Measurement of the ratio of branching fractions of the decays Λb0 → ψ(2S)Λ and Λb0 → J/ψΛ

Using pp collisions corresponding to 3 fb−1 integrated luminosity, recorded by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV, the ratio of branching fractions ℬΛb0→ψ2SΛ/ℬΛb0→J/ψΛ=0.513±0.023stat±0.016syst±0.011ℬ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathrm{\mathcal{B}}\left({\Lambda}_b^0\to \psi (2S)\Lambda \right)/\mathrm{\mathcal{B}}\left({\Lambda}_b^0\to J/\psi \Lambda \right)=0.513\pm 0.023\left(\mathrm{stat}\right)\pm 0.016\left(\mathrm{syst}\right)\pm 0.011\left(\mathrm{\mathcal{B}}\right) $$\end{document} is determined. The first uncertainty is statistical, the second is systematic and the third is due to the external branching fractions used.


LHCb detector
The LHCb detector [15,16] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks.The detector includes a high-precision tracking system consisting of a siliconstrip vertex detector (VELO) surrounding the pp interaction region [17], 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 [18] placed downstream of the magnet.The tracking system provides a measurement of the momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV/c.The minimum distance of a track to a primary vertex (PV), the impact parameter (IP), is measured with a resolution of (15 + 29/p T ) µm, where p T is the component of the momentum transverse to the beam, in GeV/c.Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors [19].Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter.Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [20].The online event selection is performed by a trigger [21], which consists of a hardware stage, based on information from the muon system, followed by a software stage, which applies a full event reconstruction.In the simulation, pp collisions are generated using Pythia [22] with a specific LHCb configuration [23].Decays of hadronic particles are described by EvtGen [24].The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [25] as described in Ref. [26].

Event selection and selection efficiencies
The J/ψ and ψ(2S) charmonium states, collectively called ψ, are reconstructed through their decay into two muons.Two tracks not originating from any PV, that are identified as oppositely charged muons, are required to form a good vertex.These muons have to fulfil various trigger requirements.At the hardware stage an event is required to contain a muon with high p T or two muons with a large product of their respective p T values.At the software stage further requirements are placed on the p T , momenta and IP of the muons.The reconstructed ψ masses must be within ±100 MeV/c 2 of their known masses [14].
The Λ candidates are reconstructed by combining a pion and a proton candidate.Due to its long lifetime, the Λ baryon can decay either inside or outside the VELO.The pion and proton can be reconstructed including hits from the VELO (long track) or without (downstream track).Combinations where the track types of pion and proton differ are not considered.Due to different momentum resolutions of these track types, some selection requirements differ between the two samples.The pion and proton candidates are required to have high momentum (> 2 GeV/c) and high p T and the tracks must be displaced from any PV.In addition, long-track proton candidates must be consistent with the proton hypothesis.The invariant mass of the pion and proton combination has to be compatible with the known Λ mass [14] and both tracks must come from a common vertex.Furthermore, the Λ candidate is required to have a decay time longer than 2 ps.
The Λ 0 b candidate is reconstructed by combining the ψ and the Λ candidates and requiring that they form a common vertex.The PV that fits best to the Λ 0 b flight direction is assigned as associated PV.It is required that the Λ 0 b momentum points back to this PV and its decay vertex is significantly displaced from this PV.Additional requirements are imposed using a kinematic fit with constrained ψ and Λ masses.For downstream-track candidates the reconstructed Λ decay time using this fit must be longer than 9 ps.The χ 2 /ndf of this kinematic fit is required to be smaller than 36/6 for long-track candidates and smaller than 26/6 for downstream-track candidates.
After the selection, about 1% of all events contain multiple candidates.Among these multiple candidates a single candidate is retained using a random but reproducible procedure.To ensure a precise efficiency determination, fiducial cuts on the Λ 0 b baryon, p T (Λ 0 b ) < 20 GeV/c and 2 < η(Λ 0 b ) < 4.5 are applied.The signal efficiency is evaluated separately for each channel and track type, using simulations and crosschecked with data.The simulation assumes unpolarised decays but is corrected using theory predictions [10] for both decay channels.Sources of inefficiencies are the geometrical acceptance of the detector, the trigger, the track reconstruction, and the candidate selection.The last three efficiencies depend on the kinematics of the Λ 0 b baryon, which is not perfectly simulated.To account for the mismodelling, these efficiencies are determined in bins of p T (Λ 0 b ) and η(Λ 0 b ).The same binning scheme, consisting of seven bins for each of the two variables, is used for both decay channels.The binning scheme is designed such that all bins are uniformly populated, with at least 100 entries in each bin.The resulting efficiency for a given candidate is determined by linear interpolation of the binned efficiency model to reduce effects arising from the choice of the binning scheme.For the interpolation, the mean value in each bin is used and additional bins are added to ensure interpolation at the boundaries.The resulting efficiency functions together with the distribution of the corresponding signal candidates are shown in Fig. 1.

Signal yield determination
The signal yield is determined using an extended unbinned maximum likelihood fit to the reconstructed Λ 0 b mass in the range 5350 to 5750 MeV/c 2 separately for both decay channels and track types.The fit model for the reconstructed Λ 0 b mass consists of several components.The signal is modelled with a double-sided Hypatia function [27], where the tail parameters are fixed to values obtained from fits to the simulation.The combinatorial background is modelled with an exponential function.A background due to B 0 → ψK 0 S decays, where the K 0 S meson decays to two pions and one of the pions is misidentified as a proton, is vetoed in the long-track sample by applying additional particle identification requirements.In the downstream-track sample this component is modelled with a kerneldensity estimation using a Gaussian kernel [28] obtained from simulated B 0 → ψK 0 S decays.Another source of background is Ξ − b → ψΞ − decays, where the Ξ − baryon decays to Λπ − and the pion is not reconstructed.Contributions from this background source are negligible in the long-track sample due to the sum of the large lifetimes of the Ξ and the Λ baryons.Thus, the Λ → pπ − decay only happens in less than 2% of the Ξ − b → ψΞ − decays inside the VELO.In the downstream-track sample this background is modelled with a kernel-density estimation using a Gaussian kernel obtained from simulated Ξ − b → ψΞ − decays.The number of observed signal events is determined from a fit to unweighted invariant-mass distributions.The resulting fit is shown in Fig. 2, separately for long and downstream tracks, and the resulting yields for each data sample are shown in Table 1.In a second fit, the efficiency-corrected yields are obtained assigning to each candidate a  track type weight given by the inverse of the efficiency.This fit to the two weighted invariant-mass distributions is shown in Fig. 3 for each data sample and the resulting efficiency-corrected signal yields for each data sample are reported in Table 2. downstream 223 000 ± 13 000 3 320 000 ± 50 000 long 280 000 ± 18 000 3 980 000 ± 80 000
Assuming lepton universality, the value for the branching fraction of ψ(2S) into two electrons, B(ψ(2S) → e + e − ) = (0.793 ± 0.017)% [14], is used in the calculation due to its lower uncertainty compared to the muon decay.Using the value for the branching fraction 2.2 % total 3.8 % total without B(cc → ) 3.1 % of J/ψ into two muons, B(J/ψ → µ + µ − ) = (5.961± 0.033)% [14] and the efficiencycorrected signal yields, given in Table 2, the ratios of branching fractions for both track types are calculated to be where the statistical uncertainty only includes the uncertainty on the measured signal yields.The results for the two classes of tracks are in good agreement and are combined using a weighted average into

Systematic uncertainties
The sources of systematic uncertainty are summarised in Table 3.The effect of each of these sources on the measured ratio is evaluated independently and is quoted as a relative uncertainty on the measured ratio of branching fractions.These relative uncertainties are summed in quadrature to obtain the total systematic uncertainty.All efficiencies are evaluated from simulated data, therefore the precision is limited by the size of the simulated dataset.This effect is determined by varying the binned efficiencies within binomial uncertainties and re-evaluating the efficiency-weighted signal yield.The result varies by 1.1 %, which is assigned as the systematic uncertainty.The effect of the chosen number of bins in both dimensions for the efficiency determination is determined by varying the numbers of bins between five and ten in each dimension independently.The largest difference compared to the baseline result is a change of 1.6% in the ratio of yields, which is assigned as systematic uncertainty.To estimate a systematic uncertainty for the trigger efficiency, kinematically similar channels with higher rates, B + → J/ψ K + and B + → ψ(2S)K + , are used [29].The resulting trigger efficiency on data is compatible with that obtained on simulation, but the systematic uncertainty due to the size of the sample used for this method is 1.2 %.The effect of using alternative fit models that describe the mass distributions are evaluated using pseudoexperiments.Candidates are generated using an alternative model and then fitted with the default model.The 1.6% relative difference between the fitted and generated yield is assigned as systematic uncertainty.The used correction on the helicity angles in simulation is taken from theory predictions [10].An alternative approach is to use the measured distributions from data and this leads to a difference of 1.3% to the baseline result, which is assigned as systematic uncertainty.The effect of neglecting peaking backgrounds for long-track candidates is evaluated by including the Ξ − b → ψΞ − and B 0 → ψK 0 S components in the long-track sample fits and letting their yields vary freely.The resulting yields for these components are compatible with zero and the variation of the signal yield is negligible.Summing these uncertainties in quadrature leads to a systematic uncertainty of 3.1 %.Another uncertainty arises from the external values for the branching fractions of the charmonium to two muon decays, which is 2.2 % [14].
The consistency of the results has been checked by repeating the analysis separately with datasets with different magnet polarities and years of data taking.In another crosscheck, the B 0 → ψK 0 S background is vetoed instead of being included in the fit.None of these checks shows a significant deviation from the baseline result.

Conclusion
In summary the ratio of branching fractions is determined to be where the first uncertainty is statistical, the second is systematic and the third is due to the uncertainty of the used ψ meson branching fractions to two leptons [14].This measurement is compatible within one standard deviation with the measurement from the ATLAS collaboration [9] and has a better precision.It confirms the discrepancy with the covariant quark model theory predictions [10,11]

Figure 1 :
Figure 1: Interpolated efficiency function for long-track candidates for (a) Λ 0 b → ψ(2S)Λ and (b) Λ 0 b → J/ψ Λ and for downstream-track candidates for (c) Λ 0 b → ψ(2S)Λ and (d) Λ 0 b → J/ψ Λ candidates.The distribution of the candidates on data is shown with black dots (each dot refers to one candidate).Statistical fluctuations of the simulated sample are contributing to the efficiency function at the phase-space boundaries, where data candidates are not affected.

Table 3 :
Relative systematic uncertainties on the ratio of branching fractions.
69National Research Centre Kurchatov Institute, Moscow, Russia, associated to 34 70 National University of Science and Technology "MISIS", Moscow, Russia, associated to 34 71 National Research Tomsk Polytechnic University, Tomsk, Russia, associated to 34 72 Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -CSIC, Valencia, Spain, associated to 40 73 Los Alamos National Laboratory (LANL), Los Alamos, United States, associated to 61 a Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil b Laboratoire Leprince-Ringuet, Palaiseau, France c P.N.Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia d Università di Bari, Bari, Italy e Università di Bologna, Bologna, Italy f Università di Cagliari, Cagliari, Italy g Università di Ferrara, Ferrara, Italy h Università di Genova, Genova, Italy i Università di Milano Bicocca, Milano, Italy j Università di Roma Tor Vergata, Roma, Italy k Università di Roma La Sapienza, Roma, Italy l AGH -University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland m LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain n Hanoi University of Science, Hanoi, Vietnam o Università di Padova, Padova, Italy p Università di Pisa, Pisa, Italy q Università degli Studi di Milano, Milano, Italy r Università di Urbino, Urbino, Italy s Università della Basilicata, Potenza, Italy t Scuola Normale Superiore, Pisa, Italy u Università di Modena e Reggio Emilia, Modena, Italy v MSU -Iligan Institute of Technology (MSU-IIT), Iligan, Philippines w Novosibirsk State University, Novosibirsk, Russia x Escuela Agrícola Panamericana, San Antonio de Oriente, Honduras y Physics and Micro Electronic College, Hunan University, Changsha City, China z Lanzhou University, Lanzhou, China aa National Research University Higher School of Economics, Moscow, Russia † Deceased