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 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  s 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

So far, top quark interactions not precisely known. Basic parameters like m t and  t. Formation and decays of toponium resonances. Top quark interactions: ttg, ttZ, tbW, ttg and ttH. Is there anomaly? Top still point-like? m t 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.

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

The analytic formula become simple in the case of M. Jezabek and J.H. Kuehn, PLB329(94) 318 Numerical calculation 1) Soft + Virtual 2) Hard part similar, but 5 th order integral. instead of calculating exact integral region, integrate 0<x b <1 and 0<x l <1. then impose the constrain of 0<x <1 and cos 2  lb ≤1. 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.

lepton distribution of (V+A) = distribution of (V-A)  s C F /  ~ double differential decay width ( without top quark spin)

top quark spin part lepton distribution of (V+A) =  distribution of (V-A) From the figure,  R effect is the largest in distribution for spin part.

For the fits, we restrict the region. 0.25<x l <0.97 and a) 0.74<x b <0.77 b) 0.77<x b <0.78 c) 0.78<x b <0.84 extract the propagator and express by cubic polynomial xbxb xlxl xlxl a)b) 1-loop correction of no spin part, a) is  for and b) is for 

0.74<x b < <x b < <x b <0.84

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

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

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

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

 R dependence in energy distribution

= c Im(    ) S, c = for tree + 1-loop The effect of T-odd term

Summary We calculate 1-loop QCD correction to top quark decay. Fit to d  /dx l dcos  and d  /dx l dx b dcos  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=p l ·(p b  s t ) the effect is 0.4% to the differential decay width.