Observation of $\Lambda_b^0\rightarrow D^+ p \pi^-\pi^-$ and $\Lambda_b^0\rightarrow D^{*+} p \pi^-\pi^-$ decays

The multihadron decays $\Lambda_b^0\rightarrow D^+ p \pi^-\pi^-$ and $\Lambda_b^0\rightarrow D^{*+} p \pi^-\pi^-$ are observed in data corresponding to an integrated luminosity of 3fb$^{-1}$, collected in proton-proton collisions at centre-of-mass energies of 7 and 8TeV by the LHCb detector. Using the~decay $\Lambda_b^0\rightarrow \Lambda_c^+ \pi^+ \pi^-\pi^-$ as a normalisation channel, the ratio of branching fractions is measured to be $$ \frac { {\mathcal{B}} ( \Lambda_b^0\rightarrow D^+ p \pi^-\pi^- ) } { {\mathcal{B}} ( \Lambda_b^0\rightarrow \Lambda_c^+ \pi^+ \pi^-\pi^- ) } \times \frac { {\mathcal{B}} ( D^+ \rightarrow K^-\pi^+\pi^+) } { {\mathcal{B}} ( \Lambda_c^+ \rightarrow p K^-\pi^+ ) } = ( 5.35 \pm 0.21 \pm 0.16 ) \% \,, $$ where the first uncertainty is statistical and the second systematic. The ratio of branching fractions for $\Lambda_b^0\rightarrow D^{*+} p \pi^-\pi^-$ and $\Lambda_b^0\rightarrow D^+ p \pi^-\pi^-$ decays is found to be $$ \frac{ {\mathcal{B}} ( \Lambda_b^0\rightarrow D^{*+} p \pi^-\pi^- )} { {\mathcal{B}} ( \Lambda_b^0\rightarrow D^{+} p \pi^-\pi^- )} \times ( {\mathcal{B}}( D^{*+} \rightarrow \pi^0 ) + {\mathcal{B}}( D^{*+} \rightarrow \gamma )) = ( 61.3 \pm 4.3 \pm 4.0 ) \% \,. $$


Introduction
Nonleptonic decays with multiple hadrons, such as Λ 0 b → D + pπ − π − and Λ 0 b → Λ + c π − π + π − , are a useful platform for testing non-perturbative quantum chromodynamics (QCD) approaches such as QCD factorisation (QCDF). At the quark level these Λ 0 b baryon decays are mediated by the weak b → ccs and b → cud transitions. 1 Calculating the rates for these decays is more challenging than for their semileptonic b → c −ν partners, since strong interactions are present in both the hadronic initial and final states. Despite these difficulties, which are due to QCD effects, substantial progress has been made in computing hadronic two-body and quasi-two-body decays; earlier calculations [1][2][3][4] have been refined in Refs. [5,6]. These theory predictions agree well with both the CDF measurement of Λ 0 b production and decays [7], and a similar LHCb measurement [8]. Formulated within the framework of QCDF, these predictions are calculated for several decay modes, Λ 0 b → Λ + c (π − , ρ − , a − 1 ), including exclusive modes where the intermediate resonance decays into a final state with multiple pions, e.g. a − 1 → π − π − π + [5]. Such decay channels contribute to the multihadron Λ 0 b → Λ + c π − π + π − decay analysed in this study. Final state protons and charm mesons are of particular interest in multihadron decays of beauty baryons, where the c-quark from the b → c transition hadronises into the final state separate from the baryon, i.e. a charm meson and a proton. This topology is not only important for charm baryon and meson spectroscopy, but also sensitive to QCD effects in beauty baryons as well as charm-quark hadronisation. However, this topology has not been widely studied. Currently, only a few decay modes of beauty baryons with the final state configuration described above are known: . The amplitude analysis of Λ 0 b → D 0 pK − decays discovered a rich resonance structure allowing the study of excited charm baryons [12]. Recently, the LHCb collaboration reported an observation of the Λ 0 b → DpK − channel with a D → K ∓ π ± decay, where the state D is a superposition of D 0 and D 0 states [13]. The CP asymmetry in this decay and the ratio of branching fractions for the Λ 0 b → (D → K − π + ) pK − and Λ 0 b → (D → K + π − ) pK − decays are also measured. In this paper, the first observation of the Λ 0 b → D + pπ − π − and Λ 0 b → D * + pπ − π − multihadron decay modes is reported. The measurements are based on proton-proton (pp) collision data, corresponding to integrated luminosities of 1 and 2 fb −1 collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV, respectively. The following ratios of branching fractions are reported where B(D * + → D + π 0 /γ) equals B(D * + → D + π 0 ) + B(D * + → D + γ), and the Λ 0 b → Λ + c π + π − π − mode with the Λ + c → pK − π + decay is used as the normalisation channel. No theory predictions are currently available for the decay modes Λ 0 b → D + pπ − π − and Λ 0 b → D * + pπ − π − .

Detector and simulation
The LHCb detector [14,15] 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 silicon-strip detectors and straw drift tubes 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 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, 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 and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers.
The online event selection is performed by a trigger system. The trigger 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 [16]. The events used in this analysis are selected at the hardware stage by requiring a cluster in the calorimeters with transverse energy greater than 3.6 GeV. The software trigger requires a two-, threeor four-track secondary vertex with a large p T sum of the particles and a significant displacement from the primary pp interaction vertices (PVs). At least one charged particle should have p T > 1.7 GeV/c and large χ 2 IP with respect to any PV, where χ 2 IP is defined as the difference in fit χ 2 of a given PV reconstructed with and without the considered track. A multivariate algorithm is used for the identification of secondary vertices consistent with the decay of a b hadron [17].
Simulated collision events are used to model the effects of the detector acceptance and the imposed selection requirements for signal decay modes. In the simulation, pp collisions are generated using Pythia [18] with a specific LHCb configuration [19]. The p T and rapidity spectra of the Λ 0 b baryons in simulation are corrected to match those for the reconstructed Λ 0 b → Λ + c π + π − π − decays, which constitute a large data sample used for normalisation. Decays of unstable particles are described by EvtGen [20], in which final-state radiation is generated using Photos [21]. A four-body phase-space decay model is used for The decay models are corrected to reproduce the ten two-and three-body mass distributions from the signals observed in data. The corrections are applied subsequently for ten mass distributions in several iterations untill convergence is achieved. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [22] as described in Ref. [23]. To account for imperfections in the simulation of charged-particle reconstruction, the track reconstruction efficiency determined from simulation is corrected using control channels in data [24].

Event selection
The Λ 0 b → D + pπ − π − and Λ 0 b → Λ + c π + π − π − decays are reconstructed using the D + → K − π + π + and Λ + c → pK − π + decay channels, respectively. The selection begins with good-quality reconstructed charged tracks that are inconsistent with being produced in a pp interaction vertex. Kaons, pions and protons, identified using information from the RICH detectors [25,26], are selected from well-reconstructed tracks within the acceptance of the spectrometer with p T > 100 MeV/c. To allow for efficient particle identification, kaons and pions are required to have a momentum between 3 and 120 GeV/c, while protons must have momenta between 9 and 120 GeV/c. The D + → K − π + π + and Λ + c → pK − π + candidates are reconstructed from selected kaon, pion and proton candidates requiring K − π + π + and pK − π + combinations to form a good quality three-prong common vertex, which is significantly separated from any PV. A reconstructed mass for the D + and Λ + c candidates is required to be within ±34 and ±24 MeV/c 2 mass windows around the known masses of the D + and Λ + c hadrons [27], respectively. These mass ranges correspond to approximately ±4σ m regions, where σ m is the mass resolution. Three-track combinations are also formed of pπ − π − and π + π − π − particle triplets, and are required to have a good-quality common vertex that is distinct from the PV. The mass of these pπ − π − and π + π − π − combinations are required to be below 4 and 3 GeV/c 2 , respectively.
The reconstructed D + and Λ + c candidates are combined with selected pπ − π − and π − π + π − candidates to form Λ 0 b candidates. Only Λ 0 b candidates with a transverse momentum above 3 GeV/c are selected for further analysis. To improve the mass resolution for the Λ 0 b candidates, a kinematic fit is performed [28], which constrains the mass of the D + and Λ + c hadron candidates to their known masses [27] and requires the Λ 0 b candidate to originate from its associated PV. A requirement on the χ 2 from this fit further suppresses background. The reconstructed Λ 0 b decay vertex is required to be distinct from the PV, with the proper decay time of the Λ 0 b candidate restricted to be above 100 µm/c. The proper decay time of the D + and Λ + c candidates calculated with respect to the reconstructed Λ 0 b decay vertex is required to be positive within the resolution. These two requirements reduce the background contributions from charmed hadrons produced directly in the pp interaction, and random combinations of tracks forming fake D + or Λ + c candidates. At least one track from the selected Λ 0 b candidate must be matched with a high energy deposit in the calorimeter system, used in the hardware-trigger stage. The mass distributions for selected Λ 0 b → D + pπ − π − and Λ 0 b → Λ + c π + π − π − candidates are shown in Figs. 1 and 2, respectively.

Signal determination
The D + pπ − π − mass distribution shown in Fig. 1 exhibits a narrow peak corresponding to the Λ 0 b → D + pπ − π − decay. In addition, a structure around 5.4 − 5.5 GeV/c 2 is visible. This structure corresponds to the Λ 0 b → D * + pπ − π − decay followed by the decay of the D * + meson into D + π 0 or D + γ states, where the neutral particle is not reconstructed. Candidates/(10 MeV/c 2 ) LHCb 3 fb −1 An extended unbinned maximum-likelihood fit to the D + pπ − π − mass distribution is performed using a function consisting of a sum of the four following contributions.
parameterised by a modified Gaussian function with power-law tails on both sides of the distribution [29,30]. The tail parameters are fixed to values obtained from simulation, while the width and peak position are allowed to vary in the fit.
The shape of the component is taken from simulation and modified by a first order positive polynomial which accounts for the unknown Λ 0 b decay model. The parameters of the polynomial function are allowed to vary in the fit.
The shape is also taken from simulation.
• A combinatorial-background component, parameterised with a positive monotonically-decreasing third-order polynomial function. Candidates/(10 MeV/c 2 ) LHCb 3 fb −1 The projection of an unbinned likelihood fit, described in the text, is superimposed.
The fit result is overlaid on Fig. 1. The signal yields for the Λ 0 b → D + pπ − π − and Λ 0 b → D * + pπ − π − decays are presented in Table 1. A similar four-component function is used to describe the Λ + c π + π + π − mass spectrum.
parameterised with a modified Gaussian function with power-law tails on both sides of the distribution [29,30]. The tail parameters are fixed to values obtained from simulation, while the width and position are allowed to vary in the fit.
→ Λ + c π 0 decay with an undetected π 0 meson. The shape is taken from simulation.
The shape is taken from simulation based on a phase-space decay model.
• A combinatorial-background component, parameterised with a positive monotonically-decreasing third-order polynomial function.
decays evaluated from fits to the D + pπ − π − and Λ + c π + π − π − mass spectra. The yields with all corrections described in the text, N cor , are also given. The uncertainties are statistical only.

Decay mode
The fit result is overlaid on Fig. 2 and the signal yield for the Λ 0 b → Λ + c π + π − π − decays is presented in Table 1.
Several corrections, described below, are applied to the fitted yields. Since the D + pπ − π − channel with a D + → K − π + π + decay and the Λ + c π + π − π − channel with a Λ + c → pK − π + decay consist of the same final state particles, there can be cross-feed between the two where true Λ This contribution is studied using background-subtracted pK − π + mass distributions from Λ 0 b → D + pπ − π − decays. The sPlot technique [31] is applied to the result of the fit described above, using the D + pπ − π − mass as the discriminating variable. The resulting background-subtracted pK − π + 1,2 mass spectra from Fig. 3. The peaks at the known mass of the Λ + c baryon correspond to true Fits are performed to these distributions with a function consisting of the following two terms.
• A first-order polynomial term models the baseline background from Λ 0 b baryon decays without a Λ + c baryon in the final state.

Efficiency and ratios of branching fractions
The ratios R D + and R D * + , defined by Eq. (1) are calculated as  Figure 4: Background-subtracted (left) π + π − π − mass distribution from Λ 0 b → Λ + c π + π − π − decays and (right) pK − π + 2 mass distribution from Λ 0 b → Λ + c → pK − π + 1 π + 2 π − π − decays. The results of the fits described in text are overlaid. and where N cor X is the corrected signal yield for decay mode X, as per Table 1, and ε X is the corresponding efficiency. This efficiency is defined as a product of the detector acceptance ε acc , reconstruction and selection efficiency ε rec&sel , efficiency of the hardware stage of the trigger ε trg and the hadron-identification efficiency ε PID , where each subsequent efficiency is defined with respect to the product of previous efficiencies. The detector acceptance, and reconstruction and selection efficiency, are determined using the simulation samples described in Sec. 2. The reconstruction and selection efficiency is corrected for a small difference in the track reconstruction efficiency between data and simulation [24]. The trigger efficiency is calculated from single-particle hadrontrigger efficiencies, which are determined separately for protons, kaons and pions from a large Λ 0 b → (Λ + c → pK − π + ) π − data sample. The hadron-identification efficiency is a combination of single-particle identification efficiencies for protons, kaons and pions determined with large calibration samples of Λ + c → pK − π + , Λ → pπ − , D * + → (D 0 → K − π + ) π + , D + s → (φ → K + K − ) π + and K 0 S → π + π − decays in data [26]. The ratios of efficiencies are, and where the uncertainties arise from the finite size of the simulation samples. Using the corrected yields from Table 1 and efficiencies from Eq. (4), the ratios R D + and R D * + are found to be and where the uncertainties are statistical only. Systematic uncertainties are discussed in Sec. 6. The background-subtracted two-and three-body mass spectra from the Λ 0 b → D + pπ − π − and Λ 0 b → D * + pπ − π − decays are shown in Figs. 5 through 8 with the expectation from phase-space simulated decays overlaid. The sPlot technique [31] is used for background subtraction using the Λ 0 b candidate mass as a discriminating variable. The analogous distributions for the Λ 0 b → Λ + c π + π − π − decays are shown in Appendix A; corresponding distributions from the corrected simulation samples, used for evaluation of the efficiencies, are also shown. Large deviations between data and phase-space based simulation are observed, demonstrating a rich structure of intermediate resonances for the decay of this study.

Systematic uncertainties
Due to the shared analysis techniques used to determine the yields for the Λ 0 b → D ( * )+ pπ − π − and Λ 0 b → Λ + c π + π − π − decays, many systematic uncertainties cancel for the ratios R D + and R D * + . The remaining contributions to systematic uncertainty are summarised in Table 2 and discussed below.
An important source of systematic uncertainty on the ratios of the branching fractions arises from the imperfect knowledge of the mass shapes of the signal and background components used in the fits. To estimate this uncertainty, several alternative models for the signal and background components are tested. For the Λ 0 b → D + pπ − π − and Λ 0 b → Λ + c π + π − π − signal shapes the tail parameters of modified Gaussian functions are varied within uncertainties, determined from fits to corresponding simulation samples. The order of the positive monotonically-decreasing polynomial function, used for modelling of the background components, is varied between two and four. The ratio of branching fractions for the D * + → D + γ and D * + → D + π 0 decays affects the shape of the Λ 0 b → D * + pπ − π − component. This ratio is varied within the known uncertainty [27,33,34]. For the Λ 0 b → D * + pπ − π − fit component, the polynomial factor that modifies the shape obtained from the simulation is removed. To account for the unknown resonance structure for the Λ 0 b → D + π + π − π − π 0 , Λ 0 b → Σ ( * )+ c π + π − π − and Λ 0 b → Λ + c π + π − π − π 0 decays, the corresponding fit components, determined from simulation, have been modified by the positive-definite linear polynomial functions. The parameters of these polynomial functions are allowed to vary in the fits. For each alternative model the ratio of event yields is determined, and the maximal deviation with respect to the default model is taken as the systematic uncertainty. This uncertainty is 1.5% and 5.7% for the ratios R D + and R D * , respectively.  Figure 5: Background-subtracted D + p, D + π − π − , pπ − π − , π − π − , and maximum and minimum pπ − mass spectra for Λ 0 b → D + pπ − π − decays. Expectations from phase-space (phsp.) and corrected (corr.) simulation are overlaid.    Figure 7: Background-subtracted D + p, D + π − π − , pπ − π − , π − π − , and maximum and minimum pπ − mass spectra for Λ 0 b → D * + pπ − π − decays. Expectations from phase-space (phsp.) and corrected (corr.) simulation are overlaid.   Source Total 2.9 6.5 yields are measured. This procedure is repeated for multiple trials to mitigate the effects of statistical fluctuations. The differences between the original mean values of R D + and R D * + and the values obtained using randomisation are found to be 0.8% and 0.7%, respectively. These differences are taken as systematic uncertainty associated with the selection of multiple candidates. The transverse momentum and rapidity spectra of Λ 0 b baryons in the simulation samples are corrected to reproduce those observed for the Λ 0 b → Λ + c π + π − π − signal in data. This correction is a source of additional uncertainty, which is evaluated with several sets of corrections obtained using different interval schemes for the p T and rapidity distributions of the Λ 0 b candidates. These corrections are applied to the simulation samples and maximal deviations of 0.2% and 0.4% are observed for the ratios R D + and R D * , respectively. These deviations are set as the systematic uncertainty due to imperfect knowledge of the production spectra of the Λ 0 b baryons.
samples are corrected to reproduce the two-and three-body signal mass distributions observed in data. Due to a large number of variables and their correlations, the method requires several iterations to converge. The corrections made for binned distributions are illustrated in Figs. 5 through 8 for the Λ 0 b → D + pπ − π − , Λ 0 b → D * + pπ − π − samples and Figs. A1 and A2 for the Λ 0 b → Λ + c π + π − π − sample. The correction procedure has been further validated by comparison of simulation and data for multiple randomly constructed linear combinations of the ten mass variables. To estimate the systematic uncertainty related to the imperfect knowledge of the decay model for Λ 0 b → D ( * )+ pπ − π − and Λ 0 b → Λ + c π + π − π − decays, the number of iterations is varied. The differences with respect to the baseline results for the R D + and R D * + ratios are assigned as systematic uncertainty due to the imperfect knowledge of the Λ 0 b → D ( * )+ pπ − π − and Λ 0 b → Λ + c π + π − π − decay models. The hadron-identification efficiency for protons, kaons and pions is estimated using large calibration samples. The uncertainty due to the finite size of the calibration samples is propagated to the ratios R D + and R D * + using pseudoexperiments. The obtained variations of 0.7% and 0.5% for the R D + and R D * + ratios, respectively, are used as the systematic uncertainty associated to the hadron identification.
There are residual differences in the reconstruction efficiency of charged-particle tracks that do not cancel completely in the ratio due to small differences in the kinematic distributions of the final-state particles. The track-finding efficiencies obtained from simulation samples are corrected using calibration modes [24]. The uncertainties related to the efficiency correction factors are propagated to the ratios of the total efficiencies using pseudoexperiments and are determined as 0.2% and smaller than 0.1% for the R D + and R D * + ratios, respectively. These values are taken as the systematic uncertainty associated with the tracking efficiency.
The hardware-trigger efficiency for protons, kaons and pions is estimated using a large Λ 0 b → (Λ + c → pK − π + ) π − calibration sample. Efficiencies from alternative calibration samples, e.g. D * + → (D 0 → K − π + ) π + decays, yield 0.9% and 0.5% variations for the R D + and R D * + ratios, respectively. These variations are taken as the systematic uncertainty due to the hardware-trigger efficiency.
The stability of the results is checked by changing the selection criteria on transverse momenta for the final state hadrons, the χ 2 from the kinematic fit and decay time for Λ 0 b candidates. The ratios R D + and R D * + vary by up to 1.9% and 2.8%, respectively, and these variation are conservatively assigned as a systematic uncertainty due to data-simulation differences not considered elsewhere. Finally, the 0.8% and 0.9% relative uncertainties from Eq. (4) are assigned as a systematic uncertainty due to the finite size of the simulated samples for the R D + and R D * + ratios, respectively.

Results and summary
The decays Λ 0 b → D + pπ − π − and Λ 0 b → D * + pπ − π − are observed using data collected with the LHCb detector in proton-proton collisions corresponding to 1 and 2 fb −1 of integrated luminosity at centre-of-mass energies of 7 and 8 TeV, respectively. Both decay modes belong to the relatively unexplored class of beauty-baryon decays where the c-quark from the b → c transition hadronises into the final state separate from the baryon, i.e. a charm meson and a proton. These multihadron decays exhibit a rich resonance structure.
Using the Λ 0 b → Λ + c π + π − π − decay as a normalisation channel, the ratios of branching fractions defined by Eq. (1) are measured to be where the first uncertainty is statistical and the second systematic. Using known branching fractions for the D + → K − π + π + and Λ + c → pK − π + decays [27] the ratio of branching fractions for the Λ 0 where the last uncertainty is due to imprecise knowledge of the branching fractions for the Λ + c and D + hadrons. The relative rate for Λ 0 b → D * + pπ + π + and Λ 0 b → D + pπ + π + decays r D * is defined as Using the known branching fractions of the D * + meson [27], the ratio r D * + is 1.90 ± 0.19. For multihadron b → c decays with a large energy release, a relative yield of the D * + and D + mesons is expected to be similar to one for the D * + and D + mesons produced via a charm quark fragmentation in high-energy hadron or e + e − interactions. A naïve spin-counting rule [35,36] predicts the ratio r D * + to be as large as 3. The relative production of D * + and D + mesons produced promptly in pp collisions at √ s = 5, 7 and 13 TeV is estimated using the cross sections of directly produced D * + and D + mesons, σ direct pp→D * + X and σ direct pp→D + X , as where σ pp→D * + X and σ pp→D + X are the measured inclusive cross sections of the promptly produced D * + and D + mesons. Assuming an independent fragmentation of the c quark into D * + and D + mesons in direct production, and averaging r pp D * + over the different proton collision energies of 5, 7, and 13 TeV [37][38][39], the value r pp D * + is 1.5 ± 0.1. The obtained value is smaller than the value of r D * + obtained from the Λ 0 b → D ( * )+ pπ − π − decays, but consistent within two standard deviations. The value for the ratio of production cross-sections of D * + and D + mesons in e + e − collisions, r e + e − D * = 1.86 ± 0.16, from Ref. [36] is obtained from a combination of measurements performed by the CLEO [40], ARGUS [41], ALEPH [42] and VENUS [43] collaborations analysing data from high energy e + e − annihilation. The similarity between these values indicates a possible correspondence between direct charm-meson production and fragmentation, and charm-meson production in the multihadron decays of beauty hadrons.
Analysis of the Λ + c π + π − π − spectra shows that Λ 0 b → Σ ( * )+ c π + π − π − decays are largely suppressed with respect to Λ 0 b → Λ + c π + π − π − decays, see Fig. 2. The relative production of charmed Σ ( * )+ c and Λ + c baryons exhibits the same trend both in e + e − annihilation [44] and in high energy hadroproduction [45]. From these measurements, a consistent picture emerges where formation and production of a light isoscalar diquark that is a scalar is more favourable during the hadronisation of heavy charm quarks, than a light isovector diquark that is an axial vector [46][47][48]. This observation supports the diquark model for heavy-flavor baryon structure and production [49].
In conclusion, Λ 0 b → D + pπ − π − and Λ 0 b → D * + pπ − π − decays are observed for the first time and their relative branching ratios are measured. Both these decays, and the Λ 0 b → Λ + c π + π − π − decays used in this analysis as a normalisation channel, demonstrate a rich resonance structure. A similarity between prompt charm-meson production and charm-meson production from multihadron decays of Λ 0 b baryons is observed. In the future, the observed decay Λ 0 b → D + pπ − π − can serve as a normalisation mode for studies of similar rare decays, e.g. Ξ 0 b → D + pK − π − and Ξ 0 b → D * + pK − π − decays.