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Physics
Letters
B
www.elsevier.com/locate/physletb
Observation
of
the
Λ
0
b
→ Λφ
decay
.
The
LHCb
Collaboration
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received 10 March 2016
Received in revised form 13 May 2016 Accepted 24 May 2016
Available online 26 May 2016 Editor: W.-D. Schlatter
The Λ0
b → Λφ decay is observed using data corresponding to an integrated luminosity of 3.0 fb−
1 recorded by the LHCb experiment. The decay proceeds at leading order via a b→sss loop
transition and
is therefore sensitive to the possible presence of particles beyond the Standard Model. A first observation is reported with a significance of 5.9 standard deviations. The value of the branching fraction is measured to be (5.18 ±1.04 ±0.35+0.67−0.62)×10−6, where the first uncertainty is statistical, the second is systematic, and the third is related to external inputs. Triple-product asymmetries are measured to be consistent with zero.
©2016 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.
1. Introduction
Inthe StandardModel (SM),the flavour-changingneutral cur-rentdecay
Λ
b0→ Λφ
proceedsviaa b→
sss loop (penguin) pro-cess. AFeynman diagramofthe gluonicpenguin that contributes to this decayat leading order is displayed in Fig. 1. This transi-tionhasbeenthesubjectoftheoreticalandexperimentalinterest inB0s andB0 decays,sincepossiblebeyondtheSMparticlesinthe
loopcouldinducenon-SMCP violation[1–3].Theprocesshasbeen probedwithdecay-time-dependentmethodsinthe B0
s
→ φφ
and B0→
KS0φ
decaymodes[4–7],whichtestforCP violationinthe in-terferencebetweenmixing anddecay.In addition,measurements ofCP violationinthedecayhavebeenperformedwiththe flavour-specific B0→
K∗0φ
channel [8].Theresultstodateareconsistent withCP conservationintheb→
sss process.Model-independently, non-SMphysicscontributionscouldappeardifferentlyinthese de-caymodes,thoughmanymodelscontainstrongcorrelations[9].Measurementswith
Λ
0b baryonsofferthepossibilitytolookforCP violationinthedecay,bothbystudyingCP asymmetriesandby means of T -odd observables. These observableshave been stud-ied ingreater detail for B0
s and B0 meson decaysthan those for
Λ
0b baryons [4,8,10,11]. Proposedmethods to studyT -odd asym-metries ofΛ
0b baryons [12] exploit the polarisation structure ofΛ
0b→ Λ
V decays,where V denotesa vectorresonance[12],and can be affected by the initialΛ
0b polarisation if non-zero. An LHCb measurement ofthe initial polarisationinΛ
b0→
J/
ψΛ
de-cayshasyieldedavalueconsistentwithzero,though polarisation atthe levelof 10% ispossible givenstatisticaluncertainties [13]. NoSM predictionexists specificallyforthe T -oddasymmetriesinΛ
0b→ Λφ
decays,thoughnolargeasymmetriesareexpectedgiven thepredictionofCP conservationinthedecaysofbeautymesons for the same transition. Measurements of CP asymmetries haveFig. 1. Feynman diagram contributing to theΛ0b→ Λφdecay.
beenperformedbyLHCb inaninclusiveanalysisof
Λ
0b→ Λ
hh de-cays[14],whereh(
h)
referstoakaonorpion,withcorrespondingCP asymmetriesmeasuredtobeconsistentwithzero.
Inthispaper,a measurementofthe
Λ
0b→ Λφ
branching frac-tion is presented using the B0→
K0S
φ
decay asa normalisationchannel, which hasa measured branching fractionof
(
7.
3+−00..76)
×
10−6 [15]. The selection requirements used to isolate the
Λ
0b→
Λφ
decaywithwell-understoodefficienciesrejectsuitable control channelsforaACP measurement.The
Λ
0b→ Λφ
sample isthenusedtoperformmeasurements oftheT -oddtriple-product asym-metries, which do not require a control channel. The results are based on pp collision data corresponding to an integrated lumi-nosityof1
.
0 fb−1 and2.
0 fb−1 collectedbytheLHCb experiment at centre-of-mass energies of√
s=
7 TeV in 2011 and 8 TeV in 2012,respectively.2. Detectorandsimulation
The LHCb detector[16,17] isa single-armforward spectrome-tercoveringthepseudorapidity range 2
<
η
<
5,designedforthehttp://dx.doi.org/10.1016/j.physletb.2016.05.077
0370-2693/©2016 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.
studyofparticles containing b orc quarks. Thedetectorincludes a high-precisiontracking systemconsisting ofa silicon-strip ver-tex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream of the magnet.Thetrackingsystemprovidesa measurementof momen-tum, p,ofchargedparticleswitharelativeuncertaintythatvaries from0.5%atlowmomentumto1.0%at200 GeV
/
c.Theminimum distanceof atrack toa primary vertex, theimpact parameter, is measuredwitha resolutionof(
15+
29/
pT)
μm,where pT isthecomponentofthe momentum transverse to thebeam, inGeV
/
c.Different typesof chargedhadronsare distinguished using infor-mationfromtworing-imagingCherenkovdetectors.Photons, elec-tronsandhadronsareidentifiedbyacalorimetersystemconsisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. The online event selec-tionisperformedbyatrigger,whichconsistsofahardwarestage, basedoninformationfromthecalorimeterandmuonsystems, fol-lowedbya softwarestage,whichapplies a fullevent reconstruc-tion. At the hardware trigger stage, events are required to have amuon with high pT ora hadron,photon or electronwith high
transverseenergyinthecalorimeters.Forhadrons, thetransverse energy threshold is 3.5 GeV. In the subsequent software trigger, atleastone chargedparticle musthave a transverse momentum
pT
>
1.
7 GeV/
c and be inconsistent with originating from a PV.Finally,the tracks of two ormore of the final-state particles are requiredto forma vertexthat issignificantly displaced fromthe PVs.The final state particles that are identified as kaons are re-quiredto havea combinedinvariantmassconsistentwiththatof the
φ
meson.Inthesimulation,pp collisionsaregeneratedusingPythia8[18] witha specificLHCb configuration[19].Decaysofhadronic parti-cles are described by EvtGen [20], inwhich final-state radiation isgenerated using Photos[21]. The interaction ofthe generated particleswiththedetector,anditsresponse,areimplemented us-ingtheGeant4toolkit[22]asdescribedinRef.[23].Thedecaysof
Λ
0b baryonsare modelledaccordingtoa phase-spacedescription. Differencesin theefficiencies of protons andanti-protons, atthe sub-percentlevel,areaccountedforwiththeGeant4 implementa-tionofthedetectordescription.3. Selection
The
Λ
0b→ Λφ
andB0→
K0S
φ
decaysarereconstructedthroughthe
Λ
→
pπ
−, KS0→
π
+π
− andφ
→
K+K− final states,where the inclusion of charge conjugate processes is implied through-out the paper.Decays ofΛ
→
pπ
− and KS0→
π
+π
− are recon-structedintwodifferentcategories. Thefirstcategory containsΛ
(K0
S)hadronsthatdecayinsidethevertexdetectoracceptanceand
thesecondcontains
Λ
(KS0)hadronsthatdecayoutside.These cat-egories are referred to as long and downstream, respectively. The highresolutionofthe vertexdetectorleads toenhanced momen-tum,vertex,andmassresolutions forcandidatesinthelong cate-goryrelativetodownstreamcandidates.Boosteddecisiontrees (BDTs)[24,25] areusedtoseparate sig-nalfrombackground.DifferentBDTsaretrainedfordecayswhere thedaughtertracksofthe
Λ
(K0S)hadronareclassifiedaslongor
downstreamand accordingto whetherthe data was collected in 2011(7 TeV)or2012(8 TeV),yieldingeightseparateBDTsintotal. Thesetofinputvariablesusedtotrainthe
Λ
0b→ Λφ
(B0→
K0Sφ
) BDTs consistsoftheΛ
0b (B0) vertex fitquality, pT,η
,thediffer-encein
χ
2ofthePVreconstructedwithandwithoutthecandidate(
χ
2IP),theflightdistancesquareddividedbytheassociatedvariance
(
χ
2FD), the angle between the momentum vector and the vector
fromthePVtothedecayvertex,the
Λ
(KS0)vertexfitquality,and thepTandη
oftheφ
andtheΛ
(KS0)hadrons.TheminimumandmaximumvaluesofthepTand
η
associatedtothefinalstatepar-ticles arealso included.In addition,the BDT trainedon thelong category usesthe
χ
2IP and
χ
FD2 oftheΛ
(KS0) withrespectto theassociated PV. A PVis reconstructed by requiring a minimum of fivegood quality tracksthat are consistent withoriginatingfrom the same location within the luminous region. Before the BDTs are trained, initial loose requirements are imposed on the input variables.TheBDTsaretrainedusingsimulatedcandidatesforthe signal and data sidebands for the background. For the training samples,thesignalregionisdefinedasbeingwithin 150 MeV
/
c2oftheknown
Λ
b0(B0)mass[26].Inaddition,theK+K−invariantmass is required to be within 20 MeV
/
c2 of the knownφ
mass andthe pπ
− invariant mass isrequiredto be within 15 MeV/
c2oftheknown
Λ
mass[26].Thesidebandsaredefinedtobewithin 500 MeV/
c2 ofthe knownΛ
0b (B0) massexcluding thesignal
re-gion.
Thefigureofmeritusedtodeterminetherequirementimposed onthe
Λ
0b→ Λφ
BDT outputisdefinedasε
/(
3/
2+
Nbkg)
[27],where
ε
isthesignal efficiency,andNbkg isthenumberofback-ground events.This figure of merit is optimised fordetection at threestandarddeviationsofdecaymodesnotpreviouslyobserved. Thesignal efficiencyisobtainedfromsimulatedsignalcandidates andthenumberofbackgroundeventsiscalculatedfromfitstothe datasidebandsinterpolatedtothesignalregion.Thisoptimisation procedureisperformedseparatelyforeachBDT.
In contrast to the
Λ
0b→ Λφ
BDTs, the optimum response re-quirement for the B0→
KS0φ
BDTs is chosen based on a figure ofmerit definedas Nsig/
Nsig
+
Nbkg,where Nsig isthe numberof signal events,estimatedfrom theBDT efficiencyon simulated datasets normalised using the known branching fraction of the
B0
→
K0S
φ
decay[15], andNbkg isthe expectednumberofback-groundcandidates inthe signal region,extrapolatedfromthe B0
sidebands.Thisfigureofmeritischosenasthe B0
→
K0S
φ
branch-ingfractioniswell measuredandisoptimisedseparatelyforeach classifier.
4. Massfitmodel
Forboth the
Λ
0b→ Λφ
and B0→
K0S
φ
decay modes, athree-dimensional fit is employed to determine the signal candidate yields. In the
Λ
0b→ Λφ
case, the three dimensions are thep
π
−K+K−, pπ
−, and K+K− invariant masses, while in the fit todeterminethe B0→
KS0φ
candidateyield,thethreedimensions aretheπ
+π
−K+K−,π
+π
−,andK+K−invariantmasses.Four components are present in the B0
→
K0S
φ
mass fit: thesignal B0
→
K0S
φ
component, the B0→
K 0SK+K− non-resonant
contribution,a
π
+π
−K+K−combinatorialcomponent,alongwith a true K0S component combined with two random kaons. The B0
→
K0SK+K− non-resonant component has been observed by
the BaBar [28], Belle [6] and LHCb [29] Collaborations. This is separatedfrom thesignal decaythrough the different K+K− in-variant mass line shapes. No significant partially reconstructed background,inwhich oneormore ofthefinal state particlesare missed,isfoundintheB0 massregion.Peakingbackgrounds,from decaysin whichatleastone ofthe final state particleshas been misidentified,aresuppressedby thenarrowK+K− masswindow aroundthe
φ
mesonandaretreatedassystematicuncertainties.The B0 signal is modelled with the same modified Gaussian
function as used in Ref. [30]. The modified Gaussian gives extra degrees of freedom to accommodate extended tails far from the mean. The
φ
signal is modelled with a relativistic Breit–Wignershape[31]convolvedwithaGaussian resolutionfunction.The K0S
signalisparametrisedbythesumoftwoGaussianfunctionswitha commonmean.DecaysfromrealB0 mesonstotheK0
SK+K−final
stateinwhichtheK+K−pairisnon-resonantaredescribedbythe sameB0 andK0
S lineshapesasthesignal,butwithaphase-space
factor to describe the non-resonant kaon pairs. The phase-space factorisgivenbytheexpression
(
m2−(
2mK)
2)/
m2,wherem isthe K+K− invariantmassandmK isfixedtothevalueofthechargedkaonmass.TheuseofaFlattéfunction[32] ratherthana phase-spacefactortodescribea possiblescalarcomponentunderthe
φ
resonanceisfoundtohaveanegligibleeffectontheresultsandis thereforenot included.Thecombinatorialbackgroundismodelled byexponentialfunctionsinallthreemassdimensions.
Asimultaneousfittothelonganddownstreamdatasetsis per-formed.The B0 resolution,modifiedGaussian tailparameters and
resolutions and fractions of the K0S Gaussian functions are con-strainedtovaluesobtainedfromafittosimulateddata,performed separately forlong anddownstreamdatasets. Thetotal yield and fractioninthedownstreamdatasetareleft asfreeparameters for eachcomponent.
The fit to the
Λ
0b→ Λφ
channel uses the same fit model as the B0→
K0S
φ
control channel: a modified Gaussian function isusedtodescribethe
Λ
0b massshape,adoubleGaussianmodelto describe theΛ
shape, and a relativistic Breit–Wigner convolved witha Gaussianresolutionfunctiontodescribethat oftheφ
res-onance. Due to the relatively unexplored mass spectra present in theΛ
b0→ Λφ
decay, the backgroundcontributions havebeen identified using the data sidebands. In the final fit, four com-ponents are present. These are the signalΛ
b0→ Λφ
component, theΛ
0b→ Λ
K+K−non-resonant componentinwhichthe K+K−dimensionisdescribedusingthephase-spacefactordefined previ-ously,combinatorialcomponentswithtrue
φ
orΛ
resonances,and acomponentthathasa combinatorialorigininallthreemass di-mensions.Combinatorialbackgroundsaremodelledbyexponential functionsineach fitdimension.As forthecaseofthe B0→
K0S
φ
fit,thetotalyieldandfractioninthedownstreamdatasetareleft asfree parametersforeachcomponent.Inaddition,thesame pa-rametersareconstrainedtosimulateddataasinthe B0
→
K0S
φ
fit. 5. BranchingfractionmeasurementThe
Λ
0b→ Λφ
branchingfractionisobtainedfromtherelationB
(Λ
0b→ Λφ) =
tot B0→K0 Sφ
tot Λ0b→Λφ
·
fd fΛ0 b·
NΛ0b→Λφ NB0→K0 Sφ·
B
(
B0→
K0φ)
2·
B
(
KS0→
π
+π
−)
B
(Λ
→
pπ
−)
,
(1)where
tot denotes the combined efficiency ofthe candidate
re-construction, the offline selection, the trigger requirements, and the efficiencyof detectoracceptance; fd(Λ0
b) denotes the fraction
ofb quarksthathadronise to B0 (
Λ
0b)hadrons. Theratioistaken
fromtheLHCb measuredvalue fΛ0
b
/
fd=
0.
387±
0.
033 [33].Theextrafactor 1
/
2 inEq.(1) accountsforthe factthat only half ofK0 mesonswilldecayas KS0 mesons.The valueofthe B0
→
K0φ
branchingfractionistakentobe
(
7.
3+−00..76)
×
10−6 [15],whilethe PDGvaluesoftheΛ
andK0S branchingfractionsareused[26].The reconstruction, selection and software trigger efficien-cies, as well as the acceptance of the LHCb detector, are deter-mined from simulatedsamples, usingdata-driven correction fac-tors where necessary. The different interaction cross-sections of the final-stateparticles with thedetector material are accounted forusingsimulateddatasets.
For the case of the hardware trigger, the efficiency of events triggeredbythesignalcandidateisdeterminedfromcontrol sam-plesofD0
→
K−π
+andΛ
→
pπ
−decays.Theefficiencyofevents triggeredindependentlyofthesignalcandidateisdeterminedfrom simulation. The agreement between data andsimulation for the distributions ofthevariablesusedintheBDT isverifiedwiththeB0
→
KS0φ
data.Data-driven corrections for the reconstruction efficiency of tracks corresponding to thelong category areobtained from J
/
ψ
samples usinga tag-and-probemethod [34]. Thisisapplied after a separate weighting to ensure agreement indetector occupancy between data and simulation. For measurements of the relative branching fractionof
Λ
0b→ Λφ
to B0→
KS0φ
,the finalstate dif-fers by substituting the proton from the decay of theΛ
with a pion.However,duetothedifferencesinthekinematicsofthe pi-ons fromtheΛ
andtheK0S decays,thedistinctcorrection factors
forbothdaughtersofthe
Λ
andKS0 areconsidered.Inadditionto thetrackreconstructionefficiency,thevertexingefficiencyof long-livedparticlescontainsdisagreementbetweendataandsimulation. Thecorrespondingcorrectionfactorsforthelonganddownstream datasetsaredeterminedseparatelyfromD0→ φ
K0S decays.
Theyieldsofthe
Λ
0b→ Λφ
signalandB0→
KS0φ
controlmode are determined fromsimultaneous extendedunbinned maximum likelihood fits tothe respectivedatasets divided accordingto the data-takingperiodandalsoaccordingtowhethertheΛ
(
K0S
)
decayproductsarereconstructedaslongordownstreamtracks. Efficien-ciesareappliedtoeachdatasetindividually.Theprojectionsofthe fit resultto
Λ
0b→ Λφ
dataare showninFig. 2.The fittedyields are 350±
24 and89±
13 forthe B0→
KS0φ
andΛ
b0→ Λφ
de-caymodes,respectively.ThestatisticalsignificanceoftheΛ
b0→ Λφ
decay,determined accordingtoWilks’ theorem[35] fromthe dif-ference in the likelihood value of the fits with and without the
Λ
0b→ Λφ
component,isfoundtobe6.
5 standarddeviations.With the systematicuncertainties discussedbelowincluded,the signif-icance of the observedΛ
0b→ Λφ
decay yield is calculated to be 5.
9 standard deviations. The projections of the fit result to theB0
→
K0Sφ
data are shownin Fig. 3. The fit is found to describe the data well in all three dimensionsand a clearpeak from the controlmodeisseen.The systematiccontributions to the branching fraction uncer-taintybudgetaresummarisedinTable 1.Thelargestcontributions tothesystematicuncertaintiesresultfromdata-drivencorrections appliedtosimulateddataalongwiththemassmodelusedto de-terminethesignalyields.
Signal mismodellingis accountedforusing a one-dimensional kernelestimateforthedescriptionofthesimulatedmass distribu-tions[36].Backgroundmismodellingisaccountedforusingalinear function.Thekernelestimateisusedinboththesignalandcontrol channelstodescribethe
Λ
0b,B0,K0S,and
Λ
lineshapes.Inordertodetermine the systematic uncertainties, 1000 pseudoexperiments aregeneratedwiththealternativemodelandaresubsequently fit-ted withthenominalmodel.The averagedifference betweenthe generatedandfittedyieldvaluesistakenasthesystematic uncer-tainty. Thisleads to uncertainties of3.0% and0.6%for thesignal andcontrolmodeyields,respectively.
Systematic uncertainties associatedwith theefficiency correc-tions from simulateddatasets areconsidered. The limitedsize of the simulated sample gives rise to an uncertainty of 2.2%. The main uncertainties in the tracking and vertexing correction fac-torsarisefromthelimitedsizeofthecontrolsample,whichleads touncertainties of0.5% and2.6%,respectively.Forthecaseofthe triggerefficiency,uncertaintiesrelatedtothesoftwaretrigger can-celbetweenthesignal andcontrolmodes, asthesoftwaretrigger decisionismadeonlyonthedecayproductsofthe
φ
meson.Un-Fig. 2. Fit
projections to the
pπ−K+K−invariant mass in the (a) long and (b) downstream datasets, the K+K−invariant mass in the (c) long and (d) downstream datasets,and the pπ−invariant mass in the (e) long and (f) downstream datasets. The total fit projection is given by the blue solid line. The blue and green dotted lines represent the φ+ Λand pure combinatorial fit components, respectively. The red and magenta dashed lines represent the Λ0
b→ Λφsignal and the Λ0b→ ΛK+K−non-resonant components, respectively. Black points represent the data. Data uncertainties are Poisson 68% confidence intervals. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
certaintiesintheefficiencyofthehardware triggerselectionsare estimatedusingdata-drivenmethods,forwhichanuncertaintyof 2.8%isapplied.The BDTsusedtoselectsignal andcontrolmodes usethesame inputvariables. Biasescould exist ifthesimulation mismodelsthesevariablesdifferentlyforsignalandcontrolmodes. Inordertoquantifythiseffect,thecontrol modeisselectedwith thesameclassifierasthesignaldecay.Thedifferenceinthe mea-suredbranchingfractionisfoundtobe4.1%.
The
Λ
0b→ Σ
0(
→ Λ
γ
)
K+K− andΛ
0b→
p K−φ
decay modes arefoundtobetheonlysignificantpeakingbackground contribu-tions.However,forthecaseoftheΛ
0b→
p K−φ
decay,the result-ingcandidatesarereconstructedinthelongdatasetonly.Withthe assumptionthatthebranchingfractionforthisdecayisthesame size asfor the signal, the contribution is<
1% compared to theΛ
0b→ Λφ
decayandfarfromtheΛ
b0signalregion,andistherefore ignored.Inordertodeterminetheshapeinthe pπ
−K+K− spec-trumoftheΛ
0b→ Σ
0K+K− decay,a sample ofΛ
0b→ Σ
0K+K−simulatedevents isused witha requirement that the K+K− in-variant mass is within 30 MeV
/
c2 of the nominalφ
mass. The inclusionofanadditionalfitcomponentusingtheshapefrom sim-ulationis foundto havea smalleffect onthe signal yield atthe levelof0.1%,whichisassignedasasystematicuncertainty.Forthe caseofthe B0→
K0S
φ
control mode,nopeakingbackgroundcon-tributionshavebeenidentified.
Thebranchingfractionratioismeasuredtobe
B
(Λ
0b→ Λφ)
B
(
B0→
K0 Sφ)
=
0.
55±
0.
11 (stat)±
0.
04 (syst)±
0.
05(
fd/
fΛ0 b).
Theuseoftheworldaveragevalueof
B(
B0→
K0S
φ)
=(
3.
65+0 .35 −0.30)
×
10−6[15]givesthefinalresultof
B
(Λ
0b→ Λφ)/
10−6=
5.
18±
1.
04 (stat)±
0.
35 (syst)+0−0..5043(
B
(
B0→
KS0φ))
±
0.
44(
fd/
fΛ0 b).
6. Triple-productasymmetries
The
Λ
0b→ Λφ
decayisaspin-1/
2 tospin-1/
2 plusvector tran-sition. Five angles are needed to describe this decay sinceΛ
0bbaryons maypotentially be produced witha transverse polarisa-tioninproton–protoncollisions[13],asshowninFig. 4.Theangle
θ
is definedas the polar angle of theΛ
baryon in theΛ
0b rest framewithrespecttothenormalvectordefinedthroughˆ
n=
p1×
pΛ0 b|
p1×
pΛ0 b|
,
(2)wherep
1isthemomentumofanincomingprotonandpΛ0 b isthemomentumofthe
Λ
0b baryon.Theanglesθ
Λ andΛ aredefined
as thepolar and azimuthal angles of the protonfrom the decay ofthe
Λ
baryon intheΛ
rest frame.The anglesθ
φ andφ are
definedasthepolarandazimuthalanglesoftheK+mesoninthe restframeofthe
φ
meson.Triple-productasymmetries,whichareoddundertime-reversal, havebeenproposedby LeitnerandAjaltouni usingtheazimuthal angles
n
i,i∈ {Λ,
φ
}
,definedas[12]Fig. 3. Fit
projections to the
π+π−K+K− invariant mass in the (a) long and (b) downstream datasets, the K+K− invariant mass in the (c) long and (d) downstreamdatasets, and the π+π−invariant mass in the (e) long and (f) downstream datasets. The total fit projection is given by the blue solid line. The green and blue dotted lines represent the combinatorial and K0
S+random K+K−fit components, respectively. The red and magenta dashed lines represent the B 0→K0
Sφsignal and the B 0→K0
SK+K− non-resonant components, respectively. Black points represent the data. Data uncertainties are Poisson 68% confidence intervals. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1
Systematic uncertainty contributions to the branch-ing fraction ratio.
Source Uncertainty (%)
Mass model 3.0
Simulation sample size 2.2
Tracking efficiency 0.5 Vertex efficiency 2.6 Hardware trigger 2.8 Selection efficiency 4.1 Peaking background 0.1 Total 6.7 cos
ni
=
eY·
ui,
(3) sinni
=
eZ· (
eY×
ui),
(4) where ui=
eZ× ˆ
ni|
eZ× ˆ
ni|
.
(5)Thebasis
{
eX,
eY,
eZ}
isdefinedintheΛ
0b restframe,inwhicheZisparallel to n,
ˆ
eX is chosen to be parallel tothe momentum oftheincomingproton,andn
ˆ
Λ(φ) isthenormalvector totheΛ(φ)
decayplane,definedthrough
ˆ
nΛ=
pp×
pπ|
pp×
pπ|
,
(6)ˆ
nφ=
pK+×
pK−|
pK+×
pK−|
.
(7)Asymmetriesincos
n
i andsinn
i,where i∈ {Λ,
φ
}
,aredefinedas Aci
=
N +,c i−
N−, c i Ni+,c+
N−,i c,
(8) Asi=
N +,s i−
N−, s i Ni+,s+
N−,i s,
(9)where N+(−),i c and N+(−),i s denotethe number ofcandidates for which thecos
n
i andsinn
i observablesare positive (negative),respectively.
The asymmetries AcΛ,s and Acφ,s are determined experimen-tallythrough asimultaneousunbinnedmaximumlikelihoodfitto datasets inwhichtherelevantobservablesare positiveand nega-tive.Thefitconstructionandobservablesareidenticaltothatused for the branching fraction measurement. However, the yields for each datasetareparametrisedintermsofthetotalyield, Nj,and
theasymmetry,Aj,forfitcomponent j as
N+j
=
N j 2(
1+
Aj),
(10) N−j=
N j 2(
1−
Aj).
(11)Distributionsofthesin
n
(Λ,φ) andcosn
(Λ,φ) observablesfromΛ
0b→ Λφ
data have beenextracted using the sPlot method [37] andareprovidedinFig. 5.Thenumericalvaluesofthefitted asym-metriesaregiveninTable 2.Mismodelling of the mass components could lead to back-groundcontaminationinthedeterminationoftheasymmetries.In
Fig. 4. Decay angles for theΛ0
b→ Λφdecay, where the angles are defined in the text.
Fig. 5. Distributions of the angular observables: (a) sinnΛ, (b) cosnΛ, (c) sinnφ, (d) cosnφfrom weightedΛ
0
b→ Λφdata.
Table 2
Asymmetries measured from Λ0b→
Λφdata events.
Asymmetry Fit value
Ac Λ −0.22±0.12 As Λ 0.13±0.12 Ac φ −0.01±0.12 As φ −0.07±0.12
the determinationof the uncertainty relatedto the mass model, twocontributionsareconsidered.Thesearethelineshapemodels andthebackgroundasymmetries.Theeffectsofthelineshapesare quantifiedusingthesamemethodasthebranchingfraction mea-surement, i.e. the generation of datasets with a one-dimensional kernel estimate of the simulation mass distributions in addition tomodificationofthe backgrounddescription.Inthenominalfit, components that are not from the
Λ
0b→ Λφ
signal have zeroasymmetries. Forbackground componentsthis isjustified dueto theuncorrelatedkinematicsoftheK+K−andp
π
−systems. How-ever, the non-resonantΛ
0b→ Λ
K+K− contribution could have non-zero asymmetries.The systematicuncertaintydueto the as-sumptionofzerobackgroundasymmetriesisdeterminedthrough comparing thenominalfit againstthe fitwithall possible asym-metriesallowedtovaryfreely.Efficiencies are found to be independent of the sin
n
i andcos
n
i observables.The systematicuncertainty dueto theangu-laracceptanceisthentakenfromthestatisticaluncertaintyinfits to thesimulated datasets,after theapplication ofan appropriate weighting toaccount forthedifferencesbetweendata and simu-lation.The resolutions oftheangularobservables arefound from simulatedeventstobe32.3 mrad and22.1 mrad forthe
n
Λ andn
φ angles, respectively. The uncertaintydueto bin migration isthen assigned assuming maximal asymmetry and leads to minor uncertainties of 0.007 for the
n
φ angle and 0.010 for then
ΛTable 3
Systematic uncertainty contributions to the triple-product asymmetries.
Source Ac Λ AΛs Acφ Aφs Mass model 0.061 0.051 0.026 0.009 Angular acceptance 0.010 0.010 0.010 0.010 Angular resolution 0.008 0.008 0.005 0.005 Total 0.062 0.053 0.028 0.014
angle. Systematic contributions to the triple-product uncertainty budgetaresummarisedinTable 3.
7. Summary
A search for the
Λ
0b→ Λφ
decay is presented based on a datasetof3.
0 fb−1collected bytheLHCb experimentin2011and 2012. Thedecayisobservedforthefirst timewithasignificance of5.
9 standarddeviations includingsystematicuncertainties.The branchingfractionisfoundtobeB
(Λ
0b→ Λφ)/
10−6=
5.
18±
1.
04 (stat)±
0.
35 (syst)+−00..4350(
B
(
B0→
KS0φ))
±
0.
44(
fd/
fΛ0b).
Triple-productasymmetriesaremeasuredtobe
AcΛ
= −
0.
22±
0.
12 (stat)±
0.
06 (syst),
AsΛ
=
0.
13±
0.
12 (stat)±
0.
05 (syst),
Acφ
= −
0.
01±
0.
12 (stat)±
0.
03 (syst),
Aφs
= −
0.
07±
0.
12 (stat)±
0.
01 (syst),
andare consistent withzero. Data collected by the LHCb exper-iment in the forthcoming years will improve the statistical pre-cision ofthesemeasurements andenable thedynamics ofb
→
stransitionsinbeautybaryonstobeprobedingreaterdetail,which willgreatlyenhancethereach ofsearchesforphysics beyondthe SM.
Acknowledgements
We express our gratitude to our colleagues in the CERN ac-celerator departments forthe excellent performance of the LHC. We thank the technical and administrative staff atthe LHCb in-stitutes. We acknowledge support from CERN and from the na-tional agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy);FOMandNWO (TheNetherlands);MNiSW andNCN (Poland);MEN/IFA (Romania); MinESand FANO(Russia); MinECo (Spain);SNSFandSER(Switzerland);NASU(Ukraine);STFC(United Kingdom); NSF (USA). We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Ger-many), INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (UnitedKingdom), RRCKIandYandexLLC(Russia), CSCS (Switzer-land),IFIN-HH(Romania),CBPF(Brazil),PL-GRID(Poland)andOSC (USA). We are indebted to the communities behind the multi-pleopen sourcesoftwarepackagesonwhichwe depend. Individ-ualgroupsormembers havereceivedsupport fromAvH Founda-tion(Germany),EPLANET,MarieSkłodowska-CurieActionsandERC (European Union), Conseil Général de Haute-Savoie, Labex ENIG-MASSandOCEVU,RégionAuvergne(France),RFBRandYandexLLC (Russia),GVA,XuntaGalandGENCAT(Spain),HerchelSmithFund, The Royal Society, Royal Commission for the Exhibition of 1851 andtheLeverhulmeTrust(UnitedKingdom).
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LHCbCollaboration