B-S(0)-(B)over-bar(S)(0) oscillations as a new tool to explore CP violation in D-S(+/-) decays

University of Groningen

B-S(0)-(B)over-bar(S)(0) oscillations as a new tool to explore CP violation in D-S(+/-) decays

Fleischer, Robert; Vos, K. Keri

Published in:

Physics Letters B

DOI:

10.1016/j.physletb.2017.04.056

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Fleischer, R., & Vos, K. K. (2017). B-S(0)-(B)over-bar(S)(0) oscillations as a new tool to explore CP

violation in D-S(+/-) decays. Physics Letters B, 770, 319-324.

https://doi.org/10.1016/j.physletb.2017.04.056

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

B

0

_s

–

B

¯

0

_s

oscillations

as

a

new

tool

to

explore

CP

violation

in

D

±

_s

decays

Robert Fleischer

a

,

b

,

∗

,

K.

Keri Vos

a

,

c

,

d a_{Nikhef,SciencePark105,NL-1098XGAmsterdam,Netherlands}

b_{DepartmentofPhysicsandAstronomy,VrijeUniversiteitAmsterdam,NL-1081HVAmsterdam,Netherlands} c_{VanSwinderenInstituteforParticlePhysicsandGravity,UniversityofGroningen,NL-9747AGGroningen,Netherlands} d_{TheoretischePhysik1,Naturwissenschaftlich-TechnischeFakultät,UniversitätSiegen,D-57068Siegen,Germany}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received2December2016

Receivedinrevisedform20April2017 Accepted24April2017

Availableonline27April2017 Editor:G.F.Giudice

CPviolation in B0

s–B¯0s oscillations isexpected atthe10−5 level inthe Standard Model butcould be

enhanced by New Physics. Using B0

s →D−s+

ν

 decays, LHCb has recently reported the new result

(0.39±0.33)×10−2ofthecorrespondingobservableas_sl.WepointoutthatothercurrentB decaydata implyas

sl= (0.004±0.075)×10−2.Inviewofthisstrongconstraint,weproposetouseBs0→D−s+

ν



and similarflavor-specificdecaysasanew tooltodetermineboththeproductionasymmetrybetween B0s andB¯0s mesons,andtheCPasymmetryinthesubsequentD±s decays.Theformerservesasinputfor

analysesofCPviolationinB0

s channels,withsignificantroomforimprovement,whilethelatteroffersan

excitinglaboratoryforNewPhysics.

©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense

(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

StudiesofCPviolationprovideinterestingtestsoftheStandard Model(SM)ofparticlephysics,wheredecaysofneutralB0

s mesons

playakey roleattheLargeHadronCollider (LHC)[1].These par-ticlesshow B0

s–B

¯

0s mixing, whichintheSM isgeneratedthrough

quantum fluctuations. New Physics (NP) may affect B0

s–B

¯

0s

mix-ingthroughcontributionsatthetreelevel,mediated,forinstance, through Z bosons,orthroughnewheavyparticlesrunninginthe loopdiagrams[2].

CPviolationinB0_s–B

¯

0_s oscillationsisdescribedbyanobservable

as_slandisvanishinglysmallintheSM[3]:

as_sl

|

SM

= (

2

.

22

±

0

.

27

)

×

10−5

,

(1)

butcould be enhancedby NP.However, inrecentyears,awealth ofexperimentalinformationon B0_s–B

¯

0_s mixingandCPviolationin

B-mesondecayswasobtained,inaccordancewiththeSM.Inview ofthisprogress,thequestionariseshowmuchspaceforNPeffects inas_sl isactuallyleftby thedata.Thisimportantissue,whichcan in fact be raised formany flavor-physics observables, is the key motivationofthefollowingdiscussion.

*

Correspondingauthor.

E-mailaddress:Robert.Fleischer@nikhef.nl(R. Fleischer).

Theobservableas

slcanbemeasuredthroughsemileptonicB0s

→

D−_s



+

ν

 andB

¯

0s

→

D+s



−

ν

¯

decays[4].IntheSM,suchtransitions areflavor-specific:

A

(

B0_s

→

D+_s



−

ν

¯



)

=

A

( ¯

B0s

→

D−s



+

ν



)

=

0

,

(2) such that the “wrong-sign” decays B0

s

→

D+s



−

ν

¯

 and B

¯

0s

→

D−_s



+

ν

 canonlyoccurthroughB0s–B

¯

0s mixing.TheLHCb

collabo-rationhasrecentlyreportedtheworld’s bestmeasurementforas

sl [5]:

as_sl

=

[0

.

39

±

0

.

26

(

stat

)

±

0

.

20

(

syst

)

]

×

10−2

,

(3) whichagreeswiththeSMprediction(1).Theaverageofthe previ-ousresultsisgivenasfollows[6]:

as_sl

= −(

0

.

48

±

0

.

48

)

×

10−2

.

(4) Here theDØresultas_sl

= −(

1.33

±

0.58)

×

10−2 _{[7],whichdiffers}

fromtheSMatthe3

σ

levelandledtoattentioninthecommunity (see,e.g.,[1,8]),wasnotincluded.

UsingmeasurementsofB0_s–B

¯

0_s mixingandCPviolationinB

de-cayscausedbyb

→

ccs processes,

¯

weshowthatas_slisconstrained –inamodel-independentway–atthe10−4 level.

Inviewofthisstrongconstraint, weproposeanewmethodto utilizeflavor-specific B0_s decays.Itallowsthedeterminationofthe

B0

s–B

¯

0s productionasymmetryandopensanewavenuetoexplore

CPviolationinD±_s decays,whichistinyintheSMbutmaybe en-hancedthroughNPeffects.TheimpactofpossibleCPviolationin http://dx.doi.org/10.1016/j.physletb.2017.04.056

0370-2693/©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

320 R. Fleischer, K.K. Vos / Physics Letters B 770 (2017) 319–324

D±_s decayshasnotbeenincludedintheLHCbresult(3).Weshall takethiseffectintoaccountinouranalysistoshowthesensitivity ofthenewstrategy.

2. Acloserlookatas

sl Theobservableas

sltakesthefollowingform[4]:

a_sls

=









₁₂(s) M(₁₂s)







sin

˜φ

s

=





s



Ms



tan

( ˜

φ

s

),

(5)

where



(₁₂s) and M₁₂(s) are the off-diagonal elements ofthe decay and mass matricesdescribing B0

s–B

¯

0s mixing,



Ms and



s are

themassanddecaywidthdifferencesofthe B0

s masseigenstates,

respectively,and

˜φ

s

=

arg

(

−

M₁₂(s)

/ 

₁₂(s)

)

(6)

is a CP-violating phase difference. As M(₁₂s) isgoverned by short-distancecontributions, NPmayhave asignificant impact. Onthe otherhand,thematrixelement



(₁₂s)

=



f

N

f



B0s

|

f



f

| ¯

B0s

,

(7)

where

N

f isaphase-spacefactor[4],isdominatedbytreedecays

causedby b

→

c

¯

cs processes,whicharefavoured bytheCabibbo– Kobayashi–Maskawa (CKM) matrix, and is hence expected to be insensitive to NP contributions [4,8,9]. Detailed theoretical stud-ies of



₁₂(s) were performed in [10] and[11,12], where the latter analyseswere motivatedinparticularby theDØresult[7].These studies found smallish room for NPeffects in



₁₂(s), also through poorlyconstrained

(

¯

sb

)(

τ τ

¯

)

operators.

TheParticleDataGroup(PDG)[13]givestheaverages



s



s

=

0

.

124

±

0

.

011

,

xs

≡



Ms



s

=

26

.

81

±

0

.

10

,

(8)

where1/ s

= (

1.510

±

0.005)

×

10−12s istheB0s lifetime.The

ex-perimentalresultsfor



s and



s

/

Ms areconsistentwiththe

SM predictions although the theoretical uncertainties are still at the20%level[3].Foradiscussion ofNPeffectson



s in

multi-Higgsandleft-right-symmetricmodels,see[10].

Inthefollowingdiscussion,we donot havetorelyon calcula-tions of



s in theSM orNPmodelsbutshallratherutilizethe

measuredvalueofthisquantity.Insertingtheexperimentalresults in(8)into(5)yields a_sls

=



(

0

.

46

±

0

.

04

)

×

10−2



×

tan

( ˜

φ

s

).

(9)

Itis interesting tonote that thenumerical pre-factorpushesthis observablealreadyintotheregimeof(3).

LetusnowexploitmeasurementsofCPviolationinB0s decays.

Using (6)and (7), andwritingthe B

¯

0

s

→

f decayamplitudes for

afinal state f

=

J

/ψφ,

D−_sD+_s

,

...

causedbyb

→

ccs processes

¯

in thefollowinggeneralway

¯

Af

= | ¯

Af

|

ei[arg(VcbV ∗ cs)+ ¯ψf]

_,

₍₁₀₎ weobtain a_sls

=





s



Ms



tan

(

φ

s

 + ).

(11)

Thephase

φ

s



istheaverageof

φ

f

= φ

SMs

+ φ

NPs

+ ψ

f

,

(12)

where

φ

sSM

= −(

2.1

±

0.1)◦ [3],

φ

NPs originatesfrom CP-violating

NPcontributionstoM(₁₂s),and

ψ

f

≡ ψ

f

− ¯ψ

f,wherethesignsof

the CP-violatingphasesentering

ψ

f arereversed withrespect to

¯ψ

f. Measurementsofmixing-induced anddirectCP asymmetries

allowtheextractionof

φ

f [14]:

A

mix

CP

(

Bs

→

f

)



1

−

A

dir_CP

(

Bs

→

f

)

2

=

η

fsin

φ

f

,

(13)

where

η

f istheCPeigenvalueofthefinalstate.Inorderto

deter-mine

φ

s



fromtheexperimentaldata,weuse

φ

s

 =

f

φ

f

/

σ

2_f

f1

/

σ

2f

±



f 1

/

σ

2_f



−1/2

,

(14)

wherethemeasured valuestaketheform

φ

f

±

σ

f [13].The

pro-cessdependenceof

φ

f entersthrough

ψ

f

= ψ

SMf

+ ψ

NPf

,

(15)

wheretheSMpiece

ψ

SM_f iscausedbydoublyCabibbo-suppressed penguin topologies,while

ψ

NP_f originatesfromNPcontributions to b

→

ccs processes.

¯

Using data for control channels,

ψ

SM_f is constrained to be at most

O(0.5

◦

)

for B0s

→

J

/ψφ

[15] and

−(

1.7+₋1₁._.7₄

)

◦forB0

s

→

D−sD+s [16].Thephaseshift



isgivenby



=

arg



f

η

fwfei(φf−φs)



(16) with wf

= (

B0s

→

f

)





1

−

A

dir_CP

(

Bs

→

f

)

1

+

A

dir CP

(

Bs

→

f

)

,

(17) where

(

B0

s

→

f

)

is therateofthecorresponding decay.As

dis-cussedin[4],anyfinalstate

|

f



canbedecomposedinitsCP-even and CP-oddcomponents

|

fCP+



and

|

fCP−



, respectively, and the sumactuallyrunsonlyoverthesestates,i.e.interferenceterms in-volving



fCP+

|

B0_s



and



fCP−

|

B0_s



dropoutinthesum.

Decays of B

¯

0

s mesons caused by b

→

cus

¯

,

ucs processes

¯

give

sub-leadingcontributionsto(7),withtheratioofthe correspond-ing CKM factors given by

λ

2Rbeiγ

≈

0.02

×

ei70

◦

,where

λ

≈

0.2 istheWolfensteinparameter, Rb

≈

0.4 isonesideoftheUnitarity

Triangle,and

γ

oneofitsangles.Theimpactofthesecontributions on thephase in(6)ishence of

O(

1◦

).

The difference

˜φ

SM_s

− φ

_sSM actually probes these terms [3], and the calculated SM value at the 2◦ level agrees with our general expectation. Assuming CP-violatingNPcontributionstothesub-leadingtreeB

¯

0_s decaysatthe 10% levelgivesatinyphaseshiftof

˜φ

satthe

O(

0.1◦

)

level,which

isirrelevantforourconsiderations.

Expressions (10)–(17) are general anddo not rely on specific assumptions for NPcontributions to theb

→

ccs transitions.

¯

The remarkable feature is that experimentaldata for CP asymmetries and decay rates allow us to determine the phase entering (11), thereby pinningdowntheobservable as_sl inamodel-independent way.

Making the plausibleassumption that NPenters only through

B0_s–B

¯

0_s mixing[4,17],itwasfoundthatthemeasurementofCP vio-lationinB0

s

→

J

/ψφ

rulesoutalargeenhancementofassl[18–20].

WecannowgobeyondthisfindingbyincludingpossibleNP con-tributionsto



₁₂(s)throughfurtherdataonCPviolation.InFig. 1,we collectthevariousLHCbresultsfor

φ

f thatarecurrentlyavailable.

Fig. 1. Compilation oftheavailablemeasurementsofφf forvariousB0s→f decays

originatingfromb¯→ ¯cc¯s processes.

Concerning the B0

s

→

J

/ψφ

decay, it is crucial to have the

pioneeringmeasurements of the differentCP-even (0,

) and CP-odd(

⊥

)final-stateconfigurations[21].TheLHCbanalysisofB0_s

→

J

/ψ

π

+

π

−[22]isactuallylargelydominatedbytheCP-oddB0

s

→

J

/ψ

f0

(980)

contribution[23,24].Thesemeasurements donot

re-vealaprocessdependencewithintheuncertaintiesandare consis-tentwiththeSMpatternoftiny valuesof

φ

f.Sinceanaccidental

cancellationbetween

φ

sNPandthe

ψ

NPf isnotplausible,we

con-cludethattheseNPphasesareall small.Thispictureisalso sup-portedby data for B0_d

→

J

/ψ

K0 modes whichdo not show any signofdirectCP violationatthe1% level; for B±

→

J

/ψ

K± de-cays,sucheffectsare evenconstrainedtovanishatthe0.3%level

[13].Shouldtherebe anaccidentalcancellationbetween

φ

_sNP and the

ψ

NP_f forsome subset offinalstates,it wouldnotaffectour analysisofas_sl asthe generalexpressions in(10)–(17)donotrely onspecificassumptionsforNPaffectingtheb

→

ccs processes

¯

and arealsovalidinthissituation.

Inthecaseof B0

s decayswithopencharm,wehaveonlyafirst

studyofCPviolationinB0_s

→

D−_sD+_s [25],whichhasasignificant uncertainty.However,wemayprobeNPalsothroughB+

→ ¯

D0D+_s. TheBellecollaboration hasmeasuredthedirect CPasymmetryof thischannelas

(0.5

±

1.5)%[26],whichshouldbecomparedwith

A

dir

CP

(

Bs

→

D−sDs+

)

= (

9.0

±

20)% anddoesnotindicateany

devia-tionfromtheSMwithhighprecision.AssumingaNPcontribution withsizableCP-violatingandCP-conservingphasedifferences,the

B+

→ ¯

D0_D+

s result corresponds to

ψ

NP_D−

sD+s

in the few degree regime, in full agreement with the data for decays of the kind

B0_s

→

J

/ψφ

discussedinthepreviousparagraph.

Theaverage ofthe measurements inFig. 1 is givenby

φ

s



=

−(

1.5

±

1.8)◦.Applying(16)tothecorrespondingfinalstatesgives



= (

2.1

±

9.0)◦,whichyields

as_sl

= (

0

.

004

±

0

.

075

)

×

10−2

.

(18) This analysiscan be refined through improved measurements of CPviolationinthevariouschannels,inparticularforB0_s

→

D−_sD+_s

and B0s

→

D∗−s Ds∗+ modes, where in the latter case – in

anal-ogy to B0

s

→

J

/ψφ

– polarization-dependent measurements are

required [27]. Analyses of CP violation in B+

→ ¯

D(∗)0_D(∗)+

s and

B_d0

→

D(_d∗)−Ds(∗)+ willfurthercomplementthepicture.Letus

con-sidera futurescenario wherewe reducethe errorofthe current measurement of

φ

_D−

sD+s by a factor of three as an experimental benchmark, which would match the current experimental preci-sion for B0

s

→

J

/ψφ,

resulting in

φ

s



= −(

1.0

±

1.6)◦,



=

(1.5

±

2.8)◦and

as_sl

= (

0

.

004

±

0

.

024

)

×

10−2

.

(19)

Fig. 2. Dependence ofas

sl onφs+  followingfrom(9)and(11).Thevertical

bandscorrespondtotheexperimentalrangein(18)and(19),whilethehorizontal bandsshowtheLHCbandHFAGresultsin(3)and(4),respectively.

In Fig. 2, we illustrate the situation for as

sl, taking also the

measurements of



s and



Ms into account. The CP violation

measurements lead toa dramatic furthersuppression ofas

sl with

respecttothenumericalfactorin(9).Whileas_sl couldstill be en-hanced withrespect to the SM prediction (1), it ison the other hand already constrained to be at least a factor of four smaller than theuncertainty ofthe LHCbmeasurement (3); therange in

(19) puts an even stronger constraint. The comparison with the LHCbandHFAGbandsshowsimpressivelythatas_slisstrongly con-strainedbycurrentlyavailable datadespitethepossibleimpactof NPcontributions.Thisfindinganswersthekeyquestionaboutthe spaceleftforNPinthisobservable.Neverthelessitwouldbe inter-estingtoconfrontthispicturewithmoreprecisemeasurementsof theas

slobservable, andnewideas ontheexperimental sidecould

resultinmoreprogressthancurrentlyforeseen. 3. Thenewstrategy

Inviewoftheconstraintsonas_slderivedintheprevioussection, flavor-specific B0s decaysofferan interesting newplayground.

As-suming(2),asisusuallydoneintheliterature,B0

s

→

D−s



+

ν

and

¯

B_s0

→

D+_s



−

ν

¯

areflavor-specifictransitions.Interestingly,these re-lations have not yet beentested by experiment. In the SM, they receive correctionsfromprocessesofhigher orderinelectroweak interactions, which are extremelysmall. But asNPmay, in prin-ciple,havesomeimpact,wegivethemostgeneralexpressionsfor therelevantobservables,allowingustosearchforviolationsof(2). To simplify the discussion, we keep only leading-order terms of smallparameters. Following[4],weintroduce

λ

= −

e−iφ(Ms)



A

( ¯

B0 s

→

D−s



+

ν



)

A

(

B0s

→

D−s



+

ν



)



,

(20)

where

φ

(_Ms)istheCP-violatingphaseassociatedwithB0

s–B

¯

0s mixing,

¯λ

involvestheCP-conjugatedecays,and



A

mix_CP

= −

2 Im

(λ

− ¯λ), 

A



= −

2 Re

(λ

− ¯λ) .

(21) The formalism isanalogousto B0

s

→

D+sK−, Bd0

→

D+

π

− decays

andis discussedindetail inRef. [28].There itis alsoshown ex-plicitlythat thecombinationoftheconvention-dependent mixing phase e−iφM(s) _{withthe amplitude ratioin (20) actually results in}

convention-independentobservables

λ

and

¯λ

.

If(2)holds,

λ,

¯λ

andtheobservablesin(21)vanish.Itisuseful todefinethetime-dependentfunctions

F_±

(

t

)

≡



A

mix

CP sin



Mst

± 

A

sinh



st

/

2

322 R. Fleischer, K.K. Vos / Physics Letters B 770 (2017) 319–324

Letusnowconsiderthefollowing“wrong-sign”asymmetryfor thetime-dependentdecayrates:

aWS

≡

( ¯

B0_s

(

t

)

→

D−_s



+

ν



)

− (

B0s

(

t

)

→

D+s



−

ν

¯



)

( ¯

B0s

(

t

)

→

D−s



+

ν



)

+ (

B0s

(

t

)

→

D+s



−

ν

¯



)

.

(23)

Fort

>

0,andtakingintoaccountthataWSisobtained

experimen-tallybymeasuringthenumberofdecayevents,ittakestheform

aWS

=

AP

(

Bs

)

+

aCP

(

+

ν



;

fDs

)

+

a

s

sl

+

F−

(

t

),

(24)

wherethetimedependenceallowsustotest(2).Ifweassume(2), thetimedependencecancelsandthetime-dependentratesin(23)

canbereplacedbytheirtime-integratedcounterparts.The produc-tionasymmetry AP

(

Bs

)

≡

σ

( ¯

B0_s

)

−

σ

(

B0_s

)

σ

( ¯

B0s

)

+

σ

(

B0s

)

,

(25) where

σ

( ¯

B0

s

)

and

σ

(

B0s

)

denoteproduction crosssections,enters

studiesofCPviolationandisanon-perturbative,hadronicquantity whichischaracteristicfortheenvironmentwherethemesonsare produced.TheLHCbmeasurement AP

(

Bs

)

= (

1.09

±

2.61

±

0.66)%

leavesalotofroomforimprovement[29].TheCPasymmetry

aCP

(

+

ν



;

fDs

)

≡

(

B0s

→

D−s

[→

fDs

]

+

ν



)

− ( ¯

B 0 s

→

D+s

[→ ¯

fDs

]

−

ν

¯



)

(

B0 s

→

D−s

[→

fDs

]

+

ν



)

+ ( ¯

B0s

→

D+s

[→ ¯

fDs

]

−

ν

¯



)

(26) ofthetime-independent decayrates(i.e.att

=

0),where fDs (

¯

fDs) isthefinalstateofthesubsequentD_s−(D+_s)decay,mayrevealnew sourcesofCPviolationandwillbediscussedindetailinSection4. TheobservableaWS canbecomplementedwiththe“right-sign”

leptonasymmetry

aRS

≡

( ¯

B0_s

(

t

)

→

D+_s



−

ν

¯



)

− (

B0s

(

t

)

→

D−s



+

ν



)

( ¯

B0s

(

t

)

→

D+s



−

ν

¯



)

+ (

B0s

(

t

)

→

D−s



+

ν



)

,

(27)

wherethefinalstatescanbeaccesseddirectly,i.e.without B0_s–B

¯

0_s

oscillationsoraviolationof(2).Ittakesthefollowingform:

aRS

=

AP

(

Bs

)

−

aCP

(

+

ν



;

fDs

)

−

F+

(

t

),

(28) wherethe time-dependentfunction allows usagaintoprobe (2). Assumingtherelationsgiventhere,aRS canbe extractedfromthe

tagged,time-integratedrates.

As we have seen in Section 2, as_sl is constrained by B-decay

data to be too small to be accessible in measurements ofdecay rateasymmetries.Ontheotherhand,wemayextract AP

(

Bs

)

and

aCP

(

+

ν



;

fDs

)

from AP

(

Bs

)

=

1 2



aWS

+

aRS

−

as_sl



,

(29) aCP

(

+

ν



;

fDs

)

=

1 2



aWS

−

aRS

−

as_sl



,

(30)

wherewe have neglected the F_±

(

t

)

termsandas_sl is constrained by(18),playinganegligiblerole.Thisanalysisopensanewwayto determineboththeCPasymmetryinB

¯

0_s decaysandtheproduction asymmetry AP

(

Bs

).

From the experimental point of view,it is interesting to con-siderthefollowinguntaggedrateasymmetry[4]:

aunt

(

t

)

≡



[

D−_s



+

ν



,

t

] − [

D+s



−

ν

¯



,

t

]



[

D−s



+

ν



,

t

] + [

D+s



−

ν

¯



,

t

]

=

aCP

(

+

ν



;

fDs

)

+

a s sl 2

−



_as sl

+

2 AP

(

Bs

)

2

 

cos

(

Mst

)

cosh

(

st

/

2

)



+

1 2



A

tanh

(

st

/

2

),

(31)

where



[

f

,

t

]

≡ (

B0_s

(

t

)

→

f

)

+ ( ¯

B0_s

(

t

)

→

f

).

TheLHCb collabo-rationemployed(31)forthetime-integrateduntaggedratesto de-termine(3).Theterminvolvingtheproductionasymmetryisthen essentially washed out dueto the rapid B_s0–B

¯

0_s oscillations [30]. However,thetimedependenceof(31)allowsalsotheextraction of

AP

(

Bs

)

andaCP

(

Bs

;

fDs

),

complementingthe determinations pro-posedabove.

We have presented ournew strategy for semileptonicdecays. However,itactuallyappliestoanyflavor-specificB0

s mode,in

par-ticularB0_s

→

D−_s

π

+.Moreover,itcanbeappliedtoanyD−_s

→

fDs decay which is experimentally accessible. In contrast to conven-tionalanalysesofCPviolationinsuchtransitions,thenewstrategy isnotaffectedbytheproductionasymmetry

AP

(

Ds

)

= (−

0

.

33

±

0

.

22

±

0

.

10

)

% (32)

betweenthe D+_s andD−_s mesons[31].Weadvocatetoimplement thenewmethodatLHCbandfuturerunsofBelleII atthe

ϒ(5S)

resonance.

4. DirectCPviolation

ThekeypointofournewstrategyisthattheD−s mesons,which

are produced inthe B

¯

0

s

→

D−s



+

ν

 transitions,will decayfurther as D−_s

→

fDs.Therefore,therateasymmetriesaresensitive toCP violationin boththe B

¯

0s andthe subsequent D−s decays.Keeping

onlyleading-ordertermsinCP-violatingeffectsintheCP asymme-trydefinedin(26),weobtain

aCP

(

+

ν



;

fDs

)

=

a (Bs) CP

|

+ν

+

a (Ds) CP

|

fDs

,

(33) where a(_CPBs)

|

_+_ν

≡

(

B 0 s

→

D−s



+

ν



)

− ( ¯

B0s

→

D+s



−

ν

¯



)

(

B0s

→

D−s



+

ν



)

+ ( ¯

B0s

→

D+s



−

ν

¯



)

(34) probesCPviolationattheB0s amplitudelevel,whereas

a(_CPDs)

|

fDs

≡

(

D−_s

→

fD_s

)

− (

D+_s

→ ¯

fDs

)

(

D−_s

→

fDs

)

+ (

D+s

→ ¯

fDs

)

(35) measuresCPviolationinthe D−_s

→

fDs processes.

Such “direct” CP asymmetries can be generated through the interference between at least two decay amplitudes with non-trivial CP-conservingandCP-violating phasedifferences [32]. The CP-conserving phasescanbe induced through stronginteractions orabsorptivepartsofloopdiagrams,whiletheCP-violatingphases areprovidedbytheCKMmatrixintheSMorNPeffects.

In theSM, a(_CPBs)

|

+ν is zeroatleading order inweak interac-tionsandtakesavanishinglysmallvaluethroughhigher-order ef-fects[33–35].EveninthepresenceofNP,thisCPasymmetry can-not take sizeablevalues.Forthenon-leptonicdecay B0_s

→

D−_s

π

+

things have to be assessed more carefully, as there may still be roomforNPatthedecayamplitudelevel[36,37]andstrong inter-actionsareatwork.Itwouldbeinterestingtomeasure

aCP

(

π

+

;

fDs

)

−

aCP

(

+

ν



;

fDs

)

=

a (Bs)

CP

|

π+ (36)

ConcerningdirectCPviolationinDsdecays,non-leptonic

chan-nels play the key role. In the SM, the CPasymmetries are small butmaybeenhanced throughNP[38,39].Predictionssufferfrom hadronicuncertainties,wherethe SU

(3)

flavorsymmetry offersa usefultool[40].

LHCb employed D∓_s

→

K+K−

π

∓ modes for the analysis of

as_sl. Consequently, the experimental result in (3) actually probes

(

as_sl

)

eff

=

assl

+

2a

(Ds)

CP

|

K+K−π∓.Using theconstraintforas_sl in (18), wemayconvert(3)into

a(_CPDs)

|

K+K−π∓

= (

0

.

19

±

0

.

17

)

×

10−2

,

(37)

which isfive times more precise than the average

(0.5

±

0.9)

×

10−2 _{[13] of CLEO measurements [41,42] and about two times}

more precise than (32), thereby illustrating the potential of the newmethod.

To probe NP, decays with penguin loop contributions, such as D+s

→

π

+K0

,

π

0K+

,

K+

φ,

are mostpromising. Taking D+s

→

π

+KS as an example [43,44], LHCb measured a(CPDs)

|

KSπ±

=

−(

0.38

±

0.46

±

0.17)%[45],whichhasanuncertaintythreetimes largerthan(37).

5. Conclusions

We are moving towards impressive new frontiers in high-precisionstudiesofCPviolation.Theglobalagreementofthe cur-rent data with the Standard Model raises the question of how much space is left for New Physics. In the case of CP violation in B0

s–B

¯

0s oscillations,we haveused experimental data to obtain

as_sl

= (

0.004

±

0.075)

×

10−2, pushing this observable well be-lowthecurrentlyaccessibleregime. Wehavepresenteda model-independent formalism in terms of CP-violating phases and de-cay rates, allowing us to further refine this range through im-proveddataforCPviolationindecaysofthekindB0

s

→

J

/ψφ

and

B0_s

→

D(s∗)+D(s∗)−.

The as_sl observable has been inthe focus for many years and was determined by means of flavour-specific B0s

→

D−s



+

ν

 de-cays. In view of our findings for as

sl, we propose a new strategy

to utilizesuch decays. It allows us to determine the B0

s

produc-tionasymmetry AP

(

Bs

)

andtheCPasymmetryaCP

(

+

ν



;

fDs

).

The currentexperimental situationfor AP

(

Bs

)

leavesroom for

signifi-cantimprovement,whileaCP

(

+

ν



;

fDs

)

isgovernedbythedirect CPviolationinD−_s

→

fDs,thereby openinganewavenueforthe explorationofthisphenomenon.

Wehavealso givenexpressions allowing usto probewhether

B0_s

→

D−_s



+

ν

 decays are actually flavor-specific. This feature, whichiscommonly used,ismostplausiblebut hasnot yetbeen testedexperimentally.

The new strategy can also be applied to other flavor-specific modes, such as B0

s

→

D−s

π

+. It shifts flavor-specific B0s decays

fromtheirwell-knownroleasprobesofCPviolationinB0

s–B

¯

0s

os-cillations to newtools for the exploration of direct CP violation, inparticularin D±_s decays.As CPviolationinthesemodesmight beenhancedbyNewPhysics,wehaveanewframeworktosearch forsuchsignatures,allowingustotakefulladvantageofthe corre-spondingphysicspotentialinthehigh-precisioneraofheavy-flavor studies.

Acknowledgements

We would like to thank Marcel Merk and Vincenzo Vagnoni forusefuldiscussions. This work is supported by the Foundation forFundamental Researchon Matter (FOM)andby the Deutsche Forschungsgemeinschaft (DFG) within research unit FOR 1873 (QFET).

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