Semileptonic decays of polarized top quarks: V+A admixture and QCD corrections Yoshiaki Umeda with...
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![Page 1: Semileptonic decays of polarized top quarks: V+A admixture and QCD corrections Yoshiaki Umeda with W. Bernreuther and M. Fuecker 1 Introduction 2 Formalism.](https://reader035.fdocuments.us/reader035/viewer/2022062809/5697bf8b1a28abf838c8b07d/html5/thumbnails/1.jpg)
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
![Page 2: Semileptonic decays of polarized top quarks: V+A admixture and QCD corrections Yoshiaki Umeda with W. Bernreuther and M. Fuecker 1 Introduction 2 Formalism.](https://reader035.fdocuments.us/reader035/viewer/2022062809/5697bf8b1a28abf838c8b07d/html5/thumbnails/2.jpg)
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
![Page 3: Semileptonic decays of polarized top quarks: V+A admixture and QCD corrections Yoshiaki Umeda with W. Bernreuther and M. Fuecker 1 Introduction 2 Formalism.](https://reader035.fdocuments.us/reader035/viewer/2022062809/5697bf8b1a28abf838c8b07d/html5/thumbnails/3.jpg)
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.
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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
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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
![Page 6: Semileptonic decays of polarized top quarks: V+A admixture and QCD corrections Yoshiaki Umeda with W. Bernreuther and M. Fuecker 1 Introduction 2 Formalism.](https://reader035.fdocuments.us/reader035/viewer/2022062809/5697bf8b1a28abf838c8b07d/html5/thumbnails/6.jpg)
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)
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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
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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
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0.74<xb<0.77
0.77<xb<0.78
0.78<xb<0.84
![Page 10: Semileptonic decays of polarized top quarks: V+A admixture and QCD corrections Yoshiaki Umeda with W. Bernreuther and M. Fuecker 1 Introduction 2 Formalism.](https://reader035.fdocuments.us/reader035/viewer/2022062809/5697bf8b1a28abf838c8b07d/html5/thumbnails/10.jpg)
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
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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
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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.
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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.
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.
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
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<O> = c Im() S, c = 0.0042 for tree + 1-loop
The effect of T-odd term
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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.