Accelerators and Colliders

Transcription

1 Accelerators and Colliders References Robert Mann: An introduction to particle physics and the standard model Tao Han, Collider Phenomenology, Particle Data Group, (J. Beringer et al., Phys. Rev. D 86, (2012)) P529 Spring,

2 Modern particle accelerators Accelerate charged particles by RF Confine and focus magnetically Synchrotrons (circular): relatively compact (synchrotron radiation rate (E/m) 4 /R: limitation for e ± ) LINACs (linear): SLAC, injectors, possible future ILC, CLIC P529 Spring,

3 Extract beam to collide in fixed target s = (p b + p t ) 2 = m 2 b + m2 t + 2E bm t May produce secondary beams, including neutrinos, antiparticles, unstable particles (π, K) P529 Spring,

4 Collision rate = σl σ = cross section L = ΦAρ t = instantaneous luminosity [L = (# beam particles /time) (# target particles/area)] Φ = flux = number beam particles/area-time = n b v (n b = number density in beam, v = velocity); A = area of beam ρ t = number target particles/area = n t L (L = target thickness) P529 Spring,

5 Colliders/storage rings: e + e (B factories, LEP, LEP II); e ± p (HERA); pp (Tevatron); heavy ion (RHIC, LHC); pp (LHC) Possible future e e + LINACs (ILC, CLIC) to avoid synchrotron radiation Different beams/particles possible than fixed target Much higher energies in CM Detectors at one or more beam intersections e +, p produced by fixed target Pre-accelerators needed; may be acceleration in collider One or two beam pipes Superconducting magnets at Tevatron, LHC P529 Spring,

6 Tevatron (Fermilab): pp, s 2 1 TeV; length 4 miles P529 Spring,

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9 LHC (LEP tunnel, CERN): pp, s 2 4 TeV 2 7; length 27 Km P529 Spring,

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12 Collision rate = Lσ, where L = instantaneous luminosity = fn 1 N 2 /(4πσ x σ y ) N 1,2 = numbers of particles per bunch f = crossing frequency (increase by multiple bunches) Colliding beam n 1 n t = 1/f σ x,y = transverse profiles of beams (4πσ x σ y = transverse area) Cross section/luminosity units (Han) σ 1 cm 2 = barn = mb = µb = nb = pb = fb L 1 cm 2 s 1 = nb 1 s 1 = pb 1 s 1 = fb 1 s 1 P529 Spring,

13 Integrated luminosity: L = Ldt; total events: Lσ 1 yr π 10 7 s 10 7 s (operation fraction) Tevatron: several fb 1 ; LHC: fb 1 P529 Spring,

14 Collider Detectors Particle ID (charge, interactions), lifetimes (displaced vertices), momentum (magnetic field), energy/resolution (calorimeters) Stopping power [MeV cm 2 /g] Lindhard- Scharff Nuclear losses µ Anderson- Ziegler Bethe µ + on Cu Radiative effects reach 1% [GeV/c] Muon momentum Radiative Radiative losses Without δ βγ [MeV/c] Minimum ionization E µc [TeV/c] Missing energy (neutrinos, lightest supersymmetric particles (dark matter?)) P529 Spring,

15 Huge detectors surround intersection point Vertex, tracking, electromagnetic calorimeters (ECAL), hadron calorimeters (HCAL), µ chambers hadronic calorimeter E-CAL beam pipe tracking ( in B field ) vertex detector muon chambers P529 Spring,

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18 Tevatron: CDF, D0; LHC: ATLAS, CMS (LHCB, ALICE) P529 Spring,

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25 Some beam fragments (along beam pipe) unobserved Observed longitudinal momentum not conserved Transverse momentum conserved (for small p t for partons) Unbalanced p T stable (or long-lived) weakly interacting particle ( missing energy ) (e.g., ν, LSP) P529 Spring,

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27 Triggering (huge rates, pileup), data storage/access, grid computing Simulation programs (Pythia, Herwig, Isajet, Madgraph, ) Jet finding algorithms P529 Spring,

28 Collider Kinematics Consider high p T events; use cylindrical coordinates p T, p z, ϕ p µ = (E, p x, p y, p z ) = (E, p T cos ϕ, p T sin ϕ, p z ) (E = m 2 + p 2, p T = p sin θ, p z = p cos θ; p p ) Rapidity: (tanh y = β z in CM) p µ = (m T cosh y, p T cos ϕ, p T sin ϕ, m T sinh y) y = 1 2 ln E + p z = ln E + p z E p z m T m T = m 2 + p 2 T = tanh 1 p z E P529 Spring,

29 Lorentz boost to frame with β 0 ẑ: y y y 0 where y 0 = 1 2 ln 1 + β 0 1 β 0 = tanh 1 β 0 y = 0 in longitudinal rest frame: β 0 = p z /E p µ = (m T, p T cos ϕ, p T sin ϕ, 0) Lorentz-invariant phase space: d 3 p E = dp xdp y dp z E = p T dp T dϕ dp z E = p T dp T dϕ dy p T, ϕ, dy = dp z /E invariant under longitudinal boosts (along ±ẑ) P529 Spring,

30 Pseudo-rapidity (easier to measure): η 1 2 ( 1 + cos θ ln 1 cos θ = ln tan θ ) 2 η y for m 0 Parametrize high-p T track by p T, ϕ, η (CMS, ATLAS: η 2.5 5) Separation between two tracks or jets (jet algorithms) (Lego plot) R = ( η) 2 + ( ϕ) 2 = (η 2 η 1 ) 2 + (ϕ 2 ϕ 1 ) 2 P529 Spring,

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32 Short Distance Processes at Hadron Colliders LHC (Tevatron): pp F + X ( pp F + X): e.g., F = 2 jets Short distance processes: large ŝ = p 2 F ; usually large momentum p T transverse to beam σ H A H B }{{} hadrons F + X = ij x A,B = (T. Han, ) ŝ/se ±y F dx A dx B f A i (x A, Q 2 )f B j (x B, Q 2 ) }{{} PDFs σ ij F (x A, x B ) }{{} hard subprocess P529 Spring,

33 p qq qq, q q q q, q q GG Gq Gq, GG q q, GG GG q q W, Z, γ f f, q q (W, Z, γ)g p q q G q q q G q p p Factorization theorems (long distance and short distance) Calculate σ ij F in perturbation theory (short) DGLAP for PDFs (Q p T or ŝ) (long) Fragmentation/hadronization (long) P529 Spring,

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35 dy (pb/gev) σ/dp 2 d T 11-1 CMS L = 34 pb 10 y <0.5 ( 3125) y <1 ( 625) 1 y <1.5 ( 125) 1.5 y <2 ( 25) 2 y <2.5 ( 5) 2.5 y <3 NLO NP (PDF4LHC) Exp. uncertainty Anti-k T R=0.5 s = 7 TeV p T (GeV) P529 Spring,