Semileptonic decays of polarized top quarks: V+A admixture an

d QCD corrections

Yoshiaki Umeda

　　 with 　 W. Bernreuther and M. Fuecker

1 Introduction

2 Formalism

3 Numerical results

4 Summary

IntroductionTop quark:Heaviest fundamental particle observedWithin the SM, decays almost 100% to b quark and W-boson

　　 decay modes: tsW(1.6×10-3), dW(1×10-4 ）Extremely unstable: Lifetime ~ 410-25s

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

So far, top quark interactions not precisely known.

• Basic parameters like mt and t.

• 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.

Formalism

Xmin : arbitrary, but small separation number. e.g. 5×10-3

After adding 1) and 2), Xmin dependence cancel Xmin should be enough small, but hard to calculate for smaller Xmin

Virtual + Z-factor : UV divergence cancelVirtual + Soft : IR divergence cancel

QCD correction: SU(3) gauge group. s(mZ)=0.119, s(mt)=0.108

min

2 )1 X

m

Ex

t

gg

min )2 Xxg

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 5th order integral.

instead of calculating exact integral region, integrate 0<xb<1 and 0<xl<1.

then impose the constrain of 0<x<1 and cos2lb≤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.

222

22

02

||)cos,,,,( )cos1 ) )

2

22

2

22

Mlbbtlblbt

tb

m

mm

l

m

mm

m

mbs mmxxcxx

m

mmdxdx

t

tb

t

tb

t

b

221

22

22

0

1

1

2

1

1

12

||)cos,cos,cos,,,,( )cos1 ) ) coscos

2

22

2

22

min

2

22

M btlbt

tb

m

mm

m

mm

x

gl

m

mm

m

mbh mmxxcxx

m

mmdddxdxdx

t

tb

t

tb

t

tb

t

b

lepton distribution of (V+A) = distribution of (V-A)

sCF/ ~ 0.046

h.c. )(

2

1

2

bWVt tb

gL R R

ls

sF

ssnF

snttb

lsl

t SFCFFCFm

Vddx

d

cos

24||

cos 1010

4g

tt

ll m

Ex

m

Ex

2

,2

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.

.

2

g h.cbW)Vβγ(αγt μtb

μ 5

2

1L R R

ls

sF

ssnF

snttb

lsl

t SFCFFCFm

Vddx

d

cos

24||

cos 1010

4g

tt

ll m

Ex

m

Ex

2

,2

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<0.84extract the propagator and express by cubic polynomial

xb

xl xl

a) b)

1-loop correction of no spin part, a) is for and b) is for

.

2

g h.cbW)Vβγ(αγt μtb

μ 5

2

1L

ls

nF

snnF

snttb

lsbl

t SFCFFCFm

Vddxdx

d

cos

24||

cos 1010

4g

,1

*,1

*,1

*1 Re( FFFF i

0.74<xb<0.77

0.77<xb<0.78

0.78<xb<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 termwith and without top quark spin.

,1

*,1

*,1

*1 Re( FFFF i

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 |Vts|<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, AFB = 0.22±0.04 (estimation in SM). |R| < 0.7 (3 deviation)

F. del Aguila et al., PRD67(2003)014009

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.

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 30-1fb 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

|Vtb|

Ar is the same as our kR.

.

2

g h.cbW)Vβγ(αγt μtb

μ 5

2

1L R R

ls

nF

snnF

snttb

lsl

t SFCFFCFm

Vddx

d

cos

24||

cos 1010

4g

R dependence in energy distribution

<O> = c Im() S, c = 0.0042 for tree + 1-loop

The effect of T-odd term

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·(pbst)

the effect is 0.4% to the differential decay width.