Precision measurement of the Lambda_b baryon lifetime

The ratio of the \Lambda b baryon lifetime to that of the B0 meson is measured using 1.0/fb of integrated luminosity in 7 TeV center-of-mass energy pp collisions at the LHC. The \Lambda b baryon is observed for the first time in the decay mode \Lambda b ->J/\psi pK-, while the B0 meson decay used is the well known B0 ->J/\psi pi+K- mode, where the pi+ K- mass is consistent with that of the K*0(892) meson. The ratio of lifetimes is measured to be 0.976 +/- 0.012 +/- 0.006, in agreement with theoretical expectations based on the heavy quark expansion. Using previous determinations of the B0 meson lifetime, the \Lambda b lifetime is found to be 1.482 +/- 0.018 +/- 0.012 ps. In both cases the first uncertainty is statistical and the second systematic.

q Università di Padova, Padova, Italy r Università di Pisa, Pisa, Italy s Scuola Normale Superiore, Pisa, Italy vi Evaluations from experimental data of fundamental parameters, such as CKM matrix elements [1], and limits on physics beyond that described by the standard model, often rely on theoretical input [2]. One of the most useful models, the heavy quark expansion (HQE) [3][4][5], is based on the operator product expansion [6]; it is used, for example, to extract values for |V ub | and |V cb | from measurements of inclusive semileptonic B meson decays [7]. In the free quark model the lifetimes of all b-flavored hadrons are equal, because the decay width is determined by the b quark lifetime. This model is too naïve, since effects of other quarks in the hadron are not taken into account [8]. Early predictions using the HQE, however, supported the idea that b-hadron lifetimes were quite similar, due to the absence of correction terms O(1/m b ). In the case of the ratio of lifetimes of the Λ 0 b baryon, τ Λ 0 b , to the B 0 meson, τ B 0 , the corrections of order O(1/m 2 b ) were found to be small, initial estimates of O(1/m 3 b ) [9,10] effects were also small, thus differences of only a few percent were expected [8,9,11]. Measurements at LEP, however, indicated that τ Λ 0 b /τ B 0 was lower: in 2003 one widely quoted average of all data gave 0.798 ± 0.052 [12], while another gave 0.786 ± 0.034 [13]. Some authors sought to explain the small value of the ratio by including additional operators or other modifications [14], while some thought that the HQE could be pushed to provide a ratio of ∼0.9 [15]. Recent measurements have shown indications that a higher value is possible [16], although the uncertainties are still large. Therefore, a precision measurement of τ Λ 0 b /τ B 0 is necessary to provide a confirmation of the HQE, or show definitively that the theory is deficient.
In this Letter we present the experimental determination of τ Λ 0 b /τ B 0 using a data sample corresponding to 1.0 fb −1 of integrated luminosity accumulated by the LHCb experiment in 7 TeV center-of-mass energy pp collisions. The Λ 0 b baryon is detected in the J/ψ pK − decay mode, while the B 0 meson is found in J/ψ π + K − decays. Mention of a particular decay channel implies the additional use of the charge-conjugate mode. This Λ 0 b decay mode has not been observed before. 1 On the other hand, the B 0 decay is well known, and we impose the further requirement that the invariant mass of the π + K − combination be within ±100 MeV of the K * 0 (892) mass, 2 in order to simplify the simulation and reduce systematic uncertainties. These decays have the same decay topology into four charged tracks, thus facilitating the cancellation of uncertainties.
The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, described in detail in Ref. [17]. Events selected for this analysis are triggered [18] 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 either of IP requirements or detachment of the J/ψ from the associated primary vertex. The simulated events used in this analysis are produced using the software described in Refs. [19] Events are preselected and then are further filtered using a multivariate analyzer based on the boosted decision tree (BDT) technique [20]. In the preselection, all hadron track candidates are required to have p T larger than 250 MeV, while for muon candidates the requirement is more than 550 MeV. Events must have a µ + µ − combination that forms a common vertex with χ 2 < 16, and an invariant mass between −48 and +43 MeV of the J/ψ mass. Candidate µ + µ − combinations are then constrained to the J/ψ mass for subsequent use in event selection. The two charged final state hadrons must have a vector summed p T of more than 1 GeV, and are also required to form a vertex with χ 2 < 10 for one degree of freedom, and a common vertex with the J/ψ candidate with χ 2 < 50 for five degrees of freedom. This b-hadron candidate must have a momentum vector that, when parity inverted, points to the primary vertex within an angle smaller than 2.56 • . Particle identification requirements differ in the two modes. We use the difference in the logarithm of the likelihood, DLL(h 1 − h 2 ), to distinguish between the two hypotheses: h 1 and h 2 as described in [21]. In the Λ 0 b decay the kaon candidate must have DLL(K − π) > 4 and DLL(K − p) > −3, while the proton must have DLL(p − π) > 10 and DLL(p − K) > −3. For the B 0 decay, the requirements on the pion candidate are DLL(π − µ) > −10 and DLL(π − K) > −10, while DLL(K − π) > 0 is required for the kaon.
The BDT selection is based on the minimum 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 impact parameter χ 2 of the Λ 0 b candidate, where the latter results from calculating the difference in χ 2 by using the hypothesis that the IP is zero. These variables are chosen with the aim of having the selection efficiency be independent of decay time. The BDT is trained on a simulated sample of either Λ 0 b → J/ψ pK − signal events and a background data sample from the mass sidebands of the Λ 0 b signal peak. It is then tested on independent samples from the same sources. The BDT selection is implemented to maximize S 2 /(S + B), where S indicates the signal and B the background event yields. This optimization includes the requirement that the Λ 0 b baryon decay time be greater than 0.5 ps. The same BDT selection is used for the B 0 → J/ψ π − K + mode.
The J/ψpK − mass distribution after the BDT selection is shown in Fig. 1. There is a large and significant signal. Backgrounds can be combinatorial in nature, but can also be formed by reflections from B meson decays where the particle identification fails. As long as these backgrounds do not peak near the Λ 0 b mass they cannot cause incorrect determinations of the Λ 0 b signal yield. The shapes of the main B meson reflections are determined from simulation and shown on Fig. 1. The shapes are smooth and do not peak in the signal region. To estimate the contributions of the reflections we take each of the candidates in the J/ψ pK − sideband regions 60 − 200 MeV on either side of the Λ 0 b mass peak, reassign proton to kaon and pion mass hypotheses, respectively, and fit the resulting signal peaks determining signal yields of 5576 ± 95 B 0 s and 1769 ± 192 B 0 decays. To translate these yields to those within ±20 MeV of the Λ 0 b peak, we use simulations of B 0 s → J/ψ K + K − with the K + K − mass distribution matched to that obtained in our previous analysis of this final state [22], and a simulation of B 0 → J/ψ π + K − decays, leading to 1186±35 J/ψ K + K − and 308±33 J/ψ π + K − reflected decays, respectively.
To determine the Λ 0 b signal yield we perform an unbinned maximum likelihood fit to the J/ψ pK − invariant mass spectrum shown in Fig. 1 in the region between 5500 and 5750 MeV. The fit function is the sum of the Λ 0 b signal component, combinatorial background and the contribution from the B 0 s → J/ψ K + K − and B 0 → J/ψ π + K − reflections. The signal is modeled by a triple-Gaussian function with common means; the effective r.m.s. width is 5.5 MeV. The combinatorial background is described by an exponential function. The event yields of the reflections are included in the fit as Gaussian constraints. The mass fit gives 15 581 ± 178 signal and 5535 ± 50 combinatorial background candidates together with 1235 ± 35 B 0 s → J/ψ K + K − and 313 ± 26 B 0 → J/ψ π + K − reflection candidates within ±20 MeV of the Λ 0 b mass peak. To view the background subtracted pK − mass spectrum, we perform fits, as described above, to the m(J/ψ pK − ) distributions in bins of m(pK − ) and extract the signal yields within ±20 MeV of the Λ 0 b mass peak. The resulting pK − mass spectrum is shown in Fig. 2. A distinct peak is observed in the pK − invariant mass distribution near 1520 MeV, together with the other resonant and non-resonant structures over the entire kinematical region. The peak corresponds to the Λ(1520) resonance [23]. Simulations of the Λ 0 b decay are weighted to reproduce this mass distribution.
The J/ψ π + K − mass spectrum, after the BDT selection, is shown in Fig. 3. There is a large signal peak at the B 0 mass and a much smaller one at the B 0 s mass. Triple-Gaussian functions each with common means are used to fit the signal peaks; the effective r.m.s. width is 6.7 MeV. An exponential function is used to fit the combinatorial background. The mass fit gives 97 506 ± 447 signal and 3660 ± 74 background candidates within ±20 MeV of the B 0 mass peak. Reflections are possible from both B 0 s → J/ψ K + K − and Λ 0 b → J/ψ pK − decays. Following the same procedure as outlined above using the sidebands of the B 0 signal we find no evidence of a reflection from the B 0 s state and a small, non-peaking, contribution of 506±19 events from the Λ 0 b state, in the B 0 signal region, that is ignored.
The decay time for each candidate is given by t = m d · p/| p| 2 , where m is the mass, d the distance vector from the primary vertex to the decay point, and p is the measured b hadron momentum. Here, we do not constrain the two muons to the J/ψ mass to avoid  systematic biases. The decay time resolutions are 40 fs for the Λ 0 b decay and 37 fs for the B 0 decay. In addition, the decay time acceptances are also almost equal. For equal acceptances, the ratio of events, R(t), as a function of decay time is given by Effects of the different decay time resolutions in the two modes are negligible above 0.5 ps. First order corrections for a decay time dependent acceptance ratio can be taken into account by modifying Eq. (1) with a linear function where a represents the slope of the acceptance ratio as a function of decay time.
The decay time acceptances for both modes are determined by simulations that are weighted to match either the pK − or π + K − invariant mass distributions seen in data, as well as to match the measured p and p T distributions of the b hadrons. In addition, we further weight the samples so that the simulation matches the hadron identification efficiencies obtained from D * + → π + (D 0 → π + K − ) events for pions and kaons, and Λ 0 → pπ − for protons.
The ratio of the decay time acceptances is shown in Fig. 4. Here we have removed the minimum requirement on decay time so we can view the distributions in the region close to zero time. The individual acceptances in both cases can be described with a linear t [ps] function above 0.5 ps. In order to minimize possible systematic effects we use candidates with decay times larger than 0.6 ps. We also choose an upper time cut of 7.0 ps, because the acceptance is poorly determined beyond this value. The acceptance ratio is fitted with a linear function between 0.6 and 7.0 ps. The slope is a = 0.0033 ± 0.0024 ps −1 , and the χ 2 /number of degrees of freedom (ndf) of the fit is 81/62.
We determine the event yields in both decay modes by fitting the invariant mass distributions in 16 bins of decay time, each bin 0.4 ps wide, using the same signal and background shapes obtained in the aforementioned mass fits. Since the bin size is approximately ten times the resolution, there is no effect due to the small difference of time resolution (<7%) between the two modes. The resulting distributions are shown in Fig. 5(a). Here the fitted signal yields in both modes are placed at the average of the decay time within a bin determined by the B 0 data in order to correct for the exponential decrease of the decay time distributions across the bin. The decay time ratio distribution fitted with the function given in Eq. (2) is shown in Fig. 5(b). The χ 2 /ndf of the fit is t [ps] 2 4 6 Yield / (0.4 ps) Whenever two uncertainties are quoted, the first is the statistical and the second systematic; the latter will be discussed below. Numerically, the ratio of lifetimes is where we use the world average value τ B 0 = 1.519 ± 0.007 ps [23]. Multiplying the lifetime ratio by this value we determine .018 ± 0.012 ps. Our result is consistent with, but higher and more accurate, than the current world average of 1.429±0.024 ps [23].
The absolute systematic uncertainties are listed in Table 1. There is 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 1 − 7 ps and using the difference with the baseline fit. To determine the acceptance slope uncertainty we vary the value of a by its error determined from the fit to the simulation samples and propagate this change to the results. For the signal shape uncertainty, we repeat the measurement of ∆ ΛB using a double-Gaussian signal shape in the mass fits. The uncertainty in the background parameterization is assigned by letting the background parameters vary in the fits to the time dependent yields and comparing the difference in final results. Effects of changes in the acceptance for the Λ 0 b mode due to the angular decay distributions are evaluated by weighting the simulation by the observed pK − helicity angle in addition to the pK − invariant mass, and redoing the analysis. The acceptance function uncertainty is evaluated by using a parabola instead of a linear function. The total systematic uncertainty is obtained by adding all of the elements in quadrature.  In conclusion, our value for τ Λ 0 b /τ B 0 = 0.976 ± 0.012 ± 0.006 shows that the Λ 0 b and B 0 lifetimes are indeed equal to within a few percent, as the original advocates of the HQE claimed [3,4,9], without any need to find additional corrections. Adding both uncertainties in quadrature, the lifetimes are consistent with being equal at the level of 1.9 standard deviations; thus we do not exclude that the Λ 0 b baryon has a longer lifetime than the B 0 meson. Using the world average measured value for the B 0 lifetime we determine τ Λ 0 b = 1.482 ± 0.018 ± 0.012 ps.