Distinguishing the low-lying vector beauty-charm meson via polarization analysis

To distinguish the low-lying vector beauty-charm meson, we systematically study the $B_c^{*}\to B_c+\gamma$, $B_c^{*}\to \ell +{\nu }_{\ell }$, and $B_c^{(*)}\to J/\psi +nh$ processes within effective theory by the helicity decomposition method. The significant difference of polarization asymmetry in $B_c^{(*)}\to J/\psi +nh$ indicates a general law in vector-to-vector and pseudoscalar-to-vector transition processes, which can be tested in current and future LHC experiments. In the end, we discuss the experiment search and discovery potential for the low-lying vector beauty-charm meson.

Figure 1

Total decay width of the low-lying vector $B_c^{*}$ meson as function of the emitted photon energy.

Figure 2

The invariant mass distribution of $m_{3\pi }$ in the $B_c^{+}\to J/\psi {\pi }^{+}{\pi }^{-}{\pi }^{+}$ process. The red points are from the LHCb measurements based on the sample corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$ data [20], while the blue line is our fitting result.

Figure 3

The reconstruction events distribution for both the $B_c\to J/\psi +2\pi$ and $B_c^{*}\to J/\psi +3\pi$ at LHCb run-2.

Figure 4

The polarization asymmetry ${\alpha }_{LT}$ is significantly different in the two processes $B_c^{*}\to J/\psi +n\pi$ and $B_c\to J/\psi +n\pi$ with $n=2$ or $n=3$. In $B_c\to J/\psi +n\pi$ decays, the polarization asymmetry ${\alpha }_{LT}$ denoting “Pseudoscalar” are not sensitive to the relative magnitude between the $n\pi$ spectra functions ${\rho }_{L,T}(q^2)$. While in $B_c^{*}\to J/\psi +n\pi$ decays, the polarization asymmetry ${\alpha }_{LT}$ is slightly sensitive to the spectra functions, where “Vector-I, Vector-II, Vector-III” represent ${\rho }_L={\rho }_T$, ${\rho }_L={\rho }_T/10$, ${\rho }_L=10{\rho }_T$, respectively.