1. Top mass and its interpretation -- theory
Standard LHC, Copenhagen, April 2012
Top mass and its interpretation -- theory
Peter Uwer
GK1504

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

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

9. 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 ?

10. 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

11. 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 / Powheg
 mass scheme could be fixed, dependence on non-perturbative effects can be improved

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

13. 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”

14.  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 ?

15. 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

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

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

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

19. 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

20. 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

21. 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

22. 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 ?

23. Thank You

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

25. 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