Top quark physics at the LHC Peter Uwer CERN Contents: Introduction Top quark physics at the LHC Spin correlations Top quark pair + Jet production Conclusion/Outlook Meeting on Particle Physics Phenomenology, CERN, 1/10/2004

Introduction  Discovery of the Higgs boson and measurement of its couplings  Top quark physics: Large number of top quarks will be produced at LHC  Good laboratory for precise analysis of top quark interactions  Test of the Standard Model at high scale Two important objectives at LHC: In fact: Top quark physics also important for Higgs discovery

The top quark in the Standard Model (1) What do we know about the top quark? Discovered 1995 at the Tevatron as last missing building block in the third family. In the SM quantum numbers are highly constrained by the structure of the SM: note:strictly speaking we have only indirect information about the top quantum numbers, no direct measurement so far!

The top quark in the Standard Model (2) In the SM the only free parameters in the top sector are: Mass of the top or Yukawa coupling, CKM matrix elements From direct measurements at the Tevatron: From unitarity (3 families!) and additional measurements: [hep-ex/ ] [PDG 04]

The top quark in the Standard Model (3) Top quark is the heaviest elementary particle known so far! Main decay in the SM: Width calculable in the SM:

Why is the top quark so interesting?  Extremly short lived: “Top quark decays before it can hadronize“  More precise measurements of the mass valuable for EW precision physics  constraints on m h  large mass:  Important background  Ideal laboratory to search for new physics Is the top just another ordinary quark? I.e. is the mass generated by the Higgs mechanism? Is it still point like? [hep-ph/ ]

Top quark production at hadron collider Top quark pair production Single top quark production

Top quark physics at the LHC LHC is a top factory: Measurements will in general not be restricted by statistics Top quark physics can be done „from the first day“ on!

What can we do at the LHC? Measure the quantum numbers and parameters of the top quark! Important observables:  tt cross section  tt  cross section  W-Polarization in top decay  ttH cross section  Single top production  Spin correlations  tt+Jet(s) production precise determination of top mass, consistency checks with theo. predictions, search for new physics in the tt invariant mass spectrum measurement of the electric charge test of the V-A structure in top decay measurement of the Yukawa coupling direct measurement of the CKM matrix element Vtb, top polarization, search for anomalous Wtb couplings weak decay of a `free’ quark, bound on the top width and V tb, search for anomalous couplings search for anomalous couplings, important background

Spin correlations in top quark pair production work done in collaboration with W.Bernreuther, A.Brandenburg and Z.G.Si

Spin correlations: Polarization versus correlation 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 Quantum mechanics: study spin density matrix *) absorptive parts at the one-loop level induce a small polarization (~1%) transverse to the scattering plane [Bernreuther,Brandenburg 93,Mahlon, Parke 96, Stelzer,Willenbrock 96, Bernreuther, Brandenburg, Si, P.U ] [Dharmaratna, Goldstein 96, Bernreuther,Brandenburg, Uwer 96]

Spin correlations: the spin density matrix

Spin correlations: Observables… Knowledge of R allows the calculation of arbitrary spin observables, i.e.: Observables of the form have simple interpretation: where ↑/↓ denote spin up/down with respect to a,b as quantization axis To measure C study for example double leptonic distributions.

Spin correlation in top quark pair production How can we measure the spin of the top quark? Basic ingredients: Top quark decays before hadronization Parity violating decay t  Wb The top quark polarization can be studied through the angular distribution of the decay products! QCD NLO corrections know! [Czarnecki,Jezabek,Kühn 91, Brandenburg, Si, Uwer 02]

Spin correlations: LO Standard Model predictions Double leptonic distribution Size of C depends on “quantization axis”: Tevatron LHC

Spin correlations: LO SM predictions (2) Interesting features: For the qq sub process an optimal quantization axis yielding 100% correlation exists: near threshold: gg and qq enter with different sign! [Mahlon, Parke 97]

Spin correlations: Results from D0 Based on six events (10822,12814,15530,26920,30317,417) D0 was able to measure the spin correlations: [hep-ex/ ] Measurement in principle possible, but limited due to small statistics!

Spin correlations: Measurement at the LHC Simulation of the spin correlations at LHC [Slabospitsky, Sonnenschein ´02] Result: without correlationswith correlations NLO needed!

In general very complicated task: Approximation: Spin correlation: NLO corrections double pole approximation calculate only factorizable contributions NLO corrections calculable: Scale dep.: TevatronLHC Tevatron [Bernreuther, Brandenburg, Si, P.U. 03,04]

Spin correlations: Conclusions Spin correlations are measurable at the LHC The SM predictions are under control The observation of the spin correlation: Important: We need also the measurement of the W-Polarization would prove the hypothesis that the top quark decays as a “free quark“ could be used to derive limits on anomalous couplings could be used to measure the properties of new resonances If we don´t see spin correlations, we might be able to obtain bounds on the top width and V tb

Spin correlations: Outlook Search for better quantization axis for gg study more precisly the effect of non-factorizable contributions Include spin correlations in wait until 2007

Top quark pair + jet NLO work done in collaboration with A.Brandenburg, S. Dittmaier and S. Weinzierl

tt+Jet Production: Motivation --- Higgs searches Higgs searches at LHC [Atlas `03] The WBF process is important over a wide Higgs mass range Important backgrounds:  Precise predictions for pp  tt + jet are necessary [Alves, Eboli, Plehn, Rainwater ’04] WW

tt+Jet Production: Motivation --- Higgs measurements “A 10 % accuracy might only be possible through a full NLO calculation” [Rainwater, Spira, Zeppenfeld ’02] [hep-ph/ ] Effects of background uncertainties on measurements tt+jets±10% ττjj ± 50% Solid line: Exp. stat. err. for 200/fb

Motivation: Cross check of alternative bckg determination Alternative ttj background determination: Extrapolation from experimental data [Cavalli et al, hep-ph/ , N.Kauer hep-ph/ ] Detailed analysis: „5-10% accurracy of background might be possible“ Very promising result, but:  Cross check with exact result from pQCD is important  Both methods/results should be used complementary

tt+Jet Production: Motivation --- Topquark physics State of the art: Extensive studies of topquark pair production at hadron collider  NLO predictions including spin effects, resummation of large logs, finite width effects Natural next step: Allows precision measurements i.e. search for anomalous gtt couplings or lepton distributions pp  tt + NLO

Motivation: Scale dependence LHC Assumption: For comparison: [Beenakker et al, ´03] Settings: gg μ/m t

Outline of the calculation In principle: No conceptual problems!  Virtual corrections  Real corrections Reduction of 5-point amplitudes Cancellation of IR-singularities Non-trivial issues...just another 1-loop calculation

Virtual corrections Calculation similar to pp  NLO [Beenakker, Dittmaier, Krämer, Plümper, Spira, Zerwas ´03] Feynmandiagram Generation Feynarts,QGRAF Standard Matrix Elements Mathematica,Form Reduction of Tensorintegrals Numerical Integration QGRAF Diagram 263 QGRAF Diagram 266 Example diagrams: Steps 1,2,4 more or less standard Step 3 involves non- trivial complications  5-point integrals 12 34

Virtual corrections: Evaluation of 5-point amplitudes One possible solution Standard reduction à la Passarino-Veltman Bottleneck: 1.Evaluation of 5-point scalar integrals in d-dimensions 2.Numerical instabilities due to vanishing Gram determinants Solution to 1. In 4 dimension 5-point integrals can be expressed in terms of 4-point integrals [Melrose ´65, van Neerven, Vermaseren ´84]  Apply above observation to regularization scheme independent integrals obtained from original ones by subtracting the singularities Alternatives : Numerical methods Analytic approaches [Oldenborgh, Vermaseren ´90, Passarino et al ´01, Bienoth, Heinrich 04] [Bern, Dixon, Kosower 93, Tarasov ´99, Giele, Glover ´04] [Beenakker et al ´03]

Virtual corrections: Evaluation of 5-point integrals General 5-point integral: Rewrite: Determination of Original Integrand Form combination of 3-point integrals from soft and coll. limits Use together with [Dittmaier ´03],

Virtual corrections: Evaluation of 5-point integrals, Examples:

Virtual corrections: Evaluation of 5-point Tensorintegrals Direct reduction, same trick as in the scalar case: with To regularize spurious UV singularities in individual terms Can be expressed in terms of N i [Denner, Dittmaier ´03]

Virtual corrections: Evaluation of 5-point Tensorintegrals General result: Lower point „tensor integrals“ With: from By discarding the ith row and jth column Tensor integrals with the ith denominator removed [Denner, Dittmaier ´03] No dangerous Gram determinants in the denominator!,

Real corrections: Amplitudes 1.Feynman diagram approach + four dimensional helicity scheme (FDH) 2.Recurrence relations a la Berends,Giele 89  Calculation of matrix elements straight forward  Two methods used: As a check: To extract soft and mass singularities we use the dipol subtraction method! [Catani,Seymour ´96, Phaf, Weinzierl ´01, Catani,Dittmaier,Seymour, Tocsanyi ´02] QGRAF Diagram 20 Phase space integration yields IR/coll. singularities Alternatives: Phase space slicing [Giele, Glover ´92, Giele, Glover, Kosower ´93] comparison with Madgraph

Real corrections: Subtraction Method Basic idea: Add and subtract a contribution which: matches pointwise the singularities is easy enough to be integrated analytically over the one-particle unresolved phase space Requirements: in all single-unresolved regions

Real corrections: Subtraction terms Due to universal structure: Generic form of individual dipol: Leading-order amplitudes Vector in color space Color charge operators, induce color correlation Spin dependent part, induces spin correlation

Real corrections: Subtraction terms Color charge operators: Matrix elements: Vector in spin- and color space Example: arbitrary! The kinematic variables are functions of the three parton momenta

Checks General philosophie: Every contribution should be checked indep., If possible using different methods and different tools Current status:  Not every thing is cross checked so far All tree amplitudes are checked Cancellation of UV and mass/soft singularities works Virtual corrections are stable Dipols are checked at individual phase space points + in singular regions  numerically stable Integration of real corrections works and is checked

First Results Cross section Settings: But we are ahead of time: “This calculation will never be done in my lifetime”, D. Rainwater cross section for LO virtual real preliminary Note: missing contribution from factorization + relicts

tt+Jet Production: Conclusions The NLO corrections to pp  tt + jets are important :  To improve the precision of the background for Higgs searches/measurements in WBF with H  WW  For precision measurements in the Topquark sector, i.e. Anomalous gtt-couplings Calculation of gg  NLO almost complete  Finish missing cross checks  Run additional checks  Remaining processes qq  ttg, qg  ttq To do: 5-point techniques work, Direct reduction of tensor integrals numerically stable, Real corrections tested, integration is stable,...

Conclusions Top quark physics is an interesting and fascinating subject. Many interesting measurements can be done at the LHC.

The End