$B\to {\chi }_{c1}(1P,2P)K$ decays in QCD factorization and X(3872)

Abstract

$B\to {\chi }_{c1}(1P,2P)K$ decays are studied in QCD factorization by treating charmonia as nonrelativistic bound states. No infrared divergences exist in the vertex corrections, while the logarithmic end-point singularities in the hard spectator corrections can be regularized by a momentum cutoff. With certain uncertainties we find that the $B\to {\chi }_{c1}(2P)K$ decay rate can be comparable to $B\to {\chi }_{c1}(1P)K$, and get $Br(B^0\to {\chi }_{c1}^{\prime }{K}^0)=Br(B^{+}\to {\chi }_{c1}^{\prime }{K}^{+})\approx 2\times 10^{-4}$. This might imply a possible interpretation for the newly discovered X(3872) that this state has a dominant $J^{PC}=1^{++}(2P)$ $c\bar{c}$ component but mixed with a substantial $D^0{\bar{D}}^{\ast 0}+D^{\ast 0}{\bar{D}}^0$ continuum component.

Comments: 5 pages, one figure, new value of decay constant f_B=216 Mev used; references added