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 Introduction: What is the LHC? Fundamentals of QCD Fundamentals of Electroweak Physics The Standard Model and the Higgs 2
What is the LHC 3
What is the LHC 4
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 5
What is the LHC The CMS (Compact Muon Solenoid) detector cms.cern.ch 6
What is the LHC The ATLAS detector atlas.ch 7
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 8
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 9
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) 10
Fundamentals of QCD Running of QCD coupling due to quantum loops leads to asymptotic freedom : 11
Fundamentals of QCD Can be understood in terms of screening and anti-screening by vacuum bubbles: 12
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 Millennium $1M Prize! Coupling constant s 10 x stronger than electromagnetic coupling EM (at Z mass) 13
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) 14
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) 15
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) 16
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 17
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 showerlike jet 18
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 19
Simulation of LHC collision Hadronization, hadron decay Hard interaction Parton showers Underlying event / multiple interactions 20
Missing transverse energy 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 21
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!) 22
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 23
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 24
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 25
The Standard Model 26
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 27
The Standard Model Scientific American 28
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 sin2 W Forward-backward asymmetries at LEP Top mass EM, weak and QCD couplings EM, Weak and s 29
Indirect mass determinations SM Higgs mass upper limit: 163 GeV Excluded by LEP Excluded by Tevatron (March 2009) Direct measurements Indirect determination 30
Higgs boson decays 31
Higgs hunting at the Tevatron CDF and D0 combined search, March 2009 32
Higgs hunting at the Tevatron CDF individual search channels, March 2009 33
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 mh2 is given by quantum loop corrections 34
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 35
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) 36
The hierarchy problem 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! 37
Summary and plan Today I have talked about: What is the LHC? Fundamentals of QCD Fundamentals of Electroweak Physics Parton density functions Parton showering, hadronization Elements of simulations of LHC collisions The Higgs mechanism The Standard Model Properties of the Higgs boson The Hierarchy problem 38
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 rd 3 lecture: Simulation at the LHC 39
Recommended reading LHC: QCD: http://public.web.cern.ch/public/en/lhc/lhc-en.html 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 40
Recommended reading The Higgs boson: Precision measurements of the Standard Model: 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: 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 41