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...

We propose a general Regge-like mass relation to describe the spectra of singly heavy hadrons with the slope ratio π : 2 between radial and orbital Regge trajectories. The hadron mass shift M → M − M Q + k s µ lQ with the heavy quark mass M Q and the reduced mass of heavy-light systems µ lQ are taken into account. The relation is successfully tested against the observed spin-averaged masses of singly heavy mesons and baryons in their radially and orbitally excited states. Some new predictions are made for more excited states.

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