Top quark physics at the LHC Theory status Peter Uwer PH-TH LHC-D Workshop  Top quark physics Bad Honnef, 03/03/2006

Theory as summarized in Beneke et al + Remark: A nice summary of top quark theory can be fund in Top Quark Physics, Beneke et al, 2000 [hep-ph/0003033 ] Here: Theory as summarized in Beneke et al + progress since then

Content: Basics Top quark pair production Single top production ttH production tt+Jet production Anomalous couplings… Conclusion

The top quark in the Standard Model Top quark is an object with quantum numbers as predicted by the Standard Model: T3 (SU(2)L) Y (U(1)Y) Q=T3+Y 1. family 2. family 3. family 1/2 1/6 2/3 -1/2 1/6 -1/3 2/3 2/3 -1/3 -1/3 Top quark interactions are completely determined by the stucture of the SM Only “2” free parameters: top mass/Yukawa coupling and CKM  Top quark properties can be precisely predicted in the SM

Almost no lower bound if additional families exist Experimental status of top quark mass and CKM matrix: From direct measurements at the Tevatron: [hep-ex/0507091] From unitarity (3 families!) and additional measurements: [PDG 04] ! Almost no lower bound if additional families exist

Top quark decay Main decay in the SM: W t b Width calculable in the SM: Two-loop QCD and one-loop EW corrections also known!

! Top quark width Theoretical uncertainty is believed to be below 1% [Beneke et al, 2000] ! Theoretical uncertainty is believed to be below 1%  Life time: “Top quark decays before it can hadronize“ [Bigi, Dokshitzer, Khoze, Kühn, Zerwas ´86]  No bound states, spin observables are “good” observables

What do we mean by the mass of a confined quark Some remarks about the top quark mass ? What do we mean by the mass of a confined quark Mass is just a parameter of the theory like for example as  Mass parameter depends on the renormalization scheme Common schemes: on-shell / pole-mass scheme MS mass Other definitions: potential subtracted mass, 1S mass, kinetic mass (used in e+e- annihilation, less useful for hadron collider)

Perturbation theory allows to switch between different schemes: Conversion between MS and Pole-mass scheme Relation known including terms of order as3 [Chetyrkin, Steinhauser] 5+1 flavour QCD, as(mz)=0.119

! Difference of 10 GeV  make sure that we know which mass we measure Due to additional infrared renormalon in pole-mass, pole mass has intrinsic uncertainty of order LQCD Pole mass not well defined beyond pert. theory, Limitation for reachable precision! For tlJ/X, where a precision of 1 GeV might be reached, additional theoretical studies useful

Top quark pair production Quark-Antiquark annihilation Gluon fusion Partonic cross sections NLO corrections also known, for some observables available in form of fits [Dawson, Ellis, Nason ’89, Beenakker et al ’89,’91,Bernreuther, Brandenburg, Si, P.U. ‘04]

Next-to-leading order corrections [Dawson, Ellis, Nason ’89] General form: QCD corrections determined by the renormalization group:

Close to threshold NLO corrections are given by: Coulomb singularity Resummation Close to threshold NLO corrections are given by: [Nason, Dawson, Ellis 88, Beenakker, kuijf, vNeerven,Smith ‘89] Large logarithmic corrections in threshold region: sum large logarithmic corrections to improve perturbation theory [Bonciani, Cacciari, Catani, Kidonakis, Laenen, Mangano, Moch, Nason, Ridolfi, Sterman…]

[Bonciani, Catani, Mangano, Nason 98] Resummation (cont’d) [Bonciani, Catani, Mangano, Nason 98] Resummation shifts slightly central value of NLO prediction  improves scale uncertainty Overall uncertainty (scale + pdf): ~12% based on CTEQ5,MRST98,99 Update using CTEQ6,… needed  tool box ?

Important contribution to the uncertainty comes from pdf´s Using the more recent CTEQ, MRST fits, uncertainty might even become larger Limitation for top mass determination from cross section measurements! Important observation: Ratios of cross sections are remarkable stable under variation of the PDF’s, uncertainty sometimes at the level of 1% Study possibility to determine the top mass via the measurement of a ratio of two cross sections.

Remarks concerning resummation Resumed predictions also available for specific single differential distributions For general observables re-summation is not available At the LHC resummation is less important compared to Tevatron

ttX included in MC@NLO (without spin-correlations!) New results since 2000 ttX included in MC@NLO (without spin-correlations!) NLO corrections for spin-dependent quantities NLO corrections to the hadronic decay of the top quark Study of off-shell and off-resonance effects in tt and tt+Jet production EW corrections to top quark pair production [Frixione, Webber] [Bernreuther, Brandenburg, Si, P.U] [Brandenburg, Si, P.U] [Kauer, Zeppenfeld] [Bernreuther, Fücker, Si 05, Kühn,Scharf,Uwer 05]

Spin correlations in top quark pair production Due to parity invariance of QCD, top’s produced in qqtt and gg tt are essentially unpolarized *) But: Spins of top quark and antiquark are correlated [Bernreuther,Brandenburg 93, Mahlon, Parke 96, Stelzer,Willenbrock 96, Bernreuther, Brandenburg, Si, P.U. 01-04] Quantum mechanics: close to threshold:  Spins are parallel or anti-parallel close to threshold

Observables like are sensitive to the top spin Quantum mechanics gg:

Spin correlations: LO Standard Model predictions Double differential distribution: Size of C depends on the “quantization axis”: Tevatron LHC mR=mF=mt=175 GeV, CTEQ6L Spin correlations can be very large!

Spin correlation: NLO corrections In general very complicated task: Approximation: double pole approximation calculate only factorizable contributions NLO corrections calculable: [Bernreuther, Brandenburg, Si, P.U. 04] Tevatron LHC mR=mF=mt=175 GeV, as(m=mt)=0.1074, CTEQ6.1M Scale dep.: Tevatron: LHC:

Off-shell effects and non-resonant tt production [Kauer, Zeppenfeld] General problem: Top quarks are treated on-shell  finite width effects are neglected Note: naïve inclusion of finite width effect often spoils gauge invariance!  theoretical issue to a specific final state also non-resonant diagrams might contribute While in general these effects should be small, for specific distributions they can be important, in particular when cuts are applied and Monte-Carlos are tuned

EW corrections to top quark pair production Although in general EW corrections are small, they can be enhanced due to the presence of large Sudakov logarithms EW corrections to top quark pair production first studied by Beenakker, Denner, Hollik, Mertig, Sack, Wackeroth ‘93  Some contributions were neglected Recently these corrections were calculated for qqtt [Bernreuther, Fücker, Si 05, Kühn,Scharf,Uwer 05] with spin! The gg process will be finished soon

Weak corrections to the total cross section: qq subprocess  for the cross section corrections are neglible For large pt corrections can become large, detailed study in preparation

Only subset of NLO corrections included Single top production One-loop corrections for inclusive cross section known (s+t)! [Stelzer, Sullivan, Willennbrock ´97, Smith, Willenbrock `96] Production rates [Beneke et al, 2000] Only subset of NLO corrections included

Important progress since [Beneke et al, 2000] NLO corrections for differential distributions [Harris, Laenen, Phaf, Sullivan, Weinzierl] Polarisation of top quark is kept, NLO decay not included m=mt Large corrections scale uncertainty of the order of 5%

s-channel production of a top quark at the Tevatron Program to calculate (partonic) distributions at NLO: Transverse momentum distribution of the b-jet at NLO Pseudorapidity distribution of the b-jet at NLO s-channel production of a top quark at the Tevatron (√S = 2 TeV) after cuts

! ? Single top quark production (s+t channel) + decay at NLO [Campbell, Ellis, Tramontano ´04] Top quark decay is included at NLO non-factorizable effects are ignored Top quark on-shell included in MCFM ! only leptonic decay considered  good description of jet activity in single top production “The inclusion of additional radiated gluon in the decay, does not change much the distribution considered” ? Artifact of specific cuts or distributions, or general feature

NLO corrections to Wt production [Campbell, Tramontano 05] NLO corrections including decay included in MCFM Corrections at LHC of the order of ±10% At the LHC results show only weak dependence on pdf Opening angle between the leptons in the transverse plane is significantly changed  important for Higgs physics

For many distributions no important difference between Single top production included in MC@NLO [Frixione, Laenen, Motylinski, Webber 05] Distributions for the pT of the hardest jet (left pane), and the pT relative to the axis of the hardest jet of those hadrons or partons in that jet (right pane). For many distributions no important difference between MC@NLO and Herwig, but…

Pt distribution of B-flavoured hadrons (no top decay!) Herwig fails at large pt because additional hart gluon emission is not considered

Top quark pair + Higgs production (not complete…) [Beneke et al, 2000] LO predictions suffer from large scale dependencies K factors of 1.2-1.5 predicted by Effective Higgs Approximation

Since 2002 NLO corrections to ttH are available [Beenakker, Dittmaier, Kramer, Plumper, Spira, Zerwas 01] [Reina, Dawson, Wackeroth 01] Calculation theoretical challenging because of Pentagon topologies K-factors: ~0.8 at Tevatron, ~1.2 at LHC Effective Higgs Approximation fails, (because of t-channel diagrams?) Scale dependence is reduced

Cross section, scale dependence [fb] [Beenakker, Dittmaier, Kramer, Plumper, Spira, Zerwas 02]

Uncertainties due to PDF: [Beenakker, Dittmaier, Kramer, Plumper, Spira, Zerwas 02] Uncertainties due to PDF: 10% at LHC, 5% at Tevatron

Differential distributions  Higgs: NLO corrections can be up to 30%

Differential distributions  Top: Top distributions have remarkable small NLO corrections

Dittmaier First results on pseudo scalar Higgs showed at Les Houches 05

 ttbb at NLO is very difficult Top quark pair + 1 Jet production at NLO [Dittmaier, P.U., Weinzierl] Rather complicated calculation due to Many diagrams Many scales Pentagon topologies QGRAF Diagram 266 QGRAF Diagram 263 Status: Not yet finished, working on cross checks  ttbb at NLO is very difficult

Anomalous couplings, new physics, rare decays… Parameterize new physics in terms of effective Lagrangian, i.e.: Theory: Size of the (anomalous) couplings including loop effects Size of anomalous couplings in specific models QCD corrections

 Not much theory input needed, basic question is experimental sensitivity to the anomalous couplings  A systematic study of QCD corrections might be useful Note: Not every type of new physics can be encoded in anomalous coupling, for specific models also full calculations are needed. For the MSSM concrete calculations are available

SM decays tWs, tWd suppressed compared to tWb: Rare decays SM decays tWs, tWd suppressed compared to tWb: for [Beneke et al, 2000] FCNC SM decays are suppressed, in extensions of the SM one can obtain much larger rates Again: Mainly the question of experimentell sensitivity, SM decays well understood

Conclusions: Theory is in a very good shape as far as top quark physics is concerned The important reactions are known at 10% level Many processes are available in tools like MCFM and MC@NLO Important contribution to the theo. uncertainty comes from PDF

Possible improvements: Top mass measurements non-factorizable corrections finite width effects Pole mass Update theoretical predictions to CTEQ6, MRST  systematic study of PDF uncertainties MC@NLO as standard framework to do NLO phenomenology? + more precise predictions + easy to use FSK subtraction  only old version of Herwig