An analysis of Bs decays in the left-right-symmetric model with spontaneous CP violation

24 February 2000

Ž .Physics Letters B 475 2000 111–119

An analysis of B decays in the left-right-symmetric model withs

spontaneous CP violation

Patricia Ball a,1, Robert Fleischer b,2

a CERN-TH, CH-1211 GeneÕa 23, Switzerlandb Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, D-22607 Hamburg, Germany

Received 16 December 1999; accepted 20 January 2000Editor: P.V. Landshoff

Abstract

q yNon-leptonic B decays into CP eigenstates that are caused by b™ccs quark-level transitions, such as B ™D D ,s s s s

Jrc h ŽX . or Jrc f, provide a powerful tool to search for ‘‘new physics’’, as the CP-violating effects in these modes are tinyin the Standard Model. We explore these effects for a particular scenario of new physics, the left-right-symmetric modelwith spontaneous CP violation. In our analysis, we take into account all presently available experimental constraints on theparameters of this model, i.e. those implied by K- and B-decay observables; we find that CP asymmetries as large asŽ .OO 40% may arise in the B channels, whereas the left-right-symmetric model favours a small CP asymmetry in thes

‘‘gold-plated’’ mode B ™Jrc K . Such a pattern would be in favour of B-physics experiments at hadron machines, whered S

the B modes are very accessible. q 2000 Elsevier Science B.V. All rights reserved.s

1. Introduction

A particularly interesting tool to search for indica-tions of ‘‘new physics’’ is provided by B -mesons

< :decays into final CP eigenstates f that originatew xfrom b™ccs quark-level transitions 1–3 ; impor-

tant examples are given by B ™DqDy , Jrc h ŽX . ors s s

Jrc f decays. The interesting feature of these modesis that their decay amplitudes do not involve – to avery good approximation – a CP-violating weakphase in the Standard Model. Moreover, the weak

0 0B – B mixing phase, which governs ‘‘mixing-in-s s

duced’’ CP violation, is negligibly small in the Stan-dard Model. Consequently, these B decays exhibits

1 E-mail: [email protected] E-mail: [email protected]

tiny CP-violating effects within the Kobayashi–Maskawa picture of CP violation, thereby represent-ing a sensitive probe for CP-violating contributionsfrom physics beyond the Standard Model.

We analyse these effects for a particular scenarioŽ . Ž .of new physics, the symmetrical SU 2 =SU 2 =L R

Ž . Ž .U 1 model with spontaneous CP violation SB–LRw x w x4,5 . In a recent paper 6 , the SB–LR model hasbeen investigated in the light of current experimentalconstraints from K- and B-decay observables. In alarge region of parameter space, the model mainlyaffects neutral-meson mixing, but does not introducesizeable ‘‘direct’’ CP violation. The sensitive observ-ables constraining the model are thus the mesonmass differences DM , DM , DM , the ‘‘indirect’’K B Bd s

CP-violating parameter e of the neutral kaon sys-K

tem, and the mixing-induced CP asymmetry

0370-2693r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0370-2693 00 00061-7

( )P. Ball, R. FleischerrPhysics Letters B 475 2000 111–119112

mix Ž .AA B ™Jrc K . In particular, it was found that,CP d S

for a set of fixed CKM parameters and quark masses,< mix Žthe model predicts a small value for AA B ™CP d

. <Jrc K below 10%, which is in agreement at theSq0.41 w x2s level with the CDF measurement 0.79 7 ,y0.44

but at variance with the Standard-Model expectationw x0.73"0.21 8 .

The new point we want to make in this letter isthat the SB–LR model predicts values also for themixing-induced CP asymmetries of the B decayss

considered here, for example B ™Jrc f, thats

largely deviate from the Standard-Model expectationof very small CP-violating effects. We show that

Ž .mixing-induced CP asymmetries as large as OO 40%may arise in these channels, whereas direct CP viola-tion stays very small. We thus face the interestingpossibility that, with all current experimental con-straints being met, new physics may just lurk aroundthe corner, and may be revealed by the pattern of CPviolation exhibited by B ™Jrc K and B ™d S s

DqDy , Jrc h ŽX . or Jrc f. This scenario, with smalls s

CP-violating effects in the former decay and largeeffects in the latter ones, would be in favour ofB-physics experiments at hadron machines, wherethe B modes are very accessible, in contrast to thes

situation at asymmetric eq–ey B-factories operatingŽ .on the F 4S resonance.

The outline of this paper is as follows: in Section2, we have a brief look at the structure of theStandard-Model decay amplitudes of the B -mesons

decays considered here, and introduce the corre-sponding CP-violating observables. The basic fea-tures of the left-right-symmetric model with sponta-neous CP violation are discussed in Section 3, andthe numerical analysis is presented in Section 4.Finally, in Section 5 we summarize our conclusions.

2. Decay amplitudes and CP-violating observables

Before we introduce the CP-violating observables,let us have a brief look at the structure of theStandard-Model transition amplitudes of B decayss

of the kind B ™DqDy , Jrc h ŽX . or Jrc f. Thes s s

new-physics contributions to the decay amplitudes ofthese channels arising within the left-right-symmetricmodel with spontaneous CP violation will be dis-cussed in Section 3.

2.1. The Standard-Model decay amplitudes

Within the Standard Model, the amplitudes of0B -meson decays caused by b™ccs quark-levels

transitions can be expressed generically as followsw x9 :

A B0 ™ f slŽ s. Ac qAc qlŽ s.Au qlŽ s.At ,Ž .Ž .s c cc pen u pen t pen

1Ž .

� q y ŽX . 4where fg D D , Jrc h , . . . is a final-state con-s scfiguration with ccss valence-quark content, Acc

denotes current–current contributions, i.e. ‘‘tree’’processes, and the amplitudes Aq describe the con-pen

tributions from penguin topologies with internal qŽ � 4.quarks qg u,c,t . These penguin amplitudes take

into account both QCD and electroweak penguinw x Ž s. )contributions 9 . The l 'V V are the usualq qs qb

CKM factors. Making use of the unitarity of theCKM matrix and applying the Wolfenstein

w xparametrization 10 , generalized to include non-lead-w x w xing terms in l 11 , we obtain 12

2 2l l0 iu igA B ™ f s 1y AA 1q ae e ,Ž .s 2ž / ž /2 1yl

2Ž .

where

AA'l2A Ac qAct , 3Ž .Ž .cc pen

with Act 'Ac yAt , andpen pen pen

Autpeniuae 'R . 4Ž .b c ctž /A qAcc pen

The quantity Aut is defined in analogy to Act , andpen pen

the relevant CKM factors are given by

1< <l' V s0.22 , A' V s0.81"0.06 ,u s cb2l

2l 1 VubR ' 1y s0.41"0.07 . 5Ž .b ž /2 l Vcb

Ž .In Eq. 2 , the CP-violating weak phase g is theusual angle of the unitarity triangle of the CKMmatrix, whereas u denotes a CP-conserving strongphase.

( )P. Ball, R. FleischerrPhysics Letters B 475 2000 111–119 113

2.2. The CP-Õiolating obserÕables

< :For a B decay into a final CP eigenstate f ,sXq y Ž . 0 0such as B ™D D or Jrc h , B – B oscilla-s s s s s

tions lead to the following time-dependent CP asym-metry:

0 0Ž . Ž .G B t ™ f y G B t ™ fŽ . Ž .s sŽ .a t 'CP 0 0Ž . Ž .G B t ™ f q G B t ™ fŽ . Ž .s s

s2 eyGst

dir mixAA B ™ f cos D M t q AA B ™ f sin D M tŽ . Ž . Ž . Ž .s s s sCP CP= ,Ž . Ž . Ž . Ž .s s s syG t yG t yG t yG tL LH He q e q AA B ™ f e y eŽ .Ž .sD G

6Ž .

where DM 'M Ž s.yM Ž s. denotes the mass differ-s H LH Ž .ence between the B mass eigenstates B ‘‘heavy’’s s

L Ž . Ž s.and B ‘‘light’’ , the G are the correspondings H ,L

decay widths, and G is defined as Gs sŽ s. Ž s. Ž .' G qG r2. In Eq. 6 , we have separatedH L

the ‘‘direct’’ from the ‘‘mixing-induced’’ CP-violat-dirŽing contributions, which are described by AA B ™CP s

. mix Ž . w xf and AA B ™ f , respectively 9 . In contrast toCP s

the B system, the width differenced

DG 'G Žq .yG Žq . 7Ž .q H L

w xmay be sizeable in the B system 13 , therebysŽ .providing the observable AA B ™ f . This quan-D G s

dirŽ .tity is not independent from AA B ™ f andCP smix Ž .AA B ™ f , but satisfies the following relation:CP s

2 2dir mixAA B ™ f q AA B ™ fŽ . Ž .CP s CP s

2q AA B ™ f s1. 8Ž . Ž .DG s

Ž .Interestingly, the observable AA B ™ f can beD G s

extracted from CP-violating effects in ‘‘untagged’’w xB rates 14,15 :s

0 0G f t 'G B t ™ f qG B t ™ fŽ . Ž . Ž .Ž . Ž .s s

AR B ™ f eyG HŽ s. tŽ .H s

qR B ™ f eyG LŽ s. t , 9Ž . Ž .L s

where

1R B ™ f s 1qAA B ™ f ,Ž . Ž .H s D G s2

1R B ™ f s 1yAA B ™ f , 10Ž . Ž . Ž .L s D G s2

and hence

R B ™ f yR B ™ fŽ . Ž .H s L sAA B ™ f s .Ž .DG s R B ™ f qR B ™ fŽ . Ž .H s L s

11Ž .

Studies of such untagged rates, where there are norapid oscillatory DM t terms present, are mores

promising than tagged rates in terms of efficiency,acceptance and purity.

Ž .Looking at 2 , we observe that the weak phasefactor eig , which is associated with the ‘‘penguinparameter’’ aeiu, is strongly Cabibbo-suppressed byl2. Consequently, there is no CP-violating weakphase present in this decay amplitude to an excellentapproximation. In this very important special case,

Ž w x.we obtain for details, see 3,9 :

AAdir B ™ f s0 , AA mix B ™ f ssinf ,Ž . Ž .CP s CP s s

AA B ™ f sycosf , 12Ž . Ž .D G s s

where f denotes a phase-convention-independents0 0combination of the CP-violating weak B – B mix-s s

ing and b™ccs decay phases. In general, we have

f sf SM qf NP , 13Ž .s s s

where the Standard-Model phase

f SM s2 arg yV ) V q2 arg V V )Ž . Ž .s t s t b cs cb

sy2l2hfy0.03 14Ž .

is negligibly small, and f NP is due to new physics.s

Within the Standard Model, the CP-violating effectsin the B decays considered here are thus very small.s

However, f NP may be sizeable in our scenario fors

new physics, as we will see in Section 4, therebyleading to significant mixing-induced CP violation.A similar feature arises also in some other scenariosfor physics beyond the Standard Model, for examplein models allowing mixing to a new isosinglet down

w xquark, as in E 2 . Unfortunately, the new-physics60 0effects reduce the magnitude of the B – B widths s

w xdifference as follows 16 :

DG sDG SM cosf , 15Ž .s s s


SM Ž .where DG sOO y15% is the Standard-Modelsw x Ž .width difference 13 . Note that 7 implies a nega-

tive Standard-Model width difference. However, thesign of DG may change in the presence of news

Ž .physics, as can be seen in 15 .The situation in the decay B ™Jrc f, which iss

very promising for B-physics experiments at hadronmachines because of its favourable experimental sig-nature, is a bit more involved than in the case of thepseudoscalar–pseudoscalar modes B ™DqDy ands s s

Jrc h ŽX ., since the final state is an admixture ofdifferent CP eigenstates. In the case of decays intotwo vector mesons, such as B ™Jrc f, it is conve-s

nient to introduce linear polarization amplitudesŽ . Ž . Ž . w x Ž .A t , A t and A t 17 . Whereas A t de-0 I H H

Ž .scribes a CP-odd final-state configuration, both A t0Ž .and A t correspond to CP-even final-state config-I

urations, i.e. to the CP eigenvalues y1 and q1,respectively. In order to disentangle them, one has tostudy angular distributions of the decay products of

w q yx w q yxthe decay chain B ™Jrc ™ l l f ™K K ,sw x 3which can be found in 18 . Let us here just give

the following time-dependent CP asymmetry, underŽ .the same assumption as was made in 12 , i.e. that

there is no CP-violating weak phase present in theB ™Jrc f decay amplitude:s

G t yG tŽ . Ž .a B t ™Jrc f 'Ž .Ž .CP s

G t qG tŽ . Ž .

1yDs

F t qDF tŽ . Ž .q y

=sin DM t sinf , 16Ž . Ž .s s

Ž . Ž .where G t and G t denote the time-dependentrates for decays of initially, i.e. at ts0, present B0-s

0and B -mesons into Jrc f final states, respectively.s

The remaining quantities are defined as

< < 2A 0Ž .HD' , 17Ž .2 2< < < <A 0 q A 0Ž . Ž .0 5

3 For a detailed discussion of new-physics effects in the corre-w xsponding observables, see 3 .

and

1 qD G tr2sF t ' 1"cosf eŽ . Ž ." s2

yD G tr2sq 1.cosf e . 18Ž . Ž .s

Ž . Ž .Note that we have F t sF t s1 for a negligi-q yble width difference DG . Obviously, the advantages

Ž .of the ‘‘integrated’’ observable 16 is that it can bemeasured without performing an angular analysis.The disadvantage is of course that – in contrast toŽ .12 – it also depends on the hadronic quantity D,which precludes a theoretically clean extraction of

Ž .f from 16 . However, this feature does not limits

the power of this CP asymmetry to search for indica-tions of new physics, which would be provided by a

Ž .measured sizeable value of 16 . Model calculationsof D, making use of the factorization hypothesis,

w xtypically give Ds0.1 . . . 0.5 18 , which is also inagreement with a recent analysis of the B ™Jrc fs

polarization amplitudes performed by the CDF Col-w xlaboration 19 . A recent calculation of the relevant

hadronic form factors from QCD sum rules on thew xlight-cone 20 yields Ds0.33 in the factorization

approximation. Consequently, the CP-odd contribu-< Ž . < 2tions proportional to A 0 may have a signifi-H

Ž .cant impact on 16 . In order to extract f froms

CP-violating effects in the decay B ™Jrc f in as

theoretically clean way, an angular analysis has to bew xperformed, as is discussed in detail in 3 .

3. The left-right-symmetric model with sponta-neous CP violation

Before discussing its predictions for CP-violatingphenomena, let us explain very shortly the essentialfeatures of the SB–LR model. It is based on the

Ž . Ž . Ž .gauge group SU 2 =SU 2 =U 1 , which cas-R L

cades down to the unbroken electromagnetic sub-Ž .group U 1 through the following simple symme-em

try-breaking pattern:

The scalar sector is highly model-dependent; for the


generation of quark masses, there has to be at leastone scalar bidoublet F , i.e. a doublet under both

Ž . Ž .SU 2 , which, by spontaneous breakdown of SU 2 RŽ .=SU 2 , acquires the VEVL

1 Õ 0² :F s . 19Ž .ž /0 w'2In general, both Õ and w are complex, which is theŽ .only source of CP violation in the model. Theparticle content of F corresponds to four particles,one analogue of the Standard-Model Higgs, twoflavour-changing neutral Higgs bosons, and oneflavour-changing charged Higgs. The masses of thesenew Higgs particles can be assumed to be degenerateto good accuracy, and were found to lie in the range

w x10.2 TeV-M -14.6 TeV 6 .H

LR symmetry implies that the left-handed quarksector of the Standard Model gets complemented bya right-handed one, with quark mixing matrices VL

< < < <and V , respectively, and V s V . In the standardR L R

Maiani convention, V contains one, V five com-L R

plex phases, which depend on the three generalizedŽ .Cabibbo-type angles ‘‘CKM angles’’ , the quarkŽ .masses, and the VEV 19 . The presence of such a

large number of weak phases, calculable in terms ofonly one non-Standard-Model variable, is what makesthe investigation of CP-violating phenomena in theSB–LR model that interesting. The left- and right-handed charged gauge bosons W and W mix withL R

each other; the mass of the predominantly right-handed mass eigenstate W , M , is found to lie in2 2

w xthe range 2.75 TeV-M -13 TeV 6 . The mixing2

angle z , defined as2< <2 Õw M1

zs , 20Ž .2 2 ž /M< < < <Õ q w 2

< < < <is rather small: as the ratio Õ r w is smaller than4 Ž .2 y41, one has z- M rM s8.5=10 . There are,1 2

however, arguments, according to which a small< < < < Ž .ratio Õ r w ;OO m rm would naturally explainb t

w xthe observed smallness of the CKM angles 21 ; inthis case, z-0.3=10y4. An experimental bound onz can in principle be obtained from the upper boundon the electromagnetic dipole moment of the neu-tron, which is due to L–R mixing; existing theoreti-

4 Which can always be achieved by a redefinition of the Higgsbidoublet F ™s F )s .2 2

cal calculations are, however, very sensitive to theprecise values of only poorly known nucleon matrixelements; 5 the present status of an experimentalbound on z is thus not quite clear, although large

Ž y4 . Žvalues of z;OO 10 appear to be disfavoured seew x.also the discussion in 6 . The fact that the new

boson masses are in the TeV range implies that theSB–LR model has no perceptible impact on Stan-dard-Model tree-level amplitudes; rather, it manifestsitself inØ W –W mixing in top-dominated penguin dia-L R

grams, enhanced by large quark mass terms fromŽspin-flips, z™z m rm similar for penguinst b.with charged Higgs particles ,

Ø Standard-Model amplitudes that are forbidden orŽheavily suppressed electric dipole moment of the.neutron, for instance ,

Ø mixing of neutral K- and B-mesons, where theŽ .2suppression factor of M rM is partially com-1 2

pensated by large Wilson coefficients or hadronicŽmatrix elements chiral enhancement in K mix-

.ing , and to which the flavour-changing Higgsbosons contribute at tree level.

We thus expect the SB–LR model to change the0 Ž .B ™ f amplitude defined in 2 in the followings

way:

AA™AA LR sl2A Ac qAc ,LR qAct qAct ,LR ,Ž .cc cc pen pen

21Ž .with

2M1c ,LR cA ;OO A ,cc ccž /M2

m mc tct ,LR c tA ;OO z A y A . 22Ž .pen pen penž /m mb b

Ž .2 y3Numerically, M rM -10 and z m rm -1 2 t b< < < <0.05 for maximum Õ r w s1, and z m rm -6=t b

y3 < < < <10 for the more likely case of Õ r w ;Ž .OO m rm . In any case, it is clear that the specificb t

LR contributions to the decay amplitude, althoughthey carry new weak phases, are heavily suppressed

Žby powers of M and M for the corresponding2 H.charged Higgs penguins . Consequently, the new

5 In addition, the Higgs contributions to the dipole moment areusually not included.


contributions of the SB–LR model to the amplitudesof the B decays considered in this letter are smalland do not yield sizeable direct CP violation. Theassumption used to calculate the CP-violating ob-

Ž . Ž .servables 12 and 16 is therefore also satisfied inthe SB–LR model, so that we may use these expres-sions in the numerical analysis given in the follow-ing section.

4. Numerical analysis

In the SB–LR model, the Standard-Model mixingmatrix gets modified by W boxes and tree-levelR

flavour-changing neutral Higgs exchange as

M Bq sM SM qM LR 'M SM 1qk eisq 23Ž . Ž .12 12 12 12

with

LR LR R R )M M V V12 12 t b tqk' , s 'arg sarg y ,qSM SM L L)ž /M M V V12 12 t b tq

24Ž .

such that the relevant observable phase f becomesq

f sf SM qarg 1qk eisq , 25Ž . Ž .q q

� 4where qg d,s . The B counterpart f to thed d

phase f can be determined in a theoretically cleans

way through mixing-induced CP violation in thew x‘‘gold-plated’’ mode B ™Jrc K 22 :d S

AA mix B ™Jrc K sysinf . 26Ž . Ž .CP d S d

To good accuracy, k is independent on the flavourw xof the spectator quark q, and is given as 6

2 27 TeV 1.6 TeVks 1.2"0.2 q1.7Ž . ž / ž /M MH 2

=

21.6 TeV0.051y0.013ln . 27Ž .½ 5ž /M2

A crucial consequence of the spontaneous break-down of the CP symmetry is that the phases of thetwo quark mixing matrices, and hence also s , canq

be calculated in terms of the quark masses, the threeŽ .CKM angles and the VEV value of F , Eq. 19 ; they

do not depend on M or M . For the technicalities,2 Hw xwe refer to Ref. 6 ; here we only state that the

² :dependence on F can be lumped into a singlew xvariable, b , which is defined as 5

< <2 wÕ sin arg ÕwŽ .bsarctan . 28Ž .2 2< < < <Õ y w

From the requirement that diagonalization of thequark mass matrices be possible, b is bounded as

w xfollows 5 :b mb

tan F .2 mt

The fact that quark mass signs are observable in theSB–LR model entails a 64-fold discrete ambiguity ofthe complex phases of V and V . The dependenceL R

of the phases on the input parameters can be ob-tained in analytical form in a linear expansion in b ,

w xthe so-called small-phase approximation 4 , which isappropriate for studying the K system. For B de-cays, however, the approximation breaks down; thefull functional dependence of s on b can only beq

w xobtained numerically and has been calculated in 6 .Experimental observables sensitive to the new-

physics contributions to the off-diagonal elementmix ŽM of the mixing matrix are, apart from AA B12 CP d

.™Jrc K , in particular the meson mass differ-S

ences DM , DM and DM , which are given byK B Bd s

< <DMs2 M . Other relevant observables are e ,12 K

which is sensitive to arg M K , the observable12Ž X .Re e re measuring direct CP violation in theK K

neutral kaon system, 6 and the upper bound on theelectromagnetic dipole moment of the neutron. With-out going into details about the respective strengthand viability of these constraints, we just quote the

w xresults of the comprehensive analysis of Ref. 6 :using the following set of Standard-Model inputparameters,

m m s170 GeV, m m s4.25 GeV,Ž . Ž .t t b b

m m s1.33 GeV, m 2 GeV s110 MeV,Ž .Ž .c c s

< <m rm s20.1, m rm s0.56, V s0.2219,s d u d u s

< < < <V s0.004, V s0.04, 29Ž .ub cb

and neglecting their uncertainties, the 64-fold phaseambiguity gets completely resolved by requiring both

w K xsin arg M and sinf to be positive, as implied by12 d

6 Because of the large hadronic uncertainties affectingŽ X .Re e re , it has only been used that a positive value of thisK K

w xobservable is implied by the most recent experimental data 23 .


mix Ž .the measured values of e and AA B ™Jrc K .K CP d S

Choosing the SB–LR model parameters M , M2 H

and b such as to reproduce the experimental valueof e , one finds that the predicted value y0.1-K

mix Ž . ŽAA B ™Jrc K -0.1 is rather small see Fig. 9CP d Sw x.in Ref. 6 but still in agreement at the 2s level

q0.44 w xwith the CDF measurement y0.79 7 . They0.41w xparameter k is found to lie in the interval 0.29,0.74 ;

w xs assumes values in 0.12,1.81 rad and s ind sw x3.23,4.58 rad.

We are now in a position to calculate the correla-tion between the mixing-induced CP asymmetries inthe decays B ™Jrc K and B ™DqDy, Jrc h ŽX .

d S s s s

within the SB–LR model. The result is given in Fig.1, which nicely shows that large CP-violating asym-metries in B ™DqDy , Jrc h ŽX . are possible in thes s s

SB–LR model, whereas mixing-induced CP viola-tion in B ™Jrc K is predicted to be small. As wed S

have already noted in Section 3, the correspondingdirect CP asymmetries remain very small, since thenew contributions of the SB–LR model to the decayamplitudes are strongly suppressed.

In Fig. 2, we show the correlation between theŽobservables of the untagged B ™ f rates fss

q y ŽX .. Ž .D D , Jrc h , which were introduced in 9 , ands s

are given by1R B ™ f s 1qcosf ,Ž . Ž .L s s2

1R B ™ f s 1ycosf . 30Ž . Ž . Ž .H s s2

As can be seen there, in the case of the SB–LRmodel, the component entering with eyG H

Ž s. t is atmost 10% of that associated with eyG L

Ž s. t. In order toŽ . Ž .extract R B ™ f and R B ™ f , a sizeable valueL s H s

of DG is required, as we already noted in Section 2.s

In Fig. 3, we show the correlation between the B0–s

mix Ž .Fig. 1. The allowed region in the space of AA B ™ Jrc KCP d Smix Ž . q ysysinf and AA B ™ f s sinf , with f s D D ,d CP s s s s

Jrc h ŽX., in the SB–LR model.

Ž .Fig. 2. The correlation between the observables R B ™ f andL sŽ . q yR B ™ f of the untagged B ™ f rates, with f s D D ,H s s s s

Jrc h ŽX., in the SB–LR model.

0B mass and width differences in the SB–LR model.s

The reduction of DG through new-physics effects,sŽ .which is described by 15 , is fortunately not very

effective in this case, whereas the mass differenceDM may be reduced significantly. Although, at firsts

glance, values of DM as small as 0.55DM SM mays s

seem to be at variance with the experimental boundy1 w xof DM )14.3 ps at 95% C.L. 24 , this is actu-s

ally not the case: with the hadronic parameters fromw x < <25 and V s0.04 with the generalized Cabibbo-t s

Ž .angles fixed from 29 , one has the theoretical pre-Ž w x .diction see 6 , e.g., for the full formula

DM SM s 14.5"6.3 psy1 .Ž .s

Combining this with the experimental bound, onehas

DM LR 14.3s) s0.53.SM 14.5q2=6.3DMs

A pattern of B mass and decay width differencess

like that emerging in the SB–LR model would be in

0 0Fig. 3. The correlation between the B –B mass and widths s

differences, normalized to their Standard-Model values, in theSB–LR model.


favour of experimental studies of the B decays ats

hadron machines, where small values of DM ands

large values of DG would be desirable. Because ofsŽ . Ž .the small ratio of R B ™ f rR B ™ f -0.1 ofH s L s

the ‘‘untagged’’ B ™ f observables, ‘‘tagged’’ stud-s

ies, allowing us to extract the mixing-induced CPmix Ž .asymmetries AA B ™ f , appear more promisingCP s

to search for indications of the SB–LR model. How-ever, in other scenarios for new physics, the situationmay be different.

Let us finally illustrate the CP-violating asymme-Ž .try 16 of the decay B ™Jrc f. In Fig. 4, we plots

this CP asymmetry as a function of t, for fixedvalues of Ds0.3, sinf sy0.38, DG rG sy0.14s s s

y1 0 0and DM s14.5 ps . Although the B – B oscilla-s s s

tions are very rapid, as can be seen in this figure, itshould be possible to resolve them experimentally,for example at the LHC. The first extremal value ofŽ .16 , corresponding to DM tspr2, is given to as

very good approximation by

1yDA B ™Jrc f s sinf , 31Ž . Ž .CP s sž /1qD

which would also fix the magnitude of the B ™sŽ .Jrc f CP asymmetry 16 in the case of a negligible

width difference DG . In Fig. 5, we show the predic-sŽ .tion of the SB–LR model for 31 as a function of

the hadronic parameter D. For a value of Ds0.3,the CP asymmetry may be as large as y25%. Thedilution through the hadronic parameter D is noteffective in the case of the CP-violating observables

Ž Ž . .Fig. 4. The time-dependent CP-asymmetry a B t ™ Jrc fCP sŽ .introduced in 16 for fixed values of Ds0.3, sinf sy0.38,s

DG rG sy0.14 and DM s14.5 psy1.s s s

Fig. 5. The prediction of the SB–LR model for the CP-violatingŽ . Ž .observable A B ™ Jrc f introduced in 31 as a function ofCP s

the hadronic parameter D.

w q yx w q yxof the B ™Jrc ™ l l f ™K K angular dis-sw xtribution, which allow us to probe sinf directly 3 .s

5. Conclusions

We have performed an analysis of mixing-in-duced CP-violating effects in B ™DqDy , Jrc h ŽX .,s s s

Jrc f decays in the SB–LR model with sponta-neous CP violation, taking into account all presentlyavailable experimental constraints on the parametersof this model, and have demonstrated that the corre-sponding CP asymmetries may be as large asŽ .OO 40% , whereas the Standard Model predicts van-

ishingly small values. Since the decay amplitudes ofthese modes are not significantly affected in theSB–LR model, direct CP violation remains negligi-ble, as in the Standard Model. From an experimentalpoint of view, B ™Jrc f is a particularly promis-s

ing mode, which is very accessible at B-physicsexperiments at hadron machines. We have proposeda simple strategy to search for indications of newphysics in this transition, which does not require an

w q yx wangular analysis of the Jrc ™ l l and f ™q yxK K decay products. In contrast to the large

mixing-induced CP asymmetries in the B channels,s

the SB–LR model predicts a small value formix Ž .AA B ™Jrc K below 10%. Since the B de-CP d S s

cays cannot be explored at the asymmetric eq–ey

Ž .B-factories operating at the F 4S resonance, such apattern would be in favour of hadronic B experi-ments. We look forward to experimental data tocheck whether this scenario is actually realized byNature.


Acknowledgements

P.B. is supported by DFG through a Heisenbergfellowship.

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An analysis of Bs decays in the left-right-symmetric model with spontaneous CP violation

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Transcript of An analysis of Bs decays in the left-right-symmetric model with spontaneous CP violation