Observation of a new baryon state in the Λb0π+π−\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Lambda}_{\mathrm{b}}^0{\pi}^{+}{\pi}^{-} $$\end{document} mass spectrum

A new baryon state is observed in the Λb0π+π−\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Lambda}_{\mathrm{b}}^0{\pi}^{+}{\pi}^{-} $$\end{document} mass spectrum with high significance using a data sample of pp collisions, collected with the LHCb detector at centre-of-mass energies s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s} $$\end{document} = 7, 8 and 13 TeV, corresponding to an integrated luminosity of 9 fb−1. The mass and natural width of the new state are measured to be m=6072.3±2.9±0.6±0.2MeV,Γ=72±11±2MeV,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\displaystyle \begin{array}{l}m=6072.3\pm 2.9\pm 0.6\pm 0.2\ \mathrm{MeV},\\ {}\Gamma =72\pm 11\pm 2\ \mathrm{MeV},\end{array}} $$\end{document} where the first uncertainty is statistical and the second systematic. The third uncertainty for the mass is due to imprecise knowledge of the Λb0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Lambda}_{\mathrm{b}}^0 $$\end{document} baryon mass. The new state is consistent with the first radial excitation of the Λb0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Lambda}_{\mathrm{b}}^0 $$\end{document} baryon, the Λb(2S)0 resonance. Updated measurements of the masses and the upper limits on the natural widths of the previously observed Λb(5912)0 and Λb(5920)0 states are also reported.


JHEP06(2020)136
Baryon State J P Ref. [16] Ref. [17] Ref. [18] Ref. [19] Λ of narrow states, Λ b (6146) 0 and Λ b (6152) 0 , was also observed by LHCb collaboration [10]. The measured masses and widths of these states are compatible with the expectations for the Λ b (1D) 0 doublet [11][12][13][14]. Recently, the CMS collaboration reported an evidence for a broad excess of events in the Λ 0 b π + π − mass spectrum in the region of 6040 − 6100 MeV corresponding to a statistical significance of four standard deviations [15]. 1 The existence of additional states in the Λ 0 b π + π − spectrum is predicted by the quark model [16][17][18], notably, in the region between the established narrow doublet states, with masses around 6.1 GeV. Quark-model predictions for the masses of the lightest Λ b and Σ ( * ) b states are shown in table 1. This paper reports the observation of a new structure in the Λ 0 b π + π − mass spectrum, as well as updated measurements of the masses and widths of the Λ b (5912) 0 and Λ b (5920) 0 states with improved precision. The analysis uses pp collision data recorded by LHCb in 2011-2018 at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of 1, 2 and 6 fb −1 , respectively.

JHEP06(2020)136
The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region [22], 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 [23,24] 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. The momentum scale of the tracking system is calibrated using samples of J/ψ → µ + µ − and B + → J/ψ K + decays collected concurrently with the data sample used for this analysis [25,26]. The relative accuracy of this procedure is estimated to be 3 × 10 −4 using samples of other fully reconstructed b-hadron, K 0 S , and narrow Υ(1S) resonance decays. Different types of charged hadrons are distinguished by the particle identification (PID) system using information from two ring-imaging Cherenkov detectors [27]. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [28].
The online event selection is performed by a trigger [29] 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 transverse momentum, p T , or a pair of opposite-sign muons with a requirement on the product of muon transverse momenta, or a hadron, photon or electron with high transverse energy in the calorimeters. The software trigger requires a two-, three-or four-track secondary vertex with at least one charged particle with a large p T and inconsistent with originating from any reconstructed primary pp collision vertex (PV) [30,31] or two muons of opposite charge forming a good-quality secondary vertex with a mass in excess of 2.7 GeV.
Simulation is required to model the effects of the detector acceptance, resolution, and selection requirements. In the simulation, pp collisions are generated using Pythia [32] with a specific LHCb configuration [33]. Decays of unstable particles are described by EvtGen [34], in which final-state radiation is generated using Photos [35]. The interaction of the generated particles with the detector, and its response, are implemented using the Geant4 toolkit [36] as described in ref. [38].

Event selection
The Λ 0 b candidates are reconstructed in the Λ 0 b → Λ + c π − and the Λ 0 b → J/ψ pK − decays. 2 The selection of the Λ 0 b candidates is similar to that used in ref.
[10]. All charged final-state particles are required to be positively identified by the PID systems. To reduce the background from random combinations of tracks, only the tracks with large impact parameter with respect to all PVs in the event are used. The Λ + c candidates are reconstructed in the pK − π + final state. The Λ 0 b → J/ψ pK − candidates are created by combining the J/ψ candidates formed of µ + µ − pairs with kaon and proton tracks. The masses of the Λ + c and J/ψ candidates are required to be consistent with the known values of the masses 2 Inclusion of charge-conjugate states is implied throughout this paper.
[GeV] of the respective states [4] and the Λ 0 b candidate is required to have a good-quality vertex significantly displaced from all PVs.
Further suppression of the background is achieved by using a boosted decision tree (BDT) classifier [39,40] implemented in the TMVA toolkit [41]. Two separate BDTs are used for the Λ 0 b → Λ + c π − and Λ 0 b → J/ψ pK − selections. The multivariate estimators are based on the kinematic properties, the reconstructed lifetime and vertex quality of the Λ 0 b candidate and on variables describing the overall consistency of the selected candidates with the decay chain obtained from the kinematic fit described below [43]. In addition, the reconstructed lifetime and vertex quality of the Λ + c → pK − π + candidate is used for the Λ 0 b → Λ + c π − decay. The PID quality, transverse momentum and pseudorapidity of the proton and kaon candidates (for Λ 0 b → J/ψ pK − ) or π − candidate (for Λ 0 b → Λ + c π − ) are also used. The BDT is trained using data, where the signal sample is obtained by subtracting the background using the sPlot technique [44], and the background sample is taken from the range 5.70 − 5.85 GeV in the Λ 0 b → Λ + c π − and Λ 0 b → J/ψ pK − mass distributions. A k-fold cross-validation technique is used to avoid introducing a bias in the evaluation [45]. A kinematic fit [43] is performed in order to improve the Λ 0 b mass resolution. The momenta of the particles in the full decay chain are recomputed by constraining the Λ + c or J/ψ mass to their known values [4] and the Λ 0 b baryon to originate from the associated PV. The mass distributions for the selected Λ 0 b → Λ + c π − and Λ 0 b → J/ψ pK − candidates are shown in figure 1. The Λ 0 b signal yield is (937.9 ± 1.6) × 10 3 and (223.0 ± 0.6) × 10 3 for Λ 0 b → Λ + c π − and Λ 0 b → J/ψ pK − decays, respectively. the Λ 0 b ππ combination, its transverse momentum, the p T of the ππ pair, the p T of each pion, as well as their PID and track-reconstruction-quality variables. For the high-mass region, the p T of the dipion system is required to exceed 250 MeV. Simulated samples of excited Λ 0 b baryons decaying into the Λ 0 b π + π − final state are used as signal training samples, while the background training sample is taken from the same-sign Λ 0 b π ± π ± combinations in data. For the low-mass region, simulated samples of Λ b (5912) 0 and Λ b (5920) 0 signal decays are used, while for the high-mass region the simulated sample consists of decays of a narrow state with mass of 6.15 GeV and natural width of 7 MeV, and a broad state with mass of 6.08 GeV and natural width of 60 MeV. A k-fold cross-validation technique is used for training. A figure of merit ε/( 5 2 + √ B) [47] is used to optimise the requirement on the BDT estimator. The Λ 0 b ππ mass resolution is improved by a kinematic fit [43] constraining the mass of the pK − π + and µ + µ − combinations to the known masses of the Λ + c baryon and J/ψ meson, respectively [4]. The mass of the Λ 0 b baryon in the fit is constrained to the central value of m Λ 0 b = 5619.62 ± 0.16 ± 0.13 MeV [48]. It is also required that the momentum vector of the Λ 0 b candidate and the momenta of both pions points back to the associated pp interaction vertex.

Analysis of the high-mass region
The distributions of the Λ 0 b π + π − and Λ 0 b π ± π ± masses in the range 5.93 < m Λ 0 b ππ < 6.23 GeV for the Λ 0 b → Λ + c π − sample with the high-mass BDT selection applied are shown in figure 2. The distributions of the same-sign Λ 0 b π ± π ± combinations are dominated by random combinations of a Λ 0 b baryon and two pions. The Λ 0 b π + π − spectrum features the contributions of two narrow Λ b (6146) 0 and Λ b (6152) 0 states as well as a broad structure just below 6.1 GeV in addition to the smooth background. This new structure is referred to as Λ * * 0 b hereafter. Figure 3 shows the same distributions for the Λ 0 b → J/ψ pK − sample, where the same features are visible.
A simultaneous binned maximum-likelihood fit with a bin width of 200 keV is performed to the six distributions shown in figures 2 and 3 in order to determine the properties of the resonant shapes. Both signal and background Λ 0 b ππ combinations could include contributions from intermediate Σ ± b and Σ * ± b states. The fitting function for the Λ 0 b π + π − spectra is the sum of five components: a combinatorial background, the two components corresponding to the combinations of Σ ± b → Λ 0 b π ± and Σ * ± b → Λ 0 b π ± with the addition of a pion from the rest of the event, and three resonant contributions for the Λ b (6146) 0 , Λ b (6152) 0 and Λ * * 0 b states. The same-sign Λ 0 b π ± π ± spectra are fitted with a function that contains only the combinatorial, Σ ± b π ± , and Σ * ± b π ± components. The combinatorial background is parameterised with a positive, increasing third-order polynomial function, whose coefficients are left free to vary in the fit. The Σ ± b π and Σ * ± b π components are described by the product of a two-body phase-space function and an exponential function, accounting for the finite width of the Σ ( * ) b states. The exponential factor is determined from the fit to the background-subtracted Σ ( * )± b π mass distributions in the 6.16 < m Λ 0 b ππ < 6.40 GeV range. The shapes of the Σ ( * )± b π components are taken to be the same in all spectra. The combinatorial background shape is fixed to be the same - in the opposite-sign Λ 0 b π + π − and same-sign Λ 0 b π ± π ± spectra, but is allowed to differ for the Λ 0 b → Λ + c π − and Λ 0 b → J/ψ pK − samples. The yields of all background components are left free to vary in the fit. A good description of both the Λ 0 b π + π + and Λ 0 b π − π − mass spectra supports the chosen background model.
A simultaneous fit, described in the text, is superimposed.
is parameterised as where ρ 3 (m) is a three-body phase space of the Λ 0 b π + π − system λ (x, y, z) stands for a Källén function [49], and m π and m Λ 0 b denote the known masses -7 -JHEP06(2020)136 where uncertainties are statistical only. The statistical significance of the Λ * * 0 b signal in Λ 0 b → Λ + c π − and Λ 0 b → J/ψ pK − samples is obtained using Wilks' theorem [50] and exceeds 14 and 7 standard deviations, respectively. The ratios of the Λ * * 0 b , Λ b (6146) 0 and Λ b (6152) 0 signal yields between the Λ 0 b → Λ + c π − and Λ 0 b → J/ψ pK − final state are larger than the ratio of their yields reported in section 3. This arises due to the differece in the p T spectra selected by the trigger for these final states which is propagated to the ππ reconstruction effects.

Analysis of the low-mass region
The Λ 0 b ππ mass spectra in the low-mass region m Λ 0 b ππ < 5.94 GeV for Λ 0 b → Λ + c π − and Λ 0 b → J/ψ pK − samples are shown in figures 5 and 6, respectively. These distributions are used to measure the properties of the Λ b (5912) 0 and Λ b (5920) 0 states. A simultaneous binned fit, with narrow bins of 50 keV width, is performed to the six distributions with the sum of the two resonance components (in Λ 0 b π + π − combinations only) and the combi-  Figure 5. Mass spectra of selected (top) Λ 0 b π + π − , (middle) Λ 0 b π + π + and (bottom) Λ 0 b π − π − combinations for the Λ 0 b → Λ + c π − sample. A simultaneous fit, described in the text, is superimposed.
lineshapes convolved with the resolution function obtained from simulation. The shape of the combinatorial background is assumed to be the same in the opposite-sign Λ 0 b π + π − and same-sign Λ 0 b π ± π ± spectra, but is allowed to differ for the Λ 0 b → Λ + c π − and Λ 0 b → J/ψ pK − samples. The results of the combined fit are presented in table 3. The natural widths of the Λ b (5912) 0 and Λ b (5920) 0 states are consistent with zero.  Figure 6. Mass spectra of selected (top) Λ 0 b π + π − , (middle) Λ 0 b π + π + and (bottom) Λ 0 b π − π − combinations for the Λ 0 b → J/ψ pK − sample. A simultaneous fit, described in the text, is superimposed.

JHEP06(2020)136
Source [  π ∓ states. To assess the associated systematic uncertainty, the fit is repeated using a more complicated function that in addition to nonresonant decays, accounts for the P-wave decays via an intermediate Σ π ∓ state, but ignores interference effects, constructed using the three-particle unitarity constraint approximated in the quasi-two-body interaction model [51] where the mass-dependent width Γ (m) is defined as .
The quasi-two-body phase-space functions ρ Σ ( * ) b π (m) for the decays via the intermediate Σ b π and Σ * b π states are where s stands for a squared mass of the Λ 0 b π pair forming the Σ where the non-negative parameters α and β account for the relative contributions from the Λ * * 0 b → Σ ± b π ∓ and Λ * * 0 b → Σ * ± b π ∓ decays, respectively. A series of fits is performed with parameters α and β varied within the ranges 0 ≤ α < 0.2, 0 ≤ β < 0.2, and α + β ≤ 0.3, consistent with figure 4. The mass of the Λ * * 0 b state is found to be very stable with respect to such variations. The fitted mass does not change more than 0.5 MeV while the fitted width increases up to 1.5 MeV. These values are taken as systematic uncertainties due to the signal parameterisation. The nominal fit does not take the variations of the detector efficiency with the Λ 0 b π + π − mass into account. An alternative fit is performed where the signal shape is multiplied by the efficiency function obtained from simulation. The difference with the nominal fit is added to the uncertainty on the signal parameterisation. Alternative parameterisations of the detector resolution functions, namely a symmetric variant of an Apollonios function [53], a double-sided Crystal Ball function [46], a modified Novosibirsk function [54,55], a Student's t-distribution and a hyperbolic secant function, cause negligible variation for the measured mass and width of the Λ * * 0 b state. The signal parameterisation uncertainty in the measurement of the masses of the low-mass states is negligible.
The uncertainty in the combinatorial background shape parameterisation is accounted for by varying the degree of the polynomial functions from 3 to 4. The uncertainty in the Σ b π and Σ * b π background functions is evaluated by modifying the parameters of the exponential parameterisation within the limits allowed by the fits to the background-subtracted Σ ( * ) b π spectra. In order to assess a possible sensitivity of the fit parameters to the features of the background shape not accounted for by the variations mentioned above, fits are performed in narrower and broader Λ 0 b ππ regions and variations are included as an additional source of systematic uncertainty.
To assess the effect of the fixed parameters of the narrow Λ b (6146) 0 and Λ b (6152) 0 states from the previous analysis [10] in the higher-mass fit, the fits are performed with the masses and the widths of each of the two states left free to vary one by one. The resulting variations of the Λ * * 0 b parameters are found to be negligible. The effect of the calibration of the momentum scale is evaluated by varying the scale within its known uncertainty [8,10,26]. All systematic uncertainties for the mass difference m Λ b (5920) 0 − m Λ b (5912) 0 are found to be negligible.
The upper limits on the natural widths of the Λ b (5912) 0 and Λ b (5920) 0 states are obtained by performing profile likelihood scans. In the calculation of the likelihood, the uncertainties in the knowledge of mass resolution are included by using various resolution models, as listed above, and by varying the mass-resolution scaling factor obtained from -13 -JHEP06(2020)136 simulations within 5% [10, 56,57] and the maximum upper limits across all variations are reported.

Results and summary
Using the LHCb data set taken in 2011-2018, corresponding to an integrated luminosity of 9 fb −1 collected in pp collisions at centre-of-mass energies of 7, 8 and 13 TeV, the Λ 0 b π + π − mass spectrum is studied with Λ 0 b baryons reconstructed in the Λ 0 b → Λ + c π − and Λ 0 b → J/ψ pK − decay modes. A new broad resonance-like state is observed with a statistical significance exceeding 14 and 7 standard deviations for Λ 0 b π + π − samples reconstructed using the Λ 0 b → Λ + c π − and Λ 0 b → J/ψ pK − decay modes, respectively. The mass difference with respect to the Λ 0 b mass and natural width of the state are determined from a combined fit to both samples and are found to be ∆m Λ * * 0 b = 452.7 ± 2.9 ± 0.5 MeV , where the first uncertainty is statistical and the second systematic. Taking the mass of the Λ 0 b baryon m Λ 0 b = 5619.62 ± 0.16 ± 0.13 MeV [48], obtained by a combination of measurements at the LHCb experiment in Λ [58] and Λ 0 b → J/ψ Λ decay modes [25,59], and accounting for the correlated systematic uncertainty, the mass of the Λ * * 0 b state is found to be Several excited Σ b (1P) states are expected with a mass close to the measured value, but the partial decay widths for Σ b (1P) states into Λ 0 b ππ are predicted to be very small [62]. If the observed broad peak corresponds to the Σ b (1P) ( * )0 state, two peaks with similar masses and widths and significantly larger yields should be visible in the Λ 0 b π ± mass spectra due to decays of the charged isospin partners Σ b (1P) ( * )± → Λ 0 b π ± . However, no signs of states with such a mass and width, and large production yields are observed in the analysis of the Λ 0 b π ± mass spectra; the observed Σ b (6097) ± states have significantly smaller natural width and relatively small yields [7]. It cannot be excluded that the observed broad structure corresponds to a superposition of more than one narrow states, but the interpretation of these states as excited Σ b resonances is disfavoured. The mass differences for the Λ b (5912) 0 and Λ b (5920) 0 states with respect to the mass of the Λ 0 b baryon are measured to be ∆m Λ b (5912) 0 = 292.589 ± 0.029 ± 0.010 MeV , where the last uncertainty is due to imprecise knowledge of the Λ 0 b mass. The mass splitting between the narrow states is The following upper limits on the natural widths are obtained: at 90% (95%) confidence level, respectively. The measurements of the parameters of the Λ b (5912) 0 and Λ b (5920) 0 states are about four times more precise and supersede those reported in ref. [8].