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

2. 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/ ]
Here:
Theory as summarized in Beneke et al +
progress since then

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

4. 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

5. 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/ ]
From unitarity (3 families!) and additional measurements:
[PDG 04] !
Almost no lower bound if
additional families exist

6. 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!

7. ! 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

8. 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)

9. 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

10. ! 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

11. 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]

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

13. 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…]

14. [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 ?

15. 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.

16. 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

17. ttX included in MC@NLO (without spin-correlations!)
New results since 2000
ttX included in (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]

18. 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 ]
Quantum mechanics:
close to
threshold:
 Spins are parallel or anti-parallel close to threshold

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

20. 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!

21. 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:

22. 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

23. 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

24. 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

25. 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

26. 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%

27. 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

28. ! ? 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

29. 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

30. For many distributions no important difference between
Single top production included in
[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
and Herwig, but…

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

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

33. 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

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

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

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

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

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

39.  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

40. 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

41.  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

42. 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

43. 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
Important contribution to the theo. uncertainty comes from PDF

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