Observation of the decay $ \Lambda_b^0\rightarrow \Lambda_c^+\tau^-\overline{\nu}_{\tau}$

The first observation of the semileptonic $b$-baryon decay $ \Lambda_b^0 \rightarrow \Lambda_c^+ \tau^-\overline{\nu}_{\tau}$, with a significance of $6.1\,\sigma$, is reported using a data sample corresponding to 3 fb$^{-1}$ of integrated luminosity, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV at the LHC. The $\tau^-$ lepton is reconstructed in the hadronic decay to three charged pions. The branching fraction ${\mathcal{B}}(\Lambda_b^0 \rightarrow \Lambda_c^+\tau^-\overline{\nu}_{\tau}) = (1.50 \pm 0.16\pm 0.25\pm 0.23)\%$ is obtained, where uncertainties are statistical, systematic and from the external branching fraction of the normalisation channel $\Lambda_b^0\rightarrow \Lambda_c^+\pi^-\pi^+\pi^-$. The ratio of semileptonic branching fractions ${\mathcal{R}}( \Lambda_c^+)\equiv {\mathcal{B}}( \Lambda_b^0 \rightarrow \Lambda_c^+ \tau^-\overline{\nu}_{\tau})/{\mathcal{B}}( \Lambda_b^0 \rightarrow \Lambda_c^+ \mu^-\overline{\nu}_{\mu})$ is derived to be $0.242 \pm 0.026 \pm 0.040\pm 0.059$, where the external branching fraction uncertainty from the channel $\Lambda_b^0\rightarrow \Lambda_c^+\mu^-\overline{\nu}_{\mu}$ contributes to the last term. This result is in agreement with the Standard Model prediction.

In the standard model of particle physics (SM) flavor-changing processes, such as semileptonic decays of b hadrons, are mediated by W ± bosons with universal coupling to leptons. Differences in the rates of decays involving the three lepton families are expected to arise only from the different masses of the charged leptons. Lepton flavor universality can be violated in many extensions of the SM with non-standard flavor structure. Since the uncertainty due to hadronic effects cancels to a large extent, the SM predictions for the ratios between branching fractions of semileptonic decays of b hadrons, such as R(D ( * ) ) ≡ B(B → D ( * ) τ − ν τ )/B(B → D ( * ) µ − ν µ ) [1][2][3], where D ( * ) and B mesons can be either charged or neutral, and , are known with uncertainties at the per cent level [4][5][6]. These ratios therefore provide a sensitive probe of SM extensions [6,7].
This Letter reports the observation of the decay Λ 0 b →Λ + c τ − ν τ and the first determination of R(Λ + c ) using τ − → π − π + π − (π 0 )ν τ decays. The inclusion of charge-conjugate modes is implied throughout. The present work closely follows the strategy of Ref. [14]. Measurements in the baryonic sector provide complementary constraints on a potential lepton flavor universality violation because of the half-integer spin of the initial state [5,6]. The Λ 0 b →Λ + c transition is determined by a different set of form factors with respect to the mesonic decays probed so far. Likewise, new physics couplings can also be different, resulting in different scenarios regarding deviations from SM expectations of R(Λ + c ) and R(D ( * ) ) [7].
A data sample of proton-proton (pp) collisions at centre-of-mass energies √ s = 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb −1 , collected with the LHCb detector is used. The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, described in detail in Refs. [16,17]. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region [18], and large-area silicon-strip detectors located upstream and downstream of the 4 Tm dipole magnet. The minimum distance of a track to a primary pp collision 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 direction, in GeV/c. The online event selection is performed by a trigger system [19], which consists of a hardware stage based on information from the calorimeter and muon systems, followed by a software stage that performs a full event reconstruction. Events are selected at the hardware stage if the particles forming the signal candidate satisfy a requirement on the energy deposited in the calorimeters or if any other particles pass any trigger algorithm. The software trigger requires a two-, three-, or four-track secondary vertex with significant displacement from any PV and consistent with the decay of a b hadron, or a three-track vertex with a significant displacement from any PV and consistent with the decay of a Λ + c baryon. A multivariate algorithm is used for the identification of secondary vertices consistent with the decay of a b hadron, while secondary vertices consistent with the decay of a Λ + c baryon are identified using topological criteria. In the simulation, pp collisions are generated using Pythia 8 [20] with a specific LHCb configuration [21]. Decays of hadronic particles are described by EvtGen [22], in which final-state radiation is generated using Photos [23]. The Tauola package [24] is used to simulate the decays of the τ − lepton into 3πν τ and 3ππ 0 ν τ final states, where 3π ≡ π − π + π − , according to the resonance chiral Lagrangian model [25] with a tuning based on the results from the BaBar Collaboration [26]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [27] as described in Ref. [28]. The signal decays are simulated using form factors that are derived from heavy-quark effective theory [29].
The Λ + c baryon candidates are reconstructed using the Λ + c → pK − π + decay mode, by combining three charged tracks compatible with proton, kaon and pion hypotheses. The τ − candidates are formed by π − π + π − combinations and include contributions from the τ − → 3πν τ and τ − → 3ππ 0 ν τ decay modes, as neutral pions are not reconstructed. The Λ + c and τ − candidates are selected based on kinematic, geometric, and particleidentification criteria. The Λ 0 b candidate is formed by combining a Λ + c and a τ − candidate. Background due to misreconstructed b hadrons, where at least one additional particle originates from either the 3π vertex or the b-hadron vertex, is suppressed by requiring a single Λ 0 b candidate per event. Tracks other than those used for the signal candidate are exploited in a multivariate algorithm to assess the signal isolation, i.e. the absence of extra tracks compatible with the 3π vertex [30]. The algorithm is trained on simulated samples of Λ 0 b →Λ + c τ − ν τ and Λ 0 b →Λ + c D 0 K − decays for signal and background, respectively; its efficiency is 20% higher than the cut-based algorithm used in Ref. [14] for the same rejection factor. Likewise, the neutral-particle energy contained in a cone centred around the direction of the τ − candidates is used to further separate signal and background processes. The τ − momentum can be determined, up to a two-fold ambiguity, from the momentum vector of the 3π system and the flight direction of the τ − candidate. The average of the two solutions is used, as discussed in Ref. [14]. The same method is used to compute the Λ 0 b momentum. This enables the computation of the invariant mass squared of the τ − ν τ lepton pair (q 2 ), and the pseudo decay time of the τ − candidate (t τ ). The variables q 2 and t τ are reconstructed with a resolution of roughly 15%, providing good discrimination between the signal and background processes.
The finite τ − lifetime causes the 3π vertex to be detached from the Λ 0 b vertex. This key feature allows the suppression of the large background, called prompt background hereafter, from b hadrons decaying to a Λ + c baryon accompanied by a 3π system being produced promptly at the b-hadron decay vertex, plus any other unreconstructed particles (X). The difference of the positions of the 3π and the Λ + c vertices along the beam direction is required to be at least 5 times larger than its uncertainty. This requirement suppresses the prompt background 10 times more than the selection used in Ref. [14], reducing this initially dominant background to a negligible level, at a price of 50% reduction of the signal efficiency.
Double-charm background processes due to Λ 0 b baryon decays into a Λ + c baryon plus another charmed hadron that subsequently decays into a final state containing three charged pions, are topologically similar to the signal and constitute the largest background source. The main contribution originates from Λ 0 b → Λ + c D − s (X) decays, with D − s decays to 3πY final states, where Y stands for any set of extra particles, such as one or two π 0 mesons. Such D − s decays have a large branching fraction (∼30%) [31]. This background is reduced principally by taking into account the resonant structure of the 3π system. The τ − → 3πν τ decays proceed predominantly through the a 1 (1260) − → ρ 0 π − decay. By contrast, the D − s → 3πY decays occur mainly through the η and η resonances. This feature, captured by the shapes of the distributions of the smaller and larger mass of the two π + π − combinations extracted from each 3π candidate, the energy carried by neutral particles within the cone around the 3π direction, and kinematic variables from partial reconstruction are exploited by means of a boosted decision tree (BDT) classifier [32, 33], as described in Ref. [14].
decay, which is obtained by removing the charged-particle isolation criterion and requiring an additional charged kaon originating from the 3π vertex; and a Λ 0 b → Λ + c D − (X) data sample, using D − →K + π − π − decays, which is obtained by assigning a kaon mass to the positively-charged pion of the τ − candidate. For all these samples, good agreement between data and simulation is observed in the distributions of the variables used in the BDT classifier.
The signal yield is measured using a three-dimensional binned maximum-likelihood fit to t τ , the BDT output, and q 2 , which are shown in Fig. 1 ; background due to misreconstructed Λ + c candidates; and combinatorial background. Template distributions for signal and background are obtained from simulation, with the exceptions of random pK − π + combinations and the combinatorial background, which are constructed from data-based control samples. The signal template accounts for both τ − → 3πν τ and τ − → 3ππ 0 ν τ decays, where the fraction of the former is fixed to 78% according to the branching fractions and selection efficiencies.
where Λ * + c denotes any excited charmed baryon state decaying into final states involving Λ + c baryon, constitutes a feeddown to the signal. Its yield fraction is constrained to be (10 ± 5)% of the signal yield, derived from the Λ * + c relative abundance as measured in the Λ 0 b → Λ * + c π − π + π − decays, their respective branching fractions in the Λ + c π 0 π 0 and Λ + c π + π − modes [31], and the corresponding selection efficiency obtained from simulation. The background originating from decays of     Fig. 3. The relative yield of each of above mentioned background processes is constrained using the results of a fit to the Λ + c π − π + π − mass distribution. The D − s decay model used in the simulation does not accurately describe the data because of the limited knowledge of the D − s decay amplitudes to 3πY final states. A correcting factor, taken from high precision B 0 → D * + D − s sample [14], is applied to each D − s branching fraction to match the π − π + π − Dalitz distributions from simulation to those observed in data.
The background originating from Λ 0 b → Λ + c D 0 (X) decays is subdivided into two contributions, depending on whether the 3π system originates from the D 0 vertex, or whether one pion originates from the D 0 vertex and the other two from elsewhere. The The components contributing to the fit model are indicated in the legend.
former contribution is constrained by the yield obtained from the Λ 0 b → Λ + c D 0 (X) control sample. The template associated to Λ + c D 0 (X) background is also validated using the data-driven sample where the D 0 → K + 3π decay is fully reconstructed. The yield of the other Λ 0 b → Λ + c D 0 (X) background component is a free parameter in the fit. The yield of the Λ 0 b → Λ + c D − (X) background is also a free parameter and its template is validated using the data-driven sample with the D − meson fully reconstructed in the K + π − π − mode.
The combinatorial background is divided into two contributions, depending on whether the Λ 0 b candidate contains a true Λ + c baryon or a random pK − π + combination. In the first case, the Λ + c and the 3π system originate from different b-hadron decays. The data sample of wrong-sign Λ 0 b candidates where the Λ + c and the 3π system have the same electric charge is used to obtain a background template. Its yield is obtained by normalising to the right-sign data in the region where the reconstructed Λ + c 3π mass is significantly larger than the known Λ 0 b mass [14]. The background not including a true Λ + c baryon is parameterised using a specific data sample originating from Λ 0 b candidates where the Λ + c candidate has a mass outside a window of 15 MeV/c 2 around the known Λ + c mass [31]. The projections of the fit on t τ and the BDT output are shown in Fig. 1. The projections on q 2 in two different BDT output ranges are shown in Fig. 2. The signal yield is N sig = 349 ± 40. The fit is repeated with all nuisance parameters related to the template shapes varying freely, while the signal yield is fixed at zero. The χ 2 variation derived from the change of the fit maximum likelihood corresponds to an increase of 6.1 σ with respect to the default fit with freely varying signal yield. This measurement signifies the first observation of the decay Λ 0 b →Λ + c τ − ν τ . A clear separation between signal and the main background originating from Λ 0 b → Λ + c D + s (X) decays is obtained, as demonstrated in the BDT distribution of Fig. 1. Figure 2 shows that the Λ 0 b → Λ + c D + s (X) background is dominant at low BDT values, while a good signal-to-background ratio is observed at high BDT output. Fig. 5 of Supplemental Material [35] shows similarly the τ decay time distribution for the same BDT intervals.
In order to reduce experimental systematic uncertainties, the Λ 0 b → Λ + c 3π decay is chosen as a normalization channel. This leads to a measurement of the ratio where N sig (N norm ) and ε sig (ε norm ) are the yield and selection efficiency for the signal (normalization) channel, respectively. The normalization channel selection is identical to that of the signal channel, except the requirement that the 3π system has a larger flight distance than that of the Λ + c candidate, which is not imposed. The yield of the normalization mode is determined by fitting the invariant-mass distribution of the Λ + c 3π candidates around the known Λ 0 b mass [31], as shown in Fig. 6 of Supplemental Material [36]. A significant contribution from excited baryons which decay to Λ + c π + π − , Λ + c π + , or Λ + c π − is explicitely vetoed from the normalization channel. As a result, the 3π dynamics ressembles that of the signal, leading to a reduced systematic uncertainty.
A normalization yield of N norm = 8584 ± 102 is found, after subtraction of a small contribution of 168 decays. This component is estimated by fitting the 3π mass distribution in the D − s mass region for candidates with a reconstructed Λ + c 3π mass in a window around the known Λ 0 b mass [31]. The normalization sample is also used to correct for differences in the Λ 0 b production kinematics between data and simulation. The reconstruction efficiencies for the τ − → 3πν τ , τ − → 3ππ 0 ν τ signal modes and normalization channel are determined using the simulation and found to be (1.37 ± 0.04) × 10 −5 , (0.82 ± 0.05) × 10 −5 , and (11.21 ± 0.11) × 10 −5 , respectively. The ratio of branching fractions is derived from Eq. 1 as where the first uncertainty is statistical and the second systematic.
where the first uncertainty is statistical, the second systematic and the third is due to the external branching fraction measurement. The branching fraction B(Λ 0 b → Λ + c µ − ν µ ) = (6.2 ± 1.4)% from the DELPHI experiment [39] updated in Ref.
[31] is used to obtain the ratio of semileptonic branching fractions R(Λ + c ) as R(Λ + c ) = 0.242 ± 0.026 ± 0.040 ± 0.059,  where the first uncertainty is statistical, the second systematic and the third is due to the external branching fractions measurements. The measured value of R(Λ + c ) is lower than but in agreement with the Standard Model prediction of 0.324 ± 0.004 [5].
The sources of systematic uncertainty of K(Λ + c ) are reported in Table 1.
, the systematic uncertainties related to the external branching fractions are added in quadrature. The uncertainty due to the limited size of the simulated samples is computed by repeatedly sampling each template with a bootstrap procedure, performing the fit, and taking the standard deviation of the resulting spread of N sig values. The limited size of the simulated samples also contributes to the systematic uncertainty in the efficiencies for signal and normalization modes. The systematic uncertainty associated with the signal decay model originates from the limited knowledge of the form factors and the τ − polarization. The form factor distributions are varied in their range allowed by measurements from Λ 0 b → Λ + c µ − ν µ decays. The contribution from the relative branching fractions and selection efficiencies of τ − → 3ππ 0 ν τ and τ − → 3πν τ decays are computed by varying their ratio within their uncertainties. Potential contribution from other τ − decay modes is investigated through a dedicated simulation including all known τ − decay modes. Feed-down contribution where the τ − is produced in association with an excited charmed baryon is computed varying in the fit the relative amount of such decays in their allowed range of (10 ± 5)%. The uncertainty due to the knowledge of the D − s decay model is estimated by repeatedly varying the correction factors of the templates within their uncertainties, as determined from the associated control sample, and performing the fit. The spread of the fit results is assigned as the corresponding systematic uncertainty.
The template shapes of the background modes depend on the dynamics of the corresponding decays. A range of template deformations [14] is performed, and the spread of the fit results is taken as a systematic uncertainty. The resulting uncertainty of 13% represents the largest single source. A similar procedure is applied to the template for the combinatorial background. The contribution from a potential bias in the fit is explored by fitting pseudoexperiments where the signal strength is varied from its SM value to a negligible amount. Other sources of systematic uncertainty arise from the inaccuracy on the yields of the various background contributions, and from the limited knowledge of the normalization channel modelling. The contribution from the removal of Λ * + c modes from the normalization channel is taken into account by varying the branching fractions of the various excited baryons decays within their measured range.
Systematic effects in the efficiencies for signal and normalization channels partially cancel in the ratio, with the remaining uncertainty being mostly due to the limited size of simulated sample. The trigger efficiency depends on the distributions of the decay time of the τ − candidates and the invariant mass of the Λ + c 3π system. These distributions differ between the signal and normalization modes, and the corresponding difference of the trigger efficiencies is taken into account.
In conclusion, the first observation of the semileptonic decay Λ 0 b →Λ + c τ − ν τ is reported with a significance of 6.1 σ, using a data sample of pp collisions, corresponding to 3 fb −1 of integrated luminosity, collected by the LHCb experiment. The measurement exploits the three-prong hadronic τ − decays with the technique pioneered by the LHCb experiment for the R(D * + ) measurement [14]. The ratio is measured to be 2.46 ± 0.27 ± 0.40, where the first uncertainty is statistical and the second systematic. The branching fraction B(Λ 0 b → Λ + c τ − ν τ ) is measured to be (1.50 ± 0.16 ± 0.25 ± 0.23)%, where the third uncertainty is due to external branching fraction measurements. A measurement of R(Λ + c ) = 0.242 ± 0.026 ± 0.040 ± 0.059 is reported. The R(Λ + c ) ratio is found to be in agreement with the SM prediction. This measurement provides constraints on new physics models, such as some of those described in Ref. [6], for which large values of R(Λ + c ) are allowed by existing R(D ( * ) ) measurements. Supplemental material for the paper "Observation of the decay Λ 0 b →Λ + c τ − ν τ " Figure 4: Distribution of the (top left) minimum π + π − mass combination formed from the pion triplet, (top right) maximum π + π − mass combination and (bottom) Λ + c π − π + π − mass, for simulated samples of Λ 0 b →Λ + c τ − ν τ (blue points) and Λ 0 b →Λ + c D − s (X) (red line) decays. Fig. 4 shows the distribution of the three most significant input variables to the BDT classifier : minimum and maximum mass of the two π + π − combinations formed from the pion triplet and Λ + c π − π + π − mass. Fig. 5 shows the τ decay time distribution for BDT output values below and above 0.66. Fig. 6 shows the invariant-mass distribution of selected Λ + c 3π candidates with a fit overlaid to extract the yield of the normalization mode.   Figure 6: Distribution of the Λ + c π − π + π − invariant mass for all candidates in the normalization channel, after removal of the Λ * + c contributions. The fit components are indicated in the legend. The signal is described by a Crystal Ball (CB) function, and the background by an exponential term. [36] See Supplemental Material for the figure showing the Λ + c π − π + π − mass distribution in the normalisation sample.