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Physics Letters B 784 (2018) 101–111Contents lists available at ScienceDirectPhysics
Letters Bwww.elsevier.com/locate/physletbObservation of the decay Λ0b→ Λ+cppπ−
Onderwater, C. J. G.; LHCb Collaboration
Published in:
Journal of High Energy Physics
DOI:
10.1016/j.physletb.2018.07.033
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Onderwater, C. J. G., & LHCb Collaboration (2018). Physics Letters B 784 (2018) 101–111Contents lists
available at ScienceDirectPhysics Letters Bwww.elsevier.com/locate/physletbObservation of the decay
Λ0b→ Λ+cppπ−. Journal of High Energy Physics, 784, 101-111.
https://doi.org/10.1016/j.physletb.2018.07.033
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Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Observation
of
the
decay
Λ
b
0
→ Λ
+
c
p p
π
−
.
LHCb
Collaboration
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received27April2018
Receivedinrevisedform29June2018 Accepted17July2018
Availableonline25July2018 Editor: W.-D.Schlatter
ThedecayΛ0b→ Λ+cp p
π
−isobservedusingpp collisiondatacollectedwiththeLHCbdetectorat centre-of-massenergiesof√s=7 and8 Tev,correspondingtoanintegratedluminosityof3 fb−1.Theratioof branchingfractionsbetweenΛb0→ Λ+cp pπ
−andΛ0b→ Λ+cπ
−decaysismeasuredtobeB(Λ0b→ Λ+cp p
π
−) B(Λ0b→ Λ+cπ
−)=0.0540±0.0023±0.0032.
Two resonant structures are observed in the Λ+c
π
− mass spectrum of the Λ0b→ Λ+cp pπ
− decays, corresponding tothe Σc(2455)0 and Σc∗(2520)0states. Theratios ofbranchingfractionswith respect tothedecayΛb0→ Λc+p pπ
−areB(Λ0b→ Σc0p p)×B(Σc0→ Λ+c
π
−) B(Λ0 b→ Λ+cp pπ
−) =0.089±0.015±0.006, B(Λ0b→ Σ∗0 c p p)×B(Σc∗0→ Λ+cπ
−) B(Λ0b→ Λ+c p pπ
−) =0.119±0.020±0.014.Inalloftheaboveresults,thefirstuncertaintyisstatisticalandthesecondissystematic.Thephasespace isalsoexaminedforthepresenceofdibaryonresonances.Noevidenceforsuchresonancesisfound.
©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
The quark model of Gell-Mann [1] and Zweig [2] classifies mesons (qq) and baryons (qqq) into multiplets, and also allows forhadronswithmorethantheminimalquark contents.In2015, LHCbobservedtwopentaquarkstatesinthedecay
Λ
0b→
J/ψ
p K−[3].Inthedecaychannel
Λ
0b→ Λ
+c p pπ
−,1charmeddibaryon res-onantstatescouldbepresent.AsdiscussedinRef. [4],suchstates could manifest via the decayΛ
0b→
p+ [
cd][
ud][
ud] =
p+
D
c+, whereD
c+ isthedibaryon statewithamassbelow4682 MeV/
c2. ThesubsequentdecayoftheD
c+dibaryoncouldproceedeithervia quark rearrangement to the final state pΣ
c0, withΣ
c0→ Λ
+cπ
−, or via string breaking to the final stateP
c0(
u¯
[
cd][
ud])
, which could involve a lighter, yet undiscoveredP
c0 pentaquark state,D
+c
→
P
c0(
u¯
[
cd][
ud])
p, withP
c0→ Λ
+cπ
− [4]. The discovery ofanyofthesedecaymodeswouldtestthe predictionsofquantum chromodynamics and the fundamental workings of the Standard Model.
1 Unlessexplicitlynoted,chargeconjugatedecaysareimplied.
InthisLetter,thefirstobservationofthedecay
Λ
b0→ Λ
+c p pπ
−,referred to as the signal channel, is reported. A measurement is made of its branching fraction relative to the normalisation channel
Λ
0b→ Λ
+cπ
−.Resonance structureswithin theΛ
+c p pπ
− systemarealsoinvestigated.Whilenoevidencefordibaryon reso-nancesisfound,significantcontributionsfromtheΣ
c(
2455)
0 andΣ
c∗(
2520)
0 resonances are found in theΛ
+cπ
− invariant massspectrum. The ratios of branching fractions between decays via these resonances, hereinafter denoted as
Σ
c0 andΣ
c∗0, and theΛ
+cp pπ
−inclusivedecayarealsoreported.Themeasurements in this Letterare basedon a data sample of pp collisions collected withtheLHCb detectoratcentre-of-massenergies of√
s=
7 Tev in 2011and√
s=
8 Tev in2012, corresponding to an integrated luminosityof3 fb−1.2. Detectorandsimulation
The LHCb detector [5,6] is a single-arm forward spectrome-tercoveringthe pseudorapidity range2
<
η
<
5,designedforthe studyofparticles containingb or c quarks.The detectorincludes a high-precision trackingsystem consistingof a silicon-stripver-https://doi.org/10.1016/j.physletb.2018.07.033
0370-2693/©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
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. Different typesofcharged hadronsare distinguished us-ing information from two ring-imaging Cherenkov (RICH) detec-tors.Photons,electrons andhadronsareidentifiedby a calorime-ter system consisting of scintillating-pad and preshower detec-tors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating lay-ersofironandmultiwireproportionalchambers.Theonlineevent selection isperformedby atrigger [7], whichconsistsofa hard-warestage,basedoninformationfromthecalorimeterandmuon systems,followedbyasoftwarestage,inwhichallcharged parti-cleswith pT
>
500(
300)
MeV/
c arereconstructedfor2011(2012) data,where pT isthetransversemomentum [7]. Atthehardware trigger stage, events are required to contain a muon or dimuon pair with high pT, or a hadron, photon or electron with high transverseenergydepositedinthecalorimeters.Thesoftware trig-ger requires a two-, three- or four-track secondary vertex with a significant displacement from any primary proton–proton in-teraction vertices (PVs). At least one chargedparticle must have a pT>
1.
7(
1.
6)
GeV/
c for2011 (2012) data,and be inconsistent withoriginating from a PV. A multivariate algorithm [8] is used fortheidentificationofsecondaryverticesconsistentwiththede-cayofab hadron.
Simulated samples of the signal, the normalisation channels and backgrounds produced in pp collisions are generated using Pythia [9] with a specific LHCb configuration [10]. Decays of hadronic particles are described by EvtGen [11], in which final-state radiationis generatedusingPhotos[12].The interaction of thegeneratedparticleswiththedetector,anditsresponse,are im-plementedusingtheGeant4toolkit [13] asdescribedinRef. [14].
3. Candidateselection
The
Λ
0b→ Λ
+c p pπ
− andΛ
0b→ Λ
+cπ
− candidates are recon-structed using the decayΛ
+c→
p K−π
+. An offline selection is applied, based on a loose preselection, followed by a multivari-ateanalysis. Tominimize the systematicuncertaintyon the ratio ofefficienciesbetweenthesignalandthenormalisationchannels, the selection criteriaon theΛ
c+ candidates are similar between thetwochannels.Reconstructed final-state particles in
Λ
b0→ Λ
+c p pπ
− andΛ
0b→ Λ
+cπ
− candidate decays are required to have amomen-tump
>
1 GeV/
c and pT>
100 MeV/
c.Protonsandantiprotonsare required to have p>
10 GeV/
c to improve particle identification. All final-state particles are also required to be inconsistent with originatingfromanyPV, by rejectingthetracks witha smallχ
2IP, where
χ
2IP is the difference in the vertex-fit
χ
2 of a given PV withorwithoutthetrackconsidered,requiring
χ
2IP
>
4.CandidateΛ
+c decaysare required tohave atleast one decayproduct with pT>
500 MeV/
c and p>
5 GeV/
c,a goodvertex-fitquality,andan invariant mass within±
15 MeV/
c2 of the knownΛ
+c mass [15]. ThescalarsumofthetransversemomentaoftheΛ
+c decayprod-uctsisrequiredtobegreaterthan1.8 GeV
/
c.The
Λ
+cπ
−candidateisreconstructedbycombiningaΛ
+c can-didatewith a pion, andthe signal candidate is reconstructed by combiningaΛ
+c candidatewitha pion,aprotonandanantipro-ton.These combinationsmustforma
Λ
0b candidatewitha good-qualityvertexandbe consistentwithoriginatingfromthe associ-atedPV,definedasthatforwhichtheΛ
0b candidatehastheleastχ
2IP. Furthermore, the
Λ
+c candidate is required to decaydown-streamofthe
Λ
0b decayvertex. TheΛ
0b decaytime,calculated ast
=
mΛ0bL
/
p, is required to be greater than 0.2 ps, where mΛ 0 b isthe mass, L is the decaylength and p is the momentum of the
Λ
0b candidate.TheΛ
0b candidateis alsorequired to haveatleast one final-state particle in the decay chain with pT>
1.
7 GeV/
c,p
>
10 GeV/
c,andhaveatleastonetracksignificantlyinconsistent withoriginatingfromtheassociated PVbyrequiring thetrackto haveχ
2IP
>
16.Final-statetracksofsignal andnormalisation chan-nelcandidatesmustpassstrictparticle-identificationrequirements based on the RICH detectors, calorimeters and muon stations. A constrainedfit [16] isappliedtothecandidatedecaychainforboth the signal andthenormalisation channels, requiringtheΛ
0b can-didate to comefrom the associatedPV andconstraining theΛ
+cparticle to its knownmass [15]. Inthe caseof thesearch of the resonant contributions,themassofthe
Λ
0b candidateisalso con-strainedtotheknownmass [15].Triggersignalsareassociatedwithreconstructedparticlesfrom the decays of the signal channel or of the normalisation chan-nel. Selection requirementscan thereforebe madeonthe trigger selection itself and on whether the decision was dueto the re-constructed candidate decay, other particles produced in the pp
collision, or a combination ofthe two. This association makes it possible to usea data-driven methodforthe correction and sys-tematic uncertainty estimation on the trigger efficiencies [7]. To take advantage ofthe similaritybetweenthe signal andthe nor-malisation channels, whichhelpsto minimize thesystematic un-certaintyontheratiooftheirefficiencies,candidatesareclassified inoneofthefollowingtwohardwaretriggercategories.Inthefirst category, calledTriggeredOnSignal(TOS), thecandidatemust in-cludeahadronconsistentwithoriginatingfromthedecayofa
Λ
+ccandidate and which deposited enough transverse energy in the calorimetertosatisfythehardwaretriggerrequirements.The typ-icalvalueofthetransverseenergythresholdisaround3.5 GeV
/
c2. As theΛ
+c baryon is aΛ
0b decay product for both the signal andthe normalisationchannels, thischoice minimizesthe differ-ence between theΛ
0b decay modes. The second category, called TriggeredIndependentofSignal(TIS),compriseseventswhich sat-isfied the hardware trigger through signatures unassociated with the completeΛ
0b decay chains, either dueto a muon withhighpT,ora hadron, photon,or electronwithhigh transverseenergy deposited inthecalorimeters.The efficienciesofthe TISandTOS requirementsaredifferent,sothedataaredividedintotwo statis-tically independentsamples, one TIS, andthe other TOS andnot TIS,whichwillbereferredtoasTOSfortherestofthisLetter.
The so-called cross-feed backgrounds, contributing under the peak of the invariant mass of the normalisation channel or of the signal channel from the B0
(
Bs0)
→
D+(
D+s)
π
− and B0(
B0s
)
→
D+(
D+s)
p pπ
− decays, respectively, with D+(
D+s)
→
K+K−π
+ or D+→
K−π
+π
+,whereeitherthekaon or pion is misidentified as a proton, are explicitly vetoed when both ofthefollowingtwo conditionsaresatisfied.First,the mass hypothesis oftheprotonfromtheΛ
+c candidateisreplacedwitheither the kaon or pion hypothesis, and the resulting invariant mass of the combination is consistent with the known D+
(
D+s)
mass [15] within
±
15 MeV/
c2. Second, theinvariant massof theΛ
+c candidateissettotheknown D+(
D+s)
mass [15],andthere-sulting invariantmassof the
Λ
b0 candidateisconsistent withthe known B0(
B0s
)
mass [15] within±
25 MeV/
c2 forΛ
0b→ Λ
+c p pπ
−decays,andwithin
±
45 MeV/
c2 forΛ
0b
→ Λ
+cπ
− decays.Further backgroundreduction isachievedusing amultivariate analysis based on a gradient boosted decision tree (BDTG) [17]. The BDTG is trained using twelve variables: the vertex-fit qual-ity ofthe
Λ
c+ andΛ
0b candidates,the decay-vertex displacementalong thebeamline betweenthe
Λ
0b andΛ
+c candidates, thethe associated PV, the
χ
2IP of the
Λ
0b candidate, the angle
be-tweenthereconstructed
Λ
0b momentumandthedirectionofflight fromthe associatedPV to the decayvertex, the smallest pT and smallestχ
2IP among the three
Λ
+c decay products, the pT andχ
2IP of the pion originating directly from the
Λ
0b decay, and thesmallest pT and smallest
χ
IP2 between the p and p originating directlyfrom theΛ
0b decay. The BDTG training is performed us-ing simulated samples for the signal, and data distributions for thebackground,withreconstructedinvariantmasswellabovethe knownΛ
b0 mass [15]. Cross-feed backgrounds from the decaysΛ
0b→ Λ
+cK+K−π
−, B0→ Λ
c+pπ
+π
− and Bs0→ Λ
+cp K+π
− areexplicitly vetoed during the BDTG-training process by requiring the difference between the reconstructed b-hadron mass and its knownmass tobe greater than
±
30 MeV/
c2. The BDTGselection isoptimizedforthefigureofmerit S/
√
S+
B,where S andB aretheexpectedsignal andbackgroundyields within
±
30 MeV/
c2 of the knownΛ
0b mass [15]. The initial value of S and B withoutBDTGselectionisobtainedfromthe
Λ
0bmassspectrumindata.No improvementinthenormalisationchannel isfoundusinga simi-larprocedure,thereforenoBDTGselectionisapplied.Asystematic uncertaintyisassessedforthischoiceinSection6.Duetothe largenumberoffinal-stateparticles inthe
Λ
0b de-cays, particles with the same charge may share track segments, representing a possible background. These tracks are referred to asclones,andaresuppressedbyrequiringthattheopeningangle betweenanysame-charged tracksin thecandidate islarger than 0.5 mrad. This selection removes 2% of candidates in the signal sampleand0.1%inthenormalisationsample. IfmultipleΛ
0b can-didatesarereconstructedinonesingleevent,onecandidateis cho-senatrandominthefollowingtwocases.First,iftheprotonfrom theΛ
+c decaysisexchangedwiththatdirectlyfromtheΛ
0b decays,formingtwocandidateswithnearlythesame
Λ
0b mass.Second,if a track fromone candidate shares a segment witha trackfrom another candidate.With these criteria, 2.5% of candidates in the signalsampleand0.1%inthenormalisationsamplearevetoed. Af-tertheseselections, 0.8%ofeventsin thesignalsample and0.2% inthenormalisationsamplecontainmultipleΛ
0bcandidates.These remaining multiplecandidates mainlyoriginate fromthe random combinationsofthefinal-statetracks,andhaveanegligible influ-enceontheestimation ofthesignal yields. No furthervetoes on thesecandidatesareapplied.4. Efficiencies
Thetotalefficienciesofthesignalandthenormalisationdecays aregivenby
total
=
a
·
rec&sel|a
·
trig|sel
·
PID
,
(1) wherea represents thegeometrical acceptance ofthe LHCb de-tector,
rec&sel|a is the efficiency of reconstruction and selection calculated on candidates in the acceptance,
trig|sel is the trig-gerefficiencyoftheselected candidates,and
PID isthe particle-identificationefficiency.Allefficienciesexcept
PID and
trig|selare determined from simulation.The particle-identification efficiency is determined from calibration data specific to each data-taking year, binned in momentum and pseudorapidity of the track in question, as well as in the multiplicity of the event [18]. The trigger efficiency is determined from a combination of simula-tion and data-driven techniques where the agreement between dataand simulationis explicitly verified usingthe normalisation sample satisfying the TIS requirement. All efficiencies are calcu-lated separately for the TIS and TOS trigger samples, and for data-takingyear,duetothedifferenceincentre-of-massenergies.
Agreementbetweendataandsimulationisimprovedby applying aper-candidateweighttothepT andrapidity, y,ofthe
Λ
0bbaryon insimulatedeventstomatchthenormalisationsampleintheTIS category, which is largely independent of trigger conditions.ThepTand y distributionsof
Λ
0bproducedinpp collisionareidentical for the signal andthe normalisation channels, so the same per-candidateweightsareappliedtothesignalsample.Thesimulatedχ
2IP ofthe final-stateparticles andthevertex-fit
χ
2 ofΛ
+c
candi-dates are weighted to reproducethe datadistributions. The ratio betweentheefficienciesofthesignalandthenormalisation chan-nels,
r,is
(
10.
00±
0.
12)
% fortheTISsampleand(
11.
39±
0.
22)
%fortheTOSsample,includinguncertaintiesduetothelimitedsize ofthesimulatedsample.
5. Fitmodelandtheratioofbranchingfractions
The yields in both the signal and the normalisation channels are determined froman unbinned extended maximum-likelihood fitto thecorresponding invariant-mass spectrawithboththe TIS andTOS samples combined.The signal is modelled by a sum of twoCrystalBallfunctions[19] withacommonmeanofthe Gaus-siancore, andwiththetailparametersfixed fromsimulation.For both the signal and the normalisation channels, the background fromrandomcombinationsof final-stateparticlesisdescribed by an exponential function, whose parameters are left free in the fits and are independent betweenthe signal and the normalisa-tionchannels.Forthenormalisationchannel,backgroundfromthe
Λ
b0→ Λ
+cρ
−decays,withρ
−→
π
−π
0ismodelledbytheconvo-lutionofan empirical thresholdfunctionwitha Gaussian resolu-tion.Thecontributionduetomisidentificationofthekaontopion from
Λ
0b→ Λ
+cK− ismodelledbyasumoftwoCrystalBallfunc-tions. Theparameters ofthesetwobackground sourcesare taken from simulation. The fits to the invariant-mass distributions for thesignal andthenormalisationchannelsareshowninFig. 1.In thisfigure,theTISandTOSsamplesarecombined.Fromthesefits, 926
±
43Λ
0b→ Λ
+cp pπ
−and(
167.
00±
0.
50)
×
103Λ
0b
→ Λ
+cπ
−decaysareobserved.
To determine the ratio of branching fractions B(Λ
0
b→Λ+cp pπ−) B(Λ0
b→Λ+cπ−)
, indicated inthe followingby
B
r,a simultaneousfit isperformedto the signal and the normalisation channels, each divided into the two independent trigger categories. The yield of the nor-malisation sample, N
(Λ
0b→ Λ
c+π
−)
, is a free parameter in thefits, whereas the yield of the signal sample is calculated as
N
(Λ
0b→ Λ
+c p pπ
−)
=
B
r×
r
×
N(Λ
0b→ Λ
c+π
−)
, wherer is the
ratio between the total efficiency of the
Λ
0b→ Λ
+cp pπ
− andΛ
b0→ Λ
+cπ
− decays. The ratio of branching fractionsB
r is thesame for the TIS and TOS subsamples and is measured to be
B
r=
0.
0542±
0.
0023.The corresponding signal yields are 677±
29 forthe TISsubsample and259
±
11 forthe TOS subsample; theyieldsinthenormalisationsampleare(
124.
9±
0.
4)
×
103 for theTISsubsampleand(
41.
9±
0.
2)
×
103 fortheTOSsubsample.6. Systematicuncertainties
The systematicuncertainties on themeasurement ofthe ratio of branching fractions are listed in Table 1. The total systematic uncertaintyisdeterminedfromthesuminquadratureofallterms. First, the uncertainty related to the background modelling is considered. In the signal sample, the exponential function is re-placedwithasecond-orderpolynomialforthebackground compo-nent.Forthenormalisationchannel,themodelisvariedby using thesumoftwoexponentialfunctions.Theresultinguncertaintyon the ratio ofbranching fractions is 0.6%. The uncertainties dueto the
Λ
0b→ Λ
+c K−shapeparametersareassessedbyincreasing theFig. 1. Invariantmassdistributionsofthe(a)Λ0
b→ Λ+cp pπ− and(b)Λ0b→ Λ+cπ− candidates.Fitresultsareoverlaidasasolidblueline.For(a),thereddottedline
representsthesignalcomponentandthegreendottedlinethebackgroundduetorandomcombinations.For(b),thereddottedlineisthesignalcomponent,thegreendotted lineistherandomcombinationbackground,thepurpledashedlineisthecontributionfromΛ0b→ Λ+cρ− andthebrowndashed–dottedlinerepresentsthecontribution
fromΛ0
b→ Λ+cK−.(Forinterpretationofthecoloursinthefigure(s),thereaderisreferredtothewebversionofthisarticle.)
Table 1
Summaryofsystematicuncertaintiesandcorrectionfactorstotheratioofbranchingfractions measurement.Alluncertaintiesaregivenasapercentageoftheratioofbranchingfractions.
Source Uncertainty (%) Correction factor
Background fit model 0.7 –
Signal fit model 0.1 –
PID efficiency 0.3 –
Tracking efficiency calibration 0.8 0.985 Kinematic range of final-state tracks 0.7 –
Hadron interaction 4.4 –
pT,y weighting 1.0 –
Trigger efficiency 2.9 –
Simulated sample size 1.3 –
Candidates with clone tracks and multiple candidates 0.2 – Veto of the reflection background 0.4 –
Λ+c Dalitz weighting 0.2 0.984
Λ+c polarization 0.3 0.987
Resonant structures 1.8 1.041
Total 6.0 0.996
widthofthe Crystal Ballfunctionsby 10%,corresponding to two standarddeviations,resultinginachangeof0.1%.Theuncertainty duetothe
Λ
0b→ Λ
c+ρ
− contributionisestimatedby varyingthe shapeparametersbyonestandarddeviation,resultinginan uncer-taintyof0.4%.Thetotaluncertaintyonthe ratioofthebranching fractionsduetothebackgroundmodellingis0.7%.Thesignal-modelparameterizationischangedtoasingle Hypa-tiafunction [20],wherethemean andwidthare allowedto float andallotherparametersaretakenfromsimulation,resultinginan uncertaintyof0.1%.
Theuncertainty onthe relativeefficiencyof theparticle iden-tification is assessed by generating pseudoexperiments. For each pseudoexperiment, efficiencies in different momentum, pseudo-rapidity and multiplicity bins are determined from independent Gaussiandistributions withmeanvaluesequaltothenominal ef-ficiencies and widths corresponding to their uncertainties. This procedure is repeated 1000 times, and the width of the result-ing efficiency is taken asthe systematic uncertainty. This proce-dure, performed separately for the TIS and TOS samples, results in a 0.13% uncertainty for both samples. Binning effects on the efficiency are estimated by halving the bin size of the momen-tumdistributions,resultinginarelativechangeof0.2%fortheTIS sampleand0.1%fortheTOSsample.The totaluncertaintyonthe relativeefficiencyfortheTISandTOSsamplesis0.24%and0.16%, respectively,corresponding toan uncertaintyof0.3% onthe ratio ofthebranchingfractions.
Tracking efficiencies are determined with simulated events weighted tomatchthe kinematicpropertiesofdedicated
calibra-tion samples. The weights are determined as a function of the kinematicvariables,separately foreachdata-taking year [21].The kinematic properties of the
Λ
c+ decay products are similar for the signal and the normalisation samples and therefore provide minorcontributionstothetotaltrackingefficiencyratio.The dom-inant contribution to the systematicuncertainty comes from the knowledge ofthe p and p tracking efficiencies,whosesystematic uncertainties are fullycorrelated. Theefficiencycorrection proce-dure gives a change inefficiency of2.0% for theTIS sample and 1.4%fortheTOSsample,yieldingatotalcorrectionfactorof0.985 for theratio ofbranching fractions, anda systematicuncertaintyof0.4% foreach ofthe p and p mainlystemming fromthefinite
sizeofthecalibrationsample [21].
Due todistinct triggerrequirements,thekinematicacceptance ofthe calibrationsamplesdiffersslightlyfromthesignal andthe normalisationchannels.Anonnegligiblefractionofcandidateshave final-state particles in a kinematic range outside of the regions covered by the calibrationsamples. About 20% of the candidates frombothchannelsfallinthiscategoryduetothelow-momentum pionfromthe
Λ
+c decay. Inaddition,10% ofthecandidatesfrom the signalchannel arealsoaffected,mainly dueto thepion orig-inating from theΛ
0b decay.For all of these outside-range candi-dates,theefficiencycorrectioninthenearestavailablebinisused. AstheeffectsforΛ
+c decayscancelintherelativeefficiency,onlythe additional 10% candidates in the signal channel contribute a 0.7%uncertaintyontherelativeefficiency.
HadronicinteractionswiththeLHCb detectorcontributean ad-ditionaluncertaintyof2.2%ontheratioofthebranchingfractions
foreach p orp (4.4%intotal),whichisobtainedfromsimulation, accountingfortheimperfectknowledgeofmaterialbudgetofthe LHCb detector[22].
Per-candidate weights depending on pT and y of the
Λ
0b baryon are applied in simulated events to improve the agree-ments betweendata andsimulation. Systematicuncertainties for theweighting dueto the finitesize of the normalisation sample areassessed withpseudoexperiments.Ineach pseudoexperiment, theweights are varied within their uncertainties, andtheresults are propagated to the ratio of branching fractions. The standard deviation of the obtained distributions is taken as a systematic uncertainty, resulting in 0.65% for the TIS sample and 0.65% for theTOS sample. Thesystematic uncertainties dueto the binning scheme of the weighting in pT and y are estimated by halving thebinsize,orusingthegradientboosting [23] [24],whichisan unbinnedmethodof weighting, tocheck the changeson the rel-ativeefficiencies.The resultingsystematicuncertaintiesare 0.43% fortheTISsampleand1.5%fortheTOSsample.Afterpropagation throughthe entirefitprocedure, thisresultsinan uncertaintyof 1.0%ontheratioofthebranchingfractions.TriggerefficienciesfortheTOSsamplesarealsoassessedusing pseudoexperiments which are propagated to the final measure-ment,resultinginafinaluncertaintyof0.1%.Thetriggerefficiency ofthe TISsample istaken fromsimulation.Its systematic uncer-taintyiscomputedfromthedifferencebetweentheTISefficiency taken from data and simulation for events which are triggered bothon the
Λ
+c candidateandalsoon other tracks unassociated tothesignaldecay.Asaresult,asystematicuncertaintyof3.9%is assignedfortherelative trigger efficiencyoftheTIS sample, cor-respondingtoanuncertaintyof2.9%ontheratioofthebranching fractions.The effect of the finite size of the simulated samples is as-sessedbyconsidering thepossiblevariationoftheefficiencywith weightedsamplesinabinof pTandrapidityofthe
Λ
0b candidate,andthecorresponding systematicuncertaintyonthe efficiencyof thesignalornormalisationchannel,TISorTOSsample,isgivenby
σ
=
ii
(
1−
i
)
Niwi/
i Niwi,
(2)wherefor each bin i, Ni is the number ofcandidates, wi is the
singleeventweight,and
i isthesingleeventefficiency.Thetotal
uncertaintyontherelativeefficiencyfortheTISandTOSsamples is1.2% and1.9%, respectively, corresponding to an uncertaintyof 1.3%ontheratioofthebranchingfractions.
Theuncertaintyduetotheremovalofcandidatesreconstructed withclonetracksandmultiplecandidatesisassessedbyapplying thesameproceduretosimulation,resultinginadifferenceof0.2%. Vetoes on the invariant mass of possible cross-feed back-groundsmaybiasthesignalmassdistributions.Anuncertaintyof 0.4%isdetermined bychangingthefitrangeofthenormalisation sampletobeginat5450 MeV
/
c2,insteadof5350 MeV/
c2.The agreement between data and simulation in the
Λ
c+→
p K−π
+ decayis alsotestedby comparing the Dalitz plot distri-butions. The normalisation sample is weighted in the m2(
p K−)
versus m2(
K−π
+)
plane. Due to the smaller sample size of the signal channel, weights obtained fromthe normalisation channel areappliedto thesignal. Theresultingprocedure rendersall dis-tributionsconsistentwithinonestatisticalstandarddeviation. The differencein theratioof branchingfractions is1.3% smallerthan thenominalresult,providing acorrection factorof0.984.An un-certainty of 0.2% is determined by using an alternative binning schemeandvaryingtheDalitz-plotweightsbytheirstatistical un-certainties.The polarization ofthe
Λ
0b particleshas beenmeasured tobe consistent withzero [25], but the weak decayof theΛ
0b baryon mayinduceapolarizationintheΛ
+c system.Inthesimulation,it is assumedthat theΛ
+c particleis unpolarized,leading to a dif-ference in angular distributions between simulation and data. A possibleeffectduetotheΛ
+c polarizationisassessedbyapplyinga weighting procedure to thedistribution of the
Λ
+c helicityan-gle,whichisdefinedastheanglebetweenthe
Λ
+c flightdirectioninthe
Λ
0b restframeandthedirectionofthep K− pairintheΛ
+crestframe.Thisweightisobtainedthroughacomparisonbetween theangulardistributionsinsimulationanddataforthesignaland the normalisation channels individually. Applying this weight to both the signal andthe normalisation channels doesnot change theefficiencywithrespecttoanyoftheotherpossibleangles,and leadstoachangeof1.1%intherelativeefficiencyfortheTOS sam-pleand1.4%fortheTISsample.Propagationoftheseuncertainties leads toacorrectionfactorof0.987ontheratioofthebranching fractions.An uncertaintyof0.3%isdetermined byusingan alter-nativebinningschemeandvaryingthesingle-candidateweightsby theirstatisticaluncertainties.
Simulateddataaregeneratedusingaphase-spacemodelforthe
Λ
b0 decay, whichdoes not take into account possible resonances in theΛ
+c p pπ
− system. Upon inspection, clearsignals from theΣ
c0 andΣ
c∗0 resonances are found,as described inSection 7. Toassess theeffect ofthese resonances, thesimulation is weighted toreproduce thedata.Weightsareapplied intwoinvariant mass dimensions,namelythe
Λ
+cπ
−invariantmassandanother invari-ant mass of any two or three body combination. Among these weighting strategies,applyingweights inm(Λ
+cπ
−)
andm(
pπ
−)
(option 1) leads to the smallest
B
r, while weights in m(Λ
+cπ
−)
andm
(
p pπ
−)
(option2)leadstothelargestB
r.Acorrectionfac-tor iscomputed asthe averageof thecentral values ofthe ratio ofbranchingfractionsforthetwooptionsdividedbythenominal branchingfraction,withanuncertaintydeterminedbyhalfthe dif-ferencebetweenthetworatiosofbranchingfractions.Thisleadsto acorrectionfactorof1.041anda resultingsystematicuncertainty of1.8%.
UncertaintiesduetotheuseoftheBDTGaretestedby repeat-ing the BDTG training andselection procedure to the normalisa-tionchannelwithoutvariablesrelatedtothe p p pair;theratioof branchingfractionsisfoundtobeconsistent.
7. Resonancestructuresinthe
Λ
+cπ
−massspectrumAs the resonant structure of
Λ
0b→ Λ
+cp pπ
− decays is unex-plored,the resonances in theΛ
+cπ
− system are studied.An un-binned maximum-likelihood fit oftheΛ
+cπ
− massis performedfor those candidates which pass all the selection criteria for the signal
Λ
b0→ Λ
+c p pπ
− decays,to determineifthere areresonant contributions. In thiscasetheΛ
0b candidateis constrainedto its knownmass [15] whenobtainingtheΛ
+cπ
− invariantmass spec-trum.Thesignal shapesofthe
Σ
c0 andΣ
c∗0 resonances aregivenasthemodulussquaredoftherelativisticBreit–Wignerfunction[15],
|
BW(
m|
M0,
0)
|
2=
1/(
M20−
m2−
iM0(
m))
2
,
(3)multiplied by m
(
m)
, and convolved with a Gaussian resolution determined fromsimulation.Here, M0 istheknown valueof theΣ
0c or
Σ
c∗0 mass [15],m istheΛ
+cπ
− invariantmass, and0 is themass-independentwidthoftheresonance,namely1.83 MeV
/
c2for the
Σ
c0 and 15.3 MeV/
c2 for theΣ
c∗0 resonance. TheFig. 2. InvariantmassoftheΛ+cπ−systemfromthedecayΛ0b→ Λ+cp pπ−.TheΣc0
andΣc∗0resonancesareindicated.Thefittothedataisshownasabluecontinuous
line,withthebackgroundcomponentshownasagreendottedline,theΣ0 c shape
shownasadashedredline,andtheΣ∗0
c shapeshownasadash-dottedmagenta
line.
(
m)
=
0×
q q0 2L+1M 0 m BL(
q,
q0,
d)
2,
(4)where L is the angular momentum in the resonance decay, q
is the momentum of the
Λ
+c baryon in theΣ
(∗)0c rest frame,
q0
≡
q(
m=
M0)
and d stands for the size of theΣ
c(∗)0parti-cles.From parityandangularmomentumconservation,it follows that L
=
1.ThewidthalsodependsontheBlatt–WeisskopffactorBL
(
q,
q0,
d)
[26],wherethevalueofd issettobe1 fm (5GeV−1 in naturalunits).TheratioofwidthsoftheGaussianresolution func-tions fortheΣ
c0 andΣ
c∗0 resonances isfixed fromsimulationtobe1.96. Thebackgroundisdescribed withanempiricalthreshold function.ThefitshowninFig.2yields59
±
10Λ
0b→ Σ
c0p p decaysand104
±
17Λ
0b→ Σ
c∗0p p decays.The relative efficiencies for the decays
Λ
0b→ Σ
0cp p, with
Σ
0c
→ Λ
+cπ
− andΛ
0b→ Σ
c∗0p p, withΣ
c∗0→ Λ
+cπ
− withre-spect to
Λ
0b→ Λ
+cp pπ
− decays are determined with ananalo-gousprocedureasthatforthe
Λ
0b→ Λ
+cp pπ
− decaysrelativetothe
Λ
0b→ Λ
+cπ
− decays,but withthetrigger samplescombinedduetolimitedsample size.The efficiencies are0
.
685±
0.
021 for theΣ
0c mode and 0
.
904±
0.
021 for theΣ
c∗0 mode, relative toΛ
0b→ Λ
+c p pπ
−.Many of the systematic uncertainties cancel out in the mea-surementof the ratioof branching fractions, withthe remaining systematic uncertainties stemming from the yield determination. Thevalueofd intheBlatt–Weisskopffactorisvariedbetween1.5 and0.5 fm,withthelargestvariationforeachresonancetakenas thesystematicuncertainty,resultingin3.4%forthe
Σ
c0 resonance and1.9%fortheΣ
c∗0 resonance.Thebackgroundshapeischangedtoa third-orderpolynomial, witha relativedifference of1.7% for the
Σ
c0 resonanceand10.6% fortheΣ
c∗0 resonancetakenasthesystematicuncertainty.Themassesandwidthsofthe
Σ
c(∗)0reso-nancesareallowedtofloatwithin onestandarddeviationoftheir knownvalues [15],resultingina 3.8%differenceoftherawyield forthe
Σ
c0 resonanceand2.2%difference fortheΣ
c∗0 resonance.Alluncertainties intherelative efficiencycancel,exceptforthose relatedtotheweightingduetoresonantstructuresinthe
Λ
+cπ
− system.Thescalingfactorof1.041,withanuncertaintyof1.8%on therelativeefficiency,whichisshowninTable1,isthereforeused hereaswell.TheresultingratiosofbranchingfractionsareB
(Λ
0b→ Σ
c0p p)
×
B
(Σ
c0→ Λ
+cπ
−)
B
(Λ
0b→ Λ
+c p pπ
−)
=
0.
089±
0.
015±
0.
006,
B
(Λ
0b→ Σ
c∗0p p)
×
B
(Σ
c∗0→ Λ
+cπ
−)
B
(Λ
0b→ Λ
+c p pπ
−)
=
0.
119±
0.
020±
0.
014,
wherethefirstuncertaintyisstatisticalandthesecondis system-atic.8. Searchfordibaryonresonances
The existence of dibaryon resonances,
D
c+→
pΣ
c0, isinvesti-gated in the
Λ
+cπ
−p mass spectrum of background-subtracteddata. The full m
(Λ
+cπ
−)
spectrum is considered, while the sig-nal regions ofΣ
c0 andΣ
c∗0 resonances are defined by theranges 2450
<
m(Λ
+cπ
−) <
2458 MeV/
c2 and2488<
m(Λ
+cπ
−)
<
2549 MeV
/
c2,respectively. Thebackground issubtracted withthesPlot technique [27]. No peaking structures are observed in the
distributions showninFig.3.Thetwo-dimensionaldistributionof
m
(Λ
+cpπ
−)
versusm(Λ
+cπ
−)
hasbeencheckedanddoesnotex-hibitanyclearstructure.
9. Conclusion
Thefirstobservationofthedecay
Λ
b0→ Λ
+c p pπ
−ispresented.Theratioofthebranchingfractionsusingthedecay
Λ
b0→ Λ
c+π
− asthenormalisationchannelismeasuredtobeB
(Λ
0b→ Λ
+c p pπ
−)
B
(Λ
b0→ Λ
+cπ
−)
=
0.
0540±
0.
0023±
0.
0032,
using data corresponding to an integrated luminosity of 3 fb−1 collectedduring2011and2012withtheLHCb detector. Contribu-tionsfromthe
Σ
c(
2455)
0andΣ
c∗(
2520)
0resonancesareobserved,and the ratios of their branching fractions with respect to the
Λ
0b→ Λ
+cp pπ
− decaysaremeasuredtobeB
(Λ
0b→ Σ
c0p p)
×
B
(Σ
c0→ Λ
+cπ
−)
B
(Λ
0b→ Λ
+c p pπ
−)
=
0.
089±
0.
015±
0.
006,
B
(Λ
0b→ Σ
c∗0p p)
×
B
(Σ
c∗0→ Λ
+cπ
−)
B
(Λ
0b→ Λ
+c p pπ
−)
=
0.
119±
0.
020±
0.
014.
In all ofthe above results, the first uncertainty is statisticaland thesecondissystematic.The massspectraofthe
Λ
+cpπ
− finalstate are alsoinspectedforpossibledibaryonresonances,butnoevidenceofpeaking struc-turesisobserved.
Acknowledgements
We express our gratitude to our colleagues in the CERN ac-celerator departments for the excellent performance of the LHC. WethankthetechnicalandadministrativestaffattheLHCb insti-tutes. WeacknowledgesupportfromCERNandfromthenational agencies:CAPES,CNPq,FAPERJandFINEP(Brazil);MOSTandNSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (TheNetherlands);MNiSW andNCN(Poland); MEN/IFA (Romania); MinES and FASO (Russia); MinECo (Spain); SNSF andSER (Switzerland); NASU(Ukraine); STFC (United King-dom); NSF(USA). We acknowledge thecomputingresources that are provided by CERN, IN2P3 (France), KIT andDESY (Germany), INFN (Italy),SURF (TheNetherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH(Romania),CBPF(Brazil),PL-GRID(Poland)andOSC(USA).
Fig. 3. Background-subtractedmassspectrumoftheΛ+cπ−p systemfromthedecayΛ0b→ Λ+cp pπ−in(a)thefullΛ+cπ−massspectrum,(b)thesignalregionoftheΣc0
resonance,and(c)thesignalregionoftheΣc∗0resonance.Inallfigures,theblackpointsaredataandtheredpointsare simulatedeventswheretheΛ0bbaryondecays
totheΛ+cp pπ− finalstate(a)basedonauniform-phase-spacemodel,(b)throughtheΣc0resonanceand(c)throughtheΣc∗0resonance.Noevidentpeakingshapesare
visible.
We are indebted to the communities behind the multiple open-sourcesoftwarepackagesonwhichwedepend. Individualgroups or members have received support from AvH Foundation (Ger-many),EPLANET,Marie Skłodowska-CurieActions andERC (Euro-peanUnion),ANR,Labex P2IOandOCEVU,andRégion Auvergne-Rhône-Alpes (France),Key Research Program of Frontier Sciences ofCAS,CASPIFI,andtheThousandTalentsProgram(China),RFBR, RSFandYandexLLC(Russia),GVA,XuntaGalandGENCAT(Spain), HerchelSmithFund,theRoyalSociety,theEnglish-SpeakingUnion andtheLeverhulmeTrust(UnitedKingdom).
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LHCbCollaboration