interaction
Parton
showers
Underlying
event / multiple
interactions
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Missing transverse energy
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Fundamental concept for hadron colliders
(will be used many times in these lectures)
Momentum fraction x1, x2 of incoming partons
→ event boosted in the lab frame
If invisible particle (e.g. neutrino) produced,
cannot determine boost along beam direction
Only the missing transverse momentum can be
measured:
where the sum is over all visible particles i
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Fundamentals of Elecroweak Physics
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Enrico Fermi explained beta decay of nuclei as
4-fermion interactions n → p e- e with mass
scale Mweak~ 90 GeV in denominator
(corresponding to intermediate vector boson!)
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Fundamentals of Elecroweak Physics
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Enrico Fermi explained beta decay of nuclei as
4-fermion interactions n → p e- e with mass
scale Mweak~ 90 GeV in denominator
(corresponding to intermediate vector boson!)
Looks like SU(2) gauge theory with massive
gauge vector bosons
Non-renormalizable, gives scattering probability
> 1 at high energies (unitarity violation)
Solution: Massless gauge bosons getting mass
from spontaneous symmetry breaking
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The Higgs mechanism
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Introduce scalar Higgs field which couples to the
massless gauge bosons and fermions
Let this field get a non-zero vacuum expectation
value due to Higgs potential
Rewrite
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The Higgs mechanism
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Gives mass to vector bosons and fermions in
proportion to their couplings to the Higgs
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Gauge fields (gauge couplings):
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Matter fields (Yukawa couplings):
Three of the four Higgs degrees of freedom
become longitudinal components of
and
mix to give Z and γ
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The Standard Model
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The Standard Model
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QCD SU(3) x Weak SU(2) x Hypercharge U(1)
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Electromagnetic A linear combination of W3 and B
Weak SU(2) dynamically broken
Three generations of weak doublet fermion
fields (left-handed doublets, right-handed singlets)
Top quark Yukawa coupling close to 1, all other
Yukawas small – no explanation for this
hierarchy within the model
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The Standard Model
Scientific American
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The Higgs boson mass
Higgs mass (and top and W masses before they
were seen) determined by precision measurements
–
Particle masses affect precision observables
through quantum loop contributions
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Examples of observables used:
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Mass and decay widths of the W and Z bosons
Branching ratios of Z boson to leptons, hadrons, bottom
Weak mixing angle sin2W
Forward-backward asymmetries at LEP
Top mass
EM, weak and QCD couplings EM, Weak and s
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Indirect mass determinations
SM Higgs mass upper limit: 163 GeV
Excluded by LEP
Excluded by Tevatron
(March 2009)
Direct measurements
Indirect determination
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Higgs boson decays
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Higgs hunting at the Tevatron
CDF and D0 combined search, March 2009
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Higgs hunting at the Tevatron
CDF individual search channels, March 2009
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The Higgs boson mass, cont.
Higgs mass
only unknown
parameter of the Standard Model
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95% CL upper limit from precision measurements
at 163 GeV
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Must be <800 GeV to conserve unitarity of weak
boson scattering (i.e. do its job)
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Like all masses in a quantum field theory, mass is
given by
where mH2 is given by quantum loop corrections
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Naturalness and the Higgs
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't Hooft: A theory is “natural” if the size of
corrections not too much larger than bare mass
“Fine-tuning”: The precision by which the bare
mass term must cancel the corrections
Corrections for elementary scalar are quadratic
in new-physics cutoff (for fermions and gauge
bosons, corrections are logarithmic)
Main loop corrections from strongest coupled
particles: top, W, Z and Higgs self-couplings
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Higgs mass corrections
New
physics
cutoff
1% fine-tuning
10% fine-tuning
The “Veltman throat”
where loop corrections
cancel(excluded by
indirect SM bounds
at >95% CL)
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The hierarchy problem
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If there is no new physics besides the Standard
Model and gravity, the cutoff scale is
~MPl~1018 GeV, giving a finetuning of 10-34
To reduce finetuning to an “acceptable” 10%
level, there must be new physics at around 1
TeV, i.e. within reach for the LHC!
More about ideas for new physics that solves
the hierarchy problem, in the next lecture!
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Summary and plan
Today I have talked about:
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What is the LHC?
–
Fundamentals of QCD
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Fundamentals of Electroweak Physics
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Parton density functions
Parton showering, hadronization
Elements of simulations of LHC collisions
The Higgs mechanism
The Standard Model
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Properties of the Higgs boson
The Hierarchy problem
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Summary and plan
Next lecture: New Physics at the LHC
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Problems with the Standard Model
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Classes of solutions to the hierarchy problem
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Supersymmetry
Extra dimentions
Little Higgs models
Other New Physics ideas
rd
3 lecture: Simulation at the LHC
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Recommended reading
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LHC:
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QCD:
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http://public.web.cern.ch/public/en/LHC/LHC-en.html
QCD and Collider Physics, Ellis, Sterling, Webber,
Cambridge 1996
Electroweak physics, Standard Model:
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An introduction to Quantum Field Theory,
Peskin, Schröder, Westview 1995
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Gauge Theory of Elementary Particle Physics,
Cheng, Li, Oxford 1988
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Recommended reading
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The Higgs boson:
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Precision measurements of the Standard Model:
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“Higgs Boson Theory and Phenomenology”,
Carena, Haber, Prog.Part.Nucl.Phys.50:63-152,2003
The LEP Electroweak Working Group,
http://lepewwg.web.cern.ch/LEPEWWG/
Higgs searches at the Tevatron:
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The CDF and D0 Higgs pages:
http://www-cdf.fnal.gov/physics/new/hdg/hdg.html
http://wwwd0.fnal.gov/Run2Physics/WWW/results/higgs.htm
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