Abstract
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 $B_c(2^3P_2)$, $B_c(2^3D_1)$, $B_c(3^3D_1)$, $B_c(4^3P_0)$, 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.
Highlights
The Bc states are composed of a bottom-charmed quarkantiquark pair, as an important family of hadron spectra was predicted in theory about 40 years ago [1]; the experimental progress towards establishing the Bc spectrum is not obvious
Except for the ground state Bc meson observed in 1998 by the CDF Collaboration at Fermilab [2], until 2018, only the ATLAS Collaboration reported evidence of an excited Bc state with a mass of 6842 Æ 9 MeV [3] consistent with the values predicted for Bcð2SÞ, while it was not confirmed by the LHCb Collaboration by using their 8 TeV data sample [4]
The poor situation of the observations and measurements of the Bc spectrum is due to the production yields being significantly smaller than those of the charmonium and bottomonium states
Summary
The Bc states are composed of a bottom-charmed quarkantiquark pair, as an important family of hadron spectra was predicted in theory about 40 years ago [1]; the experimental progress towards establishing the Bc spectrum is not obvious. Using the newly measured masses of Bcð1SÞ and Bcð2SÞ from the CMS Collaboration [5] and the 1S hyperfine splitting determined from the lattice QCD [36,37,38] as constraints, we calculate the Bc mass spectrum up to the 6S multiplet with a nonrelativistic linear potential model. Bc states lying above the DB threshold may have enough possibilities to be produced at LHC, and they are easy to be established in the DðÃÞBðÃÞ hadronic final states, to give useful references for the LHC observations, we further calculate the OZI-allowed strong decays of the higher Bc states within the widely used 3P0 model [63,64,65].
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