Observation of Overlapping Spin-1 and Spin-3 D̄ 0 K − Resonances at Mass 2 . 86

Original citation: LHCb Collaboration (Including: Back, J. J., Blake, Thomas, Craik, Daniel, Dossett, D., Gershon, Timothy J., Kreps, Michal, Langenbruch, C., Latham, Thomas, O’Hanlon, D. P, Pilar, T., Poluektov, Anton, Reid, Matthew M., Silva Coutinho, R., Wallace, Charlotte and Whitehead, M. (Mark)). (2014) Observation of overlapping spin-1 and spin-3 D ̄0K− resonances at mass 2.86 GeV/c2. Physical Review Letters, Volume 113 (Number 16). Article number 162001.

Studies of heavy meson spectroscopy provide an important probe of quantum chromodynamics. The observations of the D * s0 (2317) − [1] and D s1 (2460) − [2] mesons led to renewed activity in the field, as their masses were found to be below the DK and D * K thresholds, respectively, in contrast to prior predictions. These states are usually interpreted as being two of the orbitally excited (1P) charm-strange states, the other two being the D s1 (2536) − and D * s2 (2573) − resonances. Several other charm-strange states, the D * s1 (2700) − , D * sJ (2860) − and D sJ (3040) − resonances, have been discovered [3][4][5][6]. However, their quantum numbers and spectroscopic assignments are not known, with the exception of the D * s1 (2700) − meson, which has spin-parity J P = 1 − and is generally believed to be a radially excited (2S) state. Reviews of the expectations in theoretical models can be found in Refs. [7][8][9][10].
A state with J P = 3 − would be a clear candidate for a member of the 1D family, i.e. a state with two units of orbital excitation. Spin-3 states have been observed in the light unflavoured [11,12] and strange [13,14] meson sectors, but not previously among heavy flavoured mesons. Production of high-spin states is expected to be suppressed in B meson decays, and has not previously been observed. However, high-spin resonances are expected to be relatively narrow, potentially enhancing their observability.
Analysis of the Dalitz plot [15] that describes the phase-space of a three-body decay is a powerful tool for spectroscopic studies. Compared to measurements based on inclusive production processes, the lower background level allows broader states to be distinguished and the well-defined initial state allows the quantum numbers to be unambiguously determined. Specifically, in B 0 s → D 0 K − π + decays, K − π + and D 0 K − resonances appear as horizontal and vertical bands in the Dalitz plot formed from the invariant masses squared m 2 (K − π + ) vs. m 2 (D 0 K − ), and the spin of the resonance can be inferred from the distribution of decays along the band. Measurement of the spin also determines the parity, since only natural spin-parity resonances can decay strongly to two pseudoscalars.
In this Letter, results of the first Dalitz plot analysis of the B 0 s → D 0 K − π + decay are summarised. The inclusion of charge conjugated processes is implied throughout the paper. The D 0 meson is reconstructed through the K + π − decay mode, which is treated as flavour-specific, i.e. the heavily suppressed B 0 s → D 0 K − π + , D 0 → K + π − contribution is neglected. The amplitude analysis technique is used to separate contributions from excited charm-strange mesons and from excited kaon states. A detailed description of the analysis can be found in Ref. [16].
The analysis is based on a data sample corresponding to 3.0 fb −1 of integrated luminosity, approximately one third (two thirds) of which was collected by the LHCb detector from pp collisions at a centre-of-mass energy of 7 (8) TeV during 2011 (2012). The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks, and is described in detail in Ref. [17]. Signal candidates are accepted if one of the final state particles deposited sufficient energy transverse to the beamline in the hadronic calorimeter to fire the hardware trigger. Events that are triggered at the hardware level by another particle in the event are also retained. The software trigger [18] requires a two-, three-or four-track secondary vertex with a large sum of the transverse momentum, p T , of the tracks and a significant displacement from all primary pp interaction vertices (PVs).
The offline selection requirements are similar to those used in Refs. [19,20] and are optimised using the B 0 → D 0 π + π − decay as a control channel. Discrimination between signal and background categories is achieved primarily with a neural network [21] trained on B 0 → D 0 π + π − data, where signal and background are statistically separated with the sPlot technique [22] using the B candidate mass as discriminating variable. A total of 16 variables are used in the network. They include the output of a "D 0 boosted decision tree" [23, 24] that identifies D 0 mesons produced in b hadron decays, together with other variables that characterise the topology and the kinematic distributions of the B decay. A requirement on the network output is imposed that reduces the combinatorial background remaining after the initial selection by a factor of five while retaining more than 90 % of the signal. The four final state tracks also have to satisfy particle identification requirements.
To improve the mass resolution, track momenta are scaled [25, 26] with calibration parameters determined by matching the observed position of the dimuon mass peak to the known J/ψ mass [27]. In addition, the momenta of the tracks from the D 0 candidate are adjusted [28] so that their combined invariant mass matches the known D 0 mass [27]. An additional B 0 s mass constraint is applied in the calculation of the Dalitz plot variables. Vetoes are applied to remove backgrounds containing D * ± mesons, and from the B 0 s → D − s π + and B 0 s → D 0 D 0 decays. Decays of B 0 s mesons to the same final state but without an intermediate charm meson are suppressed by the D 0 boosted decision tree criteria and an additional requirement that the D 0 candidate vertex is displaced by at least 1 mm from the B 0 s decay vertex. The signal and background yields are obtained from an extended unbinned maximum likelihood fit to the invariant mass distribution of B 0 s → D 0 K − π + candidates in the range 5200-5900 MeV/c 2 . In addition to signal decays and combinatorial background, the fit model includes components to describe: partially reconstructed B 0 s → D * 0 K − π + decays, with D * 0 → D 0 π 0 or D 0 γ and the π 0 or γ not included in the reconstruction; B 0 → D 0 K − π + decays; and B 0 → D ( * )0 π + π − and Λ 0 b → D ( * )0 pπ + [29] decays with misidentification of a final state particle. Contributions from other B 0 s and B 0 decays are negligible.
The signal and B 0 → D 0 K − π + shapes are each modelled with the sum of two Crystal Ball [30] functions which share a common mean and have tails on opposite sides. The combinatorial background is modelled using a linear function. Non-parametric functions are used to describe the shapes of B 0 These shapes are determined from simulated events reweighted to account for the known Dalitz plot distributions of the background decays [20,29] and particle identification and misidentification probabilities.
The results of the fit are shown in Fig. 1. Within a signal region of µ B 0 s ± 2.5σ 1 , where the peak position µ B 0 s and core width σ 1 = 12.7 ± 0.2 MeV/c 2 are taken from the results of the fit, there are 12 954 candidates. Of these, 11 302 ± 159 are signal decays, while 948 ± 59 are combinatorial background, 363 ± 133 are B 0 → D ( * )0 π + π − decays and 300 ± 82 are   fitted with a model that includes both signal and background components. The Dalitz plot distribution of combinatorial background is obtained from a sideband region above the signal peak in the B 0 s candidate mass, while those for B 0 → D ( * )0 π + π − and Λ 0 b → D ( * )0 pπ + backgrounds are obtained from simulation reweighted in the same way as their B 0 s candidate mass shapes.
The signal model is defined by considering many possible contributions and removing those that do not significantly affect the fit. It contains 15 resonant or nonresonant amplitudes added coherently in the isobar model formalism. These include the K * (892) 0 , K * (1410) 0 , K * 2 (1430) 0 and K * (1680) 0 resonances. The K − π + S-wave is modelled using the LASS shape [31], which combines the K * 0 (1430) 0 resonance with a slowly varying  [32,33] and each amplitude includes Blatt-Weisskopf barrier form factors [34].
The signal model is multiplied by an efficiency function and normalised to unity when integrated across the Dalitz plot. The efficiency is determined as a function of Dalitz plot position from samples of simulated events with corrections applied for known discrepancies between data and simulation in the efficiencies of the trigger, track reconstruction and particle identification. The trigger efficiency correction is applied separately for candidates in events triggered at hardware level by the signal decay products and for those triggered independently. The largest source of efficiency variation across the Dalitz plot arises due to a rapid decrease of the probability to reconstruct low momentum particles. The particle identification requirements lead to a maximum efficiency variation of about ±20 %, while other effects are smaller.
The largest components in terms of their fit fractions, defined as the ratio of the integrals over the Dalitz plot of a single decay amplitude squared and the total amplitude squared, are the K * (892) 0 (28. Projections of the data and the unbinned maximum likelihood fit result are shown in Fig. 3. To assess the significance of the two states near m(D 0 K − ) ≈ 2860 MeV/c 2 , the fit is repeated with either one or two resonant amplitudes with different spins. All other combinations give values of negative log-likelihood more than one hundred units larger than the default fit. A comparison of the angular distributions in the region near m(D 0 K − ) ≈ 2860 MeV/c 2 of the data and the best fits with the spin-1 only, spin-3 only and both resonances is presented in Fig. 4. Large samples of pseudoexperiments are generated with signal models corresponding to the best fits including only spin-1 or only spin-3 amplitudes, and each pseudoexperiment is fitted under both the one-and two-resonance hypotheses. By extrapolating the tails of the distributions of the difference in negative  where the first uncertainty is statistical, the second is due to experimental systematic effects and the third due to model variations. The largest sources of uncertainty arise from varying the K − π + S-wave description and, for the D * s1 (2860) − width, from removing the K * (1680) 0 and B * + v components from the model. The results for the D * s2 (2573) − mass and width are determined with significantly better precision than previous measurements. Those for the parameters of the D * s1 (2860) − and D * s3 (2860) − resonances must be considered first measurements, since previous measurements of the properties of the D * sJ (2860) − state [3,5,6] involve an unknown admixture of at least these two particles. The results for all the complex amplitudes determined by the Dalitz plot fit, as well as derived quantities such as branching fractions of the resonant contributions and detailed descriptions of the systematic uncertainties, are given in Ref. [16].
In summary, results of the first amplitude analysis of the B 0 s → D 0 K − π + decay show, with significance of more than 10 standard deviations, that a structure at m(D 0 K − ) ≈ 2.86 GeV/c 2 contains both spin-1 and spin-3 components. The masses of the D * s1 (2860) − and D * s3 (2860) − states are found to be similar, while a larger width of the spin-1 state than that of the spin-3 state is preferred. The results support an interpretation of these states being the J P = 1 − and 3 − members of the 1D family, though the 1 − state may be partially mixed with the vector member of the 2S family to give the physical D * s1 (2700) − and D * s1 (2860) − states. The discovery of the D * s3 (2860) − resonance represents the first observation of a heavy flavoured spin-3 particle, and the first time that a spin-3 state is seen to be produced in B decays. This demonstrates that the spectroscopy of the 1D families of heavy flavoured mesons can be studied experimentally.