Top mass and its interpretation -- theory Standard Model @ LHC, Copenhagen, 10.-13. April 2012 Top mass and its interpretation -- theory Peter Uwer GK1504

Some basic facts about theory parameters …and their determination. Top-quarks don’t appear as asymptotic states, (no free quarks due to confinement) No parameter determination without theory Top-quark mass is “just” a parameter like as, only defined in a specific theory/model i.e. SM renormalisation scheme dependent, only indirect determination possible through comparison (fit): theory   experiment Scheme dependence encoded in theor. predictions

Different mass definitions Pole mass scheme MS mass Chose constants minimal to cancel 1/e poles in 1S mass [Hoang, Teubner 99] Position of would-be 1S boundstate Potential subtracted (PS) mass [Beneke 98] Each scheme well defined in perturbation theory  conversion possible

Conversion between schemes Example: Pole mass   MS mass: No meaningful parameter determination without at least NLO theory Important: Difference can be numerically significant [Chetyrkin,Steinhauser 99] Difference is formally of higher order in coupling constant

Good choices — Bad choices Perturbative expansion may converge better using specific scheme (resummation of large logs…) Example: tt in e+e- , threshold scan peak position gets large corrections in perturbation theory when pole mass is used NLO resummation improved behaviour for short distance mass, i.e. 1S mass, PS mass Remnant of would-be boundstate

Good choices — Bad choices Scheme might be ill defined beyond perturbation theory Example: Renormalon ambiguity in pole mass [Bigi, Shifman, Uraltsev, Vainshtein 94 Beneke, Braun,94 Smith, Willenbrock 97] ! “There is no pole in full QCD” Pole mass has intrinsic uncertainty of order LQCD

Requirements for a precise quark mass determination Checklist: Observable should show good sensitivity to m Observable must be theoretically calculable  NLO corrections ! Theory uncertainty must be small small non-perturbative corrections Observable must be “experimentally accessible” Well defined mass scheme

„In theory there is no difference between theory and practice. In practice there is.“ [Yogi Berra]

Template method & kinematic reco. [for details talk by Martijin Mulders] In present form: Distribution: invariant masses of top quarks Relies mostly on parton shower predictions No NLO so far available (?) Main issues: Corrections due to color reconnection / non perturbative physics ( mass of color triplet…) Precise mass definition ?

Non-perturbative effects Non-perturbative effects at the LHC [Skands,Wicke ‘08] Simulate top mass measurement using different models/tunes for non-perturbative physics / colour reconnection different offset for different tunes! Non-perturbative effects result in uncertainty of the order of 500 MeV blue: pt-ordered PS green: virtuality ordered PS offset from generated mass

Template method Possible improvements: Different distibutions, any distribution sensitive to mt could be used… Compare with NLO templates, or even better NLO + shower a la MC@NLO / Powheg  mass scheme could be fixed, dependence on non-perturbative effects can be improved

Template method – reachable precision [Stijn Blyweert, Moriond 2012] Dominant uncertainty as long as distributions relying on jets are used

Matrix element method [for details talk by Martijin Mulders] Per event likelihood based on full matrix element and transfer function Main issues: Only leading-order matrix elements are used  mass scheme is not fixed, higher corrections not taken into account Method depends on the quality of the “modeling”

 extension of the matrix element method beyond leading order Possible improvements:  extension of the matrix element method beyond leading order first steps, see C.Williams, J. Campbell and W. Giele [Moriond QCD 2012]  mass scheme could be fixed, higher order effects can be taken into account Reachable precision ?

Alternative Methods Top mass from total cross section Top mass from Mlb Top mass from jet rates In all cases: Higher orders are taken into account Mass scheme is unambiguously fixed

First direct determination of the MS mass [Langenfeld, Moch, P.U. 09] Tevatron, D0 precision limited by weak sensitivity to mt and PDF uncertainties

PDF uncertainties – mt from cross section [Aldaya, Lipka, Naumann-Emme, HCP 2011] 1.4 GeV

Mlb in leptonic top-quark decays [R. Chierici, A. Dierlamm CMS Note 2006/058]

Refinements of Mlb NLO corrections improved predictions [Biswas, Melnikov, Schulze 10] NLO corrections improved predictions in principle different mass schemes possible Further investigations required  Promising option

Short term perspective ? Possible to improve template method  Usage of different / additional distributions  Extend template to NLO accuracy Matrix element method Improvements technically more involved, longer time scale… Start using additional observables

Summary Tremendous progress in the recent past Given the small experimental uncertainties precise interpretation of the measured mass matters Various options to improve current measurements Important to use different approaches to have independent cross checks

Questions to experimentalist Plans to extend template method ? Status of Mlb method ? How computing intensive is the matrix element method? NLO extension feasible ? How is the scheme issue addressed ? Theory support ?

Thank You

Top mass from jet rates Preliminary [Aioli, Fuster, Irles, Moch, Uwer, Vos ’11] Preliminary

Recent progress: Jetmass in e+e- Study high energetic tops in different hemispheres [Hoang 07,08] factorisation in hard scattering and soft functions Double differential invariant mass distribution: Input Non-perturbative corrections shift peak by ~2.4 GeV and broaden the distribution