Physics of the Large Hadron Collider Lecture 1: …Physics of the Large Hadron Collider Lecture 1: Fundamentals of the LHC Johan Alwall, SLAC Michelson lectures at Case Western Reserve

Physics of the Large Hadron Collider

Lecture 1: Fundamentals of the LHC

Johan Alwall, SLAC

Michelson lectures at Case Western ReserveApril 13-16, 2009

Johan Alwall - Fundamentals of the LHC 2

Outline

● Introduction: What is the LHC?● Fundamentals of QCD● Fundamentals of Electroweak Physics● The Standard Model and the Higgs


What is the LHC


What is the LHC


What is the LHC

● 14 TeV proton-proton collider ● 27 km (17 miles) in circumference● Luminosity: Initial: 1033 /cm2s (10 fb-1/year)

Nominal: 1034 /cm2s (100 fb-1/year)● 4 detectors:

– ATLAS, CMS: general-purpose detectors

– ALICE: Specialized for heavy-ion collisions

– LHC-B: One-arm large- detector for bottom-quark physics


What is the LHC

The CMS (Compact Muon Solenoid) detector

cms.cern.ch


What is the LHC

The ATLAS detector

atlas.ch


What is the LHC

Real ATLAS events (from startup run)

“Splash” event, when the LHC beamwas steered into a magnet upstreamfrom the detector Cosmic ray muon event

Images from atlas.ch


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


Fundamentals of QCD

● 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)


Fundamentals of QCD

Running of QCD coupling due to quantum loops leads to “asymptotic freedom”:


Fundamentals of QCD

Can be understood in terms of screening and anti-screening by vacuum bubbles:


Fundamentals of QCD

● At low energy (~1 GeV) QCD is confining– No free color charges

– Quarks/gluons always confined in hadrons

– 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

● Coupling constant s 10 x stronger than

electromagnetic coupling EM (at Z mass)

Millennium $1M Prize!


Parton distribution functions

● 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)





● Increases as power-law for small x and logarithmically for large Q2

● Behaviour governed by DGLAP equation (Dokshitzer-Gribov-Lipatov-Altarelli-Parisi)


Splitting functions and DGLAP

QCD bremsstrahlung – logarithmic divergences as energy fraction z → 0 and virtuality k2 → 0

– Leading contribution from the soft and collinear regions of phase space

– 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


Parton showering

● 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 shower-like “jet”


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


Simulation of LHC collision

Hard interaction

Partonshowers

Hadronization,hadron decay

Underlying event / multiple interactions


Missing transverse energy

● Fundamental concept for hadron colliders(will be used many times in these lectures)

● Momentum fraction x1, x

2 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


Fundamentals of Elecroweak Physics

● 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!)


Fundamentals of Elecroweak Physics

● 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


The Higgs mechanism

● 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


The Higgs mechanism

● Gives mass to vector bosons and fermions in proportion to their couplings to the Higgs– Gauge fields (gauge couplings):

– Matter fields (Yukawa couplings):

● Three of the four Higgs degrees of freedom become longitudinal components of

● and mix to give Z and γ


The Standard Model


The Standard Model

● QCD SU(3) x Weak SU(2) x Hypercharge U(1)

– 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


The Standard Model

Scientific American


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

– Examples of observables used:● Mass and decay widths of the W and Z bosons ● Branching ratios of Z boson to leptons, hadrons, bottom

● Weak mixing angle sin2W

● Forward-backward asymmetries at LEP● Top mass

● EM, weak and QCD couplings EM

, Weak

and s


Indirect mass determinations

Indirect determination

Direct measurementsSM Higgs mass upper limit: 163 GeV

Excluded by LEP Excluded by Tevatron(March 2009)


Higgs boson decays


Higgs hunting at the Tevatron

CDF and D0 combined search, March 2009


Higgs hunting at the Tevatron

CDF individual search channels, March 2009


The Higgs boson mass, cont.

Higgs mass only unknown parameter of the Standard Model– 95% CL upper limit from precision measurements

at 163 GeV

– Must be <800 GeV to conserve unitarity of weak boson scattering (i.e. do its job)

– Like all masses in a quantum field theory, mass is given by

where mH

2 is given by quantum loop corrections


Naturalness and the Higgs

● '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


Higgs mass corrections

New physics cutoff

1% fine-tuning

10% fine-tuning The “Veltman throat”where loop correctionscancel(excluded by indirect SM boundsat >95% CL)


The hierarchy problem

● If there is no new physics besides the Standard Model and gravity, the cutoff scale is~M

Pl~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!


Summary and plan

Today I have talked about:– What is the LHC?

– Fundamentals of QCD● Parton density functions● Parton showering, hadronization● Elements of simulations of LHC collisions

– Fundamentals of Electroweak Physics● The Higgs mechanism

– The Standard Model● Properties of the Higgs boson● The Hierarchy problem


Summary and plan

Next lecture: New Physics at the LHC– Problems with the Standard Model

– Classes of solutions to the hierarchy problem● Supersymmetry● Extra dimentions● Little Higgs models

– Other New Physics ideas

3rd lecture: Simulation at the LHC


Recommended reading

● LHC:– http://public.web.cern.ch/public/en/LHC/LHC-en.html

● QCD:– QCD and Collider Physics, Ellis, Sterling, Webber,

Cambridge 1996

● Electroweak physics, Standard Model:– An introduction to Quantum Field Theory,

Peskin, Schröder, Westview 1995

– Gauge Theory of Elementary Particle Physics, Cheng, Li, Oxford 1988


Recommended reading

● The Higgs boson:– “Higgs Boson Theory and Phenomenology”,

Carena, Haber, Prog.Part.Nucl.Phys.50:63-152,2003

● Precision measurements of the Standard Model:– The LEP Electroweak Working Group,

http://lepewwg.web.cern.ch/LEPEWWG/

● Higgs searches at the Tevatron:– The CDF and D0 Higgs pages:

http://www-cdf.fnal.gov/physics/new/hdg/hdg.html http://www-d0.fnal.gov/Run2Physics/WWW/results/higgs.htm

Documents

Physics of the Large Hadron Collider Lecture 1: …Physics of the Large Hadron Collider Lecture 1: Fundamentals of the LHC Johan Alwall, SLAC Michelson lectures at Case Western Reserve