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Semileptonic decays of polarized top quarks: V+A admixture and QCD corrections

Semileptonic decays of polarized top quarks: V+A admixture and QCD corrections. Yoshiaki Umeda with W. Bernreuther and M. Fuecker 1 Introduction 2 Formalism 3 Numerical results 4 Summary. Introduction. Top quark: Heaviest fundamental particle observed

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Semileptonic decays of polarized top quarks: V+A admixture and QCD corrections

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  1. Semileptonic decays of polarized top quarks: V+A admixture and QCD corrections Yoshiaki Umeda withW. Bernreuther and M. Fuecker 1 Introduction 2 Formalism 3 Numerical results 4 Summary

  2. Introduction Top quark:Heaviest fundamental particle observed Within the SM, decays almost 100% to b quark and W-boson decay modes: tsW(1.6×10-3), dW(1×10-4） Extremely unstable: Lifetime ~ 410-25s Decays too fast to form hadronic bound states.  The properties of a naked quark can be studied. The dynamics of top quark production and decay are described by perturbative QCD. All the spin information of top quark  transfer to its decay products. life time << spin flip time or emitting gluon

  3. So far, top quark interactions not precisely known. • Basic parameters like mt and Gt. • Formation and decays of toponium resonances. • Top quark interactions: ttg, ttZ, tbW, ttg and ttH. Is there anomaly? • Top still point-like? • mt due to usual Higgs mechanism? • In this talk, I will show • Calculate 1-loop QCD correction. • Fit to 1-loop QCD correction. • Study the effect of V+A coupling. • Study the effect of CP-odd terms.

  4. Formalism QCD correction: SU(3) gauge group. as(mZ)=0.119, as(mt)=0.108 Xmin : arbitrary, but small separation number. e.g. 5×10-3 Virtual + Z-factor : UV divergence cancel Virtual + Soft : IR divergence cancel After adding 1) and 2), Xmin dependence cancel Xmin should be enough small, but hard to calculate for smaller Xmin

  5. The analytic formula become simple in the case of M. Jezabek and J.H. Kuehn, PLB329(94) 318 Numerical calculation 1) Soft + Virtual instead of calculating exact integral region, integrate 0<xb<1 and 0<xl<1. then impose the constrain of 0<xn<1 and cos2qlb≤1. 2) Hard part similar, but 5th order integral. For MC integration, I use vegas (cornell univ.) and bases(KEK). For the calculation of matrix element, I use FORM. FORM is excellent for algebraic calculation and pattern matching.

  6. double differential decay width ( without top quark spin) asCF/p ~ 0.046 lepton distribution of (V+A) = n distribution of (V-A)

  7. top quark spin part lepton distribution of (V+A) = -n distribution of (V-A) From the figure, kR effect is the largest in n distributionfor spin part.

  8. For the fits, we restrict the region. 0.25<xl<0.97 and a) 0.74<xb<0.77 b) 0.77<xb<0.78 c) 0.78<xb<0.84 extract the propagator and express by cubic polynomial 1-loop correction of no spin part, a) is aa for and b) is for ab. a) b) xb xl xl

  9. 0.74<xb<0.77 0.77<xb<0.78 0.78<xb<0.84

  10. The fits to one-loop correction. The vector, axial-vector and interference term with and without top quark spin. Fits to the one-loop correction. Vector and interference part with top spin.

  11. The constraint of kR The Lagrangian for third family quark is The most stringent constraint: CLEO bsg experiment. |kR|< 0.04 F.Larios, M.A.Perez and C.-P.Yuan, PLB457(1999)334 bsg experiment constrain CC of kL and kR But this constraint use the condition |kL|< 0.2 and |Vts|<0.04.  |kR| can be larger than 0.04 LEP/SLC data constrain CC of kL and NC of kL and kR. Thus deviation of SM tbW coupling require the deviation of SM ttZ coupling.

  12. The best way to observe kR directly is FB asymmetry. F. del Aguila et al., PRD67(2003)014009 For 2fb-1, AFB = 0.22±0.04 (estimation in SM).  |kR| < 0.7 (3s deviation) The second way is to observe the cross section of single top production. The cross section is proportional to |Vtb|2 (SM). Single top is almost 100% polarized (SM). Anomalous coupling can be observed.

  13. kR effect  cross section become large.If |Vtb| is away from 1  cross section become small.Tevatron run3 (30fb-1) error of |Vtb| is 5%LHC (10fb-1/year) error of |Vtb| is 2% for 30-1fbAt LHC, 3milion single top / year will be produced. (s=300pb)At Tevatron, 60,000 single top / year will be produced (s=2pb) |Vtb| A.P. Heinson et al., PRD56(1996)3114 Ar is the same as our kR.

  14. kR dependence in energy distribution

  15. The effect of T-odd term <O> = c Im(a*b) S, c = 0.0042 for tree + 1-loop

  16. Summary • We calculate 1-loop QCD correction to top quark decay. • Fit to d/dxldcos and d/dxldxbdcos are performed. • Calculate the |R| effect to V-A coupling. |R|<0.04 from b s experiment but the effect is 2% for |R|=0.1 • Calculate the expectation value of O=pl·(pbst) the effect is 0.4% to the differential decay width.

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