Recently, the LHCb Collaboration observed two new bottom baryons, the Ξ b (6227) − and the Σ b (6097) ± , which arouses considerable interest in their inner structures. Stimulated by this, we re-examine the low-lying spectrum of the singly heavy baryons in the heavy quark-diquark picture. Our computation indicates that a linear Regge relation, which is derived from the rotating string model, is sufficient to describe the mass spectrum of all observed singly heavy baryons, predicting that the quantum numbers of the charmed baryons Σ c (2800) and the charm-strange baryon Ξ ′ c (2930), which remain unknown experimentally, are preferably J P = 3/2 − . Similar calculations for the bottom partners support that the newly observed baryons Σ b (6097) − and Ξ ′ b (6227) − are the 1P-wave excitations of the baryons Σ b and Ξ ′ b with J P = 3/2 − . PACS numbers: 14.40.Be, 12.40.Nn, 12.39.Ki ′ b (6227) − . Finally, the paper ends with the discussions and summary in Sec. V. II. SPIN-INDEPENDENT MASSES FOR SINGLY HEAVY BARYONSThe notion of Regge trajectory or Regge mass relation for hadrons, which connects high energy scattering and the spectrum of hadrons in general theory [14], provides us a powerful way to organize the whole spectrum of a given family of the hadrons. In the case of light hadrons, the Regge trajectories are commonly believed to be linear and parallel, and these features are also tested to be true roughly for the SH hadrons in Ref. [24] provided that the hadron mass undergoes a shift M → M − M Q , with M Q the heavy quark mass. As such, one can estimate the spin-averaged masses of Σ c and Ξ ′ c in their P-wave states with the help of the trajectory information of the partner baryons, Λ c and Ξ 0 c , which has the rich data experimentally, and so forth.

We study the Regge-like spectra of light mesons in a relativized quark model. An analytical mass formula is presented for the light unflavored mesons with the help of auxiliary field method, by which a quasi-linear Regge-Chew-Frautschi plot is predicted for the orbitally excited states. We show that the trajectory slope is proportional to the inverse confining parameter 1/a up to a factor depending on the strong coupling α s when the orbital quantum number L is large. The result is tested against the experimental data of the spectra of the meson families π/b,ρ/a,η/h and ω/f in the (L,M 2 ) planes, with the fitted parameters consistent with that in the literatures.

In this work, we study the Regge-like spectra of excited singly heavy mesons by proposing a general Reggelike mass relations in which the slope ratio α ′ /β ′ between the radial and angular-momentum Regge trajectories is π/2 and the hadron mass undergoes a shift including the heavy quark mass and an extra binding energy between heavy quark and strange anti-quark. The relation is successfully tested against the observed spin-averaged data of the singly heavy mesons in their radially and angularly excited states. Some new predictions are made for more excited excitations and the discussion is given associated with the QCD string (flux tube) picture. I. INTRODUCTIONDuring the last two decades, heavy meson spectroscopy has been greatly enlarged due to the discovery of numerous excited charm and charm-strange states (charm mesons hereafter) by the B-Factory experiments BaBar, Belle, CLEO and recently by the LHCb experiment [1]. One of recent examples is the observations of the heavy mesons B(5970) by the CDF Collaboration in the B + π − and B 0 π + mass distributions [2] and the B J (5960) by the LHCb Collaboration in the Bπ mass distributions [3]. The first observation determined the mass of the B (5970) resonances to be 5978 ± 5 ± 12 MeV for the neutral state and to be 5961 ± 5 ± 12 MeV for the charged state. The second observation, giving the mass of 5969.2 ± 2.9 ± 5.3 MeV for the neutral state and 82.3 ± 7.7 ± 9 : 4 MeV for the charged state for B J (5960), seems to be consistent with the B(5970) in their properties, and they may be the same state. Another example is the observation of the charmed states of D J (3000) by the LHCb Collaboration in the Dπ mass distribution data from pp collision [4,5]. These experimental findings arouses theoretical interests to explore and accommodate the newly-discovered states with various approaches, e.g., with the potential quark models [6-18], Lattice QCD [19,20] and other approaches (see Ref.[21] for a recent review). For the B(5970), the two main interpretations exist, with the assignments 2 3 S 1 [22] and the candidate of 1 3 D 3 state [23]. For the D J (3000) and D * J (3000), there are the different interpretations, the D(3 1 S 0 ) and the D(3 3 S 1 ) states, respectively, or the candidates of D(1F) or D(2P). For the D * 2 (3000) the prediction favoring D(3 3 P 2 ) was given [24].In Ref. [25], a comprehensive analysis was made for the whole singly heavy systems of mesons and baryons using the Regge-like mass relation,with M Q the heavy quark mass, supporting that all heavy-light hadrons fall on straight lines in a "shifted" orbital trajectory plane: M → M − M Q , with the slope (α) nearly half of that for the light hadrons. Here, L is the orbital angular momentum of the hadron system. This reflects that the notion of Regge trajectory, which is widely-used in light-flavor sector and stems * Electronic address: jiadj@nwnu.edu.cn from the well-known Regge theory of the scattering matrix [26], remains to be useful in the spectra of the heavy flavor hadrons if one shifts the h...