Available on the CERN CDS information server CMS PAS BPH-18-005

CMS Physics Analysis Summary

Contact: cms-pag-conveners-bphysics@cern.ch 2019/03/25

Study of the B+ → J/ψΛp decay in proton-proton collisionsat√

s = 8 TeV

The CMS Collaboration

Abstract

A study of the B+ → J/ψΛp decay is reported, using proton-proton collision datacollected at

√s = 8 TeV by the CMS experiment at the LHC, corresponding to an

integrated luminosity of 19.6 fb−1. The ratio of branching fractions B(B+→J/ψΛp)B(B+→J/ψK∗+) is

measured to be 1.054± 0.057 (stat)± 0.028 (syst)± 0.011(B)%, where the first uncer-tainty is statistical, the second is systematic, and the third reflects the uncertaintiesin the world-average branching fractions. The invariant mass distributions of J/ψΛ,J/ψp, and Λp systems produced in the B+ → J/ψΛp decay are investigated andfound to be inconsistent with the pure phase space hypothesis. The analysis is ex-tended by using a model-independent angular amplitude analysis, which shows thatthe inclusion of contributions from excited kaons in the Λp system does improve thedescription of the observed invariant mass distributions.

1. Introduction 1

1 IntroductionThe first evidence for the B+ → J/ψΛp decay was published by the BaBar Collaboration [1],along with a measurement of its branching fraction of (12+9

−6) × 10−6. (In all the notationsused, the charge-conjugate states are implied throughout the paper.) Later, the B+ → J/ψΛpdecay was observed by the Belle Collaboration and its branching fraction was measured tobe (11.7± 2.8+1.8

−2.3) × 10−6 [2], resulting in the world-average branching fraction of B(B+ →J/ψΛp)=(11.8± 3.1) × 10−6 [3]. The B+ → J/ψΛp decay was the first example of a B mesondecay into baryons and a charmonium state. Originally, the interest to this decay mode wasinspired by the possibility to explain [4] an excess of the low-momenta J/ψ mesons producedin inclusive B → J/ψ + X decays [5, 6], which was not consistent with the predictions fromnonrelativistic quantum chromodynamics (QCD) calculations [7]. An additional motivation tostudy this decay is to search for new intermediate resonances in the J/ψΛ, J/ψ p and Λp systems[1, 8].

Recently, the LHCb Collaboration reported the first observation of the baryonic Bc decay B+c →

J/ψ ppπ+ [9]. Several searches for the B0s → J/ψ pp [10] and the B0 → J/ψ pp [1, 2, 10] decays

have been performed by the B factories and LHCb as well, followed by the observation ofthese decays by the LHCb collaboration [11]. The interest in these decay modes is becausethey allow to study the invariant mass spectra of a charmonium-baryon system. Such a studyin the Λ0

b → J/ψ pK− decay resulted in the observation by the LHCb Collaboration [12] ofnew multiquark states consistent with pentaquarks: P+

c (4380) and P+c (4450), decaying into

J/ψ p. Subsequently, LHCb has observed the Ξ−b → J/ψΛK− decay, but the signal yield was notsufficient to perform an intermediate resonance analysis [13].

To explore an advantage of the large integrated luminosities of proton-proton (pp) collisionsand the large production cross section of bb pairs at the CERN LHC, the CMS experiment hasdeveloped an efficient trigger on the displaced J/ψ → µ+µ− decays. The availability of thistrigger allowed CMS to conduct a search for new exotic multiquark states in the J/ψΛ andJ/ψ p systems produced in the B+ → J/ψΛp decay. In addition to a search for new resonances,this new measurement of baryonic B meson decays provides information on the dynamics ofsuch decays that would help to improve theoretical descriptions of baryonic B decays.

In this paper, we report on a study of the B+ → J/ψΛp decay using a data sample of ppcollisions collected by the CMS experiment at

√s = 8 TeV, corresponding to an integrated

luminosity of 19.6 fb−1. The decay B+ → J/ψK∗+ (K∗+ → K0Sπ+) is chosen as the normalization

channel, as it is measured with high precision and has a similar decay topology to the B+ →J/ψΛp decay. The ratio of the branching fractions is measured using the following formula:

B(B+ → J/ψΛp)B(B+ → J/ψK∗+)

=N(B+ → J/ψΛp)B(K∗+ → K0

Sπ+)B(K0S → π+π−)ε(B+ → J/ψK∗+)

N(B+ → J/ψK∗+)B(Λ→ pπ+)ε(B+ → J/ψΛp), (1)

where N(B+ → J/ψX(Y)) and ε(B+ → J/ψX(Y)) correspond to the number of the B+ → J/ψX(Y)decays observed in data and the total efficiency to reconstruct this decay, respectively. In addi-tion, we investigate the invariant mass distributions of J/ψΛ, J/ψ p, and Λp systems producedin the B+ → J/ψΛp decay.

2

2 The CMS DetectorThe central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diame-ter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and striptracker, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadroncalorimeter, each composed of a barrel and two endcap sections. Forward calorimeters extendthe pseudorapidity coverage provided by the barrel and endcap detectors. Muons are detectedin gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid.

The main subdetectors used for the present analysis are the silicon tracker and the muon sys-tem.

The silicon tracker measures charged particles within the pseudorapidity range |η| < 2.5. Dur-ing the LHC running period used in this paper, the silicon tracker consisted of 1440 silicon pixeland 15 148 silicon strip detector modules. For nonisolated particles of 1 < pT < 10 GeV and|η| < 1.4, the track resolutions are typically 1.5% in pT and 25–90 (45–150) µm in the transverse(longitudinal) impact parameter [14]

Muons are measured within |η| < 2.4, with detection planes made using three technologies:drift tubes, cathode strip chambers, and resistive-plate chambers. Matching muons to tracksmeasured in the silicon tracker results in a relative transverse momentum resolution, for muonswith pT < 10 GeV used in this analysis, of 0.8–3.0%, depending on the muon |η| [15].

Events of interest are selected using a two-tiered trigger system [16]. The first level (L1), com-posed of custom hardware processors, uses information from the calorimeters and muon de-tectors to select events at a rate of around 100 kHz within a time interval of less than 4 µs. Thesecond level, known as the high-level trigger (HLT), consists of a farm of processors running aversion of the full event reconstruction software optimized for fast processing, and reduces theevent rate to around 1 kHz before data storage.

A more detailed description of the CMS detector, together with a definition of the coordinatesystem used and the relevant kinematic variables, can be found in Ref. [17].

3 Data sample and event selectionData were collected with a dedicated two-level trigger (L1 and HLT), optimized for the se-lection of B hadrons decaying to J/ψ(µ+µ−). The L1 trigger required two oppositely chargedmuons, each with pT > 3 GeV and |η| < 2.1. At the HLT, a J/ψ candidate decaying into a µ−µ+

pair displaced from the interaction point was required. Each muon pT was required to be atleast 4 GeV and the pT of the dimuon pair was required to be greater than 6.9 GeV. The J/ψ can-didates reconstructed from the dimuon pairs were required to have invariant mass between2.9 and 3.3 GeV. The three-dimensional (3D) distance of closest approach of the two muons toeach other was required to be less than 0.5 cm. The dimuon vertex fit with the transverse decaylength significance Lxy/σLxy > 3 was further required, where Lxy and σLxy are, respectively, thedistance between the beam axis and the common vertex in the transverse plane, and its uncer-tainty. Finally, the secondary-vertex fit probability, calculated using the χ2 and the number ofdegrees of freedom of the vertex fit, was required to exceed 10%, while the angle ρ between thedimuon transverse momentum vector and the line connecting the primary and the secondaryvertices was required to satisfy cos ρ > 0.9.

In the subsequent analysis, individual muon candidates are required to have pT > 4 GeV and|η| < 2.1. Two oppositely charged muon candidates are paired and required to originate from a

3. Data sample and event selection 3

common vertex. Dimuon candidates with invariant mass within 150 MeV of the world-averageJ/ψ mass [3] are selected.

To reconstruct a B+ candidate, the reconstructed J/ψ candidate is combined with positivelycharged track satisfying the high-purity requirement [18] assigned the proton mass hypothesis,and a Λ candidate. The Λ candidates are formed from dispaced two-prong vertices under theassumption of Λ→ pπ+ decay, as described in Ref. [19]. Daughter particles of the Λ candidateare refitted to a common vertex, with the requirement of the vertex fit probability to exceed 1%.The proton mass is assigned to the leading (in pT) daughter track. To select the candidates inthe Λ signal region the following additional requirement is applied:|M(pπ+)−MPDG

Λ| < 2σΛ

eff,

where the effective Λ signal width σΛeff = 3.671 MeV is measured in data by fitting the M(pπ+)

distribution with a sum of two Gaussian functions with a common mean value.

Since particle identification is not possible, the reflection from K0S candidates is present in

Λ → pπ+ sample. Its contribution is removed by imposing an additional requirement on theinvariant mass of these two tracks, where both are assigned a pion mass: |M((p→ π−)π+)−MPDG

K0S| > 2σ

K0S

eff , where the effective K0S signal width σ

K0S

eff = 9.17 MeV is measured in data by

fitting the M(π+π−) distribution with a sum of two Gaussian functions with a common meanvalue.

As the last step of the reconstruction, the kinematic vertex fit of the Λ candidate, the pro-ton track, and the dimuon pair, with the dimuon mass constrained to the world-average J/ψmass [3] is performed; this vertex is referred as the B vertex. The selected candidates are re-quired to have pT(J/ψ) > 7 GeV, pT(Λ) > 1 GeV, and pT(p) > 1 GeV. The following require-ment is used to select the B+ candidates consistent with originating from the primary vertex(PV): cos α(B+, PV) > 0.99, where cos α(B+, PV) is the cosine of the angle between the B+

candidate momentum and the vector from the PV to the B vertex. The following requirement

on the B vertex displacement is further applied: Lxy(B+)σLxy(B+)

> 3, where Lxy(B+) is the distance

between the primary and B vertices, and σLxy(B+) is its uncertainty. The B+ candidate kinematicvertex fit probability is required to exceed 1%. The Λ candidate is required to be consistentwith originating from the B+ decay by requiring cos(αΛ,B+) > 0.

Multiple pp interactions per bunch crossing (pileup) are present in the data, with an averagemultiplicity of 20. The hard scattering vertex in the event is chosen as the PV with the highestcosine of the pointing 3D angle to the B vertex. The right-sign requirement is applied to thefinal combination, i.e., the candidates where the proton candidate has the same sign as the Λdaughter proton are rejected.

The normalization decay channel B+ → J/ψK∗+ (K∗+ → K0Sπ+) candidates are selected using

the same reconstruction chain. The identical requirements were used to select the J/ψ candidateand the π+ track. The selection of the K0

S candidates is the same as for the Λ candidates, except

that the mass window for K0S daughter pions is required to satisfy |M(π+π−)−MPDG

K0S| < 2σ

K0S

eff .

The contribution from Λ→ pπ+ decay is removed with an additional requirement: |M((π− →p)π+)−MPDG

Λ| > 2σΛ

eff.

To calculate the reconstruction efficiency a study based on simulated signal events is per-formed. The events are generated with PYTHIA v6.424 [20]. The B meson decays are mod-eled using EVTGEN v1.3.0 [21] for both the B+ → J/ψΛp and B+ → J/ψK∗+ decays. Theevents are then passed through a detailed CMS detector simulation based on GEANT4 [22].

4

Matching of the reconstructed candidates to the generated particles is performed by requiring∆R =

√(∆η)2 + (∆φ)2 < 0.004 (0.03) for muon (proton, π+, Λ, and K0

S) candidates, where ∆ηand ∆φ are the differences in the pseudorapidity and azimuthal angle (in radians), respectively,between the momenta of the reconstructed and generated particles.

4 Signal yields for the B+→ J/ψΛp and B+→ J/ψK∗+ decays

4.1 B+→ J/ψΛp signal yield

The invariant mass distribution of the selected B+ → J/ψΛp candidates is shown in Fig. 1 (up-per). An unbinned extended maximum-likelihood fit to a signal plus background hypothesisis performed to this distribution. The signal component is modeled with a sum of three Gaus-sian functions with a floating common mean and an overall normalization, while the widthsand the relative normalizations of the three Gaussian functions are fixed to the values obtainedfrom the simulation. The background component is parameterized by a threshold polynomialfunction: (x − x0)α, where x0 = MPDG

Λ+ MPDG

J/ψ + MPDGp . The fit results in a signal yield of

452± 23 events and the B+ mass value of 5.27922± 0.00017 GeV, which is in a good agreementwith the world-average value of 5.27925± 0.00026 GeV [3].

4.2 B+→ J/ψK∗+ signal yield

Figure 1 (lower left) shows the observed B+ → J/ψK0Sπ+ invariant mass distribution with

the requirement on the K0Sπ+ invariant mass to fall inside the ±200 MeV window around the

world-average K∗(892)+ mass [3]. The points show the data and the curve corresponds tothe result of the fit. The B+ signal is modeled with a sum of two Gaussian functions with acommon mean and all parameters floating in the fit, while the background is described by asecond-order Bernstein polynomial.

In order to evaluate the pure K∗(892)+ contribution, avoiding the consideration of other res-onances in the K0

Sπ+ final state, the background-subtracted M(K0Sπ+) distribution shown in

Fig. 1 (lower right) is fitted in the range of ±200 MeV around the K∗(892)+ mass. Backgroundsubtraction is performed using the sPlot technique [23]. The mass resolution of the K∗(892)+

peak is negligible in comparison with the natural width; therefore the relativistic Breit–Wignerfunction is used as the signal model, and the threshold polynomial function as the non-K∗(892)+

component: (x− xK∗0 )α, where xK∗

0 = MPDGK0

S+ MPDG

π+ .

To obtain the number of B+ → J/ψK∗(892)+ decays for the branching fraction ratio calculation,the normalization of the signal Breit-Wigner component in the ±50 MeV range around theK∗(892)+ mass is calculated, resulting in the yield of 20863± 357 events.

5 Efficiency calculationThe efficiency is calculated for each decay channel using simulated samples described in Sec-tion 3. It is calculated as the ratio between the numbers of the reconstructed to generatedevents. The efficiency includes the trigger efficiency, reconstruction efficiency, and the detectoracceptance. The efficiency ratio, which is used in the branching fraction ratio measurement iscalculated to be ε(B+→J/ψK∗+)

ε(B+→J/ψΛp)= 1.347± 0.023, where the uncertainty reflects the limited number

of events in the simulated samples.

For the study of 2-body intermediate invariant masses in the B+ → J/ψΛp decay, the effi-

6. Evaluation of the systematic uncertainties 5

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Figure 1: Invariant mass distribution of the selected B+ → J/ψΛp candidates (upper). TheJ/ψK0

Sπ+ (lower left) and K0Sπ+ (lower right) invariant mass distributions in the B+ → J/ψK∗+

decay. The points are data and the curves are results of the fits described in the text. The verticallines in the last plot indicate the K∗+ invariant mass window used for the normalization, asdescribed in the text.

ciency is calculated as the function of two variables: cosine of the Λp (K∗) system helicityangle, which is defined as the angle between the Λ and B+ momentum vectors in the Λp sys-tem rest frame (see Fig. 3), cos(θK∗), and the invariant mass of the Λp system, M(Λp). Thetwo-dimensional (2D) efficiency is calculated as the ratio of the 2D histogram at the reconstruc-tion level to the simulated 2D histogram. The efficiency correction is performed on data byapplying the 1

ε(M(Λp),cos(θK∗ ))weight to each event. Efficiency values at each point in 2D space

are evaluated using bilinear interpolation algorithm. The values inside the border bins of the2D space are assumed to be the values at the centers of the corresponding bins.

6 Evaluation of the systematic uncertainties

In this section we discuss the sources of the systematic uncertainty in the ratio B(B+→J/ψΛp)B(B+→J/ψK∗+) ,

defined by Eq. (1). Since the signal B+ → J/ψΛp and the normalization B+ → J/ψK∗+ decayshave the same topology, the systematic uncertainties related to the muon reconstruction, trackreconstruction, and the trigger efficiency are cancelled in the ratio of the branching fractions.Other systematic uncertainties are discussed below.

The systematic uncertainty related to the choice of the background model is estimated sepa-rately for the fits to the J/ψΛp, J/ψK0

Sπ+, and K0Sπ+ invariant mass distributions. The variation

of the background model includes Bernstein polynomials of the first, second, and third orderfor the J/ψK0

Sπ+ invariant mass distribution; and (x− x0)α function multiplied by the Bernstein

6

polynomials of the first and second order for the J/ψΛp and K0Sπ+ invariant mass distributions.

The second source of the uncertainty is the uncertainty in the signal invariant mass resolution.In the baseline fits, the resolution functions are obtained from the simulation in the case ofB+ → J/ψΛp decay. The associated uncertainty is estimated by varying the widths in theranges defined by their uncertainties derived from simulation. For the B+ → J/ψK∗+ decay,the systematic uncertainty originating from an ambiguity of the signal model is estimated byapplying different signal models when fitting the J/ψK0

Sπ+ invariant mass distribution, such asthe sum of two or three Gaussian functions, or a double Crystal Ball function [24, 25].

For each of the variations, the largest deviation in the measured signal yield is used as thesystematic uncertainty. Variations of signal and background component are performed inde-pendently. The statistical uncertainty in the relative efficiency from simulation related to to thelimited sizes of the simulated samples is considered as an additional source of the systematicuncertainty.

Table 1 summarizes individual systematic uncertainties, as well as the total systematic uncer-tainty, calculated as the quadratic sum of the individual sources.

Table 1: Summary of the relative systematic uncertainties in the B(B+→J/ψΛp)

B(B+→J/ψK∗+) ratio.

Source Relative uncertainty, %Background model in the M(J/ψΛp) distribution 1.1

Background model in the M(J/ψK0Sπ+) distribution 0.1

Signal model in the M(J/ψΛp) distribution 1.1Signal model in the M(J/ψK0

Sπ+))distribution 0.6Non-K∗+ component in the M(K0

Sπ+) distribution 1.2Simulated sample size 1.7

Total systematic uncertainty 2.7

7 Measurement of the B(B+→J/ψΛp)B(B+→J/ψK∗+)

ratio

Using the world-average [3] values of B(K∗+ → K0π+) = 0.66660 ± 0.00006, B(K0S →

π+π−) = 0.692 ± 0.005, B(Λ → pπ+) = 0.639 ± 0.005, the relative efficiency described inSection 5, and signal yields N(B+ → J/ψΛp) = 452± 23 and N(B+ → J/ψK∗+) = 20863± 357,

the ratio B(B+→J/ψΛp)B(B+→J/ψK∗+) is measured using Eq. (1) to be (1.054 ± 0.057 (stat) ± 0.028 (syst) ±

0.011(B)) × 10−2, where the first uncertainty is statistical, the second is systematic (Sec. 6),and the third is due to the uncertainties in the world-average branching fractions of the decaysinvolved.

From this ratio and the world average value of B(B+ → J/ψK∗+) = (1.43± 0.08)× 10−2 [3],the branching fraction B(B+ → J/ψΛp) = (15.07± 0.81 (stat)± 0.40 (syst)± 0.86(B))× 10−6 iscomputed. This measurement is the most precise to date.

8 Study of J/ψΛ, J/ψ p and Λp mass spectra8.1 Model-independent approach

The invariant mass distributions of the J/ψΛ, J/ψ p, and Λp two-body combinations of theB+ → J/ψΛp decay products are investigated. Background subtraction is performed using the

8. Study of J/ψΛ, J/ψ p and Λp mass spectra 7

sPlot technique. Figure 2 shows the invariant mass distributions of the J/ψΛ, J/ψ p, and Λpsystems. To account for the event selection efficiency, each event is assigned a weight equalto 1

ε(M(pΛ),cos(θK∗ )), where ε(M(Λp), cos(θK∗)) is obtained from simulation, as described in Sec-

tion 5. The efficiency-corrected invariant mass distributions are fitted with the phase spacehypothesis (shown by the black dashed line) obtained from generator-level simulation. Thedata are poorly described by the pure phase space hypothesis in all three distributions. Thedegree of incompatibility between the data and the pure phase space fit is measured using thelikelihood ratio method and is determined to be at least 5.5, 6.1, and 3.4 standard deviations forthe J/ψΛ, J/ψ p, and Λp mass distributions, respectively. More details of the significance esti-mation can be found in Section 8.3. It is concluded that none of these three mass spectra couldbe described by a pure 3-body nonresonant phase space hypothesis, which is an indication ofmore complex dynamics in the B+ → J/ψΛp decay.

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Figure 2: The invariant mass distributions of the J/ψ p (upper left), J/ψΛ (upper right), andΛp (lower) systems from the B+ → J/ψΛp decay. The points are efficiency-corrected andbackground-subtracted data. Superimposed curves are obtained from simulation: the redcurve represents the phase space distribution corrected by the Λp angular structure with theinclusion of the first eight moments corresponding to the resonances in the Λp system with themaximum spin S = 4; the dashed red curve is the fit to the phase space distribution reweightedaccording to the 1D cos θK∗ distribution, which is defined as the H1 hypothesis and explainedin Section 8.3; the black dashed line corresponds to the pure phase space fit.

There are at least three known K∗+ resonances that can decay to Λp listed in Table 2 [3]. Eventhough these resonances are beyond the kinematic region of the B+ → J/ψΛp decay, the tailsfrom these broad excited kaon states can contribute to the two-body invariant mass distribu-tions, altering the pure phase space shapes.

To test this hypothesis, we use a model-independent approach first introduced by the BaBar

8

B+

K*+J/ψμ+

μ− p

ΛθJ/ψ θK*

ϕ

Figure 3: The illustration of decay angles in B+ → J/ψΛp decay.

Collaboration [26] and later used by the LHCb Collaboration [27] in the search for the Z(4430)resonance in the ψ(2S)π+ invariant mass spectrum and to support the existence of pentaquarkstates P+

c (4380) and P+c (4450) in J/ψp system [28]. This method allows to test whether the

contributions from a reflection of the resonant Λp angular amplitudes in the J/ψΛ and J/ψ pspectra are sufficient to describe the data. The distribution in cosine of the K∗ (Λp) helicityangle defined as the angle between Λ momentum and B+ momentum in the Λp rest frame,cos(θK∗), is shown in Fig. 4. It is clear that the distribution is not flat and has a structure thatcould affect the two-body invariant mass distributions under study.

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Figure 4: The background-subtracted and efficiency-corrected cos(θK∗) distribution on dataand simulation.

Table 2: Known excited K∗ states [3] that can decay to Λp.Resonance Mass [MeV] Natural width [MeV] JP

K∗4(2045)+ 2045± 9 198± 30 4+

K∗2(2250)+ 2247± 17 180± 30 2−

K∗3(2320)+ 2324± 24 150± 30 3+

In each M(Λp) bin, the cos(θK∗) distribution can be expressed as an expansion in terms ofLegendre polynomials:

dNd cos θK∗

=lmax

∑j=0〈PU

j 〉Pj(cos θK∗), (2)

where lmax depends on the maximum angular momentum needed to describe the data, Pj areLegendre polynomials, 〈PU

j 〉 are unnormalized Legendre moments (moments, in the follow-ing). The Legendre moments contain the full angular information of the Λp system and can be

8. Study of J/ψΛ, J/ψ p and Λp mass spectra 9

expressed using the following formula obtained by projecting Eq. (2) on the Legendre polyno-mial basis:

〈PUj 〉 =

Nreco

∑i=1

1εi Pj(cos θi

K∗), (3)

where Nreco is the number of selected events in each M(Λp) bin, εi = εi(cos θiK∗ , M(Λp)) is the

efficiency correction obtained as described in Section 5.

If we consider the observed resonances decaying to Λp listed in Table 2 up to a maximumspin S = 4, we should include the first eight moments (lmax = 8) to fully describe the ampli-tudes of these resonances and the interference between them. The dependence of the first eightmoments on M(Λp) is shown in Fig. 5.

8.2 Simulation reweighting according to the observed angular structure in theΛp system

To investigate whether the reflection of the Λp angular structure is sufficient to describe thedata, the reweighting of the simulated signal sample is performed and the result is comparedwith the background-subtracted and efficiency-corrected data. The simulated sample that doesnot include the detector effects is used for reweighting. This is justified because the efficiencycorrection is already applied to data. The mass structure in Λp is imposed to the simulationby applying to each event in the simulation a weight proportional to the ratio between theobserved data and simulation. To calculate the weights responsible for the angular structure,the moments discussed in the previous section are used in the following way:

wi = 1 +lmax

∑j=1〈PN

j 〉Pj(cos θiK∗), (4)

where 〈PNj 〉 =

2〈PUj 〉

Ncorrreco

are the normalized Legendre moments and Ncorrreco is the number of recon-

structed events in each M(Λp) bin.

The templates obtained after applying the weights given by Eq. (4) to simulation are then fit-ted to the efficiency-corrected and background-subtracted data. Results are shown in Fig. 2(in red solid line). As seen in the figure, the M(Λp) distribution in data is well described bythe reweighted simulation, which is expected by construction of the weights, given that thesimulation is reweighted to reproduce the mass spectrum observed in data. The M(Λp) dis-tribution is not affected by the wi weights since the integrals of the individual Pj(x) functionsover the full range in cos θK∗ are equal to zero. It is evident that the description of the M(J/ψΛ)and M(J/ψ p) data distributions is improved after accounting for the angular and invariantmass structure in the Λp system in simulation. The compatibility of data with the reweightedsimulation sample is quantified using likelihood method, as discussed in the next section.

8.3 Significance calculation

In this section the quality of data description with both the pure phase space and the phasespace augmented with the eight Legendre moment hypothesis is quantified using the likeli-hood ratio. To test the compatibility of data with the hypothesis including the first eight Leg-endre moments in the Λp system (H0), 2000 pseudoexperiments are generated, according to

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Figure 5: The dependence of first eight unnormalized Legendre moments on M(Λp).

the probability density function corresponding to this hypothesis FX(H0), where X stands forthe invariant mass of the system. The additional FX(H1) probability density function is de-fined as a function, which accounts for all of the features in the cos θK∗ data distribution, andis obtained by reweighting the pure phase space simulation according to the function fittedto the cos θK∗ distribution in data. Therefore, the FX(H1) hypothesis reflects the total angular

9. Summary 11

structure of Λp system and provides the best description of the M(J/ψΛ) and M(J/ψ p) in-variant mass spectra. The logarithm of the likelihood ratio is used to define the test statistic2∆NLL = −2 ∑N

i=1 log FX(H0)FX(H1)

, where the sum runs over the events in each pseudoexperimentor in data.

The 2∆NLL distribution from pseudoexperiments is fitted with a Gaussian function, the 2∆NLLdatavalue calculated using collision. The significance of the H0 hypothesis incompatibility withdata is calculated as the number of standard deviations between the observed 2∆NLLdata valueand the mean value of 2∆NLL distribution from pseudoexperiments.

The same test is performed to quantify the data incompatibility with the pure phase spacehypothesis. The only difference in the already described procedure, is that the H0 hypothesisis based on the pure phase space assumption.

There are number of systematic uncertainty sources that could contribute to the significancecalculation. First is the function used for the description of the background component inthe M(J/ψΛp) distribution, which enters through the sPlot background subtraction procedureperformed using that fucntion. This uncertainty is estimated by using two additional modelsfor the background component in the M(J/ψΛp) spectrum: the baseline model multiplied by aBernstein polynomial of the first or second order.

Another source of systematic uncertainty are the statistical fluctuations in the 2D efficiencycalculations. To test how the significance is affected by these fluctuations, additional parame-terizations of the 2D efficiency are used: a histogram with wider bins and a fit to the efficiencydistribution with 2D Bernstein polynomials, the uncertainties obtained from the 2D fit alsotaken into account. The last source of systematic uncertainty considered is the requirement on

the reflected invariant mass of the Λ candidate daughters |M((p→ π−)π+)−MPDGK0

S| > 2σ

K0S

eff .To test the effect of this requirement, the significance calculation is repeated without applyingthis selection.

Under the variations discussed above, the significance of the incompatibility of data with thepure phase space hypothesis is found to vary from 6.1 to 8.0 standard deviations for the J/ψ pmass spectrum, from 5.5 to 7.4 standard deviations for the J/ψΛ mass spectrum, and from 3.4 to4.6 standard deviations for the Λp mass distribution. The significance of data incompatibilitywith the phase space hypothesis augmented with eight Legendre moments, varies from 1.3 to2.8 (2.7) standard deviations for the J/ψ p (J/ψΛ) invariant mass spectrum.

9 SummaryUsing the data set of proton-proton collisions, collected by the CMS experiment at

√s = 8 TeV

and corresponding to an integrated luminosity of 19.6 fb−1, we measured the branching frac-

tion ratio B(B+→J/ψΛp)B(B+→J/ψK∗+) = (1.054 ± 0.057 (stat) ± 0.028 (syst) ± 0.011(B)) × 10−2. Using the

world-average branching fraction of the B+ → J/ψK∗+ decay, we obtained B(B+ → J/ψΛp) =(15.07± 0.81 (stat)± 0.40 (syst)± 0.86(B))× 10−6. The study of two-body invariant mass distri-butions of the B+ → J/ψΛp decay products was performed, showing that the spectra can not besatisfactory modeled with a phase space distribution. The incompatibility with the phase spacehypothesis is more than 5.5, 6, and 3.4 standard deviations for the J/ψΛ, J/ψ p, and Λp massspectra, respectively. A model-independent approach was used to conclude that the agreementis improved significantly, and is within three standard deviations, once the contribution fromK∗ resonances with spins up to 4 in the Λp system is accounted for.

12

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