Studies of dark sector & B decays involving $\tau$ at Belle and Belle II

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by  Gianluca Inguglia

Studies of dark sector & B decays involving τ at
Belle and Belle II
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2 Gianluca Inguglia∗†

n DESY
a E-mail: [email protected]
J

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The Belle II experiment aims to record 50 ab−1 data with the high luminosity to be provided
]
x bytheSuperKEKBenergy-asymmetrice+e collider. Theanticipatedhighstatisticsdataenables
e
- us to perform studies of B decays involving τ leptons such as B+ →τ+ν and B→D(∗)τ+ν
p τ τ
e modes. Theprecisemeasurementsofbranchingfractionandoftheτ leptonpolarizationinthese
h
BdecaysprovideaverysensitiveindirectsearchforachargedHiggsboson. BelleIIsensitivity
[
for the charged Higgs is complementary to direct searches at ATLAS and CMS. With the large
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v datasampleandbyusingdedicatedtriggerstheBelleIIexperimentisexpectedtoexploredark
8 sectorbysearchingforvisibleandinvisibledecaysofthedarkphotonandthedarkHiggsboson,
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2 andbyalsosearchingforlowmassdarkmatterwithunprecedentedprecision.
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38thInternationalConferenceonHighEnergyPhysics
3-10August2016
Chicago,USA
∗Speaker.
†Afootnotemayfollow.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
Studiesofdarksector&Bdecaysinvolvingτ atBelleandBelleII GianlucaInguglia
1. Bdecaysinvolvingτ
1.1 B→τν
The SM decay rate Γ for the decay B→τν is calculated in terms of the Fermi constant G ,
F
the mass of the m and m of the B meson and of the τ lepton, the B meson decay constant and
B τ
lifetime f andτ ,respectively. Thiscanbewrittenas
B B
G2m m2f2 m2
Γ(B+→τ+ν )= F B τ B|V |2(1− l )τ . (1.1)
τ 8π ub m2 B
B
New physics beyond the SM can enhance this particular decay. In the supersymmetric two Higgs
doubletsmodel(2HDM)thedecayrateshowninEq.1.1assumetheform
G2m m2f2 m2 tan2β m2
Γ(B+→τ+ν )= F B τ B|V |2(1− τ)×(1− B )2 (1.2)
τ 8π ub m2 1+ε˜ tanβ m2
B 0 H±
where tanβ defines ratio of the vacuum expectation values (vev) for two Higgs doublets and m
H±
is the mass of the predicted charged Higgs bosons [1]. Data collected by the Belle detector in
e+e− collisions taking place at the mass of the ϒ(4S) have been used to search for B+ →τ+ν
τ
(andchargeconjugated). Theϒ(4S)isknowntodecaytoB+B− pairswithBR(ϒ(4S)→B+B−)=
0.514±0.006, consequently a search for B+ → τ+ν relies on the capabilities of software and
τ
detector to (fully) reconstruct one B meson (B ) to infer the flavour of the other (B ). Dif-
rec sig
ficulties in the reconstruction of B+ → τ+ν arise mainly from two factors. First the complex
τ
algorithms implemented to reconstruct the B affects the reconstruction efficiency lowering it,
rec
second the B+ →τ+ν signal events are characterised by large missing energy due to the pres-
τ
ence of neutrinos in the final state (one or two neutrinos in hadronic or leptonic τ decays, re-
(cid:113)
spectively). B candidates are selected using the standard variables M = E2 −P2 and
rec bc beam B
∆E = E −E , where E and p are the energy and momentum of the reconstructed B me-
B beam B B
son and E the beam energy in CM system. Once B candidates have been reconstructed,
beam rec
charged tracks are selected to identify the τ decays for example in the following final states:
τ+→µ+νν¯,e+νν¯,π+ν ,π+π0ν,π+π+π−ν. ThesignatureoftheB→τν decayisthensearched
as an excess of events in the E (= E −E −E ) distribution defining the energy de-
ECL tot Brec tracks
position in the electromagnetic calorimeter and that is peaked around zero for signal events. A
slight excess of events has been observed by the Belle Experiment in two independent analy-
ses using hadronic and semileptonic decays of the B , and due to limited statistics upper lim-
rec
its have been set to BR < (1.79+0.56(stat)+0.46(syst)) for hadronic tagged B [2] and to
B→τν −0.49 −0.51 rec
BR <(1.25±0.28±0.27)×10−4 and BR <(1.54±0.38±0.37)×10−4 for semilep-
B→τν B→τν
tonictaggedB [3]at90%confidencelevel(C.L.). With50ab−1 ofdatathatwillbecollectedby
rec
theBelleIIexperimentwithinthenextyearsandwithimproveddetectorandsoftware,onewould
expect to be able to further constrain this decay to BR <4×10−5 and to observe at 5 σ
B+→τ+ντ
statistical significance the decay B+ →µ+ν (in this last case a 5 σ observation is expected with
µ
justsome5ab−1 ofdata)asshowninTable.1.
1.2 B→D(∗)τν
The semileptonic decay B → D∗τ+ν is a b → c transition proceeding via the emission of
τ
a virtual W+ boson in a tree level decay topology. NP can affect this decay in different ways,
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Studiesofdarksector&Bdecaysinvolvingτ atBelleandBelleII GianlucaInguglia
Table 1: Observed (Belle) and expected (Belle II) precision in the determination of BR(B+ →τ+ν ) for
τ
differenttaggingmodesincludingstatistical,systematic,andtotaluncertainties(inpercent).
Process Statistical Systematic Total
(reducible,irreducible)
BR(B→τν)(hadronictag)
711fb−1 38.0 (14.2,4.4) 40.8
5ab−1 14.4 (5.4,4.4) 15.8
50ab−1 4.6 (1.6,4.4) 6.4
BR(B→τν)(semileptonictag)
711fb−1 24.8 (18,+6.0) +31.2
−9.6 −32.2
5ab−1 8.6 (6.2,+6.0) +12.2
−9.6 −14.4
50ab−1 2.8 (2.0,+6.0) +6.8
−9.6 −10.2
modifyingforexampleeithertheBRortheτ polarization. IfNPdependsonthemassscaleandit
isproportionaltoitasforthecaseforachargedHiggsboson,inthecalculationofbranchingratio
B→D∗τ+ν a term in which theW+ boson is replaced by a charged Higgs boson H+ has to be
τ
added, and due to the proportionality to the mass the effect is expected to be more pronounced in
decays involving a τ-lepton in the final state with respect to the other two lighter leptons, making
suchaneffectdetectable[4]. AnalternativepossibilityofNPaffectingtheBRwithrespecttothe
chargedHiggsbosonisrepresentedbyanadditionaltransition(interferingwiththeSM)inwhich
avirtualleptoquarkisproducedintheprocessb→ν h˜∗ andsubsequentdecayh˜∗→cτ [5].
τ
Twoveryimportantquantitiesthatcharacterisethesedecay(s)areR(D)andR(D∗)definedas
Γ(B→D(∗)τ+ν )
R(D(∗))= τ (1.3)
Γ(B0→D(∗)l+ν )
l l=µ,e
thatcanbemeasuredexperimentallyandforwhichveryprecisepredictionsfromtheSMexist:
R(D)=0.297±0.017, (1.4)
R(D∗)=0.252±0.003. (1.5)
Results reported by the Belle (hadronic tag), BABAR (hadronic tag) and LHCb Collaborations
while in agreement with each other have shown a significant deviation from the SM predictions
shown in Eqs. 1.4 and 1.5 and their averages are R(D∗) = 0.322±0.018±0.012 and R(D) =
0.391±0.041±0.028 [6]. The deviation of the combined results on R(D) and R(D∗) is then
found to be 3.9 σ from SM prediction. At Belle the strategy for the selection of event candidates
proceedsviaatwostepsprocess. Firstanalgorithmbasedonthehierarchicalreconstructionofthe
B usingNeuroBayesisapplied,thenacheckisperformedontheremainingparticlesseeninthe
rec
detectortoevaluatewhethertheseareconsistentwithsignalsignatureornot. Recentlynewresults
fromtheBelleCollaborationbasedonsemileptonicdecaysoftheB havebeenreleasedinwhich
rec
R(D∗)=0.302±0.030±0.011showinganimprovementoverpreviouslypublishedresults[7]. The
newresultsarecompatiblewithboththeSMandthetype-II2HDMfortanβ/m (cid:39)0.7GeV−1 (to
H
becomparedtotanβ/m (cid:39)0.5GeV−1 obtainedforthehadronictaganalysis). Figure1showthe
H
mentioned results together with their (private, preliminary) combination and with the projection
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Studiesofdarksector&Bdecaysinvolvingτ atBelleandBelleII GianlucaInguglia
Table2: Observed(Belle)andexpected(BelleIIassuminghadronictaggedB mesons.) precisioninthe
rec
determinationofR(D(∗))includingstatistical,systematic,andtotaluncertainties(inpercent).
Process Statistical Systematic Total
(reducible,irreducible)
R(D)
423fb−1 13.1 (9.1,3.1) 16.2
5ab−1 3.8 (2.6,3.1) 5.6
50ab−1 1.2 (0.8,4.4) 3.4
R(D∗)
423fb−1 7.1 (5.2,1.9) 9.0
5ab−1 2.1 (1.5,1.9) 3.2
50ab−1 0.7 (0.5,1.9) 2.1
of Belle results to Belle II luminosities. This decay is also sensitive to the tensor operator in
leptoquarks (LQ) models, in particular the R LQ model is a good model for compatibility test
2
and assuming M (cid:39)1 TeV/c2 results show that this model with Wilson coefficientC =+0.36
LQ T
is disfavoured. This study is limited by the efficiencies in the full reconstruction and suffer by
dominant systematic effects arising from the limited MC sample used for defining the PDF shape
and from limited knowledge of probability density function (PDF) shapes in B → D∗∗lν . One
l
can expect that with larger data and MC samples and with improved software at Belle II one will
achievealargeimprovementinthedeterminationofR(D)andR(D∗)asshowninTable2.
Figure1:1-sigmacontourplotofR(D)vs.R(D∗)showingtheresultsfromBabar(black),LHCb(orizzontal
cyanband)Belle(combinedsemi-leptonicandhadronictag,blue)andtheirprivatepreliminarycombination
(red). InyellowisshowntheprojectionofthetheBelleresultstoBelleIIfullluminosity(i.e. 50ab−1).
0.5
)
*
D
R( BBeellllee ICI oPmrobjeincatitoionn ICHEP 2016 Preliminary
0.45
Babar
LHCb
World Combination
0.4 SM prediction: PRD92 054410 (2015), PRD85 094025 (2012)
0.35
0.3
0.25
1 s contours
0.2
0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
R(D)
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Studiesofdarksector&Bdecaysinvolvingτ atBelleandBelleII GianlucaInguglia
2. Darksectorsstudies
2.1 Darkphoton
ThedarkphotonA(cid:48) isthemediatorofahypotheticaldarkforcerelatedtoaU(1)(cid:48) extensionof
theSM.KineticmixingbetweentheSMphotonγ andA(cid:48),εFY,µνFD withkineticmixingstrength
µν
ε should exist in the interaction Lagrangian and may allow for interactions between SM and dark
matter. DarkmatterparticleswouldthenbeneutralunderSU(3) ×SU(2) ×U(1) andcharged
C L Y
underU(1)(cid:48) whileSMparticleswouldbeneutralunderU(1)(cid:48) andtheA(cid:48)−γ kineticmixingterm
D
wouldallowA(cid:48) todecaytoSMparticleswithverysmallcouplings. Duetotheexpectedlowmass
ofA(cid:48) (intherangeatafewMeV/c2 toafewGeV/c2 [9]),A(cid:48) couldbeproducedine+e− collisions
atBandτ-charmfactoriesorindedicatedfixedtargetexperimentsinprocessesthatwoulddepend
on its mass and its lifetime. In e+e− collisions the dark photon is searched for in the reaction
e+e− →γ A(cid:48), with subsequent decays of the dark photon to SM final states A(cid:48) →l+l−, h+h−
ISR
(l =leptons, h =hadrons) or to dark matter A(cid:48) → χχ¯, depending on kinematic constraints. The
signatures of its production and decays are characterised either by the presence of an energetic
photoninthefinalstateplustwooppositelychargedtrackswithinvariantmassequivalenttothatof
thedarkphotonorbyamono-energeticphoton(foron-shellproduction). Inthiscase,ifsistheCM
s−M2
energy of the collision, the final state is a photon with an energy E = √A(cid:48), plus missing energy
γ 2 s
in the case of decays to dark matter. For SM decays of A(cid:48) an additional possibility derives from
its lifetime. In fact for a short-lived A(cid:48) one would expect the dark photon to decay promptly near
the interaction region but in case of long-lived A(cid:48) the decay can happen far from the production
point. In the latter case the two tracks would form a vertex at a significantly displaced position
with respect to the interaction region. Searches for A(cid:48) are ongoing and are challenged by high
backgroundlevels(promptdecays),bylowtriggerefficiencies(displaceddecays),andbytheneed
ofasinglephotontrigger(decaysintodarkmatter)thatwasnotavailableattheBelleexperiment,
butwillbeimplementedatBelleII.IfA(cid:48) isnotobservedwiththeavailableBelledata,itispossible
to anticipate that dark photon decays, to any of the discussed final states, with kinetic mixing
ε (cid:39)10−4 willbewellwithinreachwiththefullBelleIIdatasample.
2.2 DarkHiggsboson
ApossiblewayforthedarkphotontoacquireitsmasscomesfromanextendedHiggssector,
In fact the SM Higgs would need to be modified to break the additional U(1)(cid:48) symmetry. This
wouldleadtoaself-interactingdarkHiggsbosonh(cid:48)withamassintheMeV/c2toGeV/c2range. In
e+e− onewouldsearchforthedarkHiggsbosoninaprocesscalleddarkHiggsstrahlung. Decays
ofh(cid:48) dependonitsmass: infactifM >2M thenitwouldmainlydecaytotwodarkphotons,if
h(cid:48) A(cid:48)
M <M <2M thenh(cid:48)→A(cid:48)A(cid:48)∗ whereA(cid:48)∗ decaysintoleptons,andifM <M thedarkHiggs
A(cid:48) h(cid:48) A(cid:48) h(cid:48) A(cid:48)
bosonislonglivedanditwouldeventuallydecaytoleptonorhadronpairs. TheBelleexperiment
hassearchedforthedarkHiggsbosoninthirteendecaychannels,tenofwhichareexclusivedecays
suchas2(π+π−)(l+l−),3(l+l−),2(l+l−)(π+π−),3(π+π−)andthreeareinclusivedecayssuchas
2(l+l−)X, where l =e,µ and X a dark photon decaying invisibly [10]. The search for the dark
photon and the dark Higgs boson has been performed in the mass ranges of 0.1-3.5 GeV/c2 and
0.2-10.5 GeV/c2, respectively. Since no significant excess of events was observed, individual and
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Studiesofdarksector&Bdecaysinvolvingτ atBelleandBelleII GianlucaInguglia
combined 90% C.L. upper limits have been placed on the product of the branching fraction times
the Born cross section, B×σ , and on the product of the dark photon coupling to the dark
Born
Higgs boson and the kinetic mixing between the SM photon and the dark photon, α ×ε2. For
D
α = 1/137, m < 8 GeV/c2, and M <1 GeV/c2, values of the mixing parameter, ε, above
D h(cid:48) A(cid:48)
8×104 areexcludedat90%C.L.[10].
2.3 Lowmassdarkmatter
Theinvisibledecayoftheϒ(1S)resonanceinvolvesneutrinoproductionviabb¯ annihilation
withBF[ϒ(1S)→νν¯](cid:39)10−5;lowmassDMshouldenhancethisBFifM >2M . The
ϒ(1S) χ
ARGUS,CLEO,BelleandBABARexperimentshavesearchedforinvisibledecaysoftheϒ(1S)
providingupperlimitstoBR(ϒ(1S)→invisible)<3.0×10−4 atthe90%C.L.[11,12,13,14].
TheBelleIIexperiment,withalargerdatasamplethanitspredecessorsthankstotheincreased
luminosity(×40Belleluminosity)andimproveddetectorperformance,willbeabletofurther
constraintheupperlimitonϒ(1S)→invisibleandeventuallyobservetheSMprocess
ϒ(1S)→νν¯ ifnonewphysicsisfound.
Duetothedisappearanceoftheϒ(1S)onehastoidentifytaggingalgorithmsthatwillbeusedto
unambiguouslyinferthepresenceoftheϒ(1S)→invisibledecay(theseare: di-piondecaysof
higherspinresonanceswithdatacollectedatenergiesequivalenttotheirmassandviaaninitial
stateradiationphotonfromdatacollectedattheϒ(4S)). Inadditiontothetaggingmodesforthis
particulardecaychannelonehastoconsideranirreduciblepeakingbackgroundduetotwo-body
decaysoftheϒ(1S)inwhichthedecayproductstraveloutsideofthedetectoracceptance. One
wouldconsiderallthetaggingmethodsmentionedbefore,undertheassumptionthatsimilaror
improvedperformanceoftheBelleIIdetectorisexpectedoverpreviousperformanceachievedby
theBelleexperiment. Thedecaysϒ(nS)→π+π−ϒ(1S)(n=2,3)mightbestudiedwithtotal
efficienciesbetween10%and20%. Table3showstheexpectedyieldsofϒ(1S)→invisiblefor
varioustaggingtechniques. ItisclearfromtheyieldsshowninTab.3thegreatdiscoverypotential
oftheBelleIIexperimentwhenlookingfornewphysicsintherareϒ(1S)→invisibledecay.
Table3:Expectedyieldsforvariousϒ(1S)taggingtechniqueswhereL istheintegratedluminosityconsid-
int
eredfortheextrapolationoftheyields,ε istheexpectedtotalefficiency,N(ϒ(1S))isthenumberofϒ(1S)
produced in the process, and N and N are the expected number of observed ϒ(1S)→invisible
ϒ(1S)→νν¯ NP
eventsassumingSM(1×10−5)andnewphysics(3×10−4)BF,respectively.
Process Lint(ab−1) ε N(ϒ(1S)) Nϒ(1S)→νν¯ NNP
ϒ(2S)→π+π−ϒ(1S) 0.2,ϒ(2S) 0.1-0.2 2.3×108 232-464 6960-13920
ϒ(3S)→π+π−ϒ(1S) 0.2,ϒ(3S) 0.1-0.2 3.2×107 32-64 945-1890
ϒ(4S)→π+π−ϒ(1S) 50.0,ϒ(4S) 0.1-0.2 5.5×106 5.5-11 165-310
ϒ(5S)→π+π−ϒ(1S) 5.0,ϒ(5S) 0.1-0.2 7.6×106 7.6-15.2 228-456
γISRϒ(2S)→(γISR)π+π−ϒ(1S) 50.0,ϒ(4S) 0.1-0.2 1.5×108 150-300 4500-9000
γISRϒ(3S)→(γISR)π+π−ϒ(1S) 50.0,ϒ(4S) 0.1-0.2 6.5×107 65-130 1950-3900
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