New physics in $\Delta \Gamma_d$

1.5 MB·English

by  Gilberto Tetlalmatzi-Xolocotzi

New physics in ∆Γ
d
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Gilberto Tetlalmatzi-Xolocotzi∗
n
InstituteforParticlePhysicsandPhenomenology,DurhamUniversity
a
J E-mail: [email protected]

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] We analyze the possibility of having new physics effects in the decay rate difference, ∆Γ , of
h d
p neutralB mesons. Threedifferentsourcesofenhancementareconsidered, CKMunitarityvio-
d
-
p lations, beyond standard model effects in the tree-level dimension six operators (d¯p)(p¯(cid:48)b) with
e p,p(cid:48) =u,c; and large enhancements of the almost unconstrained operators (d¯b)(τ¯τ). We find
h
[ that deviations of several hundred per cent from the standard model prediction of ∆Γ are not
d

1 excludedbycurrentexperimentaldata.
v
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i
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FlavorfulWaystoNewPhysics-FWNP,
28-31October2014
Freudenstadt-Lauterbad,Germany
∗Speaker.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
Newphysicsin∆Γ GilbertoTetlalmatzi-Xolocotzi
d
1. Introduction
There is a longstanding discrepancy between experimental results for the like-sign dimuon
asymmetry measured by the D0 Collaboration [1]-[4] and the corresponding standard model pre-
dictions [5]-[9]. In [10] an interesting connection between the dimuon asymmetry and the decay
rate difference of neutral B mesons was suggested: the measured enhancement of the dimuon
d
asymmetrycouldalsobeexplainedbyanenhanceddecayratedifferenceoftheneutralB mesons.
d
Moreover, ∆Γ , is currently only weakly constrained by direct measurements. This was the mo-
d
tivation for the study in [11] where indirect experimental constraints on possible new physics en-
hancementsof∆Γ werestudied;wepresentherethemainfindingsof[11].
d
2. NeutralBmixing
DuetoelectroweakinteractionstheneutralstatesB andB¯ oscillateintoeachother,thetime
d d
evolutionofthissystemisgivenbysolvingtheSchrödinger-likeequation
d (cid:32)|B (cid:105)(cid:33) (cid:32)|B (cid:105)(cid:33) i (cid:32)Md −iΓd11 Md −iΓd12(cid:33)
i d =Σd d where Σd =M − Γ = 11 2 12 2 . (2.1)
dt |B¯d(cid:105) |B¯d(cid:105) d 2 d Md∗−iΓd12∗ Md −iΓd11
12 2 11 2
Diagonalizing Σd gives the physical eigenstates {|B >,|B >} with the masses Md,Md and the
H L H L
decay rates Γd,Γd. To provide a mathematical description of the mixing process it is useful to
H L
define the observables ∆M =Md −Md and ∆Γ =Γd −Γd. Theoretically ∆M and ∆Γ can be
d H L d H L d d
calculatedfromthecomponentsofΣd accordingtotheformulas
(cid:16) Md (cid:17)
∆M ≈2|Md | and ∆Γ ≈2|Γd |cos(φ ) where φ =arg − 12 . (2.2)
d 12 d 12 d d Γd
12
Only ∆M and ∆Γ are directly accessible in experiment, the phase φ can be calculated from the
d d d
measurementofthesemileptonicasymmetry
(cid:12)Γd (cid:12)
ad =(cid:12) 12(cid:12)sin(φ ). (2.3)
sl (cid:12)Md (cid:12) d
12
BycombiningdatafromBelle,BABAR,D0,DELPHIandLHCbthefollowingdirectexperimental
boundfor∆Γ isavailable
d
∆ΓHFAG
d = (0.1±1.0)%[12] (2.4)
Γ
d
whichcanbecomparedtothestandardmodelprediction
∆ΓSM
d = (0.42±0.08)%[5].
Γ
d
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Newphysicsin∆Γ GilbertoTetlalmatzi-Xolocotzi
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3. Sourcesofenhancementfor∆Γ
d
3.1 CKMunitarityviolations
Letλd=V∗V ,fromtheunitarityofthe3×3CKMmatrixthefollowingconditionissatisfied
q qd qb
λd+λd+λd =0. Howeverindifferentextensionsofthestandardmodelthepreviousequalityis
u c t
brokenaccordingtoλd+λd+λd =δd ;forinstancein4thfamilystudiesδd ≈10−2 leading
u c t CKM CKM
toapotentialenhancementfactoron∆Γ of300%.
d
3.2 Current-currentstandardmodeloperators
Inthissectionweconsiderthepossibilityofhavingnewphysicseffectsintreelevelstandard
modeloperatorsanditsconsistencywithrecentexperimentalobservations, asimilarstudyandits
implicationsovertheCKMphaseγ hasbeendiscussedin[13].
WeareconcernedwiththefollowingeffectiveHamiltonian
H current,|∆B|=1 = 4√GF ∑ V∗ V ∑ Cpp(cid:48)(µ)Qpp(cid:48)+h.c. (3.1)
eff pd p(cid:48)b i i
2
p,p(cid:48)=u,c i=1,2
with
Qpp(cid:48) = (d¯αpβ) (p¯(cid:48)βbα) ,
1 V−A V−A
Qpp(cid:48) = (d¯αpα) (p¯(cid:48)βbβ) . (3.2)
1 V−A V−A
NewphysicseffectswillproduceshiftsoverthestandardmodelWilsoncoefficientsaccordingto
Cpp(cid:48) = CSM+∆Cpp(cid:48). (3.3)
1,2 1,2 1,2
pp(cid:48)
Toconstrainthevaluesof∆C weconsiderdifferentobservablesdependingontheuptypequark
1,2
structureindicatedbythelabels pp(cid:48)inEqns. (3.1)and(3.2). Themostimportantboundsarisefrom
theoperatorsrelatedwiththetransitionsb→uu¯d,b→cu¯d andb→cc¯d withWilsoncoefficients
Cuu,Cuc andCcc respectively. ThedecaysB→ππ,B→πρ andB→ρρ providelimitsfor∆Cuu.
To calculate the bounds on ∆Cuc the relevant processes are B¯ →D∗+π− and B0 →D(∗)0h0 with
h0 =π0,η orω. Regarding that the decay width of the B meson is dominated by the transition
d
b→cu¯d an extra constraint for ∆Cuc can be imposed from the decay rate itself. The shift ∆Ccc
is bounded by the process B→X γ, the observable sin(2β) and the semileptonic asymmetry ad
d sl
defined in Eqn. (2.3). We visualize graphically the parameter space available for new physics by
plottingtherealandimaginarypartsof∆Cqq(cid:48),asanexamplewepresenttheresultsfor∆Ccc inthe
1,2 2
leftpanelofFig. (1).
qq(cid:48)
Finallytheeffectsof∆C over∆Γ canbeestimatedbyusingEqns. (2.2)and(3.3)togetherwith
1,2 d
theexpression
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Newphysicsin∆Γ GilbertoTetlalmatzi-Xolocotzi
d
4 4 (cid:45)20 (cid:45)10 (cid:45)3 20
(cid:45)20
(cid:45)10
2 2
(cid:45)3
(cid:76) (cid:76)
W W
M M 0 0
SM SM
cc(cid:68)C2 0 (cid:72) cc(cid:68)C2 0 (cid:72)10 5 1 1 5 10
m m 0
I I 0
(cid:45)2 (cid:45)2 (cid:45)3
(cid:45)10
(cid:45)20
(cid:45)4 (cid:45)4 20 (cid:45)3 (cid:45)10 (cid:45)20
(cid:45)4 (cid:45)2 0 2 (cid:45)4 (cid:45)2 0 2
Re(cid:68)Ccc M Re(cid:68)Ccc M
2 W 2 W
Figure 1: Left panel: Allowed(cid:72)par(cid:76)ameter space in the Re ∆Ccc-Im∆Ccc plane. (cid:72)The(cid:76)constraints shown
2 2
correspondtoB→X γ (Blue),ad (Green)andsin(2β)(Red). Theregioncontainedwithinthedashedblack
d sl
linerepresentthecombinedconstraintsfromthedifferentobservables. Rightpanel: contoursof∆Γ /∆ΓSM
d d
alongwiththecombinedconstraints.
1 (cid:18) (cid:90) (cid:104) (cid:105)(cid:19)
Γd = <B¯ |Im i d4xTˆ H current,∆B=1(x)H current,∆B=1(0) |B >
12 2M d eff eff d
Bd
(cid:16) (cid:17)
= − λ2Γcc,d(Ccc,Ccc)+2λ λ Γuc,d(Cuc,Cuc)+λ2Γuu,d(Cuu,Cuu) . (3.4)
c 12 1 2 c u 12 1 2 u 12 1 2
The enhancement factors can be read by plotting the contour lines for ∆Γ /∆ΓSM, we provide
d d
an example of this strategy in the right panel of Fig. (1). Our calculations show that there is
room for new physics inCuu andCuc leading to enhancement factors of 1.6 in both cases. The
1,2 1,2
most interesting result arises from Ccc where an enhancement factor of 14 is allowed by current
2
experimentalresults. Alltheboundswerecalculatedat90%C.L..
3.3 Operators(d¯b)(τ¯τ)
In the third part of our analysis we consider the effective operators (d¯b)(τ¯τ), they are well
suppressedwithinthestandardmodel,howevertheyarenotquiteconstrainedbytheexperimental
dataavailablenowadays;theapproachfollowedinthissectionisanalogoustothestudyperformed
forB mesonsin[14]. HerewetakeintoaccountthefollowingeffectiveHamiltonian
s
4G
H b→dτ+τ− =− √Fλd∑C (µ)Q (3.5)
eff t i,j i,j
2
i,j
andstudythescalar,vectorandtensorDiracstructuresof(d¯b)(τ¯τ)
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Newphysicsin∆Γ GilbertoTetlalmatzi-Xolocotzi
d
Q = (cid:0)d¯P b(cid:1)(τ¯P τ),
S,AB A B
Q = (cid:0)d¯γµP b(cid:1)(cid:0)τ¯γ P τ(cid:1), (3.6)
V,AB A µ B
Q = (cid:0)d¯σµνP b(cid:1)(cid:0)τ¯σ P τ(cid:1)
T,A A µν A
withWilsoncoefficientsC ,C andC respectively. Followingthenotationof[14]: A,B=
S,AB V,AB T,A
(cid:17)
R,LandP =(1±γ /2.
R,L 5
To get bounds on the Wilson Coefficients we use direct and indirect constraints. Direct bounds
arise from particle transitions where the chain b→dτ+τ− appears at tree level; indirect estima-
tions are derived from processes where the terms given in Eqns. (3.6) arise as a consequence
of operator mixing, loop level corrections or both. The direct category includes the processes
B →τ+τ−,B→X τ+τ− andB+→π+τ+τ−. Inthefirstcasethefollowingexperimentalbound
d d
is available Br(B →τ+τ−)<4.1×10−3 [15]. In the second and third cases currently there are
d
notexperimentalmeasurementsforthebranchingratios. Howeverwecanestimateanupperlimit
fortheseobservablesbyconsideringthespaceavailablefornewB decays,i.e. thosethathavenot
d
(cid:16) (cid:17) (cid:16) (cid:17)
beenmeasuredyet. Tofulfillthistaskwecomparetheratio τBs −1 against τBs −1 and
τBd SM τBd exp
ignorenewphysicseffectsintheB sector;ourresultisBr(B →X )≤1.5%. FromB →τ+τ−
s d new d
wegetchiralityindependentboundsforC andC ,whereasfromB→X τ+τ−andB+→π+τ+τ−
S V d
wegetconstraintsforalltheDiracstructuresshowninEqns. (3.6). Indirectboundsarecalculated
fromthebranchingratiosoftheprocessesB →X γ andB+→π+µ+µ−. InthecaseofB →X γ
d d d d
the tensor element in Eqns. (3.6) mixes with the operator mediating the transition b→dγ. For
the process B+ → π+µ+µ− there are contributions from mixing between the vector and tensor
componentsofEqns. (3.6)andtheoperatorsresponsibleforthechainsb→dγ andb→dl+l−.
To quantify the effects of our (d¯b)(τ¯τ) operators over ∆Γ we first parametrize the new physics
d
contributionsinΓd throughthefactor∆˜
12 d
Γd = Γd,SM∆˜ . (3.7)
12 12 d
The relationship between ∆˜ and the Wilson coefficients of the operators in Eqns. (3.6) is estab-
d
lishedbythefollowinginequalities
|∆˜ | < 1+(0.41+0.13)|C (m )|2
d S,AB −0.08 S,AB b
|∆˜ | < 1+(0.42+0.13)|C (m )|2 (3.8)
d V,AB −0.08 V,AB b
|∆˜ | < 1+(0.42+0.13)|C (m )|2
d T,A −0.08 T,A b
here we are assuming single operator dominance; i.e. we are analyzing the effect of only one op-
eratorfromEqns. (3.6)atatimebyswitchingonthecorrespondingWilsoncoefficientandsetting
theotherstozero. Thesubindexof|∆˜ |inEqns. (3.8)indicatestheoperatorunderstudy.
d
Wefinallyarrivetothefollowingenhancementfactorsat90%C.L.
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Newphysicsin∆Γ GilbertoTetlalmatzi-Xolocotzi
d
10 B (cid:174)Τ(cid:43)Τ(cid:45)
d
B(cid:174)X Τ(cid:43)Τ(cid:45)
7 d
B(cid:43)(cid:174)Π(cid:43)Τ(cid:43)Τ(cid:45)
V 5
M (cid:200)
S(cid:71)d 4
(cid:68)
(cid:144)
(cid:71)d 3
(cid:68)
(cid:200)
2
AllowedregionfromB (cid:174)Τ(cid:43)Τ(cid:45)
d
1
2.(cid:180)10(cid:45)6 0.00001 0.0001 0.001 0.01
Br
Figure2: Boundsontheenhancementfactorfor∆Γ asafunctionoftheimprovementontheexperimental
d
limits over the branching ratios for the processes B →τ+τ− (purple), B →X τ+τ− (blue) and B →
d d d d
π+τ+τ− (red). Onlytheeffectinducedbythevectorialversionofthe(d¯b)(τ¯τ)operatorsisshownat90%
C.L..
|∆˜ | ≤ 1.6
d S,AB
|∆˜ | ≤ 3.7 (3.9)
d V,AB
|∆˜ | ≤ 1.2.
d T,R
Strongerboundsfor|∆˜ |canbeestablishedifupperlimitsforthebranchingratiosoftheprocesses
d
B →τ+τ−, B→X τ+τ− and B+ →π+τ+τ− are reduced experimentally; this effect is shown
d d
explicitlyinFig. (2)forthevectorstructureofthe(d¯b)(τ¯τ)operators.
4. Likesigndimuonasymmetry
ExperimentallytheD0collaborationhasmeasuredtherawlikesigndimuonchargeasymmetry
A=A +A [1]-[4], afterremovingthebackgroundsA theremainingcomponentA isthe
CP bkg bkg CP
resultofCPviolationarisingfromneutralBmesoninteractions. Before2013itwasassumedthat
A wascausedonlybyCPviolationinmixingbetweentheB andB¯ statesleadingto
CP d d
A ∝Ad =C ad +C as . (4.1)
CP sl d sl s sl
The terms ad,s are the semileptonic asymmetries andC are proportionality constants depending
sl d,s
on the production fractions, oscillation parameters and decay widths of B . Based on this inter-
d,s
pretation D0 reported in 2011 a measurement for Ad that was in disagreement with the standard
sl
modelpredictionby3.9σ [3].
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Newphysicsin∆Γ GilbertoTetlalmatzi-Xolocotzi
d
Recently the contribution of CP violation in interference between decays with and without mix-
ing was included in the analysis of A . According to [10] this implies the replacement of Eqn.
CP
(4.1)by
∆Γ ∆Γ
A ∝Ad +C d +C s, (4.2)
CP sl Γd Γ Γs Γ
d s
here ∆Γs ishighlysuppressedbytheconstantC incomparisonwiththecontributiondueto ∆Γd.
Γs Γs Γd
InprincipleEqn. (4.2)maysuggestthatthetensionbetweentheoryandexperimentforA could
CP
beeliminatedif∆Γ getsenhancedthroughnonstandardmodelphysics. Howeveramoredetailed
d
study reveals that Eqn. (4.2) is the first approximation towards the inclusion of CP violation in
interference;insteadofhavingacompletedependenceon∆Γ itisexpectedthattherelevantcon-
d
tribution to the interference depends on the components Γcc and Γuc, see Eqn. (3.4), in a more
12 12
convolutedwaythantheonegivenin∆Γ [16];thispossibilityiscurrentlyunderfurtherinvestiga-
d
tion[17].
5. Conclusions
Wehaveexploredthepossibilityofhavingnewphysicseffectson∆Γ withintheHeavyQuark
d
Expansion. Firstly we found that by breaking the unitarity of the CKM matrix by 10−2 we can
have a deviation of 300% with respect to the standard model expectation on∆Γ . Our analysis of
d
dimensionsixtreelevelstandardmodeleffectiveoperatorsshowsinterestingdeviationsover∆ΓSM,
d
the most remarkable example is given by (d¯c)(c¯b) where an enhancement factor of 14 is allowed
bycurrentexperimentaldata. Finallyinthecaseoftheeffectiveoperators(d¯b)(τ¯τ)wehavefound
that ∆Γ can be nearly 4 times bigger than in the standard model. We mentioned that as a first
d
approximation there is a relationship between ∆Γ and the dimuon asymmetry A measured by
d CP
D0,describingbrieflypossiblecorrectionsthatcouldbeusefulinreducingthegapbetweentheory
andexperimentforA . Thuswestronglymotivatesomefurtherexperimentalstudiesof∆Γ .
CP d
6. Acknowledgements
I would like to thank to the organizers for an interesting and motivating workshop. Many
thankstoU.NiersteandG.Borissovforusefuldiscussionsconcerningthelike-signdimuonasym-
metry. I am also grateful with A. Lenz for proofreading this manuscript and with CONACyT,
Mexico,forfinanciallysupportingmyPhDprogram.
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d
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