搜档网
当前位置:搜档网 › Polarized Single Top Quark Production in egamma Collision and Anomalous Wtb Couplings

Polarized Single Top Quark Production in egamma Collision and Anomalous Wtb Couplings

Polarized Single Top Quark Production in egamma Collision and Anomalous Wtb Couplings
Polarized Single Top Quark Production in egamma Collision and Anomalous Wtb Couplings

a r X i v :0709.0365v 2 [h e p -p h ] 24 F e

b 2008

Polarized Single Top Quark Production in eγCollision and

Anomalous W tb Couplings

B.S ?ahin ?and ˙I.S ?ahin ?

Department of Physics,Faculty of Sciences,Ankara University,06100Tandogan,Ankara,Turkey

Abstract

We investigate the potential of eγcollisions to probe anomalous W tb couplings via the polarized single top quark production process e +γ→t ˉb ˉνe .We ?nd 95%con?dence level limits on the

anomalous coupling parameters F 2L and F 2R with an integrated luminosity of 500fb ?1and

?dilec@https://www.sodocs.net/doc/418159271.html,.tr ?

isahin@https://www.sodocs.net/doc/418159271.html,.tr

I.INTRODUCTION

The standard model(SM)has been tested with good accuracy and it has been proved to be successful in the energy scale of the present colliders.However,it is generally believed that SM is embedded in a more fundamental theory(new physics)in which its e?ects can be observed at higher energy scales.The top quark is the heaviest fermion in the SM. Its mass is at the electroweak symmetry-breaking scale.Because of its large mass,the top quark and its couplings are expected to be more sensitive to new physics than other particles [1].Therefore precision measurements of top quark couplings will be the crucial test of the structure of the SM.A deviation of the couplings from the expected values would indicate the existence of new physics beyond the SM.

In this work we analyzed anomalous W tb andγW tb couplings in the single top production process e+γ→tˉbˉνe.Since the top quark is very heavy,its weak decay time is much shorter than the typical time for the strong interactions to a?ect its spin[2].Therefore the information on its polarization is not disturbed by hadronization e?ects but transferred to the decay products.The angular distribution of the top quark decay involves correlations between top decay products and top quark spin:

1

dcosθ=

1

√2m

w

Wμνˉtσμν(F2L P?+F2R P+)b]+h.c.(2) where

W μν=D μW ν?D νW μ,D μ=?μ?ieA μ

P ?=

1

2

(γμγν?γνγμ)(3)

In the SM,the (V-A)coupling F 1L corresponds to the Cabibbo-Kobayashi-Maskawa (CKM)matrix element V tb ,which is very close to unity and F 1R ,F 2L and F 2R are equal to zero.The (V+A)coupling F 1R is severely bounded by the CLEO b →sγdata [7]at a level such that it will be out of reach at expected future colliders.Therefore we set F 1L =0.999and F 1R =0as required by present data [8].The magnetic type anomalous couplings are related to the coe?cients C tW Φand C bW Φ[5]in the general e?ective lagrangian by

F 2L =

C tW Φ

Λ2g

F 2R =

C bW Φ

Λ2g

(4)

where Λis the scale of new physics.Natural values of the couplings F 2L (R )are in the region [1]of

√v

~0.1

(5)

and do not exceed unitarity violation bounds for |F 2L (R )|~0.6[4].

There are many detailed discussions in the literature for W tb couplings in the single and

pair top quark production.The single top quark production cross section for the process e +e ?→W tb has been discussed below and the above the t ˉt

threshold [9]and for the process e +e ?→e ˉνtb at CERN LEP2[10]and linear e +e ?collider [11]energies.Pair top production processes for a future linear collider have been investigated in e +e ?and γγcollisions [12].

W tb couplings have also been investigated at Fermilab Tevatron and CERN LHC [13,14].In ep collision,the W tb couplings were analyzed for polarized top quarks via the process ep →t ˉb ˉν+X [15].It was shown that polarization leads to a signi?cant improvement in the sensitivity limits.In the literature there have been several studies of anomalous W tb couplings in eγcollisions [16].Di?erent from these studies we take into account top quark spin polarization along the direction of various spin bases to improve the sensitivity limits.

II.CROSS SECTIONS OF POLARIZED TOP QUARKS IN THE eγCOLLISION

Research and development of linear e+e?colliders have been progressing and the physics potential of these future machines is under study.After linear colliders have been constructed their operating modes of eγandγγare expected to be designed[17,18].A real gamma beam is obtained through Compton backscattering of laser light o?a linear electron beam, where most of the photons are produced at the high energy region.The luminosities for eγandγγcollisions turn out to be of the same order as the one for e+e?[19],so the cross sections for photoproduction processes with real photons are considerably larger than the virtual photon case.In our calculations we consider three di?erent center of mass energies √

g(ζ)[1?y+

1

ζ(1?y)

+

4y2

ζ?

8

2

+

8

2(ζ+1)2

(7)

withζ=4E e E0/M2e.E0is the energy of the initial laser photon and E e is the energy of the initial electron beam before Compton backscattering.y is the fraction that represents the ratio of the scattered photon and initial electron energy for the backscattered photons moving along the initial electron direction.The maximum value of y reaches0.83when ζ=4.8,in which case the backscattered photon energy is maximized without spoiling the luminosity.The integrated cross section over the backscattered photon spectrum is given by

σ(s)= 0.83y min fγ/e(y)?σ(?s)dy(8) where y min=m2t

V-A structure,the top quarks produced are highly polarized.It was shown in ref.[20]that the top quark possesses a high degree of spin polarization when its spin decomposition axis is along the incoming e+beam.In the e?ective Lagrangian approach,there are?ve tree level diagrams;one of them contains an anomalousγW tb vertex,which is absent in the SM (Fig.1).

The top quark possesses a large mass,so its helicity is frame dependent and changes under a boost from one frame to another.The helicity and chirality states do not coincide with each other and there is no reason to believe that the helicity basis will give the best description of the spin of top quarks.Therefore it is reasonable to study other spin bases better than helicity for the top quark spin.

The spin four-vector of a top quark is de?ned by

sμt=( p t· s′

m t(E t+m t)

p t)(9)

where(sμt)RF=(0, s′)in the top quark rest frame.Top quark spinors are the eigenstates of the operatorγ5(γμsμt):

[γ5(γμsμt)]u(p t,±s)=±u(p t,±s)(10) Using eq.(10)one can easily obtain the spin projection operator:

?Σ(s)=1

p?

s′=λ

( β· p) β?Eγ β(13)

β2

where βis the velocity of the top quark in the e+e?cm system.In the cross section calculations we have performed a boost to obtain p?at each point in phase space.

One can see from Fig.2-5the in?uence of the top quark spin polarizations on the devia-

tions of the total cross sections from their SM value at

dσ e+γ→tˉbˉνe→b?+ν?ˉbˉνe =1(2π)32E3d3p4(2π)32E5d3p6(2π)32E7

×(2π)4δ4 i p i? f p f (14) where p i=p1,p2are the momenta of the incoming fermions and p f=p3,p4,p5,p6,p7are the momenta of the outgoing fermions.|M|2is the square of the full amplitude,which is averaged over the initial spins and summed over the?nal spins.The full amplitude can be expressed as follows:

|M|2(2π)4δ4 i p i? f p f = d4q

q2?m2t+im tΓt(16) M a(s t)is the amplitude for the process e+γ→tˉbˉνe with an on shell t quark.M b(s t)is the decay amplitude for t→b?+ν?.The square of the decay amplitude summed over the?nal fermion spins is given by

|M b(s t)|2=2g4w

dσ e+γ→tˉbˉνe→b?+ν?ˉbˉνe = dσ e+γ→↑tˉbˉνe dΓ(↑t→b?+ν?)

Γ(t→b?+ν?) BR t→b?+ν? (18) where BR(t→b?+ν?)is the leptonic branching ratio for the top quark.Up and down arrows indicate the spin up and spin down cases along a speci?ed spin quantization axis,respectively. dΓ(↑t→b?+ν?)and dΓ(↓t→b?+ν?)are di?erential decay rates for polarized top quarks. The unpolarized rate is given by;dΓ(t→b?+ν?)=dΓ(↑t→b?+ν?)+dΓ(↓t→b?+ν?).

Top quark polarization can be determined by measuring the angular distribution of out-going charged lepton in the top rest frame.It is possible to obtain from the expression(18) the polarized production cross section as a coe?cient of the angular distribution by a?tting procedure.In this paper we ignore the problems associated with the reconstruction of the top rest frame.We assume that the top quark rest frame can be reconstructed.

IV.SENSITIVITY TO ANOMALOUS COUPLINGS

We have obtained95%C.L.limits on the anomalous coupling parameters F2L and F2R √

using aχ2analysis at

s=0.5TeV and by a factor of1.5at

s=0.5TeV and by a factor of2at

unpolarized(total)case.At

s=1TeV.The most

sensitive bounds are obtained at

[1]R.D.Peccei,X.Zhang,Nucl.Phys.B337,269(1990);

R.D.Peccei,S.Peris and X.Zhang,Nucl.Phys.B349,305(1991).

[2]I.Bigi,Y.Dokshitzer,V.Khoze,J.Kuhn and P.Zerwas,Phys.Lett.B181,157(1986).

[3]W.Buchmuller and D.Wyler,Nucl.Phys.B268,621(1986);

K.Hagiwara,S.Ishihara,R.Szalapski and D.Zeppenfeld,Phys.Rev.D48,2182(1993).

[4]G.J.Gounaris,F.M.Renard and C.Verzegnassi,Phys.Rev.D52,451(1995);

G.J.Gounaris,F.M.Renard,and N.D.Vlachos,Nucl.Phys.B459,51(1996).

[5]K.Whisnant,J.Yang,B.Young and X.Zhang,Phys.Rev.D56,467(1997);

J.M.Yang and B.Young,Phys.Rev.D56,5907(1997).

[6]G.Kane,https://www.sodocs.net/doc/418159271.html,dinsky and C.-P.Yuan,Phys.Rev.D45,124(1992).

[7]M.S.Alam et al.(CLEO Collaboration),Phys.Rev.Lett.74,2885(1995);

https://www.sodocs.net/doc/418159271.html,rios,M.A.Perez and C.-P.Yuan Phys.Lett B457,334(1999).

[8] D.E.Groom,et al.,Eur.Phys.J.C15,1(2000).

[9]S.Ambrosanio and B.Mele,Z.Phys.C63,63(1994);

N.V.Dokholian and G.V.Jikia,Phys.Lett.B336,251(1994).

[10]K.Hagiwara,M.Tanaka and T.Stelzer,Phys.Lett.B325,521(1994);

E.Boos et al.,Phys.Lett.B326,190(1994).

[11] E.Boos et al.,Z.Phys.C70,255(1996);

A.Bienarchik,K.Cieckiewicz and K.Kolodziej,hep-ph/012253.

[12] B.Grzadkowski and Z.Hioki,Phys.Rev.D61,014013(1999);

B.Grzadkowski and Z.Hioki,Nucl.Phys.B585,3(2000);

B.Grzadkowski,Z.Hioki,K.Ohkuma and J.Wudka Phys.Lett.B593,189(2004);

P.Batra and T.M.P.Tait,Phys.Rev.D74,054021(2006).

[13] D.Dicus and S.Willenbrock,Phys.Rev.D34,155(1986);

C.-P.Yuan,Phys.Rev.D41,42(1990);

S.Cortese and R.Petronzio,Phys.Lett.B253,494(1991);

G.V.Jikia and S.R.Slabospitsky,Phys.Lett.B295,136(1992);

R.K.Ellis and S.Parke,Phys.Rev.D46,3785(1992);

G.Bordes and B.van Eijk,Z.Phys.C57,81(1993);

D.O.Carlson and C.-P.Yuan,Phys.Lett.B306,386(1993);

D.O.Carlson,

E.Malkawi and C.-P.Yuan,Phys.Lett.B337,145(1994);

G.Bordes and B.van Eijk,Nucl.Phys.B435,23(1995);

T.Stelzer and S.Willenbrock,Phys.Lett.B357,125(1995);

R.Pittau,Phys.Lett.B386,397(1996);

M.C.Smith and S.Willenbrock,Phys.Rev.D54,6696(1996);

D.Atwood,S.Bar-Shalom,G.Eilam and A.Soni,Phys.Rev.D54,5412(1996);

C.S.Li,R.J.Oakes and J.M.Yang,Phys.Rev.D55,5780(1997);

G.Mahlon and S.Parke,Phys.Rev.D55,7249(1997);

A.P.Heinson,A.S.Belyaev and E.E.Boos,Phys.Rev.D56,3114(1997);

T.Stelzer,Z.Sullivan and S.Willenbrock,Phys.Rev.D56,5919(1997);

D.Atwood,S.Bar-Shalom,G.Eilam and A.Soni,Phys.Rev.D57,2957(1998);

T.Stelzer,Z.Sullivan and S.Willenbrock,Phys.Rev.D58,094021(1998);

A.S.Belyaev,E.E.Boos and L.V.Dudko,Phys.Rev.D59,075001(1999);

T.M.P.Tait and C.-P.Yuan,Phys.Rev.D63,014018(2000);

J.A.Aguilar-Saavedra et al.,Eur.Phys.J.C50,519(2007).

[14] E.Boos,L.Dudko and T.Ohl,Eur.Phys.J.C11,473(1999).

[15]S.Ata?g and B.S?ahin,Phys.Rev.D73,074001(2006).

[16] E.Boos,A.Pukhov,M.Sachwitz and H.J.Schreiber,Phys.Lett.B404,119(1997);

J.-J.Cao,et al.Phys.Rev.D58,094004(1998);

Q.-H.Cao and J.Wudka,Phys.Rev.D74,094015(2006).

[17] C.Akerlof,Ann Arbor Report No.UM HE81-59(1981);

J.A.Aguilar-Saavedra et al.,TESLA Technical Design Report,DESY-2001-011.

[18]T.L.Barklow,in Proceedings of the1990Summer Study on Research Directions for the Decade

(Snowmass,Colorado,1990),and SLAC Report No.SLAC-PUB-5364(1990).

[19]I.F.Ginzburg et al.,Nucl.Instrum.Methods205,47(1983);ibid.219,5(1984).

[20] B.Sahin and I.Sahin,hep-ph/0708.3905.

[21]T.Kaneko in“New Computing Techniques in Physics Research”,ed.D.Perret-Gallix,W.

Wojcik,Edition du CNRS,1990;

MINAMI-TATEYA group,“GRACE manual”,KEK Report92-19,1993;

F.Yuasa et al.,Prog.Theor.Phys.Suppl.138(2000)18.

FIG.1:Tree level Feynmann diagrams for the process e +γ→t ˉb ˉνe .

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-0.15

-0.1-0.05

0 0.05 0.1 0.15σ(p b )

F 2R

1.5 TeV

Total

anti b-beam ↓anti b-beam ↑

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-0.15

-0.1-0.05

0 0.05 0.1 0.15

σ(p b )

F 2L

1.5 TeV

Total

anti b-beam ↓anti b-beam ↑

FIG.2:The integrated cross section of the process e +γ→t ˉb ˉνe as a function of the anomalous

couplings F 2R and F 2L at center of mass energy

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-0.15

-0.1-0.05

0.05 0.1 0.15σ(p b )

F 2R

1.5 TeV

Total e +

-beam ↑e +-beam ↓

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-0.15

-0.1-0.05

0 0.05 0.1 0.15

σ(p b )

F 2L

1.5 TeV

Total

e +-beam ↑e +

-beam ↓

FIG.3:The same as Fig.2,but the top quark spin decomposition axis is along the e +-beam.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-0.15

-0.1-0.05

0 0.05 0.1 0.15σ(p b )

F 2R

1.5 TeV

Total γ-beam ↑γ-beam ↓

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-0.15

-0.1-0.05

0 0.05 0.1 0.15

σ(p b )

F 2L

1.5 TeV

Total γ-beam ↑γ-beam ↓

FIG.4:The same as Fig.3,but the top quark spin decomposition axis is along the γ-beam.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-0.15

-0.1-0.05

0 0.05 0.1 0.15σ(p b )

F 2R

1.5 TeV

Total helicity (L)helicity (R)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16-0.15

-0.1-0.05

0 0.05 0.1 0.15

σ(p b )

F 2L

1.5 TeV

Total helicity (L)helicity (R)

FIG.5:The same as Fig.4,but for the top quark helicity basis.

TABLE I:Sensitivity of the eγcollision to anomalous couplings at 95%C.L.for the decomposition axis of the top quark spin along the e +-beam,γ-beam,ˉb -beam and helicity directions.Only one

of the couplings is assumed to deviate from the SM at a time.

γ-beam Up -0.04,0.05-0.05,0.05Down

-0.11,0.05

-0.15,0.15

Helicity Right -0.16,0.04-0.09,0.09Left

-0.05,0.21

-0.08,0.08

TABLE II:The same as table I,but for

γ-beam

Up-0.02,0.02-0.02,0.02 Down-0.02,0.04-0.10,0.10

Helicity

Right-0.04,0.02-0.04,0.04 Left-0.01,0.21-0.03,0.03

TABLE III:The same as table II,but for

γ-beam

Up-0.02,0.01-0.02,0.02 Down-0.01,0.03-0.11,0.11

Helicity

Right-0.02,0.01-0.03,0.03 Left-0.01,0.18-0.02,0.02

相关主题