1. Top Quark and New Physics at Hadron Colliders
李重生
北京大学物理学院理论物理研究所
2010威海高能物理暑期论坛暨“QCD与强子物理”研讨会
07 Aug 山东大学(威海）

2. Outline Introduction Top Quark in the SM and Beyond Supersymmetry
Extra Dimensions
Summary

3. Introduction The “Successful” Standard Model
Comparing measurements and theoretical prediction of electroweak precision observables
1. The electroweak sector of SM is tested at the one-loop ,even two-loop level. ( at the level of 1% and less).
2.The consistency of SM is checked by comparing direct measurements with indirect determinations of input parameters, e.g and
3. Global SM fit to all electroweak data from LEPEWWG

4. Problems in the Standard Model
Electroweak symmetry breaking mechanism ?
Hierarchy problem.
Too many free parameters
Flavor / Family problems and fermion masses problem
Neutrinos mass and oscillations
Dark matter …
All these call for a more fundamental theory, and SM is just its low energy approximation New physics beyond SM
LHC is running!
The LHC, with its center-of-mass energy of 14 TeV (7 TeV) and its high
luminosity , offers the best prospects for discovering new physics
beyond the SM.
Mass searching at LHC can reach about 3 TeV.
Most of new physics models predicts phenomena at TeV
scale.

5. Cross Sections and Production Rates (LHC)
Rates for L = 1034 cm-2 s-1: (LHC)
Inelastic proton-proton
reactions: / s
bb pairs / s
tt pairs / s
W  e n / s
Z  e e / s
Higgs (150 GeV) / s
Gluino, Squarks (1 TeV) / s
LHC is a factory for:
top-quarks, b-quarks, W, Z, ……. Higgs, ……
The only problem: you have to detect them !

6. The Top Quark in the SM and Beyond
Top is the heaviest quark in the SM:
Sensitive to EW symmetry breaking
Only fermion with a “natural ”Yukawa coupling
In addition, the SM predicts
--So the top has one dominant decay mode: t → W+ b. (NLO QCD corrections: C.S.Li, et al. PRD,1991)
Top spin information is well kept
among its decay products
Most of the interest in
top quark physics comes
from the potential to find
non-standard effects

7. What Can We Learn From The Top Quark?
Questions
Measurements
What is the Higgs boson mass?
Single top cross section
Constraints on Wtb couplings
Searches for H+ →tb, t→H+b
Do we understand heavy flavor production in QCD?
Search for FCNC
Top quark pair cross section
Are there more than
three fermion generations?
Top quark mass
Forward-backward charge
asymmetry
Are there new
massive particles?
Mtt distribution
Search for t’ quark
Does top quark has the expected couplings?
W boson helicity
Top quark branching fractions

8. Precise predictions on top quark cross section
Top quark pair production cross section
Currently the best predictions is resummation at NNLL+NLO matching:
Beneke, Falgari, Schwinn, 2009
Czakon, Mitov, Sterman, 2009
Ahrens, Ferroglia, Neubert, Pecjak, Li Lin Yang , 2010
Traditional framework
SCET framework
Invariant mass distribution
Top quark velocity distribution

9. Single top production cross section with NNLL resummation ( s and t channel )
Precise measurement of single top cross section is a important task of both Tevatron and LHC in the following years.
We need more precise theoretical prediction to compare with experiment!
We perform a complete NNLL threshold resummation for s-channel single top production in the framework of soft-collinear-effective theory. (Hua Xing Zhu, Chong Sheng Li, Jian Wang, Jia Jun Zhang, arXiv: )
Schematically, we show in the framework of SCET that the cross section in the threshold limit factorized as:

10. SCET approach vs. Traditonal approach
Resummation in SCET has advantage over tranditonal approach of resummation as following reasons:
Completely separates the effects associated with different scales in the problem.
Avoid the Landau-pole ambiguities inherent in the traditional approach.
Using conventional RG equations to resum logarithms of scale ratios.
Especially, the momentum space resummation in SCET(Neubert, 2005) is simpler comparing with the Mellin moment space approach.

11. Basics of SCET
SCET is an effective theory describing collinear and soft interaction (Bauer,Fleming, Pirjol, Rothstein, Stewart)
Collinear quark and gluon field
Soft and collinear interaction decoupled by field redefinition
SCET Lagrangian factorized:

12. Factorization: step 1-integrated out the hard function
Idea:
Match the full theory cross section onto SCET by integrating out hard momentum mode.
SCET is constructed to reproduce the long distance physics, and thus short distance physics is not described by the dynamics of the effective field theory.
The short distance information carried by hard mode is absorbed into Wilson coefficient, the hard function (H)
After full theory match onto SCET at the hard scale , hard function (H) can be obtained

13. Factorization: step 2-integrated out the jet function
Usually final state jet has larger invariant mass: collinear gluon need to be integrated out.
The jet function J is the final state analog of the parton distribution functions.
In general, Jet function describe how the final partons from the hard interaction evolve into the observed jets, and contain all dependence on the actual jet algorithm. But we use the inclusive algorithm.
After integrate out the final state collinear gluons at the scale

14. Factorization: step 3-integrated out the soft function
The remaining parton interact with soft gluon through eikonal interaction, and can be absorbed into soft Wilson line by field redefinition.
The soft function S describes the emission of soft partrons from the soft Wilson line.
If we define the soft scale
Then one can perturbatively calculate it and avoid the Landau pole problem.
Match at

15. Factorization: step 4, match onto PDFs
Finally, the remaining initial state collinear effects is matched onto the SCET PDFs:
Match at scale

16. PDFs Description of factorization Hard function Jet function
Soft function
Large logarithms of scale ratio: ,
Resummed by RGE!
Note: Factorization scale is not necessarily lower than the soft scale, jet scale!

17. Hard Function
Soft Function
Jet Function
Hard function is the amplitudes square of full theory QCD corrections, which
encode the short distance physics which are not captured by SCET.
Soft function is the matrix of Wilson lines along beam, jet and top quark
directions. It describe soft gluon interaction between different partons.
Jet function is the matrix of collinear fields associate with the jet.
Each of these function obey certain RG evolution equation. Resummation is achieved via computing these function at its appropriate scale and then evolving to the same scale by RG equation.

18. After matching in momentum space approach, the resummed total cross section is given by
The cross section in blue color is our best prediction. We can see that the resummation effects enhance the NLO cross section by about 3%-5%. The total uncertainties is obtained from varying the hard, soft, jet and factorization scale separately by a factor ½ and 2, and then adding up the individual variations in quadrature.

19. T-channel

20. Preliminary numerical results at Tevatron
Our combined (s+t channel) predictions are consistent with the Tevatron results (D0 and CDF average value) so far.

21. Forward-backward Asymmetry of Top Quark Pair
Recent measurements of the forward-backward assymmetry in top quark pair production at the Fermilab Tevatron have shown a significant positive deviation from the small value predicted in the SM. The recent value reported by CDF, base on 3.2fb-1 of integrated luminosity, is
Interference of box and tree diagrams.
While the SM NLO QCD predicts (Kuhn,et.al.,1998,1999; Bowen, et.al.,2006;Antunano, et.al., 2008;Almeida,et.al.,2008):
Interference of initial state radiation of final state radiation.
In the SM assymmetry arises at O( )
Where is the event number of top quark with y>0.

22. Forward-bacjward asymmetry at D0 and CDF (from ICHEP 2010 slides)
results
results
The discrepancy with respect to the SM reduces from 2 sigma to 1.7 sigma, still room for new physics!

23. Implication of top quark forward-backward assymetry
QH Cao, et.al., Phys.Rev.D81:114004,2010:
… After combining the forward-backward asymmetry with the measurement of the top pair production cross section and the ttbar invariant mass distribution at the Tevatron, we find that an axial vector exotic gluon G’ of mass about 1 TeV or 2 TeV or a W’ of mass about 2 TeV offer an improvement over the SM. The other models considered do not fit the data significantly better than the SM.
They also emphasize a few points that have long been ignored in the literature:
heavy resonance width effects;
renormalization scale dependece;
NLO corrections to the ttbar invariant mass spectrum.

24. Possible solution to top quark forward-backward assymmetry?
The forward-backward asymmetry of top quark production at the Tevatron in warped extra dimensional models (A. djouadi, et.al., arXiv: )
They explain the top quark forward-backward assymmetry by the contributions of Kaluza-Klein excitations of gauge bosons (gluons at the Tevatron and electroweak bosons at LEP) in warped extra dimensional models in which the fermions are localized differently along the extra dimension so that the gauge interactions of heavy third generation fermions are naturally different from that of light fermions.
Non-zero top quark forward-backward assymmetry originates from non-zero axial coupling of KK-excitation to light and heavy qaurk

25. Axigluon as possible explanation for top quark forward-backward asymmetry ( Frampton, J. Shu, K. Wang, Phys.Lett.B683: ,2010 )
In their model extended color model SU(3)X(SU(3), axial gluon couples to light and heavy quark via
The key feature of their model is that
while
The unique feature of this model: rise and fall behavior of
Axigluon cannot explain the observed top quark forward-backward asymmetry (Chivukula, Simmons, C.-P. Yuan, arXiv: )
Chivukula,Simmons, Yuan
They consider the constraint from neutral Bd meson mixing and requiring the extended color sector remaing perturbative essentially make the axigluon unlikely to be the source of observed top quark forward-backward asymmetry.
: mixing angle of the extended color sector.
: mass of the axigluon
Frampton, Shu, Wang

26. Single top quark production via anomalous couplings
Any new physics effect involved in top quark FCNC processes can be incorporated into an effective Lagrangian in a model independent way:
It should be noted that very recent data from D0 collaboration has set
upper limits on the top quark FCNC couplings (D0 Collaboration,
Phys. Rev. Lett. 99,191802(2007))
The upper limits on the anomalous
coupling parameters at 95% C.L. are:

27. Direct top quark production
This is the most sensitive process to t-g-c anomalous couplings!
NLO QCD: J.J. Liu,
C.S.Li and L.L. Yang,
PRD72, (2005):
Threshold resummation effects L.L.Yang, C.S.Li, Y. Gao, and J.J. Liu, PRD,73, (2006)

28. Top quark decay via anomalous couplings at the NLO in QCD
To be consistent, besides obtaining limits on the coupling constants, we should deduce limits on the BRs as well. Moreover, experimentalists are more interest in measuring BRs.
without mixing : J.J.Zhang, C.S. Li, et al., Phys.Rev.Lett,102,072001, 2009, aiXiv:
with mixing: J.J.Zhang, C.S. Li, et al., arXiv:
Constraints from Tevatron measurement
Using the upper limits of FCNC couplings measured by D0 and CDF and our predictions at the NLO in QCD, the following constraints on the branching ratios can be obtained
CDF D0

29. Relations between branch ratio and FCNC couplings at NLO in QCD J. J
Relations between branch ratio and FCNC couplings at NLO in QCD J.J.Zhang, C.S. Li, et al., Phys.Rev.Lett,102,072001,2009
D0 constraints
ATLAS sensitivity
Fig4. Branching ratio as function of
Fig as functions of Branching ratio

30. Sensitivities at the LHC:
When considering the mixing effects of FCNC operator, the decay branching ratio of t->qg doesn’t change, while t->qZ and t-> qү are modified. In particular, mixing effects changes the running of anomalous coupling. (J.J.Zhang, C.S. Li, et al., arXiv: )
Sensitivities at the LHC:
Low Luminosity 10 fb-1 ,without mixing
High Luminosity 100 fb-1 , without mixing
Low Luminosity 10 fb-1 ,with mixing
High Luminosity 100 fb-1 , with mixing

32. Single top production via the anomalous couplings : pp-> t+jet
There are three channels which contribute at tree level, gu  tg, gg  tubar, and q(u,ubar)u  tq(u,ubar).
The main backgrounds arise from SM single top production, top pair production, W plus jets production and Multijets production. (Tao Han et al., 1998)
NLO QCD corrections:
Jun Gao, Chong Sheng Li, et al., PRD 2009
Assuming κtug/Λ=κtcg/Λ=0.01TeV-1 , and set the leading light jet pT cut to be 20 GeV.
Cross section (pb)
tug (Tev)
tcg
(Tev)
tug
(LHC) LO
0.09
0.006
7.1
1.1
NLO
0.14
0.010
9.2
1.8
K factor
1.5
1.7
1.3
1.6
Black: LO Red: NLO

33. Heavy resonance production and decay into top quark pair at LHC
V. Barger, Tao Han, and D.G.E. Walker, PRL (2008); R. Frederix and F. Maltoni, JHEP(2009); Y. Bai and Z. Han, JHEP(2009)
To explore the connections between the new physics and the top quark, one possibility is to study the top quark pair invariant mass distribution and look for possible resonances since many new physics models predict the existence of a new resonance with a mass around TeV, which can decay into a top quark pair. And it is possible to extract the spin and coupling information of the resonance from the top quark polar angle distributions and the spin correlations of the top quark pair.
We calculated the complete NLO QCD corrections to a heavy resonance production and decay into top quark pair at the LHC, where the resonance could be either a RS KK graviton G or an extra gauge boson Z’.
Jun Gao, Chong Sheng Li, Bo Hua Li, C.-P. Yuan and Hua Xing Zhu, PRD (2010)

34. K factors of the total cross sections
The solid and dotted lines correspond to including the total NLO corrections and the corrections from production part alone, respectively.
Top pair invariant mass distribution
The solid line corresponds to the LO result, and the other lines correspond to the NLO ones.

35. Polar angle distributions
The generic coupling of Z’ to fermion can be written as
Z’1
Z’2
Z’3
Z’4

37. Search for SUSY at the LHC
The masses of the SUSY particles are not predicted; Theory has many additional new parameters (on which the masses depend). However, charginos/neutralinos are usually lighter than squarks/sleptons/gluinos.
Present mass limits : m (sleptons, charginos) > GeV LEP II
m (squarks, gluinos) > ~ 250 GeV Tevatron Run 1
m (LSP, lightest neutralino) > ~ GeV LEP II
SUSY signals
tops and large :
jets and :
like-sign dileptons :
dileptons + jet :
tri-leptons :

38. Strong production
Beenakker, Höpker, Spira, Zerwas, 1997;
Berger, Klasen, Tait, 1999.
Squarks and gluinos, cross sections comparable to QCD cross sections at the same mass scale. Inclusive search using multijets plus missing ET, typical selection: N jet > 4, ET > 100, 50, 50, 50 GeV, ET miss > 100 GeV .
LHC reach for Squark- and Gluino masses:
1 fb  M ~ GeV
10 fb  M ~ GeV
100 fb  M ~ GeV
TeV-scale SUSY can be found quickly !

39. Charginos and Stop associated production
NLO QCD predictions for productions
The total cross sections can reach 1 pb in the favorable parameter
space , and in other cases they generally vary from 10fb to several
hundred fb.
The QCD NLO corrections enhance the LO results significantly,
which are in general a few ten percent, and vastly reduce the
dependence of the total cross sections on the renormalization/factorization
scale.
Li Gang Jin, Chong Sheng Li, et al., PLB 561(2003)135, EPJC30(2003) 77

40. Charginos and Neutralinos associated production
Gaugino pair production via electroweak processes (small cross sections, ~0.1 – 0.5 pb, however, small expected background, trileptons final states, “Golden” SUSY signature)
For small gaugino masses (~100 GeV/c2) one needs to be sensitive to low PT leptons

41. NLO (SUSY) QCD corrections
Threshold resummation effects in the associated production of chargino and neutralino at hadron colliders.
NLO (SUSY) QCD corrections
W. Beenakker, et al., (1999)
S. Hao, et. al., (2006)
Chong Sheng Li, et al., PRD77 (2008)
Threshold Resummation effects
Chong Sheng Li, et al., PRD77 (2008)

42. Single- slepton production in R-parity violating SUSY
Resonant production of a single slepton can lead to interesting phenomenology at hadron colliders.
A charged slepton can decay into a neutralino and a charged lepton, and neutralino can subsequently decay into a charged lepton and two jets via couplings.
Because of the Majorana nature of neutralino, the two leptons can have either opposite or same charges. The case of two leptons of the same charges is more interesting due to the absence of large SM background.
After suitable cuts the R-parity violation signals can be clearly distinguished from the suppressed SM and SUSY backgrounds.
H. K. Dreiner, et al. (2001).

43. qT-Resummation in Single-Slepton Production at the LHC
R-parity violating L:
NLO QCD corrections:
D. Choudhury et al., (2003)
Li Lin Yang , Chong Sheng Li, et al., PRD 72 (2005)
NLO SUSY-QCD corrections:
Dreiner et al., (2006)
QCD parts agree
qT-Resummation:

44. Warped Extra Dimensions Large Extra Dimensions
Search for Extra Dimensions at the LHC
Introduction of extra dimensions
According to the topology/geometry of the space – time manifold,
the models can be classified into two classes:
“Flat” (factorizable) ED
Large ED(Arkani-hamed, Dvali & Dimopoulos)
TeV-1 ED(variant of LED)
Universal ED(Appelquist, Cheng&Dobrescu)
“Warped” (non-factorizable) ED(Randall and Sundrum
Extra Dimensions
Flat Extra Dimensions
Warped Extra Dimensions
Large Extra Dimensions
Split fermions
RS model
Universal
TeV-1 ED
Arkani-Hamed, Dimopoulos, and Dvali, PLB, 1998.
Randall and Sundrum, PRL, 1999 44

45. Can LHC probe extra dimensions ?
Much recent theoretical interest in models with extra dimensions
(Explain the weakness of gravity (or hierarchy problem) by extra
dimensions)
New physics can appear at the TeV-mass scale,
i.e. accessible at the LHC
Example: Search for direct Graviton production
SM wall
Bulk G
 Jets or Photons with ETmiss

46. LED Phenomenology at the LHC (1)The virtual graviton exchange
Summing over all KK modes will lead to enhancement of cross sections. The sum is UV divergent and sensitive to the UV cut.
(2) Graviton emission as missing energy
Vertices
Photon graviton associated production at the LHC may be a interesting way to directly search for signal of the ADD model for it is clean at hadron colliders.

47. Z pair production at the LHC in LED
The Z pair production can get additional contributions through s-channel exchange of KK gravitons at the LHC. Z pair decays to four leptons final states provides a golden signature at the LHC.
We use the partial wave unitarity to discuss the constraints on the process energy scale in order to give a self-consistent calculations.
The J-partial wave amplitudes are
For g g  Z Z, the only nonvanishing partial wave amplitudes correspond to J=2. All the amplitudes contribute to the imaginary part of g g elastic scattering amplitudes according to the optical theorem, so the partial wave unitarity leads to
LED contributions to the Z pair production total cross sections at the LHC.
Jun Gao, Chong Sheng Li, et al., PRD80 (2009)

48. According to our MC simulation analysis, the kinematic distributions of the LED signal are greatly different from the SM backgrounds, and the LHC can probe the LED scale MS up to TeV for the Z pair production process.
4 lepton invariant mass distribution
leading lepton transverse momentum distribution
The total cross sections of the LED signals after all the cuts. The horizontal lines indicate the cross sections needed for a 3σ detection of the signal.

49. Graviton and photon associated production at the LHC
It is one of the most important channel for the direct detection of the graviton, and the resulting signature of single photon plus large missing transverse energy are rather clean at hadron colliders. LO MC analysis shows that the LHC can probe the LED scale MD up to about 3 TeV (CMS TDR).
G.F. Giudice et al., Nucl.Phys.B,1999
Dependence of the cross section on missing transverse momentum (left) and the transverse momentum of photon (right).
The NLO QCD corrections enhance the cross sections significantly, about 30-50% for δ=2 and 10-30% for δ=4. Thus it can increase the experimental reach of the LED scale.
Xiangdong Gao, Chong Sheng Li et al., PRD81:036008,2010.

50. Graviton production associated with a jet at the LHC
Becase of the large QCD coupling, it’s also very important to investigate the graviton production associated with a hard jet. Searches for the process at the LHC will be able to extend the sensitivity to the fundamental scale Ms into the multiple TeV region. (Vacavant, et.al.,2001; X.G. Wu,et.al.,2008;CMS collaboration, 2010)
The NLO QCD corrections to this process has been performed by S. Karg, M. Kramer, Qiang Li, D. Zeppenfeld, (PRD81:094036,2010 ). The NLO results stabilize the theoretical predictions and significantly reduces the scale uncertainty to a level of approximately 10%.

51. The Randall-Sundrum Scenario
Warped extra dimensions
Its metric tensor can be written as:
The extra dimension (5th-dim) y is “warped”.
RS vs. LED
Same: Only the graviton propagate in the bulk.
Different:
1. Warped (RS) vs. flat (LED)
2. The unevenly spaced KK spectrum for the graviton (RS) vs. the evenly spaced KK spectrum (LED).
3. Each resonance has an 1/TeV order couplings (RS) vs. the sum of all the KK gravitons gives an 1/TeV couplings (LED).
L.Randall and R.Sundrum, Phys. Rev. Lett. 83, 3370 (1999).

52. RS Phenomenology
The individual KK graviton are heavy and strong coupled to the SM particles, and its effects can be detected at the LHC.
The data analysis on the Drell-Yan and dijet process, as well as EW precise test strongly constrain the parameter space of RS model.
Its phenomenology at the LHC has been extensively studied in literatures (e.g. Rizzo. et al). It is shown that the diphoton channel can be used to detect the graviton mass up to 2~3TeV.
Rizzo. et al.,2001
The invariant mass distribution for the Drell-Yan Process at the LHC

53. Same-sign top pair production in RS model of flavor at LHC
The nonuniversal couplings between fermions and KK gauge bosons will lead to observable tree-level flavor changing neutral current effects.
For the same-sign dilepton channel, by imposing suitable cuts the backgrounds can be suppressed to about 0.03 fb, which can lead to a sizable signal/backgrounds ratio, about The discovery limit of the flavor violation parameter εu can reach 0.1 for gtR=5gs, MG1=1 TeV and 10 fb-1 integrated luminosity, 0.06 for 300 fb-1.
Jun Gao, Chong Sheng Li, et al., PRD78 (2008)

55. Soft Gluon Resummation Effects in Single Graviton Production at the LHC
In the RS model, the lightest massive graviton can have a mass of several hundred GeV, and maybe produced copiously at LHC, then decay into observable particles and hence be detected.
Dependence of the K-factor for the first KK graviton excitation mode direct production at the LHC on m1.
The transverse momentum distribution of the first KK graviton excitation mode from pp → G process at the LHC.
Qiang Li, Chong Sheng Li, et al., PRD74 (2006)

56. Summary
As the LHC will produce abundant top-quark events, precise predictions on top quark pair (single top quak) cross section in the SM are important for discovering the non-standard effects. And top quark FCNC interaction is a very good probe of new physics beyond the SM.
Various new physics models (Supersymmetry, Extra Dimension, etc.) all have definite signals at the LHC, and the LHC has the ability to discover them.
Distinguishing different extensions of the SM and making precise measurement of the new physics parameters with high accuracy may depend on future ILC.

57. Thanks!