Collider Phenomenology From basic knowledge to new physics searches

Transcription

1 Collider Phenomenology From basic knowledge to new physics searches Tao Han University of Wisconsin Madison Lecture series, TsingHua University, Beijing, China (July 26 30, 2006)

2 Collider Phenomenology From basic knowledge to new physics searches Tao Han University of Wisconsin Madison Lecture series, TsingHua University, Beijing, China (July 26 30, 2006) I. Colliders and Detectors II. Basics Techniques and Tools for Collider Physics III. An e + e Linear Collider IV. Hadron Colliders V. New Physics Searches at Hadron Colliders

3 I. Colliders and Detectors The energy: (A). High-energy Colliders: E cm s { 2E1 2E 2 in the c.m. frame p 1 + p 2 = 0, 2E1 m 2 in the fixed target frame p 2 = 0. s (p 1 + p 2 ) 2 = { (E1 + E 2 ) 2 in the c.m. frame p 1 + p 2 = 0, m m (E 1E 2 p 1 p 2 ).

4 I. Colliders and Detectors The energy: (A). High-energy Colliders: E cm s { 2E1 2E 2 in the c.m. frame p 1 + p 2 = 0, 2E1 m 2 in the fixed target frame p 2 = 0. s (p 1 + p 2 ) 2 = { (E1 + E 2 ) 2 in the c.m. frame p 1 + p 2 = 0, m m (E 1E 2 p 1 p 2 ). The luminosity: Colliding beam n 1 n t = 1/f L fn 1 n 2 /a, in units of #particles/cm 2 /s cm 2 s 1 = 1 nb 1 s 1 10 fb 1 /year.

5 Current and future high-energy colliders: Hadron s L δe/e f #/bunch L Colliders (TeV) (cm 2 s 1 ) (MHz) (10 10 ) (km) Tevatron p: 27, p: LHC %

6 Current and future high-energy colliders: Hadron s L δe/e f #/bunch L Colliders (TeV) (cm 2 s 1 ) (MHz) (10 10 ) (km) Tevatron p: 27, p: LHC % e + e s L δe/e f polar. L Colliders (TeV) (cm 2 s 1 ) (MHz) (km) ILC % 3 80,60% CLIC % ,60% 33 53

7 Current and future high-energy colliders: Hadron s L δe/e f #/bunch L Colliders (TeV) (cm 2 s 1 ) (MHz) (10 10 ) (km) Tevatron p: 27, p: LHC % e + e s L δe/e f polar. L Colliders (TeV) (cm 2 s 1 ) (MHz) (km) ILC % 3 80,60% CLIC % ,60% (B). An e + e Linear Collider The collisions between e and e + have major advantages: The system of an electron and a positron has zero charge, zero lepton number etc., = it is suitable to create new particles after e + e annihilation. With symmetric beams between the electrons and positrons, the laboratory frame is the same as the c.m. frame, = the total c.m. energy is fully exploited to reach the highest possible physics threshold.

8 With well-understood beam properties, = the scattering kinematics is well-constrained. Backgrounds low and well-undercontrol. It is possible to achieve high degrees of beam polarizations, = chiral couplings and other asymmetries can be effectively explored.

9 With well-understood beam properties, = the scattering kinematics is well-constrained. Backgrounds low and well-undercontrol. It is possible to achieve high degrees of beam polarizations, = chiral couplings and other asymmetries can be effectively explored. Disadvantages Large synchrotron radiation due to acceleration, ( E ) 4. E 1 R m e Thus, a multi-hundred GeV e + e collider will have to be made a linear accelerator. This becomes a major challenge for achieving a high luminosity when a storage ring is not utilized; beamsstrahlung severe.

10 (C). Hadron Colliders LHC: the next high-energy frontier Hard Scattering outgoing parton proton underlying event outgoing parton final-state radiation proton underlying event initial-state radiation

11 (C). Hadron Colliders LHC: the next high-energy frontier Hard Scattering outgoing parton proton underlying event outgoing parton final-state radiation proton underlying event initial-state radiation Advantages Higher c.m. energy, thus higher energy threshold: S = 14 TeV: M 2 new s = x 1 x 2 S M new 0.2 S 3 TeV.

12 Higher luminosity: /cm 2 /s 100 fb 1 /yr. Annual yield: 1B W ± ; 100M t t; 10M W + W ; 1M H 0...

13 Higher luminosity: /cm 2 /s 100 fb 1 /yr. Annual yield: 1B W ± ; 100M t t; 10M W + W ; 1M H 0... Multiple (strong, electroweak) channels: q q, gg, qg, b b colored; Q = 0, ±1; J = 0,1,2 states; WW, WZ, ZZ, γγ I W = 0,1,2; Q = 0, ±1, ±2; J = 0,1,2 states.

14 Higher luminosity: /cm 2 /s 100 fb 1 /yr. Annual yield: 1B W ± ; 100M t t; 10M W + W ; 1M H 0... Multiple (strong, electroweak) channels: q q, gg, qg, b b colored; Q = 0, ±1; J = 0,1,2 states; WW, WZ, ZZ, γγ I W = 0,1,2; Q = 0, ±1, ±2; J = 0,1,2 states. Disadvantages Initial state unknown: colliding partons unknown on event-by-event basis; parton c.m. energy unknown: E 2 cm s = x 1 x 2 S; parton c.m. frame unknown. largely reply on final state reconstruction.

15 Higher luminosity: /cm 2 /s 100 fb 1 /yr. Annual yield: 1B W ± ; 100M t t; 10M W + W ; 1M H 0... Multiple (strong, electroweak) channels: q q, gg, qg, b b colored; Q = 0, ±1; J = 0,1,2 states; WW, WZ, ZZ, γγ I W = 0,1,2; Q = 0, ±1, ±2; J = 0,1,2 states. Disadvantages Initial state unknown: colliding partons unknown on event-by-event basis; parton c.m. energy unknown: E 2 cm s = x 1 x 2 S; parton c.m. frame unknown. largely reply on final state reconstruction. The large rate turns to a hostile environment: Severe backgrounds!

16 Higher luminosity: /cm 2 /s 100 fb 1 /yr. Annual yield: 1B W ± ; 100M t t; 10M W + W ; 1M H 0... Multiple (strong, electroweak) channels: q q, gg, qg, b b colored; Q = 0, ±1; J = 0,1,2 states; WW, WZ, ZZ, γγ I W = 0,1,2; Q = 0, ±1, ±2; J = 0,1,2 states. Disadvantages Initial state unknown: colliding partons unknown on event-by-event basis; parton c.m. energy unknown: E 2 cm s = x 1 x 2 S; parton c.m. frame unknown. largely reply on final state reconstruction. The large rate turns to a hostile environment: Severe backgrounds! Our primary job!

17 (D). Particle Detection: The detector complex: hadronic calorimeter E-CAL beam pipe tracking ( in B field ) vertex detector muon chambers

18 What we see as particles in the detector: (a few meters) For a relativistic particle, the travel distance: τ d = (βcτ)γ (300 µm)( s ) γ

19 What we see as particles in the detector: (a few meters) For a relativistic particle, the travel distance: τ d = (βcτ)γ (300 µm)( s ) γ stable particles directly seen : p, p, e ±, γ quasi-stable particles of a life-time τ s also directly seen : n,λ, K 0 L,..., µ±, π ±, K ±...

20 What we see as particles in the detector: (a few meters) For a relativistic particle, the travel distance: τ d = (βcτ)γ (300 µm)( s ) γ stable particles directly seen : p, p, e ±, γ quasi-stable particles of a life-time τ s also directly seen : n,λ, K 0 L,..., µ±, π ±, K ±... a life-time τ s may display a secondary decay vertex, vertex-tagged particles : B 0,±, D 0,±, τ ±...

21 What we see as particles in the detector: (a few meters) For a relativistic particle, the travel distance: τ d = (βcτ)γ (300 µm)( s ) γ stable particles directly seen : p, p, e ±, γ quasi-stable particles of a life-time τ s also directly seen : n,λ, K 0 L,..., µ±, π ±, K ±... a life-time τ s may display a secondary decay vertex, vertex-tagged particles : B 0,±, D 0,±, τ ±... short-lived not directly seen, but reconstructable : π 0, ρ 0,±..., Z, W ±, t, H... missing particles are weakly-interacting and neutral: ν, χ 0, G KK...

22 For stable and quasi-stable particles of a life-time τ s, they show up as

23 A closer look:

24 A closer look: Theorists should know: For charged tracks : p/p p, typical resolution : p/(10 4 GeV ). For calorimetry : E/E 1 E, typical resolution : (5 80%)/ E.

25 For vertex-tagged particles τ s, heavy flavor tagging: the secondary vertex:

26 For vertex-tagged particles τ s, heavy flavor tagging: the secondary vertex: Typical resolution: d µm or so need at least two charged tracks, that are not colinear. For theorists: just multiply a tagging efficiency ǫ b 40 60% or so.

27 For short-lived particles: τ < s or so, make use of kinematics to reconstruct the resonance.

28 For short-lived particles: τ < s or so, make use of kinematics to reconstruct the resonance. For missing particles: make use of energy-momentum conservation to deduce their existence. (or transverse direction only for hadron colliders.)

29 What we see for the SM particles Leptons Vetexing Tracking ECAL HCAL Muon Cham. e ± p E µ ± p p τ ± e ± h ± ; 3h ± µ ± ν e, ν µ, ν τ Quarks u, d, s c D e ± h s µ ± b B e ± h s µ ± t bw ± b e ± b + 2 jets µ ± Gauge bosons γ E g W ± l ± ν p e ± µ ± q q 2 jets Z 0 l + l p e ± µ ± q q (b b) 2 jets

30 ( How to search for new particles? Leptons (e, µ) y98014_416dpauss rd ( H Z Z * 4 leptons 0 H ZZ 4l 0 χ χ + n lept.+ x Missing E T ( * ( Photons H Z' ll W' lν γγ (H ) γγ g 0 h + x h 0 0 unpredicted discovery V,ρ WZ TC lνll g n jets + E M T n leptons + X q similar H ZZ νν H WW lνlν H, A H +, h ττ τν H WW lνjj H ZZ lljj ZZ llττ H WW lνlν H g, q b jets + X WH lνbb tth lνbb+x Jets Taus b- Jet-tag

31 Homework: Exercise 1.1: For a π 0, µ, or a τ respectively, calculate its decay length for E = 10 GeV. Exercise 1.2: An event was identified to have µ +, µ along with some missing energy. What can you say about the kinematics of the system of the missing particles? Consider for both an e + e and a hadron collider. Exercise 1.3: A 120 GeV Higgs boson will have a production cross section of 20 pb at the LHC. How many events per year do you expect to produce for the Higgs boson with a designed LHC luminosity /cm 2 /s? Do you expect it to be easy to observe and why?

32 II. Basic Techniques and Tools for Collider Physics (A). Scattering cross section For a 2 n scattering process: σ(ab n) = 1 2s M 2 dpsn, dps n (2π) 4 δ 4 P s = P 2 = 2 n p i i=1 where M 2 dynamics; dps n kinematics., n p i Π n i=1 i=1 1 d 3 p i (2π) 3, 2E i

33 (B). Phase space and kinematics One-particle Final State a + b 1: dps 1 (2π) d3 p 1 2E 1 δ 4 (P p 1 ). = π p 1 dω 1 δ 3 ( P p 1 ). = 2π δ(s m 2 1 ). where the last equal sign made use of the identity d 3 p 2E = d 4 p δ(p 2 m 2 ).

34 (B). Phase space and kinematics One-particle Final State a + b 1: dps 1 (2π) d3 p 1 2E 1 δ 4 (P p 1 ). = π p 1 dω 1 δ 3 ( P p 1 ). = 2π δ(s m 2 1 ). where the last equal sign made use of the identity Kinematical relations: d 3 p 2E = d 4 p δ(p 2 m 2 ). P p a + p b = p 1, E cm 1 = s in the c.m. frame, s = (p a + p b ) 2 = m 2 1.

35 (B). Phase space and kinematics One-particle Final State a + b 1: dps 1 (2π) d3 p 1 2E 1 δ 4 (P p 1 ). = π p 1 dω 1 δ 3 ( P p 1 ). = 2π δ(s m 2 1 ). where the last equal sign made use of the identity Kinematical relations: d 3 p 2E = d 4 p δ(p 2 m 2 ). P p a + p b = p 1, E cm 1 = s in the c.m. frame, s = (p a + p b ) 2 = m 2 1. The phase-space volume is 2π.

36 Two-particle Final State a + b 1 + 2: dps 2. = 1 (2π) 2 δ4 (P p 1 p 2 ) d3 p 1 d 3 p 2 2E 1 2E 2 1 p cm 1 (4π) 2 dω 1 = 1 p cm 1 s (4π) 2 dcos θ 1 dφ 1 s = 1 1 4π2 λ1/2 ( 1, m2 1 s, m2 2 s ) dx 1 dx 2.

37 Two-particle Final State a + b 1 + 2: dps 2. = 1 (2π) 2 δ4 (P p 1 p 2 ) d3 p 1 d 3 p 2 2E 1 2E 2 1 p cm 1 (4π) 2 dω 1 = 1 p cm 1 s (4π) 2 dcos θ 1 dφ 1 s = 1 1 4π2 λ1/2 ( 1, m2 1 s, m2 2 s ) dx 1 dx 2. The magnitudes of the energy-momentum of the two particles are fully determined by the four-momentum conservation: p cm 1 = pcm 2 = λ1/2 (s, m 2 1, m2 2 ) 2, E1 cm s = s + m2 1 m2 2 2, E2 cm s = s + m2 2 m2 1 2, s λ(x, y, z) = (x y z) 2 4yz = x 2 + y 2 + z 2 2xy 2xz 2yz.

38 Two-particle Final State a + b 1 + 2: dps 2. = 1 (2π) 2 δ4 (P p 1 p 2 ) d3 p 1 d 3 p 2 2E 1 2E 2 1 p cm 1 (4π) 2 dω 1 = 1 p cm 1 s (4π) 2 dcos θ 1 dφ 1 s = 1 1 4π2 λ1/2 ( 1, m2 1 s, m2 2 s ) dx 1 dx 2. The magnitudes of the energy-momentum of the two particles are fully determined by the four-momentum conservation: p cm 1 = pcm 2 = λ1/2 (s, m 2 1, m2 2 ) 2, E1 cm s = s + m2 1 m2 2 2, E2 cm s = s + m2 2 m2 1 2, s λ(x, y, z) = (x y z) 2 4yz = x 2 + y 2 + z 2 2xy 2xz 2yz. The phase-space volume of the two-body is scaled down with respect to that of the one-particle by a factor just like a loop factor. dps 2 1 s dps 1 (4π) 2.

39 Consider a 2 2 scattering process p a + p b p 1 + p 2, the Mandelstam variables are defined as s = (p a + p b ) 2 = (p 1 + p 2 ) 2 = E 2 cm, t = (p a p 1 ) 2 = (p b p 2 ) 2 = m 2 a + m2 1 2(E ae 1 p a p 1 cos θ a1 ), u = (p a p 2 ) 2 = (p b p 1 ) 2 = m 2 a + m 2 2 2(E ae 2 p a p 2 cos θ a2 ), s + t + u = m 2 a + m 2 b + m2 1 + m2 2.

40 Consider a 2 2 scattering process p a + p b p 1 + p 2, the Mandelstam variables are defined as s = (p a + p b ) 2 = (p 1 + p 2 ) 2 = E 2 cm, t = (p a p 1 ) 2 = (p b p 2 ) 2 = m 2 a + m2 1 2(E ae 1 p a p 1 cos θ a1 ), u = (p a p 2 ) 2 = (p b p 1 ) 2 = m 2 a + m 2 2 2(E ae 2 p a p 2 cos θ a2 ), s + t + u = m 2 a + m 2 b + m2 1 + m2 2. The two-body phase space can be thus written as dps 2 = 1 (4π) 2 dt dφ 1 s λ 1/2 ( 1, m 2 a /s, m2 b /s).

41 Exercise 2.1: Assume that m a = m 1 and m b = m 2. Show that t = 2p 2 cm (1 cos θ a1 ), u = 2p 2 cm(1 + cos θa1 ) + (m2 1 m2 2 )2, s where p cm = λ 1/2 (s, m 2 1, m2 2 )/2 s is the momentum magnitude in the c.m. frame. This leads to t 0 in the collinear limit. Exercise 2.2: A particle of mass M decays to two particles isotropically in its rest frame. What does the momentum distribution look like in a frame in which the particle is moving with a speed β z? Compare the result with your expectation for the shape change for a basket ball.

42 Three-particle Final State a + b : 1 dps 3 (2π) 5 δ4 (P p 1 p 2 p 3 ) d3 p 1 d 3 p 2 d 3 p 3 2E 1 2E 2 2E 3. = p 1 2 d p 1 dω 1 1 p (23) 2 (2π) 3 2E 1 (4π) 2 dω 2 m 23 = 1 (4π) 3 λ1/2 ( 1, m2 2 m 2, m m 2 23 ) 2 p 1 de 1 dx 2 dx 3 dx 4 dx 5. dcos θ 1,2 = 2dx 2,4, dφ 1,2 = 2πdx 3,5, 0 x 2,3,4,5 1, p cm 1 2 = p cm 2 + pcm 3 2 = (E1 cm )2 m 2 1, m 2 23 = s 2 se cm 1 + m2 1, p23 2 = p23 3 = λ1/2 (m 2 23, m2 2, m2 3 ) 2m 23,

43 Three-particle Final State a + b : 1 dps 3 (2π) 5 δ4 (P p 1 p 2 p 3 ) d3 p 1 d 3 p 2 d 3 p 3 2E 1 2E 2 2E 3. = p 1 2 d p 1 dω 1 1 p (23) 2 (2π) 3 2E 1 (4π) 2 dω 2 m 23 = 1 (4π) 3 λ1/2 ( 1, m2 2 m 2, m m 2 23 ) 2 p 1 de 1 dx 2 dx 3 dx 4 dx 5. dcos θ 1,2 = 2dx 2,4, dφ 1,2 = 2πdx 3,5, 0 x 2,3,4,5 1, p cm 1 2 = p cm 2 + pcm 3 2 = (E1 cm )2 m 2 1, m 2 23 = s 2 se cm 1 + m2 1, p23 2 = p23 3 = λ1/2 (m 2 23, m2 2, m2 3 ) 2m 23, The particle energy spectrum is not monochromatic. The maximum value (the end-point) for particle 1 in c.m. frame is 1 = s + m2 1 (m 2 + m 3 ) 2 2, m 1 E 1 E1 max, s E max 1 = λ1/2 (s, m 2 1,(m 2 + m 3 ) 2 ) 2, 0 p 1 p max 1. s p max

44 More intuitive to work out the end-point for the kinetic energy, recall the direct neutrino mass bound in β-decay: K1 max = E1 max m 1 = ( s m 1 m 2 m 3 )( s m 1 + m 2 + m 3 ) 2. s

45 Recursion relation P n: p 1 p 2... p n 1 p p n 1, n p n

46 Recursion relation P n: p 1 p 2... p n 1 p p n 1, n p n dps n (P; p 1,..., p n ) = dps n 1 (P; p 1,..., p n 1,n ) For instance, dps 2 (p n 1,n ; p n 1, p n ) dm2 n 1,n. 2π dps 3 = dps 2 (i) dm2 prop 2π dps 2 (f).

47 Breit-Wigner Resonance andthe Narrow Width Approximation An unstable particle of mass M and total width Γ V, the propagator is 1 R(s) = (s MV 2)2 + Γ 2. V M2 V Consider an intermediate state V a bv b p 1 p 2. By the reduction formula, the resonant integral reads Variable change (m max ) 2 =(m a m b ) 2 (m min ) 2 =(m 1 +m 2 ) 2 dm2. tan θ = m2 M 2 V Γ V M V, resulting in a flat integrand over θ (m max ) 2 (m min ) 2 (m 2 MV 2)2 + Γ 2 V M2 V dm 2 = θ max θ min dθ Γ V M V.

48 In the limit (m 1 + m 2 ) + Γ V M V m a Γ V, θ min = tan 1 (m 1 + m 2 ) 2 M 2 V Γ V M V π, θ max = tan 1 (m a m b ) 2 M 2 V Γ V M V 0, then the Narrow Width Approximation 1 (m 2 M2 V )2 + Γ 2 V M2 V π Γ V M V δ(m 2 M 2 V ).

49 In the limit (m 1 + m 2 ) + Γ V M V m a Γ V, θ min = tan 1 (m 1 + m 2 ) 2 M 2 V Γ V M V π, θ max = tan 1 (m a m b ) 2 M 2 V Γ V M V 0, then the Narrow Width Approximation 1 (m 2 M2 V )2 + Γ 2 V M2 V π Γ V M V δ(m 2 M 2 V ). Exercise 2.3: Consider a three-body decay of a top quark, t bw b eν. Making use of the phase space recursion relation and the narrow width approximation for the intermediate W boson, show that the partial decay width of the top quark can be expressed as Γ(t bw b eν) Γ(t bw) BR(W eν).

50 Traditional Trace Techniques: You should be good at this QFT course! With algebraic symbolic manipulations: REDUCE FORM MATHEMATICA, MAPLE... Helicity Techniques: More suitable for direct numerical evaluations. Hagiwara-Zeppenfeld: best for massless particles... (NPB) CalCul Method (by T.T. Wu et al., Parke-Mangano: Phys. Report); Homework III-3: Work out the helicity amplitude for e + e ZZ.

51 Calculational Tools Monte Carlo packages for phase space integration: (1) VEGAS by P. LePage: adaptive important-sampling MC integration (2) SAMPLE, RAINBOW, MISER... Automated software for matrix elements: (1) REDUCE an interactive program designed for general algebraic computations, including to evaluate Dirac algebra, an old-time program, (2) FORM by Jos Vermaseren: A program for large scale symbolic manipulation, evaluate fermion traces automatically, and perform loop calculations,s commercially available at form

52 (3) FeynCalc and FeynArts: Mathematica packages for algebraic calculations in elementary particle physics. (4) MadGraph: Helicity amplitude method for tree-level matrix elements available upon request or Example: Standard Model particles include: Quarks: d u s c b t d u s c b t Leptons: e- mu- ta- e+ mu+ ta+ ve vm vt ve vm vt Bosons: g a z w+ w- h Enter process you would like calculated in the form e+ e- a. (return to exit MadGraph.) a a w+ w- Generating diagrams for 4 external legs There are 3 graphs. Writing Feynman graphs in file aa wpwm.ps Writing function AA WPWM in file aa wpwm.f.

53 Automated evaluation of cross sections: (1)MadGraph/MadEvent and MadSUSY: Generate Fortran codes on-line! (2) CompHEP: computer program for calculation of elementary particle processes in Standard Model and beyond. CompHEP has a built-in numeric interpreter. So this version permits to make numeric calculation without additional Fortran/C compiler. It is convenient for more or less simple calculations. It allows your own construction of a Lagrangian model! kryukov (3) GRACE and GRACE SUSY: (4) Pandora by M. Peskin: C++ based package for e + e, including beam effects.

54 Generators/PANDORA.htm The program pandora is a general-purpose parton-level event generator which includes beamstrahlung, initial state radiation, and full treatment of polarization effects. (An interface to PYTHIA that produces fully hadronized events is possible.) This version includes the SM physics processes: e + e l + l, q q, γγ, t t, Zγ, ZZ, W + W Zh, ν νh, e + e h, ν νγ γγ l + l, q q, t t, e + e, W + W, h eγ eγ, ez, νw e e e e. and some illustrative Beyond the SM processes: e + e Z l + l, q q KK gravitons l + l, q q, γγ, ZZ, W + W γ graviton M ρ TC W + W.

55 Numerical simulation packages: (1) PYTHIA: PYTHIA and JETSET are programs for the generation of high-energy physics events, i.e. for the description of collisions at high energies between elementary particles such as e+, e-, p and pbar in various combinations. Together they contain theory and models for a number of physics aspects, including hard and soft interactions, parton distributions, initial and final state parton showers, multiple interactions, fragmentation and decay. torbjorn/pythia.html (2) ISAJET ISAJET is a Monte Carlo program which simulates p-p, pbar-p, and e-e interactions at high energies. It is based on perturbative QCD plus phenomenological models for parton and beam jet fragmentation. isajet