1. ITP of Peking University Aug 25, 2009 ITP of Peking University Aug 25, 2009

2.  1, Introduction  2, FCNC single top production  3, Numerical results  4, Conclusion

3.  Top quark: star of the Hadron Colliders 1, Discovered by CDF and D0 in 1995. For 14 years, we have measured its mass, spin, decay properties, pair production cross sections, distributions and FB asymmetry and also single top production rate @Tevatron. 2, LHC is a top factory, with a rate of 830 pb for top pair production and 320 pb for single top production. Measuring top properties is one of the most important missions for the LHC, including production rates, masses, helicities, spin correlations, CKM matrix elements, rare decay, electric charge and Yukawa coupling. To prove SM predictions or find NP hints. Rapid decay ~0.4 × 10 -24 s Large mass ~171GeV The heavier you are, the closer to the Lord.

4.  Single top production in the SM: Wg fusion: 245±27 pb S.Willenbrock et al., Phys.Rev.D56, 5919 Wt: 62.2 pb A.Belyaev, E.Boos, Phys.Rev.D63, 034012 W* 10.2±0.7 pb M.Smith et al., Phys.Rev.D54, 6696 1, A measurement of the production cross section provides the only direct measurement of the top decay width and the CKM matrix element |V tb | 2 ; 2, Measuring the spin polarization of single-top quarks can be used to test the V-A structure of the top quark EW charged current interaction; 3, The presence of various new physics may be inferred by observing deviations from the predicted rate of the single-top signal and by comparing different production modes. Also important background for Higgs search. 4, Different production modes can be measured separately due to different final states and kinematic distributions. The s-channel mode is very sensitive to an exotic charged boson which couples to top and bottom. And the FCNC processes can have a drastic effect on the t-channel mode. (Tevatron-for-LHC Report: Top and Electroweak Physics, arXiv:0705.3251)

5.  Top FCNC couplings: 1, Highly suppressed in SM, BR(t->c γ ) ≈4.6×10 -14, BR(t->cg) ≈4.6×10 -12. 2, Receive significant contributions from various new physics models: (C.S. Li et al., Phys. Rev. D49: 293(1994); J.J. Liu, C.S. Li et al., Phys Lett B599: 92(2004); J. A. Aguilar - Savedra, Acta Phys. Polon. B35: 2695 (2004); J.J. Cao, Z.H. Xiong and Jin Min Yang, Phys. Rev. Lett. 88:111802(2002).)

6.  Effective operator method (model-independent): New interactions with a scale Λ will manifest themselves at energies below Λ through small deviations from the SM, which can be described by an effective Lagrangian containing non- renormalizable SU(3) × SU(2) × U(1) invariant operators. The dimension 5 terms break baryon and lepton number conservation, and are thus not usually considered. If we restrict ourselves to the operators that include a single top quark, gluons and others. Then the most studied one is After spontaneous symmetry breaking, the above one generate a dimension 5 flavor-changing chromo-magnetic operator, for phenomenology study, one always choose the FCNC Lagrangian to be (W. Buchmuller and D. Wyler, Nucl. Phys. B268, (1986), 621)

7.  Test the FCNC tu(c)g coupling at Hadron Colliders: 1, Through top rare decay, t  u(c)g, unlike the tu(c) γ or tu(c)Z couplings, due to the large QCD backgrounds, this channel is not so efficient. NLO QCD effects have been considered. (Tao Han et al., Phys. Lett. B385:311(1996); Tim Tait and C.-P. Yuan, Phys. Rev. D55, (1997) 7300; ATLAS collaboration, Eur. Phys. J. C999(2007); C.S. Li et al., Phys. Rev. Lett. 102: 072001(2009). )

8. 2, Through direct top production, pp( pbar)  t, high order QCD effects including threshold resumation have been studied. (M. Hosch et al., Phys. Rev. D56, 5725(1997); J. A. Aguilar - Savedra, Acta Phys. Polon. B35: 2695 (2004); J.J. Liu, C.S. Li et al., Phys. Rev. D72: 074018(2005); L.L. Yang, C.S. Li et al., Phys. Rev. D73:074017(2006); CDF collaboration, Phys. Rev. Lett. 102:151801(2009). ) CDF direct search result using W plus one jet: The CDF collaboration have adopted the NLO QCD and resumation results, given by: J.J. Liu, C.S. Li et al., Phys. Rev. D72: 074018(2005); L.L. Yang, C.S. Li et al., Phys. Rev. D73:074017(2006); C.S. Li et al., Phys. Rev. Lett. 102: 072001(2009).

9. 3, Through single top production, pp( pbar)  t + jets, theoretical predictions are only presented at tree level. High order QCD effects are needed in order to give a more precise measurement of the FCNC couplings. Our main goal. This work investigates the NLO QCD effects, and next step will be threshold resumation effects. (Ehab Malkawi and Tim Tait, Phys. Rev. D54, 5758(1996); Tao Han et al., Phys. Rev. D58, 073008(1998); P. M. Ferreira and R. Santos, Phys. Rev. D73, 054025(2006); D0 collaboration, Phys. Rev. Lett. 99:191802(2007). ) D0 direct search result through single top production:

10.  @Tree level: FCNC vertices Feynman diagrams for different subprocesses There are 3 main subprocesses which contribute at hadron colliders, g u  t g, g g  t ubar, and q u  t q, similar for tcg coupling. @LHC, for tug coupling, g u channel is dominant ~80%, while for tcg coupling, g c and g g channel contribute about 50% each. @Tevatron, for tug coupling, g u and q u channel contributes ~70% and ~30%, separately, while for tcg coupling, 3 channel contribute almost equally.

11.  @NLO-QCD 1,We use conventional dimensional regularization (CDR) in d=4-2 ε space- time dimensions to regulate both the IR and UV divergences. 26 box diagrams 68 triangle diagrams 65 bubble diagrams 2, To cancel all the UV divergences we need to introduce the renormalization of the FCNC coupling constant κ using MSbar scheme, also the running of κ. 3, There are 58 independent real correction diagrams in total. Generally, two kinds of method to separate the IR divergences: Ⅰ, Phase slicing method, like two cut-off; Ⅱ, Subtraction method, like dipole. Here we use the latter one. PS: more intuitive, more physics, bad numerical precision due to big number cancellation. DIP: more formal, more general, greatly improve the numerical convergence. (Stefano Catani et al., Nucl. Phys. B627:189, 2002)

12.  Final state signal and kinematics  Possible backgrounds We leave the top quark undecayed, so the final state contains one top quark plus possible one or two (only @NLO) light jets. For the light jet selection, we require its P T >20GeV, | η | 20GeV. Our calculation are pure NLO at parton level, no showering, no hadronization. JJ t PP(P bar) The main backgrounds arise from SM single top production, top pair production, W plus jets production and Multijets production. Since we mainly concern the NLO QCD effects, we don’t consider them here.

13.  Total cross section: We use the cteq6m PDF, choose the renormalization and factorization scale to be m t, and set κ tug / Λ = κ tcg / Λ =0.01TeV -1.

15.  Scale dependence and theoretical uncertainty:

19.  Transverse momentum distribution of the leading light jet:

21.  Rapidity distribution of the leading light jet:

23.  Energy distribution of the top quark:

25.  Invariant mass distribution of the top quark and leading light jet:

27.  Distributions of the jet multiplicities:

29.  In conclusion, we have studied the NLO QCD effects to the single top production process through model-independent FCNC couplings at hadron colliders.  The NLO QCD corrections greatly reduce all the scale dependences, which make the theoretical predictions more stable and more accurate.  The NLO K factor are found to be 1.2~1.7 for different cases. Since the total cross sections are proportional to the square of the FCNC couplings, so our results will increase the experimental sensitivity to the FCNC couplings by about 10%~30%.  We investigate the NLO corrections to several important kinematic distributions, which will be helpful for the experimentalist to separate the signal from backgrounds.  Further investigation on the threshold resummation effects may needed.

30. God is there! t Z W