Precision measurement of the ratio of the Λ 0 b to B 0 lifetimes

The LHCb measurement of the lifetime ratio of the Λ 0 b baryon to the B 0 meson is updated using data corresponding to an integrated luminosity of 3.0 fb − 1 collected using 7 and 8 TeV centre-of-mass energy pp collisions at the LHC. The decay modes used are Λ 0 b → J /ψ pK − and B 0 → J /ψ π + K − , where the π + K − mass is consistent with that of the K ∗ 0 ( 892 ) meson. The lifetime ratio is determined with unprecedented precision to be 0 . 974 ± 0 . 006 ± 0 . 004, where the ﬁrst uncertainty is statistical and the second systematic. This result is in agreement with original theoretical predictions based on the heavy quark expansion. Using the current world average of the B 0 lifetime, the Λ 0 b lifetime is found to be 1 . 479 ± 0 . 009 ± 0 . 010 ps. the by 3 .


Introduction
The heavy quark expansion (HQE) is a powerful theoretical technique in the description of decays of hadrons containing heavy quarks. This model describes inclusive decays and has been used extensively in the analysis of beauty and charm hadron decays, for example in the extraction of Cabibbo-Kobayashi-Maskawa matrix elements, such as |V cb | and |V ub | [1]. The basics of the theory were derived in the late 1980s [2]. For b-flavored hadrons, the expansion of the total decay width in terms of powers of 1/m b , where m b is the b quark mass, was derived a few years later [3]. These developments are summarized in Ref. [4]. It was found that there were Some authors sought to explain the small value of the ratio by including additional operators or other modifications [11], while others thought that the HQE could be pushed to provide a ratio of about 0.9 [12], but not so low as the measured value. Recent measurements have obtained higher values [13]. In fact, the most precise previous measurement from LHCb, 0.976 ± 0.012 ± 0.006 [14], based on 1.0 fb −1 of data, agreed with the early HQE expectations.
In this paper we present an updated result for τ Λ 0 b /τ B 0 using data from 3.0 fb −1 of integrated luminosity collected with the LHCb detector from pp collisions at the LHC. Here we add the 2.0 fb −1 data sample from the 8 TeV data to our previous 1.0 fb −1 7 TeV sample [14]. The data are combined and analyzed together. Larger simulation samples are used than in our previous publication, and uncertainties are significantly reduced.
The Λ 0 b baryon is detected in the J /ψ pK − decay mode, discovered by LHCb [14], while the B 0 meson is reconstructed in J /ψ K * 0 (892) decays, with K * 0 (892) → π + K − . 1 These modes have the same topology into four charged tracks, thus facilitating cancellation of systematic uncertainties in the lifetime ratio. The LHCb detector [15] 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 silicon-strip vertex 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 siliconstrip detectors and straw drift tubes [16] placed downstream. The combined tracking system provides a momentum measurement with relative uncertainty that varies from 0.4% at 5 GeV to 0.6% at 100 GeV, and impact parameter resolution of 20 μm for tracks with large transverse momentum, p T . 2 Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov (RICH) detectors [17]. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are iden- 1 Charge-conjugate modes are implicitly included throughout this Letter. 2 We use natural units withh = c = 1. tified by a system composed of alternating layers of iron and multiwire proportional chambers [18]. The trigger [19] consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction.

Event selection and b hadron reconstruction
Events selected for this analysis are triggered by a J /ψ → μ + μ − decay, where the J /ψ is required at the software level to be consistent with coming from the decay of a b hadron by use of either impact parameter (IP) requirements or detachment of the reconstructed J /ψ decay position from the associated primary vertex.
Events are required to pass a cut-based preselection and then are further filtered using a multivariate discriminator based on the boosted decision tree (BDT) technique [20]. To satisfy the preselection requirements the muon candidates must have p T larger than 550 MeV, while the hadron candidates are required to have p T larger than 250 MeV. Each muon is required to have χ 2 where χ 2 IP is defined as the difference in χ 2 of the primary vertex reconstructed with and without the considered track. Events must have a μ + μ − pair that forms a common vertex with χ 2 < 16 and that has an invariant mass between −48 and +43 MeV of the known J /ψ mass [1]. Candidate μ + μ − pairs are then constrained to the J /ψ mass to improve the determination of the J /ψ momentum. The two charged final state hadrons must have a vector summed p T of more than 1 GeV, and form a vertex with χ 2 /ndf < 10, where ndf is the number of degrees of freedom, and a common vertex with the J /ψ candidate with χ 2 /ndf < 16. Particle identification requirements are different for the two modes. Using information from the RICH detectors, a likelihood is formed for each hadron hypothesis. The difference in the logarithms of the likelihoods, DLL(h 1 − h 2 ), is used to distinguish between the two hypotheses, h 1 and h 2 [17]. In the Λ 0 b decay the kaon candidate must have DLL(K − π) > 4 and DLL(K − p) > −3, while the proton candidate must have DLL(p − π) > 10 and DLL(p − K ) > −3.
The BDT selection uses the smaller value of the DLL(μ − π) of the μ + and μ − candidates, the p T of each of the two charged hadrons, and their sum, the Λ 0 b p T , the Λ 0 b vertex χ 2 , and the χ 2 IP of the Λ 0 b candidate with respect to the primary vertex. The choice of these variables is motivated by minimizing the dependence of the selection efficiency on decay time; for example, we  Fig. 2. For B 0 candidates we also require that the invariant π + K − mass be within ±100 MeV of the K * 0 (892) mass.
In order to measure the number of signal events we need to ascertain the backgrounds. The background is dominated by random track combinations at masses around the signal peaks, and their shape is assumed to be exponential in invariant mass. Specific backgrounds arising from incorrect particle identification, called "reflections", are also considered. In the case of the Λ 0 b decay, these are B 0 where the pion is misidentified as a proton. There is also a double misidentification background caused by swapping the kaon and proton identifications.
To study these backgrounds, we examine the mass combina- events are used to find the shapes of these reflected backgrounds in the J /ψ pK − mass spectrum. Using the event yields found in data and the simulation shapes, we estimate 5603 ± 90 B 0 s → J /ψ K + K − and 1150 ± 59 B 0 → J /ψπ + K − reflection candidates within ±20 MeV of the Λ 0 b peak. These numbers are used as Gaussian constraints in the mass fit described below with the central values as the Gaussian means and the uncertainties as the widths. Following a similar procedure we find 1138 ± 48 doublymisidentified Λ 0 b decays under the Λ 0 b peak. This number is also used as a Gaussian constraint in the mass fit.
To determine the number of Λ 0 b signal candidates we perform an unbinned maximum likelihood fit to the candidate J /ψ pK − invariant mass spectrum shown in Fig. 2(a). The fit function is the sum of the Λ 0 b signal component, combinatorial background, the contributions from the B 0 The signal is modeled by a triple-Gaussian function with common means. The fraction and the width ratio for the second and third Gaussians are fixed to the values obtained in the fit to Fig. 2(b). The effective r.m.s. The pK − mass spectrum is consistent with that found previously [14], with a distinct peak near 1520 MeV, together with the other broad resonant and nonresonant structures that cover the entire kinematic region.
The B 0 candidate mass distribution can be polluted by the re- Following a similar procedure as for the analysis of the Λ 0 b mass spectra, we take into account the reflection under the B 0 peak. Fig. 2(b) shows the fit to the J /ψπ + K − mass distribution. There are signal peaks at both B 0 and B 0 s masses on top of the background. A triple-Gaussian function with common means is used to fit each signal. The shape of the B 0 s → J /ψπ + K − mass distribution is taken to be the same as that of the signal B 0 decay. The effective r.m.s. width is 6.5 MeV. An exponential function is used to fit the combinatorial background. The shape of the Λ 0 b → J /ψ pK − reflection is taken from simulation, the yield being Gaussian constrained in the global fit to the expected value.
The mass fit gives 340 256 ± 893 signal and 11 978 ± 153 background candidates along with a negligible 573 ± 27 contribution of Λ 0 b → J /ψ pK − reflection candidates within ±20 MeV of the B 0 mass peak. All other reflection contributions are found to be negligible.

Measurement of the
The decay time, t, is calculated as where m is the reconstructed invariant mass, p the momentum and d the flight distance vector of the particle between the production and decay vertices. The b hadron is constrained to come from the primary vertex. To avoid systematic biases due to shifts in the measured decay time, we do not constrain the two muons to the J /ψ mass. The decay time distribution of the Λ 0 b → J /ψ pK − signal can be described by an exponential function convolved with a resolution where t is the true decay time, multiplied by an acceptance function, The ratio of the decay time distributions of Λ 0 b → J /ψ pK − and B 0 → J /ψ K * 0 (892) is given by The advantage of measuring the lifetime through the ratio is that the decay time acceptances introduced by the trigger requirements, selection and reconstruction almost cancel in the ratio of  [14]. They are both small enough in absolute scale, and similar enough for differences in resolutions between the two modes not to affect the final result. Thus, where Δ ΛB ≡ 1/τ Λ 0 b − 1/τ B 0 is the width difference and R(0) is the normalization. Since the acceptances are not quite equal, a correction is implemented to first order by modifying Eq. (4) with a linear function where a represents the slope of the acceptance ratio as a function of decay time.
The decay time acceptance is the ratio between the reconstructed decay time distribution for selected events and the generated decay time distribution convolved with the triple-Gaussian decay time resolutions obtained from the simulations. In order to ensure that the p and p T distributions of the generated b hadrons are correct, we weight the simulated samples to match the data distributions. The simulations do not model the hadron identification efficiencies with sufficient accuracy for our purposes. Therefore we further weight the samples according to the hadron identification efficiencies obtained from D * + → π + D 0 , D 0 → K − π + events for pions and kaons, and Λ → pπ − for protons. The Λ 0 b → J /ψ pK − sample is also weighted using signal yields in bins of m(pK − ).
The decay time acceptances obtained from the weighted simulations are shown in Fig. 4(a). The individual acceptances in both cases exhibit the same behaviour. The ratio of the decay time acceptances is shown in Fig. 4(b). For decay times greater than 7 ps, the acceptance is poorly determined, while below 0.4 ps the individual acceptances decrease quickly. Thus, we consider decay times in the range 0.4-7.0 ps. A χ 2 fit to the acceptance ratio with a function of the form C (1 + at) between 0.4 and 7 ps, gives a slope a = 0.0066 ± 0.0023 ps −1 and an intercept of C = 0.996 ± 0.005.
In order to determine the ratio of Λ 0 b to B 0 lifetimes, we determine the yield of b hadrons for both decay modes using unbinned maximum likelihood fits described in Section 2 to the b hadron mass distributions in 22 bins of decay time of equal width between 0.4 and 7 ps. We use the parameters found from the time integrated fits fixed in each time bin, with the signal and background yields allowed to vary, except for the double misidentification background fraction that is fixed.
The resulting signal yields as a function of decay time are shown in Fig. 5. The subsequent decay time ratio distribution fitted with the function given in Eq. (5) is shown in Fig. 6. A χ 2 fit is used with the slope a = 0.0066 ps −1 fixed, and both the normalization parameter R(0), and Δ ΛB allowed to vary. The fitted value of the reciprocal lifetime difference is Δ ΛB = 17.9 ± 4.3 ± 3.1 ns −1 . Table 1 Systematic uncertainties on the Δ ΛB , the lifetimes ratio τ Λ  Whenever two uncertainties are quoted, the first is statistical and second systematic. The latter will be discussed in Section 4. The χ 2 /ndf of the fit is 20.3/20. The resulting ratio of lifetimes is where we use the world average value 1.519 ± 0.007 ps for τ B 0 [1]. This result is consistent with and more precise than our previously measured value of 0.976 ± 0.012 ± 0.006 [14]. Multiplying the lifetime ratio by τ B 0 , the Λ 0 b baryon lifetime is

Systematic uncertainties
Sources of the systematic uncertainties on Δ ΛB , τ Λ 0 b /τ B 0 and the Λ 0 b lifetime are summarized in Table 1. The systematic uncertainty due to the signal model is estimated by comparing the results between the default fit with a triple-Gaussian function and a fit with a double-Gaussian function. We find a change of Δ ΛB = 1.5 ns −1 , which we assign as the uncertainty. Letting the signal shape parameters free in every time bin results in a change of 0.4 ns −1 . The larger of these two variations is taken as the systematic uncertainty on the signal shape.
The uncertainties due to the background are estimated by comparing the default result to that obtained when we allow the exponential background parameter to float in each time bin. We also replace the exponential background function with a linear function; the resulting difference is smaller than the assigned uncertainty due to floating the background shape. The systematic uncertainty due to the normalization of the double misidentification background is evaluated by allowing the fraction to change in each time bin.
The systematic uncertainties due to the acceptance slope are estimated by varying the slope, a, according to its statistical uncertainty from the simulation. An alternative choice of the acceptance function, where a second-order polynomial is used to parametrize the acceptance ratio between Λ 0 b → J /ψ pK − and B 0 → J /ψ K * 0 (892), results in a smaller uncertainty. There is also an uncertainty due to the decay time range used because of the possible change of the acceptance ratio at short decay times. This uncertainty is ascertained by changing the fit range to be 0.7-7.0 ps and using the difference with the baseline fit. This uncertainty is greatly reduced with respect to our previous publication [14] due to the larger fit range, finer decay time bins, and larger signal sample.
In order to correctly model the acceptance, which can depend on the kinematics of the decay, the Λ 0 b → J /ψ pK − simulation is weighted according to the m(pK − ) distribution observed in data.
As a cross-check, we weight the simulation according to the twodimensional distribution of m(pK − ) and pK − helicity angle and assign the difference as a systematic uncertainty. In addition, the PDG value for the B 0 lifetime, τ B 0 = 1.519 ± 0.007 ps [1], is used to calculate the Λ 0 b lifetime; the errors contribute to the systematic uncertainty. The total systematic uncertainty is obtained by adding all of the contributions in quadrature.

Conclusions
We determine the ratio of lifetimes of the Λ 0 b baryon and B 0 meson to be This is the most precise measurement to date and supersedes our previously published result [14]. It demonstrates that the Λ 0 b lifetime is shorter than the B 0 lifetime by −(2.6 ± 0.7)%, consistent with the original predictions of the HQE [2,4,5,21,22], thus providing validation for the theory. Using the world average measured value for the B 0 lifetime [1], we determine which is the most precise measurement to date.
LHCb has also made a measurement of τ Λ 0 b using the J /ψΛ final state obtaining 1.415 ± 0.027 ± 0.006 ps [23]. The two LHCb measurements have systematic uncertainties that are only weakly correlated, and we quote an average of the two measurements of 1.468 ± 0.009 ± 0.008 ps.

Acknowledgements
We are thankful for many useful and interesting conversations with Prof. Nikolai Uraltsev who contributed greatly to theories describing heavy hadron lifetimes; unfortunately he passed away before these results were available. We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and