Measurement of the branching ratio $\Gamma(\Lambda_b^0 \rightarrow \psi(2S)\Lambda^0)/\Gamma(\Lambda_b^0 \rightarrow J/\psi\Lambda^0)$ with the ATLAS detector

An observation of the $\Lambda_b^0 \rightarrow \psi(2S) \Lambda^0$ decay and a comparison of its branching fraction with that of the $\Lambda_b^0 \rightarrow J/\psi \Lambda^0$ decay has been made with the ATLAS detector in proton--proton collisions at $\sqrt{s}=8\,$TeV at the LHC using an integrated luminosity of $20.6\,$fb$^{-1}$. The $J/\psi$ and $\psi(2S)$ mesons are reconstructed in their decays to a muon pair, while the $\Lambda^0\rightarrow p\pi^-$ decay is exploited for the $\Lambda^0$ baryon reconstruction. The $\Lambda_b^0$ baryons are reconstructed with transverse momentum $p_{\rm T}>10\,$GeV and pseudorapidity $|\eta|<2.1$. The measured branching ratio of the $\Lambda_b^0 \rightarrow \psi(2S) \Lambda^0$ and $\Lambda_b^0 \rightarrow J/\psi \Lambda^0$ decays is $\Gamma(\Lambda_b^0 \rightarrow \psi(2S)\Lambda^0)/\Gamma(\Lambda_b^0 \rightarrow J/\psi\Lambda^0) = 0.501\pm 0.033 ({\rm stat})\pm 0.019({\rm syst})$, lower than the expectation from the covariant quark model.


Introduction
The Λ 0 b baryon properties have been extensively studied at the Large Hadron Collider (LHC) [1][2][3][4][5][6][7].The decay channel Λ 0 b → J/ψ(µ + µ − )Λ 0 (pπ − ) 1 has been primarily used by the LHC experiments in these studies, although a number of other Λ 0 b decay channels have been exploited by the LHCb experiment.In particular, a measurement of the differential branching fraction and angular analysis of the rare decay Λ 0 b → µ + µ − Λ 0 was performed by LHCb [8,9] following observation of this decay by the CDF experiment [10] at the Tevatron collider.However, no results for the decay mode Λ 0 b → ψ(2S )Λ 0 have yet been reported, although a measurement of the decay properties would be useful for verification of theoretical predictions [11].
The Λ 0 b → ψ(2S )Λ 0 branching fraction should be of the same order as that of the decay Λ 0 b → J/ψΛ 0 as suggested by the branching fraction values of the B 0 , B + and B 0 s meson decays to ψ(2S )/J/ψ and either a pseudoscalar (K 0 , K + , η) or vector (K * 0 , K * + , φ) meson.The branching ratios of such B meson decays to ψ(2S )X and J/ψX are within the 0.5-0.8range [12], and are generally reproduced by factorisation calculations [13].The only available theoretical calculation of the branching ratio of the Λ 0 b → ψ(2S )Λ 0 and Λ 0 b → J/ψΛ 0 decays, performed in the framework of the covariant quark model [14], predicts 0.8 with an uncertainty of approximately 0.1 [11].
An observation of the Λ 0 b → ψ(2S )Λ 0 decay and a measurement of the branching ratio of the Λ 0 b → ψ(2S )Λ 0 and Λ 0 b → J/ψΛ 0 decays is reported in this Letter.The J/ψ and ψ(2S ) mesons are reconstructed in their decays to a muon pair, while the Λ 0 → pπ − decay is exploited for the Λ 0 baryon reconstruction.The Λ 0 b baryons are reconstructed with transverse momentum p T > 10 GeV and pseudorapidity |η| < 2.1.

The ATLAS detector, data and Monte Carlo simulation samples
A detailed description of the ATLAS detector can be found elsewhere [15].A brief outline of the components most relevant to this analysis is given below.
The ATLAS detector has a three-level trigger system [16]: the hardware-based Level-1 system and the two-stage High Level Trigger (HLT).For this measurement, dimuon triggers are used.At Level-1, the dimuon triggers search for patterns of MS hits corresponding to dimuons passing various p T thresholds.Since the rate from the low-p T dimuon triggers was too high, prescale factors were applied to reduce their output rates.The data sample used in this analysis was collected using three dimuon triggers with p T thresholds of 4 GeV for both muons, 4 GeV and 6 GeV for the two muons, and 6 GeV for both muons.At the HLT, the dimuon triggers used require muons with opposite charges and dimuon mass in the range 2.5 < m(µ + µ − ) < 4.3 GeV.This analysis uses 20.6 fb −1 of proton-proton collision data with a centre-of-mass energy of 8 TeV recorded by the ATLAS detector at the LHC in 2012.The uncertainty on the integrated luminosity is ±2.8%.It is derived following the same methodology as that detailed in [17].The event sample is processed using the standard offline ATLAS detector calibration and event reconstruction code.There are typically a few primary vertex candidates in each event due to multiple collisions per bunch crossing.Only events with at least four reconstructed tracks with p T > 0.4 GeV and at least one reconstructed primary vertex candidate are kept for further analysis.
To model inelastic pp events containing 3 four large samples of Monte Carlo (MC) simulated events are prepared using the PYTHIA 8.1 [18] MC generator.The B 0 MC samples are needed to control reflections from B 0 decays to the Λ 0 b signal distributions.The generation is based on leading-order matrix elements for all 2 → 2 QCD processes.Initial-and final-state parton showering is used to simulate higher-order processes.Generated events with both muons from J/ψ or ψ(2S ) decays having transverse momenta above 3.5 GeV and pseudorapidities within ±2.5, and, for Λ 0 b MC samples, with the Λ 0 transverse momentum above 1 GeV are passed through a full simulation of the detector using the ATLAS simulation framework [19] based on GEANT4 [20,21] and processed with the same reconstruction program as used for the data.An emulation of the three triggers used for the data collection is applied to the MC samples.The angular decay distributions of the Λ 0 b → J/ψ(µ + µ − )Λ 0 (pπ − ) decay are modelled using the helicity amplitudes measured by ATLAS [2].For the Λ 0 b → ψ(µ + µ − )Λ 0 (pπ − ) decay, the helicity amplitudes are set to the predicted values [11].
3 Event and Λ 0 b candidate selection

Charmonium candidate selection
Events are required to contain at least two muons identified by the MS with tracks reconstructed in the ID.
The reconstructed muons are required to match the muon candidates identified by the trigger.The muon track parameters are taken from the ID measurement alone, since the MS does not significantly improve the precision in the momentum range relevant for the charmonium measurements presented here.To ensure accurate measurements, each muon track must contain at least six SCT hits and at least one Pixel hit.Muon candidates satisfying these criteria are required to have opposite charges and a successful fit to a common vertex with χ 2 /N dof < 10, where χ 2 is the fit quality with the number of degrees of freedom N dof = 1.Events with m(µ + µ − ) values within ±200 MeV intervals around the J/ψ and ψ(2S ) world average masses [12] are used to search for Λ 0 → pπ − candidates.

Λ 0 and Λ0 candidate selection
In all events with J/ψ or ψ(2S ) candidates, pairs of tracks from particles with opposite charge are combined to form Λ 0 candidates.Each track is required to have at least one Pixel or SCT hit.Only pairs successfully fitted to a common vertex with χ 2 /N dof < 5 are kept.The track with larger momentum is assigned the proton mass hypothesis since the proton always has a larger momentum than the pion for Λ 0 baryons with momenta larger than 0.3 GeV.To suppress combinatorial background the following requirements are used: • |z 0 (p)| < 25 mm, where z 0 (p) is the proton longitudinal impact parameter with respect to the dimuon vertex.MC studies show the requirement produces no loss of signal.
• L BL xy (Λ 0 ) > 7 mm, where L BL xy (Λ 0 ) is the transverse decay length 4 of the Λ 0 candidate measured from the beam line.
Events with m(pπ − ) values within an interval of ±20 MeV around the Λ 0 world average mass [12] are kept for further analysis.

Λ 0 b reconstruction
Tracks of the selected charmonium and Λ 0 candidates are simultaneously refitted with the dimuon and dihadron masses constrained to the world average masses of J/ψ (m J/ψ ) or ψ(2S ) (m ψ(2S ) ) and Λ 0 (m Λ 0 ) [12], respectively.The combined momentum of the refitted Λ 0 track pair is required to point to the dimuon vertex.To control B 0 reflections to the Λ 0 b signal distributions, a B 0 decay topology fit is also attempted for each track quadruplet successfully fitted to the Λ 0 b topology, i.e. the pion mass is assigned to both hadron tracks and the dihadron mass is constrained to the world average mass of K 0 S [12].To suppress combinatorial and B 0 backgrounds the following requirements are used: is the Λ 0 b world average mass [12].The primary vertex candidate with at least three tracks and the smallest value of the three-dimensional impact parameter of the Λ 0 b candidate is selected as the actual primary vertex.
The muon transverse momenta and pseudorapidities are required to be in the ranges with high values of the trigger and reconstruction acceptances: The kinematic range of the Λ 0 b measurement is fixed to The invariant mass distribution m(J/ψΛ 0 ), calculated using track parameters from the Λ 0 b topology fits, is shown in Figure 1  The m(J/ψΛ 0 ) and m(J/ψK 0 S ) distributions are simultaneously fitted to sums of signal and two-component background distributions.The signals are described by modified Gaussian functions [22].The modified Gaussian function is defined as where x = |(m − m 0 )/σ|.This functional form, introduced to take into account the non-Gaussian tails of resonant signals, describes both data and MC signals well.The signal position, m 0 , and width, σ, as well as the number of the signal events are free parameters of the fit.The non-resonant backgrounds in the distributions are described by independent exponential functions.The mutual B 0 and Λ 0 b reflections are described by MC templates normalised to the numbers of B 0 and Λ 0 b hadrons obtained in the fit.The reflection normalisations are corrected for small losses (2-6%) of Λ 0 b and B 0 hadrons that passed the Λ 0 b reconstruction but failed the B 0 reconstruction.The corrections are obtained using MC simulation.A similar fit is performed for the m(ψ(2S )Λ 0 ) and m(ψ(2S )K 0 S ) distributions.In the analysis of the combined Λ 0 b and Λ0 b samples, the ratio of the MC Λ 0 b and Λ0 b events is set to the data ratio obtained in the separate Λ 0 b → J/ψΛ 0 and Λ0 b → J/ψ Λ0 fits (Figure 1).The Λ 0 b and Λ0 b fitted yields are 3523 ± 89 and 3414 ± 92, respectively, providing the ratio 1.03 ± 0.04(stat).
The results of the fits for the combined Λ 0 b and Λ0 b samples are summarised in Table 1.The Λ 0 b mass values obtained from the fits of the m(J/ψΛ 0 ) and m(ψ(2S )Λ 0 ) distributions agree with each other and with the world average Λ 0 b mass value [12].The signal widths are different, reflecting the difference in charmonium masses in the two decay channels, in agreement with the MC expectations.The quality, χ 2 /N dof , of the Λ 0 b → J/ψΛ 0 and Λ 0 b → ψ(2S )Λ 0 signal fits are 1.0 and 1.1, respectively.To verify that the observed Λ 0 b signals correspond to the Λ 0 b → J/ψΛ 0 and Λ 0 b → ψ(2S )Λ 0 decays the signal reconstruction is repeated with only one mass constraint for either the dimuon or the dihadron track pair in the cascade fit and the Λ 0 b mass is calculated using the mass-difference method.In the case that the dihadron mass is fixed to the Λ 0 mass, the Λ 0 b mass is calculated as m(µ with those in Table 1. Figure 4 shows the m(µ + µ − ) distributions for the Λ 0 b → J/ψΛ 0 and Λ 0 b → ψ(2S )Λ 0 candidates reconstructed with the mass constraint for the dihadron pair and selected within ±3σ sig around the world average Λ 0 b mass.Clear signals from J/ψ and ψ(2S ) are seen.The m(µ + µ − ) distributions are fitted to a sum of an exponential function describing the background and a modified Gaussian function describing the signal.The signal yields are found to be N J/ψ = 9770 ± 120 and N ψ(2S ) = 724 ± 45. Figure 5 shows the m(pπ − ) distributions for the Λ 0 b candidates reconstructed with the mass constraint for the dimuon pair and selected within ±3σ sig around the world average Λ 0 b mass.Clear signals from Λ 0 are seen.The m(pπ − ) distributions are fitted to a sum of a threshold function describing the background and a modified Gaussian function describing the signal.The threshold function has the form where m p and m π − are the proton and pion masses, respectively, and A, B, C and D are free parameters.The Λ 0 signal yields are found to be 7710 ± 120 and 702 ± 38 for the Λ 0 b → J/ψΛ 0 and Λ 0 b → ψ(2S )Λ 0 candidates, respectively.The numbers of signal charmonium and Λ 0 events are larger than the numbers of the corresponding Λ 0 b signal events because the backgrounds are partly due to genuine charmonium and Λ 0 states.
The numbers of Λ 0 b signal events in the two decay modes, reported in Table 1, are corrected for detector effects and selection efficiencies as N cor = N sig /A, where N cor is the corrected number and A is the MC acceptance.The MC events with the ψ(2S )/J/ψ muons having transverse momenta above 3.5 GeV and pseudorapidities within ±2.5, and Λ 0 transverse momentum above 1 GeV, passed through the detector simulation and event reconstruction, are used to correct the numbers of signal events in the fiducial range, defined as follows: The acceptances are calculated as the ratio of the number of reconstructed Λ 0 b signal events passing all selection requirements in the above fiducial range to the number of Λ 0 b baryons in the same decay mode and fiducial range at the MC generator level.These acceptances are 4.16 ± 0.02(stat)% and 4.30 ± 0.03(stat)% for the Λ 0 b → J/ψΛ 0 and Λ 0 b → ψ(2S )Λ 0 decays, respectively.In the fiducial range, the ratio of the corrected numbers of Λ 0 b signal events in the two decay modes is 0.0841 ± 0.0055(stat).Then the numbers are corrected, using generator-level MC samples with no requirements on the µ ± and Λ 0 selection, from the above fiducial range to the kinematic range of the Λ 0 b measurement 1.The acceptances of the latter corrections are 7.57±0.06(stat)%and 9.61±0.07(stat)%for the Λ 0 b → J/ψΛ 0 and Λ 0 b → ψ(2S )Λ 0 decays, respectively.Finally, the branching ratio of the two Λ 0 b decays is calculated as where B is the branching fraction of the corresponding charmonium decay to a lepton pair.In the case of J/ψ, the branching fraction B(J/ψ → µ + µ − ) = 0.05961 ± 0.00033 [12] is used.For B(ψ(2S ) → + − ), the branching fraction B(ψ(2S ) → e + e − ) = 0.00789 ± 0.00017 is used, assuming lepton universality, because it is measured with better precision than in the muon channel, B(ψ(2S ) → µ + µ − ) = 0.0079 ± 0.0009 [12].
Five groups of systematic uncertainty sources are considered.The effect of each group on the measured ratio, obtained by adding in quadrature the effects of independent sources, is shown in parentheses: • The uncertainty originating from the MC statistical uncertainty (±1.3%).
The measured branching ratio of the two Λ 0 b decays is where the contributions from the first four groups of systematic uncertainty are added in quadrature.The uncertainty due to the uncertainties of the charmonium branching fractions B is quoted separately.The luminosity uncertainty, uncertainties of the muon and hadron track reconstruction and the vertexing uncertainties cancel out in the ratio.The bias in the measured ratio due to contributions from the rare decay Λ 0 b → µ + µ − Λ 0 is estimated using the LHCb measurement [9] of the rare decay's differential branching fraction to be below 0.5% and thus neglected.Consistent ratio values are found when calculated in bins of p T (Λ 0 b ) or separately for Λ 0 b and Λ0 b baryons.The measured ratio lies in the range 0.5-0.8found for the branching ratios of analogous B meson decays [12].The only available calculation for the branching ratio of the two Λ 0 b decays (0.8 ± 0.1 [11]) exceeds the measured value.

Figure 1 :Figure 2 :Figure 3 :
Figure 1: The invariant mass distributions m(J/ψΛ 0 ) (left plot) and m(J/ψ Λ0 ) (right plot) for selected Λ 0 b and Λ0 b candidates, respectively.The solid histograms represent the fit results (see text).The Λ 0 b signals (dashed lines) and the B 0 reflections are also shown.
separately for the selected Λ 0 b and Λ0 b candidates.Clear signals with similar size are seen in the two distributions around the world average mass of the Λ 0 b baryon.Figures 2 and 3 show the m(J/ψΛ 0 ) and m(ψ(2S )Λ 0 ) distributions for the combined sample of the Λ 0 b and Λ0 b candidates.The invariant mass distributions m(J/ψK 0 S ) and m(ψ(2S )K 0 S ) from the B 0 topology fits are also shown.Clear signals are seen in the m(J/ψΛ 0 ) and m(ψ(2S )Λ 0 ) distributions 5 around the world average mass of the Λ 0 b baryon.There are also signals in the m(J/ψK 0 S ) and m(ψ(2S )K 0 S ) distributions near the world average mass of the B 0 meson [12].The B 0 signals are smaller than the Λ 0 b signals due to the selection requirements.

4 Figure 4 :
Figure 4: The m(µ + µ − ) distributions for Λ 0 b → J/ψΛ 0 candidates (left plot) and Λ 0 b → ψ(2S )Λ 0 candidates (right plot) after full selection, without a mass constraint on the charmonium mass in the cascade fit.The spectra are fitted with a sum of an exponential function and a modified Gaussian function.

Figure 5 :
Figure 5: The m(pπ − ) distributions for Λ 0 b → J/ψΛ 0 candidates (left plot) and Λ 0 b → ψ(2S )Λ 0 candidates (right plot) after full selection, without a mass constraint on the Λ 0 mass in the cascade fit.The spectra are fitted with a sum of a threshold function and a modified Gaussian function.

•
Dependence on the Λ 0 b production model (±0.1%).The uncertainty is obtained by varying the MC p T (Λ 0 b ) and |η(Λ 0 b )| distributions while preserving agreement with the data distributions, varying the MC ratio of Λ 0 b and Λ0 b baryons in the range allowed by the separate data fits (Section 3), varying the lifetimes of the Λ 0 and Λ 0 b baryons in the ranges of their uncertainties [12].• Dependence on the Λ 0 b polarisation model (±1.1%).The uncertainty is obtained by varying the MC Λ 0 b → J/ψ(µ + µ − )Λ 0 (pπ − ) helicity amplitudes in the range of their uncertainties [2], and by changing the MC Λ 0 b → ψ(µ + µ − )Λ 0 (pπ − ) helicity amplitudes to those measured by ATLAS for the Λ 0 b → J/ψ(µ + µ − )Λ 0 (pπ − ) decay [2].• The uncertainty of the signal extraction procedures (±2.8%).The uncertainty is determined by changing the background parameterisations to second order polynomials and by reducing the ranges used for the signal fits by 20 MeV from either left or right side, independently for the two Λ 0 b signals.In addition, the corrections of the reflection normalisations, obtained from MC simulation, are varied by half of their values.This uncertainty is affected by statistical fluctuations.

Table 1 :
The numbers of signal events, N sig , signal masses, m sig , and signal widths, σ sig , obtained by the fits (see text).Only statistical uncertainties are shown.
Also at Department of Physics, King's College London, London, United Kingdom b Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan c Also at Novosibirsk State University, Novosibirsk, Russia d Also at TRIUMF, Vancouver BC, Canada e Also at Department of Physics, California State University, Fresno CA, United States of America f Also at Department of Physics, University of Fribourg, Fribourg, Switzerland g Also at Departamento de Fisica e Astronomia, Faculdade de Ciencias, Universidade do Porto, Portugal h Also at Tomsk State University, Tomsk, Russia i Also at CPPM, Aix-Marseille Université and CNRS/IN2P3, Marseille, France j Also at Universita di Napoli Parthenope, Napoli, Italy k Also at Institute of Particle Physics (IPP), Canada l Also at Particle Physics Department, Rutherford Appleton Laboratory, Didcot, United Kingdom m Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia n Also at Louisiana Tech University, Ruston LA, United States of America o Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain p Also at Graduate School of Science, Osaka University, Osaka, Japan q Also at Department of Physics, National Tsing Hua University, Taiwan r Also at Department of Physics, The University of Texas at Austin, Austin TX, United States of America s Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia t Also at CERN, Geneva, Switzerland u Also at Georgian Technical University (GTU),Tbilisi, Georgia v Also at Manhattan College, New York NY, United States of America w Also at Hellenic Open University, Patras, Greece x Also at Institute of Physics, Academia Sinica, Taipei, Taiwan y Also at LAL, Université Paris-Sud and CNRS/IN2P3, Orsay, France z Also at Academia Sinica Grid Computing, Institute of Physics, Academia Sinica, Taipei, Taiwan aa Also at School of Physics, Shandong University, Shandong, China ab Also at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia ac Also at Section de Physique, Université de Genève, Geneva, Switzerland ad Also at International School for Advanced Studies (SISSA), Trieste, Italy ae Also at Department of Physics and Astronomy, University of South Carolina, Columbia SC, United States of America a f Also at School of Physics and Engineering, Sun Yat-sen University, Guangzhou, China ag Also at Faculty of Physics, M.V.Lomonosov Moscow State University, Moscow, Russia ah Also at National Research Nuclear University MEPhI, Moscow, Russia ai Also at Department of Physics, Stanford University, Stanford CA, United States of America a j Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary ak Also at University of Malaya, Department of Physics, Kuala Lumpur, Malaysia a * Deceased