Semileptonic decays of B-c meson to a P-wave charmonium state chi(c) or h(c)

The semileptonic decays of meson B-c to a P-wave charmonium state chi (c)(P -3(J)) or h(c)(P-1(1)) are computed. The results show that the decays are s izable so they are accessible in Tevatron and LHC, especially, with the det ectors LHCB and BTeV in the foreseeable future, and of them, the one to the P-1(1) charmonium state potentially offers us a novel window to see the un confirmed h(c) particle. In addition, it is pointed out that since the two charmonium radiative decays chi (c)(P-3(1,2)) --> J/psi + gamma have sizabl e branching ratios, the cascade decays of the concerned decays and the char monium radiative decays may affect the result of observing B-c meson throug h the semileptonic decays B-c-->J/psi +l+v(i) substantially.