Observation of the $\Lambda_b^0\to\Lambda\phi$ decay

The $\Lambda_b^0\to\Lambda\phi$ decay is observed using data corresponding to an integrated luminosity of 3.0fb$^{-1}$ recorded by the LHCb experiment. The decay proceeds at leading order via a $b\to s\bar{s}s$ loop transition and is therefore sensitive to the possible presence of particles beyond the Standard Model. A first observation is reported with a significance of $5.9$ standard deviations. The value of the branching fraction is measured to be $(5.18\pm1.04\pm0.35\,^{+0.67}_{-0.62})\times10^{-6}$, where the first uncertainty is statistical, the second is systematic, and the third is related to external inputs. Triple-product asymmetries are measured to be consistent with zero.


Introduction
In the Standard Model (SM), the flavour-changing neutral current decay Λ 0 b → Λφ proceeds via a b → sss loop (penguin) process.A Feynman diagram of the gluonic penguin that contributes to this decay at leading order is displayed in Fig. 1.This transition has been the subject of theoretical and experimental interest in B 0 s and B 0 decays, since possible beyond the SM particles in the loop could induce non-SM CP violation [1][2][3].The process has been probed with decay-time-dependent methods in the B 0 s → φφ and B 0 → K 0 S φ decay modes [4][5][6][7], which test for CP violation in the interference between mixing and decay.In addition, measurements of CP violation in the decay have been performed with the flavour-specific B 0 → K * 0 φ channel [8].The results to date are consistent with CP conservation in the b → sss process.Model-independently, non-SM physics contributions could appear differently in these decay modes, though many models contain strong correlations [9].
Measurements with Λ 0 b baryons offer the possibility to look for CP violation in the decay, both by studying CP asymmetries and by means of T -odd observables.These observables have been studied in greater detail for B 0 s and B 0 meson decays than those for Λ 0 b baryons [4,8,10,11].Proposed methods to study T -odd asymmetries of Λ 0 b baryons [12] exploit the polarisation structure of Λ 0 b → ΛV decays, where V denotes a vector resonance [12], and can be affected by the initial Λ 0 b polarisation if non-zero.An LHCb measurement of the initial polarisation in Λ 0 b → J/ψ Λ decays has yielded a value consistent with zero, though polarisation at the level of 10% is possible given statistical uncertainties [13].No SM prediction exists specifically for the T -odd asymmetries in Λ 0 b → Λφ decays, though no large asymmetries are expected given the prediction of CP conservation in the decays of beauty mesons for the same transition.Measurements of CP asymmetries have been performed by LHCb in an inclusive analysis of Λ 0 b → Λhh decays [14], where h(h ) refers to a kaon or pion, with corresponding CP asymmetries measured to be consistent with zero.
In this paper, a measurement of the Λ 0 b → Λφ branching fraction is presented using the B 0 → K 0 S φ decay as a normalisation channel, which has a measured branching fraction of (7.3 +0.7  −0.6 ) × 10 −6 [15].The selection requirements used to isolate the Λ 0 b → Λφ decay  process that contributes to this decay is given in Figure 1.This is therefore the same of the phase has provided a value of sss s = 0.17 ± 0.15(stat) ± 0.03(syst) rad [1].The 37 SM can also be tested with triple product asymmetries, which also provide a measure of

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CP violation [2].For the case of the B 0 s !decay, which is a pseudo-scalar to vector 39 vector transition, the triple product asymmetries exploit the helicity angles of the decay 40 to isolate the interference terms between the CP -even and CP -odd polarisations.The two 41 CP -even polarisations therefore allow for two triple product asymmetries, denoted by A U 42 and A V .An LHCb measurement of these triple product asymmetries has provided values 43 of A U = 0.003 ± 0.017(stat) ± 0.006(syst) and A V = 0.017 ± 0.017(stat) ± 0.006(syst) [1], 44 that are currently limited by statistical uncertainties.

Detector and simulation
The LHCb detector [16,17] 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 silicon-strip detectors and straw drift tubes placed downstream of the magnet.The tracking system provides a measurement of 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, the impact parameter, 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.Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter.The online event selection is performed by a trigger, which 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.At the hardware trigger stage, events are required to have a muon with high p T or a hadron, photon or electron with high transverse energy in the calorimeters.For hadrons, the transverse energy threshold is 3.5 GeV.In the subsequent software trigger, at least one charged particle must have a transverse momentum p T > 1.7 GeV/c and be inconsistent with originating from a PV.Finally, the tracks of two or more of the final-state particles are required to form a vertex that is significantly displaced from the PVs.The final state particles that are identified as kaons are required to have a combined invariant mass consistent with that of the φ meson.
In the simulation, pp collisions are generated using Pythia8 [18] with a specific LHCb configuration [19].Decays of hadronic particles are described by EvtGen [20], in which final-state radiation is generated using Photos [21].The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [22] as described in Ref. [23].The decays of Λ 0 b baryons are modelled according to a phase-space description.Differences in the efficiencies of protons and anti-protons, at the sub-percent level, are accounted for with the Geant4 implementation of the detector description.

Selection
The Λ 0 b → Λφ and B 0 → K 0 S φ decays are reconstructed through the Λ → pπ − , K 0 S → π + π − and φ → K + K − final states, where the inclusion of charge conjugate processes is implied throughout the paper.Decays of Λ → pπ − and K 0 S → π + π − are reconstructed in two different categories.The first category contains Λ (K 0 S ) hadrons that decay inside the vertex detector acceptance and the second contains Λ (K 0 S ) hadrons that decay outside.These categories are referred to as long and downstream, respectively.The high resolution of the vertex detector leads to enhanced momentum, vertex, and mass resolutions for candidates in the long category relative to downstream candidates.
Boosted decision trees (BDTs) [24,25] are used to separate signal from background.Different BDTs are trained for decays where the daughter tracks of the Λ (K 0 S ) hadron are classified as long or downstream and according to whether the data was collected in 2011 (7 TeV) or 2012 (8 TeV), yielding eight separate BDTs in total.The set of input variables used to train the ) vertex fit quality, p T , η, the difference in χ 2 of the PV reconstructed with and without the candidate (χ 2 IP ), the flight distance squared divided by the associated variance (χ 2 FD ), the angle between the momentum vector and the vector from the PV to the decay vertex, the Λ (K 0 S ) vertex fit quality, and the p T and η of the φ and the Λ (K 0 S ) hadrons.The minimum and maximum values of the p T and η associated to the final state particles are also included.In addition, the BDT trained on the long category uses the χ 2 IP and χ 2 FD of the Λ (K 0 S ) with respect to the associated PV.A PV is reconstructed by requiring a minimum of five good quality tracks that are consistent with originating from the same location within the luminous region.Before the BDTs are trained, initial loose requirements are imposed on the input variables.The BDTs are trained using simulated candidates for the signal and data sidebands for the background.For the training samples, the signal region is defined as being within 150 MeV/c 2 of the known Λ 0 b (B 0 ) mass [26].In addition, the K + K − invariant mass is required to be within 20 MeV/c 2 of the known φ mass and the pπ − invariant mass is required to be within 15 MeV/c 2 of the known Λ mass [26].The sidebands are defined to be within 500 MeV/c 2 of the known Λ 0 b (B 0 ) mass excluding the signal region.The figure of merit used to determine the requirement imposed on the Λ 0 b → Λφ BDT output is defined as ε/(3/2 + N bkg ) [27], where ε is the signal efficiency, and N bkg is the number of background events.This figure of merit is optimised for detection at three standard deviations of decay modes not previously observed.The signal efficiency is obtained from simulated signal candidates and the number of background events is calculated from fits to the data sidebands interpolated to the signal region.This optimisation procedure is performed separately for each BDT.
In contrast to the Λ 0 b → Λφ BDTs, the optimum response requirement for the B 0 → K 0 S φ BDTs is chosen based on a figure of merit defined as N sig / N sig + N bkg , where N sig is the number of signal events, estimated from the BDT efficiency on simulated datasets normalised using the known branching fraction of the B 0 → K 0 S φ decay [15], and N bkg is the expected number of background candidates in the signal region, extrapolated from the B 0 sidebands.This figure of merit is chosen as the B 0 → K 0 S φ branching fraction is well measured and is optimised separately for each classifier.

Mass fit model
For both the Λ 0 b → Λφ and B 0 → K 0 S φ decay modes, a three-dimensional fit is employed to determine the signal candidate yields.In the Λ 0 b → Λφ case, the three dimensions are the pπ − K + K − , pπ − , and K + K − invariant masses, while in the fit to determine the B 0 → K 0 S φ candidate yield, the three dimensions are the π + π − K + K − , π + π − , and Four components are present in the B 0 → K 0 S φ mass fit: the signal S component combined with two random kaons.The B 0 → K 0 S K + K − non-resonant component has been observed by the BaBar [28], Belle [6] and LHCb [29] collaborations.This is separated from the signal decay through the different K + K − invariant mass line shapes.No significant partially reconstructed background, in which one or more of the final state particles are missed, is found in the B 0 mass region.Peaking backgrounds, from decays in which at least one of the final state particles has been misidentified, are suppressed by the narrow K + K − mass window around the φ meson and are treated as systematic uncertainties.
The B 0 signal is modelled with the same modified Gaussian function as used in Ref. [30].The modified Gaussian gives extra degrees of freedom to accommodate extended tails far from the mean.The φ signal is modelled with a relativistic Breit-Wigner shape [31] convolved with a Gaussian resolution function.The K 0 S signal is parametrised by the sum of two Gaussian functions with a common mean.Decays from real B 0 mesons to the K 0 S K + K − final state in which the K + K − pair is non-resonant are described by the same B 0 and K 0 S line shapes as the signal, but with a phase-space factor to describe the nonresonant kaon pairs.The phase-space factor is given by the expression (m 2 − (2m K ) 2 )/m 2 , where m is the K + K − invariant mass and m K is fixed to the value of the charged kaon mass.The use of a Flatté function [32] rather than a phase-space factor to describe a possible scalar component under the φ resonance is found to have a negligible effect on the results and is therefore not included.The combinatorial background is modelled by exponential functions in all three mass dimensions.
A simultaneous fit to the long and downstream datasets is performed.The B 0 resolution, modified Gaussian tail parameters and resolutions and fractions of the K 0 S Gaussian functions are constrained to values obtained from a fit to simulated data, performed separateley for long and downstream datasets.The total yield and fraction in the downstream dataset are left as free parameters for each component.
The fit to the Λ 0 b → Λφ channel uses the same fit model as the B 0 → K 0 S φ control channel: a modified Gaussian function is used to describe the Λ 0 b mass shape, a double Gaussian model to describe the Λ shape, and a relativistic Breit-Wigner convolved with a Gaussian resolution function to describe that of the φ resonance.Due to the relatively unexplored mass spectra present in the Λ 0 b → Λφ decay, the background contributions have been identified using the data sidebands.In the final fit, four components are present.These are the signal Λ 0 b → Λφ component, the Λ 0 b → ΛK + K − non-resonant component in which the K + K − dimension is described using the phase-space factor defined previously, combinatorial components with true φ or Λ resonances, and a component that has a combinatorial origin in all three mass dimensions.Combinatorial backgrounds are modelled by exponential functions in each fit dimension.As for the case of the B 0 → K 0 S φ fit, the total yield and fraction in the downstream dataset are left as free parameters for each component.In addition, the same parameters are constrained to simulated data as in the B 0 → K 0 S φ fit.

Branching fraction measurement
The Λ 0 b → Λφ branching fraction is obtained from the relation where tot denotes the combined efficiency of the candidate reconstruction, the offline selection, the trigger requirements, and the efficiency of detector acceptance; f d(Λ 0 b ) denotes the fraction of b quarks that hadronise to B 0 (Λ 0 b ) hadrons.The ratio is taken from the LHCb measured value f Λ 0 b /f d = 0.387 ± 0.033 [33].The extra factor 1/2 in Eq. 1 accounts for the fact that only half of K 0 mesons will decay as K 0 S mesons.The value of the B 0 → K 0 φ branching fraction is taken to be (7.3 +0. 7 −0.6 ) × 10 −6 [15], while the PDG values of the Λ and K 0 S branching fractions are used [26].The reconstruction, selection and software trigger efficiencies, as well as the acceptance of the LHCb detector, are determined from simulated samples, using data-driven correction factors where necessary.The different interaction cross-sections of the final-state particles with the detector material is accounted for using simulated datasets.
For the case of the hardware trigger, the efficiency of events triggered by the signal candidate is determined from control samples of D 0 → K − π + and Λ → pπ − decays.The efficiency of events triggered independently of the signal candidate is determined from simulation.The agreement between data and simulation for the distributions of the variables used in the BDT is verified with the B 0 → K 0 S φ data.Data-driven corrections for the reconstruction efficiency of tracks corresponding to the long category are obtained from J/ψ samples using a tag-and-probe method [34].This is applied after a separate weighting to ensure agreement in detector occupancy between data and simulation.For measurements of the relative branching fraction of Λ 0 b → Λφ to B 0 → K 0 S φ, the final state differs by substituting the proton from the decay of the Λ with a pion.However, due to the differences in the kinematics of the pions from the Λ and the K 0 S decays, the distinct correction factors for both daughters of the Λ and K 0 S are considered.In addition to the track reconstruction efficiency, the vertexing efficiency of long-lived particles contains disagreement between data and simulation.The corresponding  correction factors for the long and downstream datasets are determined separately from D 0 → φK 0 S decays.The yields of the Λ 0 b → Λφ signal and B 0 → K 0 S φ control mode are determined from simultaneous extended unbinned maximum likelihood fits to the respective datasets divided according to the data-taking period and also according to whether the Λ (K 0 S ) decay products are reconstructed as long or downstream tracks.Efficiencies are applied to each dataset individually.The projections of the fit result to Λ 0 b → Λφ data are shown in Fig. 2. The fitted yields are 350 ± 24 and 89 ± 13 for the B 0 → K 0 S φ and Λ 0 b → Λφ decay modes, respectively.The statistical significance of the Λ 0 b → Λφ decay, determined according to Wilks' theorem [35] from the difference in the likelihood value of the fits with and without the Λ 0 b → Λφ component, is found to be 6.5 standard deviations.With the systematic uncertainties discussed below included, the significance of the observed Λ 0 b → Λφ decay yield is calculated to be 5.9 standard deviations.The projections of the fit  result to the B 0 → K 0 S φ data are shown in Fig. 3.The fit is found to describe the data well in all three dimensions and a clear peak from the control mode is seen.
The systematic contributions to the branching fraction uncertainty budget are summarised in Table 1.The largest contributions to the systematic uncertainties result from data-driven corrections applied to simulated data along with the mass model used to determine the signal yields.
Signal mismodelling is accounted for using a one-dimensional kernel estimate for the description of the simulated mass distributions [36].Background mismodelling is accounted for using a linear function.The kernel estimate is used in both the signal and control channels to describe the Λ 0 b , B 0 , K 0 S , and Λ line shapes.In order to determine the systematic uncertainties, 1000 pseudoexperiments are generated with the alternative model and are subsequently fitted with the nominal model.The average difference between the generated and fitted yield values is taken as the systematic uncertainty.This leads to uncertainties of 3.0% and 0.6% for the signal and control mode yields, respectively.Systematic uncertainties associated with the efficiency corrections from simulated datasets are considered.The limited size of the simulated sample gives rise to an uncertainty of 2.2%.The main uncertainties in the tracking and vertexing correction factors arise from the limited size of the control sample, which leads to uncertainties of 0.5% and 2.6%, respectively.For the case of the trigger efficiency, uncertainties related to the software trigger cancel between the signal and control modes, as the software trigger decision is made only on the decay products of the φ meson.Uncertainties in the efficiency of the hardware trigger selections are estimated using data-driven methods, for which an uncertainty of 2.8% is applied.The BDTs used to select signal and control modes use the same input variables.Biases could exist if the simulation mismodels these variables differently for signal and control modes.In order to quantify this effect, the control mode is selected with the same classifier as the signal decay.The difference in the measured branching fraction is found to be 4.1%.
The Λ 0 b → Σ 0 (→ Λγ)K + K − and Λ 0 b → pK − φ decay modes are found to be the only significant peaking background contributions.However, for the case of the Λ 0 b → pK − φ decay, the resulting candidates are reconstructed in the long dataset only.With the assumption that the branching fraction for this decay is the same size as for the signal, the contribution is < 1% compared to the Λ 0 b → Λφ decay and far from the Λ 0 b signal region, and is therefore ignored.In order to determine the shape in the pπ events is used with a requirement that the K + K − invariant mass is within 30 MeV/c 2 of the nominal φ mass.The inclusion of an additional fit component using the shape from simulation is found to have a small effect on the signal yield at the level of 0.1%, which is assigned as a systematic uncertainty.For the case of the B 0 → K 0 S φ control mode, no peaking background contributions have been identified.
The branching fraction ratio is measured to be The use of the world average value of B(B 0 → K 0 6 Triple-product asymmetries The Λ 0 b → Λφ decay is a spin-1/2 to spin-1/2 plus vector transition.Five angles are needed to describe this decay since Λ 0 b baryons may potentially be produced with a transverse polarisation in proton-proton collisions [13], as shown in Fig. 4. The angle θ is defined as the polar angle of the Λ baryon in the Λ 0 b rest frame with respect to the normal vector defined through where p 1 is the momentum of an incoming proton and p Note that the basis {ẽ X , ẽY , ẽZ } defines the ⇤ b rest frame, in which ẽZ is parallel to ẽ3 , 120 and ñ⇤(V ) is the normal vector to the ⇤(V ) decay plane 1 , defined through Asymmetries in cos ni and sin ni , where i 2 {⇤, }, are defined as Triple-product asymmetries, which are odd under time-reversal, have been proposed by Leitner and Ajaltouni using the azimuthal angles Φ n i , i ∈ {Λ, φ}, defined as [12] cos where The basis { e X , e Y , e Z } is defined in the Λ 0 b rest frame, in which e Z is parallel to n, e X is chosen to be parallel to the momentum of the incoming proton, and nΛ(φ) is the normal vector to the Λ(φ) decay plane, defined through Asymmetries in cos Φ n i and sin Φ n i , where i ∈ {Λ, φ}, are defined as where N +(−),c i and N +(−),s i denote the number of candidates for which the cos Φ n i and sin Φ n i observables are positive (negative), respectively.
The asymmetries A c,s Λ and A c,s φ are determined experimentally through a simultaneous unbinned maximum likelihood fit to datasets in which the relevant observables are positive and negative.The fit construction and observables are identical to that used for the branching fraction measurement.However, the yields for each dataset are parametrised in terms of the total yield, N j , and the asymmetry, A j , for fit component j as Distributions of the sin Φ n (Λ,φ) and cos Φ n (Λ,φ) observables from Λ 0 b → Λφ data have been extracted using the sPlot method [37] and are provided in Fig. 5.The numerical values of the fitted asymmetries are given in Table 2.
Mismodelling of the mass components could lead to background contamination in the determination of the asymmetries.In the determination of the uncertainty related to the mass model, two contributions are considered.These are the line shape models and the background asymmetries.The effects of the line shapes are quantified using the same method as the branching fraction measurement, i.e. the generation of datasets with a onedimensional kernel estimate of the simulation mass distributions in addition to modification of the background description.In the nominal fit, components that are not from the Λ 0 b → Λφ signal have zero asymmetries.For background components this is justified due  to the uncorrelated kinematics of the K + K − and pπ − systems.However, the non-resonant Λ 0 b → ΛK + K − contribution could have non-zero asymmetries.The systematic uncertainty due to the assumption of zero background asymmetries is determined through comparing the nominal fit against the fit with all possible asymmetries allowed to vary freely.
Efficiencies are found to be independent of the sin Φ n i and cos Φ n i observables.The systematic uncertainty due to the angular acceptance is then taken from the statistical uncertainty in fits to the simulated datasets, after the application of an appropriate weighting to account for the differences between data and simulation.The resolutions of the angular observables are found from simulated events to be 32.3 mrad and 22.1 mrad for the Φ n Λ and Φ n φ angles, respectively.The uncertainty due to bin migration is then assigned assuming maximal asymmetry and leads to minor uncertainties of 0.007 for the Φ n φ angle and 0.010 for the Φ n Λ angle.Systematic contributions to the triple-product uncertainty budget are summarised in Table 3.

Summary
A search for the Λ 0 b → Λφ decay is presented based on a dataset of 3.0 fb −1 collected by the LHCb experiment in 2011 and 2012.The decay is observed for the first time with a significance of 5.9 standard deviations including systematic uncertainties.The branching fraction is found to be B(Λ 0 b → Λφ)/10 −6 = 5.18 ± 1.04 (stat) ± 0.35 (syst) +0.50 −0.43 (B(B 0 → K 0 S φ)) ± 0.44 (f d /f Λ 0 b ).Triple-product asymmetries are measured to be A c Λ = −0.22 ± 0.12 (stat) ± 0.06 (syst), A s Λ = 0.13 ± 0.12 (stat) ± 0.05 (syst), A c φ = −0.01 ± 0.12 (stat) ± 0.03 (syst), A s φ = −0.07± 0.12 (stat) ± 0.01 (syst), and are consistent with zero.Data collected by the LHCb experiment in the forthcoming years will improve the statistical precision of these measurements and enable the dynamics of b → s transitions in beauty baryons to be probed in greater detail, which will greatly enhance the reach of searches for physics beyond the SM.

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In the Standard Model (SM), the flavour-changing neutral current (FCNC) decay ⇤ b !⇤ 30 proceeds via a b !ßs penguin process.A Feynman diagram of the gluonic penguin

32 as
the B 0 s !decay, which is a golden mode for the LHCb upgrade.New particles 33 entering the penguin loop could induce non-SM CP violation.In the B 0 s !decay, this 34 is tested through the measurement of CP violation in the interference between mixing 35 and decay, characterised through the CP -violating phase, sss s .An LHCb measurement 36

Figure 2 :
Figure 2: Fit projections to the pπ − K + K − invariant mass in the (a) long and (b) downstream datasets, the K + K − invariant mass in the (c) long and (d) downstream datasets, and the pπ − invariant mass in the (e) long and (f) downstream datasets.The total fit projection is given by the blue solid line.The blue and green dotted lines represent the φ + Λ and pure combinatorial fit components, respectively.The red and magenta dashed lines represent the Λ 0 b → Λφ signal and the Λ 0 b → ΛK + K − non-resonant components, respectively.Black points represent the data.Data uncertainties are Poisson 68% confidence intervals.

Figure 3 :
Figure3: Fit projections to the π + π − K + K − invariant mass in the (a) long and (b) downstream datasets, the K + K − invariant mass in the (c) long and (d) downstream datasets, and the π + π − invariant mass in the (e) long and (f) downstream datasets.The total fit projection is given by the blue solid line.The green and blue dotted lines represent the combinatorial and K 0 S + random K + K − fit components, respectively.The red and magenta dashed lines represent the B 0 → K 0 S φ signal and the B 0 → K 0 S K + K − non-resonant components, respectively.Black points represent the data.Data uncertainties are Poisson 68% confidence intervals.

Figure 3 :
Figure 3: Decay angles for the ⇤ b !⇤ decay, where the angles are defined in the text.

Figure 4 :
Figure 4: Decay angles for the Λ 0 b → Λφ decay, where the angles are defined in the text.

Table 1 :
Systematic uncertainty contributions to the branching fraction ratio.

Table 3 :
Systematic uncertainty contributions to the triple-product asymmetries.