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. 2010 山东大学 ( 威海）. Outline. Introduction Top Quark in the SM and Beyond Supersymmetry Extra Dimensions Summary. Introduction. The “Successful” Standard Model.
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07 Aug. 2010 山东大学(威海）
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
All these call for a more fundamental theory, and SM is just its low energy approximation New physics beyond SM
luminosity , offers the best prospects for discovering new physics
beyond the SM.
reactions: 109 / s
Rates for L = 1034 cm-2 s-1: (LHC)
LHC is a factory for:
top-quarks, b-quarks, W, Z, ……. Higgs, ……
The only problem: you have to detect them !
Sensitive to EW symmetry breaking
Only fermion with a “natural ”Yukawa coupling
--So the top has one dominant decay mode: t → W+ b. (NLO QCD corrections: C.S.Li, et al. PRD,1991)
among its decay products
top quark physics comes
from the potential to find
MeasurementsWhat Can We Learn From The Top Quark?
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
Search for t’ quark
Doestop quark has the expected couplings?
W boson helicity
Top quark branching fractions
Currently the best predictions is resummation at NNLL+NLO matching:
Invariant mass distribution
Top quark velocity distribution
Single top production cross section with NNLL resummation ( s and t channel )
Schematically, we show in the framework of SCET that the cross section in the threshold limit factorized as:
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
Usually final state jet has larger invariant mass: collinear gluon need to be integrated out.
The jet function Jis 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
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.
Finally, the remaining initial state collinear effects is matched onto the SCET PDFs:
Match at scale
Large logarithms of scale ratio: ,
Resummed by RGE!
Note: Factorization scale is not necessarily lower than the soft scale, jet scale!
encode the short distance physics which are not captured by SCET.
directions. It describe soft gluon interaction between different partons.
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.
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.
While the SM NLO QCD predicts (Kuhn,et.al.,1998,1999; Bowen, et.al.,2006;Antunano, et.al., 2008;Almeida,et.al.,2008):
Where is the eventnumber of top quark with y>0.
The discrepancy with respect to the SM reduces from 2 sigma to 1.7 sigma, still room for new physics!
The forward-backward asymmetry of top quark production at the Tevatron in warped extra dimensional models (A. djouadi, et.al., arXiv:0906.0604)
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 .
Axigluon as possible explanation for top quark forward-backward asymmetry( Frampton, J. Shu, K. Wang,Phys.Lett.B683:294-297,2010 )
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
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:1007.0260)
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
Any new physics effect involved in top quark FCNC processes can be incorporated into an effective Lagrangian in a model independent way:
upper limits on the top quark FCNC couplings (D0 Collaboration,
Phys. Rev. Lett. 99,191802(2007))
coupling parameters at 95% C.L. are:
This is the most sensitive process to t-g-c anomalous couplings!
C.S.Li and L.L. Yang,
couplings at the NLO in QCD
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
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
Fig4. Branching ratio as function of .
Fig.5 as functions of Branching ratio
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:1004.0898)
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)
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.
Black: LO Red: NLO
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 massdistribution 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 itis possible to extract the spin and coupling information of theresonance from the top quark polar angle distributions and the spincorrelations of the top quark pair.
Jun Gao, Chong Sheng Li, Bo Hua Li, C.-P. Yuan and Hua Xing Zhu, PRD (2010)
The solid and dotted lines correspond to including the total NLO corrections and the corrections from production part alone, respectively.
The solid line corresponds to the LO result, and the other lines correspond to the NLO ones.
The generic coupling of Z’ to fermion can be written as
Present mass limits : m (sleptons, charginos) > 90-103 GeV LEP II
m (squarks, gluinos) > ~ 250 GeV Tevatron Run 1
m (LSP, lightest neutralino) > ~ 45 GeV LEP II
tops and large :
dileptons + jet + :
jets and :
like-sign dileptons :
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-1 M ~ 1500 GeV
10 fb-1 M ~ 1900 GeV
100 fb-1 M ~ 2500 GeV
TeV-scale SUSY can be found quickly !
NLO QCD predictions for productions
space , and in other cases they generally vary from 10fb to several
which are in general a few ten percent, and vastly reduce the
dependence of the total cross sections on the renormalization/factorization
Li Gang Jin, Chong Sheng Li, et al., PLB 561(2003)135, EPJC30(2003) 77
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
Threshold resummation effects in the associated production of chargino and neutralino at hadron colliders.
W. Beenakker, et al., (1999)
S. Hao, et. al., (2006)
Chong Sheng Li, et al., PRD77 (2008) 034010
Chong Sheng Li, et al., PRD77 (2008) 034010
Resonant production of a single slepton can lead to interesting phenomenology at hadron colliders.
H. K. Dreiner, et al. (2001).
R-parity violating L:
NLO QCD corrections:
D. Choudhury et al., (2003)
Li Lin Yang , Chong Sheng Li, et al., PRD 72 (2005) 074026
NLO SUSY-QCD corrections:
Dreiner et al., (2006)
QCD parts agree
Li Lin Yang , Chong Sheng Li, et al., PRD 72 (2005) 074026
Large Extra Dimensions
Flat Extra Dimensions
Warped Extra Dimensions
According to the topology/geometry of the space – time manifold,
the models can be classified into two classes:
Arkani-Hamed, Dimopoulos, and Dvali, PLB, 1998.
“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
Randall and Sundrum, PRL, 1999
BulkCan LHC probe extra dimensions ?
(Explain the weakness of gravity (or hierarchy problem) by extra
i.e. accessible at the LHC
Example: Search for direct Graviton production
Jets or Photons with ETmiss
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
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.
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.
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) 016008.
Z pair production at the LHC in LED
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 4.3-5.6 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.
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).
Xiangdong Gao, Chong Sheng Li et al., PRD81:036008,2010.
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).
Warped extra dimensions
Its metric tensor can be written as:
The extra dimension (5th-dim) yis “warped”.
Rizzo. et al.,2001
The invariant mass distribution for the Drell-Yan Process at the LHC
Jun Gao, Chong Sheng Li, et al., PRD78 (2008) 096005
The transverse momentum distribution of the first KK graviton excitation mode from pp → G process at the LHC.
Dependence of the K-factor for the ﬁrst KK graviton excitation mode direct production at the LHC on m1.
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.
Qiang Li, Chong Sheng Li, et al., PRD74 (2006) 056002