Using the newly measured masses of B c (1S ) and B c (2S ) from the CMS Collaboration and the 1S hyperfine splitting determined from the lattice QCD as constrains, we calculate the B c mass spectrum up to the 6S multiplet with a nonrelativistic linear potential model. Furthermore, using the wave functions from this model we calculate the radiative transitions between the B c states within a constituent quark model. For the higher mass B c states lying above DB threshold, we also evaluate the Okubo-Zweig-Iizuka (OZI) allowed two-body strong decays with the 3 P 0 model. Our study indicates that besides there are large potentials for the observations of the low-lying B c states below the DB threshold via their radiative transitions, some higher mass B c states, such as B c (2 3 P 2 ), B c (2 3 D 1 ), B c (3 3 D 1 ), B c (4 3 P 0 ), and the 1F-wave B c states, might be first observed in their dominant strong decay channels DB, DB * or D * B at the LHC for their relatively narrow widths.PACS numbers:

The open-charm strong decays of higher charmonium states up to the mass of the 6P multiplet are systematically studied in the 3 P 0 model. The wave functions of the initial charmonium states are calculated in the linear potential (LP) and screened potential (SP) quark model. The decay widths for most of the well-established charmonium states above the open-charm thresholds can be reasonably described. By comparing our quark model calculations with the experimental observations we also discuss the nature of some of the newly observed charmonium-like states. It is found that (i) the ψ(4415) may favor the ψ(4S ) or ψ 1 (3D) assignment. There may exist two highly overlapping vector charmonium states around 4.4 GeV; (ii) In the LP model the J PC = 1 −− Y(4660) resonance and the J PC = 0 ++ X(4500) resonance may be assigned as the ψ(5S ) and χ c0 (4P), respectively; (iii) The newly observed state X * (3860) can be assigned as the χ c0 (2P) state with a narrow width of about 30 MeV; (iv) It seems to be difficult to accommodate the X(4140) and X(4274) states in the same potential model as excited χ c1 states. (v) The X(3940) resonance can be assigned as the η c (3S ) state; (vi) The vector charmonium-like states Y(4230/4260, 4360) and scalar X(4700) cannot be described by any conventional charmonium states self-consistently in our model. PACS numbers:

In this work, we calculate the sub-leading power contributions to the radiative leptonic D → γ ν decay. For the first time, we provide the analytic expressions of next-toleading power contributions and the error estimation associated with the power expansion of O(Λ QCD /m c ). In our calculation, we adopt two different models of the D-meson distribution amplitudes φ + D,I and φ + D,II . Within the framework of the QCD factorization as well as the dispersion relation, we evaluate the soft contribution up to the next-toleading logarithmic accuracy, and the higher-twist contribution from the two-particle and three-particle distribution amplitudes is also considered. Finally, we find that all the sub-leading power contributions are significant at λ D (µ 0 ) = 354 MeV, and the nextto-leading power contributions will lead to 143% in φ + D,I and 120% in φ + D,II corrections to leading power vector form factors with E γ = 0.5 GeV. As the corrections from the higher-twist and local sub-leading power contributions will be enhanced with the growing of the inverse moment, it is difficult to extract an appropriate inverse moment of the Dmeson distribution amplitude. The predicted branching fractions are (1.88 +0.36 −0.29 ) × 10 −5 for φ + D,I and (2.31 +0.65 −0.54 ) × 10 −5 for φ + D,II , respectively.

151 +0.091 −0.043 th. +0.017 −0.02 exp. |V cs | = 0.89 +0.467 −0.234 th.