B_{d,s}^0 -- K^{()} K-bar^{()} CP phase alpha and New Physic

a r X i v :h e p -p h /0208144v 1 14 A u g 2002UdeM-GPP-TH-02-105

B 0d,s →K (?)ˉK (?):CP phase αand New Physics 1

Alakabha Datta and David London

Laboratoire Ren′e J.-A.L′e vesque,Universit′e de Montr′e al,C.P.6128,succ.centre-ville,Montr′e al,QC,Canada H3C 3J7(February 1,2008)Abstract The decays B 0d,s →K (?)ˉK (?)can be used to measure the angle αof the CKM unitarity triangle.The theoretical error from SU (3)breaking is expected to be small,so that the determination of αis clean.Moreover,since B 0d,s →K (?)ˉK (?)are pure penguin decays,they are particularly sensitive to the presence of new physics.

1CP phaseαfrom B0d,s→K(?)ˉK(?)

The?rst evidence of CP violation in the B system was recently observed with the mea-surement of one of the angles of the Cabibbo-Kobayashi-Maskawa(CKM)unitarity triangle: sin2β=0.78±0.08[1],which is consistent with the standard model(SM).Future e?orts will focus on the measurement of the remaining two angles of the unitarity triangle,αand γ,in order to test the SM explanation of CP violation.

There are two standard techniques for the extraction ofα.The?rst method uses the CP asymmetry in B0d(t)→π+π?to obtainα.Unfortunately,there is a penguin contribution, making it necessary to perform an isospin analysis of B→ππdecays[2].This requires the measurement of B0d→π0π0,which is expected to have a small branching ratio.Hence,it may be di?cult to obtainαusing this method.The second method uses a Dalitz-plot analysis of B0d(t)→ρπ→π+π?π0decays[3].However,the unknown non-resonant background and the correct description ofρ→ππdecays are factors that can seriously a?ect a clean determination ofαusing this method.

In this talk,we present a new method for determiningα[4].As a starting point,consider the pure b→d penguin decay B0d→K0ˉK0,for which the underlying quark transition is ˉb→ˉdsˉs.The amplitude for B0

→K0ˉK0,A d,can be written as

d

A d=P u V d u+P c V d c+P t V d t

=(P u?P c)V d u+(P t?P c)V d t,(1) where V d q≡V?qb V qd,and P u,c,t are the penguin amplitudes.In passing from the?rst line to the second,we have used the unitarity of the CKM matrix,V?ub V ud+V?cb V cd+V?tb V td=0,to eliminate the V?cb V cd term.The amplitudeˉA d describing the conjugate decayˉB0d→K0ˉK0 can be obtained from the above by changing the signs of the weak phases.

By making time-dependent measurements of B0d(t)→K0ˉK0,one can obtain the three observables

1

X≡

|A d|2?|ˉA d|2

2

Z I≡Im e?2iβA?dˉA d .(2)

The three independent observables depend on four theoretical parameters:P uc≡|P u?P c|, P tc≡|P t?P c|,the relative weak phase between the two amplitudes,α,and the relative strong phase.Hence one cannot obtain CP phase information from these measurements[5]. However,substituting Eq.1in Eq.2,one can obtain

Z R cos2α+Z I sin2α?X

P2tc|V d t|2=

where

Z R≡Re e?2iβA?dˉA d . The quantity Z R is related to the three observables in Eq.2by

Z2

R =X2?Y2?Z2

I

.(4)

Now consider a second pure b→d penguin decay of the form B0d→K?ˉK?.Here K?represents the ground state vector meson,K?(892),or any excited neutral kaon,such as K1(1270),etc.This second decay can be treated in a similar fashion as the?rst one above, with unprimed parameters and observables being replaced by primed ones.One can then combine measurements of the two decays to obtain

r d≡P2tc

Z′

I

sin2α+Z′

R

cos2α?X′

=f(α).(5)

The equation above,r d=f(α),could then be solved forαif we knew r d.Note that the CKM elements on the left-hand side of Eq.3cancel in constructing the ratio r d.

Information about the ratio r d can be obtained by measuring B0s decays to the same?nal states K0ˉK0and K?ˉK?.Consider?rst the decay B0s→K0ˉK0.This is described by a b→s penguin amplitude,A s,which is given by

A s=P(s)u V s u+P(s)c V s c+P(s)t V s t

?(P(s)t?P(s)c)V s t,(6) where V s q≡V?qb V qs,and P s u,c,t are the penguin amplitudes.In writing the second line,we have again used the unitarity of the CKM matrix to eliminate the V?cb V cs piece.Furthermore, the V?ub V us piece is negligible:|V?ub V us|?|V?tb V ts|.Thus,the measurement of the branching ratio for B0s→K0ˉK0yields|P s t?P s c||V s t|.Similarly one can obtain|P′s t?P′s c||V s t|from the branching ratio for B0s→K?ˉK?.In this way,we can measure

r s≡

P(s)tc2

ambiguities in the extraction ofα.However,by comparing several pairs of processes,the discrete ambiguities can be eliminated.In fact,with one theoretical assumption,all the discrete ambiguities can be removed with a single pair of processes[4].

This method can also be used when the?nal state is not self-conjugate.For example, one can consider the decays B0d→K0ˉK?and B0d→K0?ˉK0[4].

From the above analysis,we therefore see that the CP phaseαcan be cleanly extracted from measurements of the decays of B0d and B0s mesons to two di?erent?nal states consisting of one neutral kaon(i.e.K0or any of its excited states)and one neutral anti-kaon(i.e.ˉK0 or any excited state).Finally,we note that the K?ˉK??nal state consists of three helicity states.Each helicity state can be then considered a distinct?nal state for the purposes of our analysis.Thus,by applying our method to two di?erent K?ˉK?helicity states,αcan be obtained from B0d,s→K?ˉK?decays alone.

The branching ratios of the pure pure b→d penguin decays B0d(t)→K(?)ˉK(?)are expected to be quite small,of order10?6.Hence this method is ideally suited to hadron colliders as they produce an enormous number of B mesons.Furthermore,in all cases,the kaon or anti-kaon can be detected using its decays to chargedπ’s or K’s only;this method does not require the detection ofπ0’s.Therefore hadron colliders will …… 此处隐藏：8574字，全部文档内容请下载后查看。喜欢就下载吧 ……