Physics at the Large Hadron Collider

Herbstschule Maria Laach, September 2005 Physics at the Large Hadron Collider Michael Krämer (RWTH Aachen) Lecture 1: Review of the Standard Model Lecture 2: SM physics at hadron colliders Lecture 3: Higgs and SUSY searches at the LHC Michael Krämer Page 1 Herbstschule Maria Laach, September 2005

Plan of Lecture 2 Particle production at hadron colliders: the Drell-Yan process W production top-quark production jet production Michael Krämer Page 2 Herbstschule Maria Laach, September 2005

Particle production at hadron colliders Example: Drell-Yan process Cross section: σ pp l + l = q dx 1 dx 2 f q (x 1 ) f q (x 2 ) ˆσ q q l + l f q, q (x) dx: probability to find (anti)quark with momentum fraction x process independent, measured in DIS ˆσ q q l + l : hard scattering cross section calculable in perturbation theory Michael Krämer Page 3 Herbstschule Maria Laach, September 2005

Particle production at hadron colliders Factorization is non-trivial beyond leading order virtual corrections real corrections UV divergences IR divergences IR divergences collinear divergences UV divergences renormalization (α s (µ ren ) etc.) IR divergences cancel between virtual and real (KLN) collinear initial state divergences can be absorbed in pdfs Michael Krämer Page 4 Herbstschule Maria Laach, September 2005

$ % # "!!! Particle production at hadron colliders Initial state collinear singularities, eg. process independent divergence in dk 2 T as k2 T 0 absorb singularity in parton densities: f q (x, µ fac ) = f q (x) + { divergent part of µ 2 fac 0 dk 2 T } Hadron collider cross section σ = dx 1 f P i (x 1, µ F ) dx 2 f P j (x 2, µ F ) n α n s (µ R ) C n (µ R, µ F ) + O(Λ QCD /Q) (Altarelli, Ellis, Martinelli 78; Collins, Soper, Sterman 82-84 and many others) Interactions between spectator partons underlying event and/ or multiple hard scattering Michael Krämer Page 5 Herbstschule Maria Laach, September 2005

Particle production at hadron colliders Scale dependence Example: rapidity distribution in pp W +X σ = dx 1 fi P (x 1, µ F ) dx 2 f P j (x 2, µ F ) [Anastasiou, Dixon, Melnikov, Petriello 03] n α n s (µ R ) C n (µ R, µ F ) finite order in perturbation theory artificial µ-dependence: dσ d ln µ 2 R N = αs n (µ R ) C n (µ R, µ F ) n=0 = O(α s (µ R ) N+1 ) scale dependence theoretical uncertainty due to HO corrections significant reduction of µ dependence at (N)NLO Michael Krämer Page 6 Herbstschule Maria Laach, September 2005

Parton luminosities Other luminosities Assuming that the total parton cross ˆσ depends only on ŝ the cross section can be written σ(s) = 1 [ ] dτ 1 dl ij ŝˆσ ij {ij} τ 0 τ s dτ where the sum runs over all relevant pairs of partons {ij} and τ x 1 x 2 The differential parton luminosity is defined as τ dl dτ = 1 0 dx 1 dx 2 [ x1 f i (x 1, ν 2 )x 2 f j (x 2, µ) + (1 2) ] δ(τ x 1 x 2 ) R.K.Ellis, St Andrews, August 2003 7 Michael Krämer Page 7 Herbstschule Maria Laach, September 2005

PDF uncertainties σ W. B lν (nb) 2.80 2.75 2.70 2.65 2.60 2.55 MRST NLO and NNLO partons NNLO NLO [Martin, Roberts, Stirling, Thorne 03] W @ Tevatron Q 2 cut = 7 GeV2 Q 2 = 10 GeV2 cut x cut = 0 0.0002 0.001 0.0025 0.005 0.01 2.50 pdf < 5% (CTEQ, MRST, Alekhin,...) Michael Krämer Page 8 Herbstschule Maria Laach, September 2005

Cross section compilation 10 9 10 9 10 8 σ tot 10 8 10 7 10 6 Tevatron LHC 10 7 10 6 10 5 10 5 σ (nb) 10 4 10 3 10 2 10 1 10 0 10-1 10-2 σ bbar σ jet (E T jet > s/20) σ W σ Z σ jet (E T jet > 100 GeV) 10 4 10 3 10 2 10 1 10 0 10-1 10-2 events/sec for L = 10 33 cm -2 s -1 10-3 σ ttbar 10-3 10-4 σ jet (E T jet > s/4) 10-4 10-5 σ Higgs (M H = 150 GeV) 10-5 10-6 σ Higgs (M H = 500 GeV) 10-6 10-7 0.1 1 10 10-7 s (TeV) Michael Krämer Page 9 Herbstschule Maria Laach, September 2005

We will have a closer look at W production top-quark production jet production Michael Krämer Page 10 Herbstschule Maria Laach, September 2005

+. ' * ) -, W -boson production at hadron colliders measurement of M W and Γ W precision test of SM σ W as a (parton) luminosity monitor &(' e.g. δ σ(pp W + W ) σ(pp W ± ) < 1%? Anticipated experimental accuracy: uncertainty now Tevatron Run II LHC δ sin 2 θ eff ( 10 5 ) 17 78 14-20 δm W [MeV] 34 27 15 δm t [GeV] 5.1 2.7 1.0 δm H /M H [%] (from all data) 58 35 18 Michael Krämer Page 11 Herbstschule Maria Laach, September 2005

W -mass measurement Consider u(p u ) + d(p d ) l + (p l ) + ν l (p ν ) /(0 3 6 0 2 1 5 4 Using the couplings from the electroweak Langrangian one obtains M(u d l + ν l ) 2 = 16( 2G F M 2 W ) 2 V ud 2 (p u p l ) 2 ((p u + p d ) 2 M 2 W )2 + M 2 W Γ2 W If we define Θ to be the l + polar angle in the W + rest frame, then and (p u p l ) 2 = M 2 W 16 (1 + cos2 Θ ) 1 σ dσ d cos Θ = 3 8 (1 + cos2 Θ ) Michael Krämer Page 12 Herbstschule Maria Laach, September 2005

W -mass measurement If the W has zero transverse momentum the polar angle is given in terms of the lepton transverse momentum, p T l : cos Θ = 1 4p2 T l M 2 W so that 1 σ dσ dp 2 T,l = 3 M 2 W 1 2p 2 T l /M 2 W 1 4p 2 T l /M 2 W The p T l distribution is strongly peaked at p T l = M W /2 (Jacobian peak). The peak is smeared out by the finite W width and non-zero W transverse momentum. Therefore, in praxis, one uses the transverse mass MT 2 = 2 p T l p T ν (1 cos ϕ lν ) which is less sensitive to the W transverse momentum. At LO, one has p T l = p T ν = p, ϕ lν = π and so M T = 2 p T l. The transverse mass distribution therefore also has a Jacobian peak, at M T = M W. Michael Krämer Page 13 Herbstschule Maria Laach, September 2005

W -mass measurement Events Transverse Mass - W Candidate 7000 Data PMCS+QCD QCD bkg D0 Run II Preliminary W-Boson Mass [GeV] 6000 5000 4000 3000 2000 1000 TEVATRON 80.452 ± 0.059 LEP2 80.412 ± 0.042 Average 80.425 ± 0.034 80 80.2 80.4 80.6 m W [GeV] χ 2 /DoF: 0.3 / 1 NuTeV 80.136 ± 0.084 LEP1/SLD 80.363 ± 0.032 LEP1/SLD/m t 80.373 ± 0.023 0 40 50 60 70 80 90 100 110 120 Transverse mass(gev) Michael Krämer Page 14 Herbstschule Maria Laach, September 2005

W transverse momentum distribution At LO the W is produced at zero transverse momentum. Higher-order processes leads to p T W > 0: q W q W q g g q The corresponding squared matrix elements are M(q q W + g) 2 = πα s 2GF M 2 W V qq 8 9 M(gq W + q ) 2 = πα s 2GF M 2 W V qq 1 3 t 2 + u 2 + 2sM 2 W tu s 2 + u 2 + 2tM 2 W su where s, t and u are the usual Mandelstam variables s = (p 1 + p 2 ) 2, t = (p 1 p 3 ) 2, u = (p 1 p 4 ) 2 Michael Krämer Page 15 Herbstschule Maria Laach, September 2005

W transverse momentum distribution The poles at t = 0 and u = 0 cause the theoretical cross section to diverge as p T 0. The leading behaviour comes from the emission of a soft gluon in the process q q W + g. Schematically dσ R dp 2 T = α s ( A ln(m 2 W /p2 T ) p 2 T + B 1 p 2 T ) + C(p 2 T ) One can show that the emission of multiple soft-gluon emission leads to large logarithms order-byorder in perturbation theory: 1 σ dσ dp 2 T 1 p 2 T [ A 1 α s ln M 2 W p 2 T + A 2 α 2 s ln 3 M 2 W p 2 T + + A n α n s ln 2n 1 M 2 W p 2 T ] + The large logarithms spoil perturbation theory at p T M W as then α s ln 2 M 2 W p 2 T > 1 and need to be summed to all orders: 1 σ dσ dp 2 T 1 dp 2 T exp ( α s 2π C F ln 2 M 2 W p 2 T ) Michael Krämer Page 16 Herbstschule Maria Laach, September 2005

W transverse momentum distribution A more complete analysis of the small p T distribution requires a proper treatment of transverse momentum conservation in multiple gluon emission and the inclusion ofnon-perturbative contributions at very small p T. (Ellis and Vesili) The problem of accurately predicting the p T distribution is generic for all Drell-Yan type processes, like eg. pp Higgs Michael Krämer Page 17 Herbstschule Maria Laach, September 2005

W -mass measurements at the Tevatron and the LHC Expectations for Tevatron run II 0.25 Statistical Uncertainties Run1, CDF & D0 statistical uncertainty δm W experiment for L = 2 fb 1 15 MeV per channel and δw (GeV / c 2 ) 0.2 0.15 δw (GeV/c 2 )= 800 + 330 L (pb -1 ) overall uncertainty δm W 40 MeV per channel and experiment for L = 2 fb 1 0.1 0.05 0 0 0.005 0.01 0.015 0.02 1/sqrt (#W) Expectations for the LHC statistical uncertainty δm W < 2 MeV for L = 10 fb 1 overall uncertainty δm W 20 MeV may be reached if lepton energy and momentum scales are known to 0.02%. main theoretical uncertainties from PDFs and multi-photon radiation effects Michael Krämer Page 18 Herbstschule Maria Laach, September 2005

Search for extra gauge bosons W, Z Many new physics models (eg. SO(10) GUTs) predict an extended gauge group and addtional heavy gauge bosons W and/or Z. Assuming SM-like couplings, the LHC can discover W and/or Z with masses up to 6 TeV here: 4 TeV W signal above M T 2.3 TeV For L = 100 fb 1 expect 160 signal and 13 background events. Michael Krämer Page 19 Herbstschule Maria Laach, September 2005

Top-quark physics Why is the top quark an interesting object to study? The top quark mass is a crucial input for electroweak precision tests. m top m b,c,s,u,d,τ,µ,e,ν : Is the top in some way exotic? The top quark may be a window to new physics: it couples strongly to scalars (like the Higgs); the top quark mass may be important for testing grand unified theories. Events containing top quarks are background for new physics signals. Michael Krämer Page 20 Herbstschule Maria Laach, September 2005

Top quark production at hadron colliders The top-quark is mainly produced through quark-antiquark annihilation and gluongluon fusion: q t q t g t g t g t + + g t g t g t Top quark production at the Tevatron/LHC is dominated by q q/gg initial states: σ NLO (pb) q q t t gg t t Tevatron ( s = 1.8 TeV p p) 4.87 ± 10% 90% 10% Tevatron ( s = 2.0 TeV p p) 6.70 ± 10% 85% 15% LHC ( s = 14 TeV pp) 803 ± 15% 10% 90% Michael Krämer Page 21 Herbstschule Maria Laach, September 2005

Top-quark production at hadron colliders NLO corrections are important (as usual): Michael Krämer Page 22 Herbstschule Maria Laach, September 2005

Top-quark decays The dominant decay of the top-quark is t W b q t W = i g 2 2 V tq γ µ (1 γ 5 ) so that Γ = G F Mt 2 ( 8π 2 V tb 2 1 M W 2 Mt 2 ) ( 1 + 2M 2 W M 2 t ) V tb 2 1.42 GeV Unitarity of the CKM matrix V tb 2 + V cb 2 + V ub 2 = 1 implies V tb 1 Top-quark lifetime τ t 5 10 25 sec Typical QCD time scale for hadron formation τ QCD 3 10 24 sec The top quark decays before it can form bound states Michael Krämer Page 23 Herbstschule Maria Laach, September 2005

Top-quark cross sections at the Tevatron 8 Cacciari et al. JHEP 0404:068 (2004) Kidonakis,Vogt PRD 68 114014 (2003) 2 Assume m t =175 GeV/c CDF Run 2 Preliminary σ(pp tt) (pb) 12 10 8 Cacciari et al. JHEP 0404:068 (2004) Cacciari et al. ± uncertainty Kidonakis,Vogt PIM PRD 68 114014 (2003) Kidonakis,Vogt 1PI Dilepton: Combined -1 (L= 200pb ) Lepton+Jets: Kinematic ANN -1 (L= 347pb ) Lepton+Jets: Soft Muon Tag -1 (L= 193pb ) 2.4 1.6 0.4 7.0 ± 2.1 ± 1.1 ± 0.4 0.8 0.9 0.4 6.3 ± 0.8 ± 0.9 ± 0.3 3.3 1.3 0.3 5.3 ± 3.3 ± 1.0 ± 0.3 6 Lepton+Jets: Vertex Tag -1 (L= 318pb ) 0.9 1.1 0.5 8.9 ± 0.9 ± 0.8 ± 0.5 4 2 0 Preliminary CDF combined tt production cross section for 200 pb @ Summer 2005 CDF+D0 combined top quark mass 166 168 170 172 174 176 178 180 2 Top Mass (GeV/c ) -1 0 MET+Jets: Vertex Tag -1 (L= 311pb ) All-hadronic: Vertex Tag -1 (L= 311pb ) Combined -1 (L= 350pb ) 1.2 1.3 0.4 6.1 ± 1.2 ± 0.9 ± 0.3 1.7 3.3 0.5 8.0 ± 1.7 ± 2.2 ± 0.4 0.4 0.4 (stat.)±(syst.)±(lumi.) 7.1±0.6±0.7± 0 2 4 6 8 10 12 14 σ(pp tt) (pb) Michael Krämer Page 24 Herbstschule Maria Laach, September 2005

Top-quark decays The ratio R = BR(t W b) BR(t W q) = V tb 2 V td 2 + V ts 2 + V tb 2 has been measured to consistent with the SM. R = 1.11 0.19 +0.21 (CDF) 1.03 0.17 +0.19 (D0) If we assume three generations then V td 2 + V ts 2 + V tb 2 = 1 and V tb = 1.05 0.09 +0.10 (CDF) 1.01 0.09 +0.09 (D0) However, assuming three generation we know 0.9990 < V tb < 0.9993 anyway... Michael Krämer Page 25 Herbstschule Maria Laach, September 2005

Measurement of V tb from single top production The production of single top quarks via weak interactions is a direct measure of V tb q W t q W q g t q b b t b W The cross section is suppressed w.r.t. QCD top pair production cross sections in pb s channel t channel W t Tevatron ( s = 2.0 TeV p p) 0.90 ± 5% 2.1 ± 5% 0.1 ± 10% LHC ( s = 14 TeV pp) 10.6 ± 5% 250 ± 5% 75 ± 10% need several fb 1 of data for observation at the Tevatron Michael Krämer Page 26 Herbstschule Maria Laach, September 2005

Top-mass measurement at the Tevatron Mass of the Top Quark (*Preliminary) Measurement M top [GeV/c 2 ] CDF-I di-l 167.4 ± 11.4 D -I di-l 168.4 ± 12.8 CDF-II di-l* 165.3 ± 7.3 CDF-I l+j 176.1 ± 7.3 D -I l+j 180.1 ± 5.3 CDF-II l+j* 173.5 ± 4.1 D -II l+j* 169.5 ± 4.7 CDF-I all-j 186.0 ± 11.5 χ 2 / dof = 6.5 / 7 Tevatron Run-I/II* 172.7 ± 2.9 150 170 190 M top [GeV/c 2 ] Tevatron run II goal: δm top = 2 GeV with L = 4 9 fb 1 Michael Krämer Page 27 Herbstschule Maria Laach, September 2005

Top physics at the LHC The top cross section at the LHC is σ tt 800 pb O(10 7 ) events in the first year Physics goals: δm top = 1 GeV with L = 100 fb 1 Observation of single top production with L = 30 fb 1 test of quantum numbers sensitivity to rare (BSM) decay modes Michael Krämer Page 28 Herbstschule Maria Laach, September 2005

Jet production Intuitively, a jet is supposed to be a spray of particles, all going approximately into one direction: Michael Krämer Page 29 Herbstschule Maria Laach, September 2005

Jet production To make this precise we need to specify a jet algorithm. The k T or Durham algorithm is widely used and defined as follows: Start with a list of momenta p µ 1, p µ 2,..., p µ N. At the start these represent the momenta of particles. (In a perturbative calculation, they are the momenta of partons.) Choose a parameter y cut (related to the jet-resolution). For each pair of final state momenta calculate y ij = 2 min{e 2 i, E 2 j } (1 cos Θ ij )/s. If y IJ = min{y ij } < y cut, combine momenta I, J into one object K with p K = p I + p J. Repeat until y IJ > y cut. the remaining objects are jets. According to this definition, an n-parton final state can give any number of jets between n (all partons well-separated) and 2 (for example, two energetic quarks accompanied by soft and collinear gluons). Michael Krämer Page 30 Herbstschule Maria Laach, September 2005

Jet production and new physics searches New physics can modify the scattering of quarks and gluons, for example through the exchange of a new heavy object, or perhaps the exchange of some of the constituents out of which quarks are made. At energies S M the details of the new particle exchange cannot be resolved and the effect of the new physics can be summarized by adding new terms to the Lagrangian of QCD. A typical term might be L = g2 M 2 ψγ µ ψ ψγ µ ψ. (The strength of the coupling between the new physics and the quarks is denoted by g 2.) Michael Krämer Page 31 Herbstschule Maria Laach, September 2005

Jet production and new physics searches To observe a deviation from the Standard Model we need either of a high-precision experiment an experiment that looks for some effect that is forbidden in the Standard Model an experiment that has moderate precision but operates at the highest possible energies As an example, consider p p jet + X as a function of the transverse energy ( p T ) of the jet. New terms in the effective Lagrangian should modify the Standard Model cross section. When the transverse energy of the jet is small compared to M, one expects Data Theory Theory g 2 E2 T M 2 The factor g 2 /M 2 is the coefficient of the new physics contribution in the effective Lagrangian. The factor E 2 T in the numerator follows because the left-hand side is dimensionless and E 2 T is the only factor with dimension of mass 2 that is available. Michael Krämer Page 32 Herbstschule Maria Laach, September 2005

Jet production and new physics searches A comparison of experimental jet cross sections and next-to-leading order QCD (as of 1996) theory is presented below. The theory works fine for E T < 200 GeV, but for 200 GeV < E T, there appears to be a systematic deviation of precisely the form anticipated in the discussion above. 1 (Data - Theory)/ Theory 0.5 0 CTEQ3M CDF (Preliminary) * 1.03 D0 (Preliminary) * 1.01-0.5 50 100 E t (GeV) 200 300 400 However, in this case the observed effect can most likely be explained by the theoretical uncertainty due to the poor knowledge of the gluon distribution in the proton at large x. Michael Krämer Page 33 Herbstschule Maria Laach, September 2005

Jet production and new physics searches A systematic study of the PDF uncertainty reveals that the data can be accommodated by adjusting the gluon density at large x Michael Krämer Page 34 Herbstschule Maria Laach, September 2005

Precision physics at the LHC Precision calculations at hadron colliders require the calculation of QCD corrections at (N)NLO; the inclusion of electroweak corrections; the resummation of large logarithmic corrections; the precision determination of input pdfs; matching of fixed order calculations with parton showers & hadronization. Michael Krämer Page 35 Herbstschule Maria Laach, September 2005

NLO calculations with parton showers N k LO calculations + allow precision test of QFTs break down for certain kinematic configurations do not provide realistic final states are limited to IR safe observables Parton shower Monte Carlo programs + include certain summations (soft/colli near emissions) + provide realistic final states do not include hard emissions are based on LO perturbation theory Aim: Perform NLO calculations with (LL) summation of soft/collinear logarithms and realistic hadronic final states match NLO calculations with parton shower Monte Carlo programs Problem of double counting: parton showers include part of the short-distance physics already included in NLO calculations See work by Frixione, Nason, Webber; MK, Mrenna, Soper Michael Krämer Page 36 Herbstschule Maria Laach, September 2005

NLO calculations with parton showers Example: dσ(pp t t)/dp t (t t) NLO provides reliable prediction at large p t (t t), but fails as p t (t t) 0 MC includes summation for p t (t t) 0, but fails at large p t (t t) Frixione, Webber Michael Krämer Page 37 Herbstschule Maria Laach, September 2005

Precision SM physics at the LHC... what we hope to see (Bentvelsen, Grünewald) Repeat the electroweak fit changing the uncertainties δm W = 15 MeV δm top = 1 GeV same central values Michael Krämer Page 38 Herbstschule Maria Laach, September 2005