polarization and angular parameters in Lambda[b]

32 Pages·2017·0.7 MB·English

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-EP-2017-331
2018/02/13
CMS-BPH-15-002
Λ
Measurement of the polarization and angular
b
parameters in Λ → J/ψΛ decays from pp collisions at
b √
s = 7 and 8TeV
8
1
0
2
b The CMS Collaboration∗
e
F

3
1

]
Abstract
x
e
-
p AnanalysisofthedecayΛ → J/ψ(→ µ+µ−)Λ(→ pπ−)isperformedtomeasurethe
e b √
h Λ polarization and three angular parameters in data from pp collisions at s = 7
b
[ Λ
and8TeV,collectedbytheCMSexperimentattheLHC.The b polarizationismea-

7 suredtobe0.00±0.06(stat)±0.06(syst)andtheparity-violatingasymmetryparam-
8 eter is determined to be 0.14±0.14(stat)±0.10(syst). The measurements are com-
0
3 paredtovarioustheoretical predictions, includingthosefromperturbativequantum
6 chromodynamics.
1
2
/
t
i SubmittedtoPhysicalReviewD
m
b
u
s
:
v
i
X
r
a
(cid:13)c 2018CERNforthebenefitoftheCMSCollaboration.CC-BY-4.0license
∗SeeAppendixAforthelistofcollaborationmembers

1
1 Introduction
The decay Λ → J/ψΛ is a rich source of information about the effect of strong interactions
b
in hadronic decays. For this particular decay, perturbative quantum chromodynamics can be
applied and therefore a systematic approach can be taken to study its characteristics. Several
techniques [1–10] are used to study and calculate the decay amplitudes and the effect of the
bquark polarization on this decay. The most interesting parameters that can be measured are
thepolarization,P,andtheparity-violatingdecayasymmetry,α ,oftheΛ . TheLHCbandAT-
1 b
LASexperimentshavereportedmeasurementsonthisdecay[11,12]. TheLHCbCollaboration
Λ Λ
measuredthe polarizationandthedecayamplitudes,whileATLASassumeda polariza-
b b
Λ
tion of zero and measured the amplitudes. In this paper, a measurement of the transverse
b
polarization is presented using the decay Λ → J/ψΛ, with J/ψ → µ+µ− and Λ → pπ−.
b
Λ
Charge-conjugate modes are implied throughout this paper unless otherwise stated. The
b
baryons used in this measurement come from both direct production in pp collisions and de-
cays of heavier bbaryons [1, 13–15]. The data were collected with the CMS detector in pp
collisionsatcenter-of-massenergiesof7and8TeV,correspondingtointegratedluminositiesof
5.2and19.8fb−1,respectively.
2 Angular distribution
TheΛ → J/ψΛdecayintotheµ+µ− pπ− finalstateisillustratedinFig.1. Inppcollisions,we
b
Λ Λ
definethepolarizationofthe asthemeanvalueofthe spinalongtheunitvector:
b b
nˆ = (cid:126)pbeam×(cid:126)pΛb , (1)
|(cid:126)pbeam×(cid:126)pΛb|
normal to its production plane, where(cid:126)p is in the direction of the counterclockwise proton
beam
beam direction [16], and (cid:126)pΛb is the Λb momentum. The decay is described by four complex
helicity amplitudes T , with λ = ±1/2 and λ = ±1,0 referring to the helicities of the
λ1λ2 1 2
Λ
and J/ψ particles, respectively. The angular distribution is a function of five decay angles
(θΛ,θp,θµ,ϕp,ϕµ)andhastheform[8]:
d5Γ (cid:0) (cid:1) 1 ∑20
dcosθΛdΩpdΩµ θΛ,θp,θµ,ϕp,ϕµ = (4π)3 i=1ui(Tλ1λ2)vi(P,αΛ)wi(θΛ,θp,θµ,ϕp,ϕµ), (2)
where w are trigonometric functions, u are bilinear combinations of the helicity amplitudes
i i
Tλ1λ2, and vi stands for 1, P, αΛ, or PαΛ; P is the Λb polarization and αΛ is the asymmetry
parameter in the decay Λ → pπ−. The angle θΛ is the polar angle of the Λ momentum rel-
ative to nˆ in the Λ rest frame; θ and ϕ are the polar and azimuthal angles of the proton,
b p p
respectively, defined with respect to the axes zˆ1 = (cid:126)pΛ/|(cid:126)pΛ| and yˆ1 = (nˆ ×(cid:126)pΛ)/|nˆ ×(cid:126)pΛ| in
Λ
the rest frame of the ; and the angles θ and ϕ are the polar and azimuthal angles, respec-
µ µ
tively, of the positively charged muon, defined with respect to the axes zˆ = (cid:126)p /|(cid:126)p | and
2 J/ψ J/ψ
(cid:0) (cid:1)
yˆ2 = nˆ ×(cid:126)pJ/ψ /|nˆ ×(cid:126)pJ/ψ| in the J/ψ rest frame. Here, (cid:126)pΛ and (cid:126)pJ/ψ are the momenta of the
Λ and J/ψ, respectively, and dΩ = d(cosθ )dϕ and dΩ = d(cosθ )dϕ are differential
p p p µ µ µ
solidangles. Assuminguniformdetectoracceptanceovertheazimuthalangles ϕ and ϕ ,the
p µ
2 3 TheCMSdetector
p
'p ✓ nˆ
p
zˆ1 ⇤ µ+
✓
yˆ1 ⇤ yˆ2
J/
⇡� xˆ1 ✓µ
nˆ ⇤b xˆ2 zˆ2 'µ
µ�
p p
Figure 1: Definition of the angles used to describe the Λ → J/ψΛ decay into the µ+µ− pπ−
b
finalstateasexplainedinthetext.
angulardistributioncanbesimplifiedthroughanintegrationoverthesetwoangles:
d3Γ (cid:90) π (cid:90) π d5Γ
(θΛ,θp,θµ) = Ω Ω (θΛ,θp,θµ,ϕp,ϕµ)dϕpdϕµ
dcosθΛdcosθpdcosθµ −π −π dcosθΛd pd µ
8
∼ ∑ui(cid:0)|Tλ1λ2|2(cid:1)vi(P,αΛ)wi(θΛ,θp,θµ).
i=1
(3)
The eight functional forms of u , v , and w are listed in Table 1. The u factors are written
i i i i
in terms of the three angular decay parameters α , α , and γ proposed in Ref. [8], and the
1 2 0
constant1,whichthemselvescanbewrittenintermsofthe T amplitudesas:
λ1λ2
1 = |T++|2+|T+0|2+|T−0|2+|T−−|2,
α1 = |T++|2−|T+0|2+|T−0|2−|T−−|2,
(4)
α2 = |T++|2+|T+0|2−|T−0|2−|T−−|2,
γ0 = |T++|2−2|T+0|2−2|T−0|2+|T−−|2,
whereα istheasymmetryparameterforthedecayΛ → J/ψΛ,α representsthelongitudinal
1 b 2
Λ
polarization of the , and γ is a parameter that depends on the longitudinal and transverse
0
Λ
polarizationsoftheJ/ψ[9]. TheCPinvarianceofEq.(3)impliesthattheparametersfor and
b
Λ
arerelatedasfollows:
b
P = −P,
α = −α ,
1 1
(5)
α = −α ,
2 2
γ = γ .
0 0
Inaddition,CPconservationinΛ → pπ− decaysimpliesthatαΛ = −αΛ [17]. Inthisanalysis,
the four parameters (P,α ,α ,γ ) are extracted from an analysis of the angular distribution
1 2 0
giveninEq.(3),whereαΛ isfixedtoitsworld-averagevalueof0.642±0.013[17].
3 The CMS detector
TheCMSdetectorisusedtostudyawiderangeofphenomenaproducedinhigh-energycolli-
sions, with its central feature being a superconducting solenoid of 6m internal diameter, pro-
viding a magnetic field of 3.8T. A silicon pixel and strip tracker, a lead tungstate scintillating
crystal electromagnetic calorimeter, and a brass and scintillator sampling hadron calorimeter,
includingacentralbarrelandendcapdetectors,arelocatedwithinthemagneticvolume.
3
Table1: FunctionsusedinEq.(3)todescribetheangulardistributioninthedecayΛ → J/ψΛ,
b
withJ/ψ → µ+µ− andΛ → pπ−.
i u v w
i i i
1 1 1 1
2 α2 αΛ cosθp
3 −α1 P cosθΛ
4 −(1+2γ0)/3 αΛP cosθΛcosθp
(cid:0) (cid:1)
5 γ /2 1 3cos2θ −1 /2
0 µ
(cid:0) (cid:1)
6 (3α1−α2)/4 αΛ cosθp 3cos2θµ−1 /2
(cid:0) (cid:1)
7 (α1−3α2)/4 P cosθΛ 3cos2θµ−1 /2
(cid:0) (cid:1)
8 (γ0−4)/6 αΛP cosθΛcosθp 3cos2θµ−1 /2
Thesilicontrackerdetectschargedparticleswithinthepseudorapidityrange|η| < 2.5. Itcon-
sists of 1440 silicon pixel and 15148 silicon strip detector modules. For nonisolated particles
with transverse momentum of 1 < p < 10GeV and |η| < 1.4, the track resolutions are typi-
T
cally1.5%in p and25–90(45–150)µminthetransverse(longitudinal)impactparameter[18].
T
Muons are detected in gas-ionization chambers within the pseudorapidity range |η| < 2.4,
withdetectionplanesmadeusingthreetechnologies: drifttubes,cathodestripchambers,and
resistive plate chambers [19]. The global event reconstruction (also called particle-flow event
reconstruction[20])consistsofreconstructingandidentifyingeachindividualparticlewithan
optimizedcombinationofallsubdetectorinformation. Inthisprocess,muonsareidentifiedas
a track in the silicon tracker consistent with either a track or several hits in the muon system,
associatedwithanenergydeficitinthecalorimeters.
Eventsofinterestareselectedusingatwo-tieredtriggersystem[21]. Thefirstlevel(L1), com-
posed of custom hardware processors, uses information from the calorimeters and muon de-
tectorstoselecteventsatarateofaround100kHzwithinatimeintervaloflessthan4µs. The
secondlevel,knownasthehigh-leveltrigger(HLT),consistsofafarmofprocessorsrunninga
versionofthefulleventreconstructionsoftwareoptimizedforfastprocessing,andreducesthe
eventratetoaround1kHzbeforedatastorage.
A more detailed description of the CMS detector, a definition of the coordinate system used
andtherelevantkinematicvariables,canbefoundinRef.[16].
4 Data and simulated events
We use data collected with a trigger designed for events containing a J/ψ meson decaying to
twomuonsthatformadisplacedvertexrelativetothemeanppcollisionpoint(beamspot). The
requirementonthedisplacementdoesnotaffecttheangulardistributionsofthereconstructed
Λ
decay products. The dimuon trigger configurations were changed during the data taking
b
at different center-of-mass energies, with increasingly stringent requirements to maintain an
acceptable trigger rate as the instantaneous luminosity increased. The requirements of the
different trigger versions are: the J/ψ candidates are selected in the invariant mass window
2.5–4.0GeVand2.9–3.3GeVdependingontheversion;theangle(β)betweenthereconstructed
momentum vector of the dimuon system and the vector pointing from the beamspot position
tothedimuonvertexmusthaveavalueofcosβ > 0.9;thedistancebetweenthebeamspotand
the dimuon vertex in the transverse plane must have a value that is at least a factor of three
µµ
largerthanitsuncertainty(standarddeviationorSD);themuonpairmustsatisfy p > 6.5or
T
6.9GeV in the different versions; the χ2 probability of the fit of the two muons to a common
vertexmustexceed0.05,0.10,or0.15fromtheearliesttothelatestversion;eachmuonmustbe
4 5 Reconstructionandeventselection
in|η(µ)| < 2.2andhave pµ > 3.5or4GeV;andthedistanceofclosestapproachofeachmuon
T
tothecommonvertexinthetransverseplanemustbelessthan0.5cm.
Simulated events of the signal decay are used to study the effects of detector acceptance and
selection on the reconstructed angular distributions. The events are generated using PYTHIA
6.4[22]forproductionandhadronization,andEVTGEN[23]isusedtodescribethebandchadron
decays. The generated events are passed through the full CMS detector simulation based on
√
GEANT4 [24]. The simulated event samples are generated to reproduce s = 7 and 8TeV
data-taking conditions, where additional simulation of pp interactions in the same or nearby
beam crossings and the impact of the HLT are included. Simulated events are reconstructed
andselectedusingthesamealgorithmsandrequirementsasusedfordata.
5 Reconstruction and event selection
The offline selection requires pairs of oppositely charged muons originating from a common
vertex to form the J/ψ candidates. The standard CMS muon reconstruction procedure [19] is
used to identify the muons. Since the trigger changed slightly over the different data-taking
periods, the offline selection is required to be more restrictive than the most-stringent trigger,
µ
and are summarized as follows: (i) each muon must have p > 4GeV and the dimuon trans-
T
verse momentum must satisfy pµµ > 8GeV; (ii) the χ2 probability must exceed 0.15; and (iii)
T
thedimuoninvariantmassmustliewithin±150MeVoftheworld-averageJ/ψmass[17]. Ad-
ditional requirements are the same as the trigger selection and, to reduce background, the J/ψ
candidatesmustsatisfycosβ > 0.99.
Λ
The candidatesareconstructedfrompairsofoppositelychargedtracksthathaveasuccessful
fit to a common vertex. Since the default CMS algorithms cannot distinguish between pions
andprotons,thehigher-andlower-momentumtracksareassumedtohavetheprotonandpion
masses [17], respectively. The selections used for Λ and K0 particles are detailed in Ref. [25].
S
They are optimized to reduce background using the following additional requirements: (i)
each track is required to have at least 6 hits in the silicon tracker and a χ2 track fit per degree
of freedom < 7; (ii) the tracks coming from the Λ decay are required to have pπ > 0.3GeV,
T
p
p > 1.0GeV; (iii) the transverse impact parameter of the tracks relative to the beamspot is
T
requiredtobegreaterthan3SD;(iv)theprobabilityofthetwo-trackvertexfitmustexceed2%;
(v)thetransverseseparationofthetwo-trackvertexfromthebeamspotisrequiredtobelarger
than 15 SD; (vi) the invariant mass of the Λ candidate is selected to lie within ±9MeV of the
pπ
world-average value [17] and satisfy p > 1.3GeV; and (vii) to reduce the contamination of
T
K0 → π+π− decays,eventsareremovediftheirinvariantmassfallswithin±20MeVoftheK0
S S
masswhentheprotoncandidateisgiventhechargedpionmass.
Λ Λ
The candidatesarefittedtoacommonvertexbycombiningtheJ/ψand candidates,with
b
Λ
therespectivemassconstraintstotheworld-averagevaluesoftheJ/ψ and masses[17]. The
Λ
selectionof candidatesisoptimizedtoreducebackgroundwiththeadditionalrequirements:
b
pJ/ψΛ > 10GeV,aχ2probabilityofthefittotheJ/ψΛvertex> 3%,andtheJ/ψΛinvariantmass
T
5.40 < mJ/ψΛ < 5.84GeV.
Toextractthenumberofsignalandbackgroundeventsandtodefinethesignalandsidebands
regions, unbinned maximum likelihood fits to the reconstructed invariant mass (m√J/ψΛ) distri-
butions are performed, using separate data sets of the Λ and Λ candidates at s = 7 and
b b
8TeV. The signal shape is modeled by two Gaussian functions with different SDs, σ and σ ,
1 2
but common mean µJ/ψΛ, and the background by a first-order polynomial. We define in the
fourdatasetsthesignalregionasµJ/ψΛ±16MeV,thelowersidebandregionas[5.46,5.54]GeV,
5
andtheuppersidebandregionas[5.70,5.78]GeV. FromthefitstheΛ yieldsare981±39and
b √
2072±55 signal events, and the Λ yields are 916±40 and 1974±53 signal events at s = 7
b
and8TeV,respectively.
6 Measurement of the polarization and angular parameters
The analysis extracts the Λ polarization, P, and the angular decay parameters α , α , and γ .
b 1 2 0
Λ
TheresultsareobtainedfromanunbinnedmaximumlikelihoodfittotheJ/ψ invariantmass
distribution and the three angular variables Θ3 = (cid:0)cosθΛ,cosθp,cosθµ(cid:1), using the extended
likelihoodfunction:
N
(cid:0) (cid:1)∏(cid:2) (cid:3)
L = exp −N −N N PDF +N PDF , (6)
sig bkg sig sig bkg bkg
where N is the total number of events, N and N are the yields of signal and background
sig bkg
events,respectively,determinedfromthefitinSection5,and PDF and PDF representthe
sig bkg
probability density functions (PDFs) for the signal and background, respectively. The PDF
sig
hastheform:
PDFsig = Fsig(Θ3)(cid:101)(Θ3)G(mJ/ψΛ), (7)
where F represents the theoretical angular distribution given by Eq. (3) and G is the sum of
sig
Λ
two Gaussian functions used to model the J/ψ invariant mass distribution, as mentioned in
Section 5. The effect of the detector on the angular distribution is taken into account by the
factor(cid:101)thatrepresentstheefficiencyasafunctionoftheangles.
To estimate the angular efficiency, simulated events of Λ → J/ψΛ decays are generated with
b
uniform distributions in cosθΛ, cosθp, and cosθµ. After full detector simulation, reconstruc-
tion,andimplementationofthefinalselectionrequirements,theslightdifferencesbetweenthe
simulatedeventsandthebackground-subtracteddataareminimizedthroughaweightingpro-
cedurewhereweightsareassignedtothesimulatedeventstomatchthedata. Theweightsare
computed with an iterative process in which, for each iteration, the histograms of a selection
variable in background-subtracted data and simulated events are used to calculate the ratio
bin-by-bin (weight) with its propagated statistical uncertainty. The final weight per event is
the product of the weights in each iteration. The efficiency distributions as a function of the
variablesarefitwithaproductofChebyshevpolynomials,wherethecoefficientsareobtained
√
for Λ and Λ at s = 7 and 8TeV in separate likelihood fits. The simulated efficiency distri-
b b √
butions and the results of these fits are shown in Fig. 2 for the Λ candidates at s = 8TeV.
b
The background PDFbkg is given by the product of a first-order polynomial P(mJ/ψΛ) for the
invariantmassandanangulardistributionfunction F (Θ ):
bkg 3
PDFbkg = P(mJ/ψΛ)Fbkg(Θ3). (8)
The background angular distributions Fbkg(Θ3) are estimated using events from the mJ/ψΛ in-
variantmasssidebands. TheyaremodeledusingChebyshevpolynomialsforcosθΛandcosθp,
Λ
andaproductoftwocomplementaryerrorfunctionsforcosθ , asshowninFig.3for can-
√ µ b
didatesat s = 8TeV.
ThecompletelikelihoodfunctioninEq.(6)ismaximizedbyfittingsimultaneouslythefourdata
√
setsforΛ andΛ at s = 7and8TeV,allowingfortheextractionofthecommonparameters
b b
P, α , α , and γ . The simultaneous fit is performed in the enriched signal mass range within
1 2 0
Λ
3.5 SDs of the mean mass. This range contains more than 99.9% of the signal events, and
b
6 6 Measurementofthepolarizationandangularparameters
ale]800 CMS ale]800 CMS ale]800 CMS
c c c
s Simulation s Simulation s Simulation
ary 600 ary 600 ary 600
bitr bitr bitr
ar ar ar
y [400 y [400 y [400
c c c
n n n
e e e
Effici200 (a) Effici200 (b) Effici200 (c)
0- 1 - 0.5 0 0.5 1 0- 1 - 0.5 0 0.5 1 0- 1 - 0.5 0 0.5 1
cosq L cosq p cos q m
Figure 2: The efficiencies as a fun√ction of (a) cosθΛ, (b) cosθp, and (c) cosθµ obtained from
simulated Λ → J/ψΛ decays at s = 8TeV. The vertical bars on the points are the statis-
b
tical uncertainties in the simulated data, and the lines show the projections of a 3D fit to the
distributionsusingChebyshevpolynomials. Thescalesoftheverticalaxesarearbitrary.
19.8 fb-1 (8 TeV) 19.8 fb-1 (8 TeV) 19.8 fb-1 (8 TeV)
3 3 3
1 CMS 1 CMS 1 CMS
0. 0. 0.
s / s / s /
nt100 nt100 nt
ve ve ve100
E E E
50 50 50
(a) (b) (c)
0- 1 - 0.5 0 0.5 1 0- 1 - 0.5 0 0.5 1 0- 1 - 0.5 0 0.5 1
cosq L cosq p cosq m
Figure3: Thebackgroundangulardistributionsof(a)cosθΛ,(b)cosθp,and(c)√cosθµareshown,
as obtained from the sidebands in the J/ψΛ invariant mass distribution at s = 8TeV. The
vertical bars on the points represent the statistical uncertainties, and the solid lines are the
resultsofthefitstodataasdescribedinthetext.
7
significantlyreducesthenumberofbackgroundevents. Asaresult,thefitislesssensitivetothe
modelingdiscussedabove. Thefitparametersforthebackgroundandefficiencydistributions
are fixed to those found in the previous fits. The signal and background mass parameters are
obtained from previous fits to the mass distribution within 10 SDs, and the numbers of signal
and backgrounds events are fixed to the propagated values in the signal mass region. The
resultingfitvaluesofthepolarizationandthethreeangulardecayparametersare:
P = 0.00±0.06,
α = 0.14±0.14,
1
α = −1.11±0.04,
2
γ = −0.27±0.08,
0
where the uncertainties are statistical only. The correlation matrix of the fitted parameters is
showninTable2. Nostrongcorrelationsarefoundamongtheseparameters. Translatingthese
valuestothesquaresofthehelicityamplitudes,theresultsare:
|T |2 = 0.05±0.04,
++
|T |2 = −0.10±0.04,
+0
|T−0|2 = 0.51±0.03,
|T−−|2 = 0.52±0.04,
wheretheuncertaintiesarestatisticalonly. TheprojectionsofthefitareshowninFigs.4and5
√
forΛ andΛ ,respectively,usingthecombineddataat s = 7and8TeV.
b b
Table2: Correlationmatrixforthefittedparameters.
Parameter P α α γ
1 2 0
P 1 −0.039 −0.029 0.116
α 1 −0.207 −0.030
1
α 1 0.285
2
γ 1
0
7 Systematic uncertainties
Varioussourcesofsystematicuncertaintythataffectthemeasurementoftheparameters P,α ,
1
α ,andγ arediscussedbelow.
2 0
Fit bias The bias introduced through the fitting procedure is studied by generating 1000
pseudo-experiments using the measured parameters as inputs. The difference between the
inputandthemeanofthefittedvaluesistakenasthesystematicuncertainty.
Asymmetry parameter αΛ This parameter is varied up and down by its uncertainty and
themaximumdeviationinthefinalresultforeachparameteristakenasthesystematicuncer-
tainty.
Model for the background mJ/ψΛ distribution An exponential function is used instead
of the first-order polynomial in the likelihood fit. The parameter of the exponential and the
background yield are varied by their uncertainties. The fit is redone taking into account this
variationonthebackgroundmodelforthemass,andthedifferencesbetweentheseresultsand
thenominalfitresultsaretakenasthesystematicuncertaintyforthissource.
8 7 Systematicuncertainties
19.8 fb-1 (8 TeV) + 5.2 fb-1 (7 TeV) 19.8 fb-1 (8 TeV) + 5.2 fb-1 (7 TeV)
400
V CMS 2 CMS
e (a) 0.800 (b)
M
/
3 s
/ 300 Data nt Data
nts FSiitgnal Eve600 FSiitgnal
e
v Background Background
E200
400
100
200
0 0
5.58 5.6 5.62 5.64 5.66 - 1 - 0.5 0 0.5 1
m (J/y L ) [GeV] cosq
p
19.8 fb-1 (8 TeV) + 5.2 fb-1 (7 TeV) 19.8 fb-1 (8 TeV) + 5.2 fb-1 (7 TeV)
600

0.2 (c) CMS 0.2600 (d) CMS

/ /

s s
t t
n n
e e
v400 v
E E400
Data
Data
Fit
Fit
Signal
200 Signal
200 Background
Background
0 0
- 1 - 0.5 0 0.5 1 - 1 - 0.5 0 0.5 1
cosq cosq
L m
Figure4: D√istributionsin(a)mJ/ψΛ,(b)cosθp,(c)cosθΛ,and(d)cosθµ forΛb candidatesinthe
combined s = 7and8TeVdata. Theverticalbarsonthepointsarethestatisticaluncertainties
inthedata,thesolidlineshowstheresultofthefit,andthedashedanddottedlinesrepresent,
respectively,thesignalandbackgroundcontributionsfromthefit.
Model for the background angular distributions Alternative parametrizations of the
background angular distributions are used to estimate the systematic uncertainty. For cosθΛ
and cosθ the alternative models comprise a superposition of Gaussian kernels, as imple-
µ
mented in Roofit RooKeysPdf [26], while for cosθ the alternative model is an error function.
p
The differences relative to the nominal results are taken as the systematic uncertainties from
themodelingofthebackgroundangulardistributions.
Model for the signal mJ/ψΛ distribution Weestimatethisuncertaintybychangingthepa-
Λ
rameters by their uncertainties, taking into account their correlations. In each sample of
√ b
and Λ at s = 7 and 8TeV, we use the parameter of the signal mass model with the largest
b
global correlation and add 1 SD to its nominal value if the correlation is positive and subtract
1 SD if the correlation is negative. The difference relative to the nominal result is quoted as a
systematicuncertainty.