$B$-to-Glueball form factor and Glueball production in $B$ decays

Abstract

We investigate transition form factors of $B$ meson decays into a scalar glueball in the light-cone formalism. Compared with form factors of $B$ to ordinary scalar mesons, the $B$-to-glueball form factors have the same power in the expansion of $1/m_B$. Taking into account the leading twist light-cone distribution amplitude, we find that they are numerically smaller than those form factors of $B$ to ordinary scalar mesons. Semileptonic $B\to Gl\bar\nu$, $B\to Gl^+l^-$ and $B_s\to Gl^+l^-$ decays are subsequently investigated. We also analyze the production rates of scalar mesons in semileptonic $B$ decays in the presence of mixing between scalar $\bar qq$ and glueball states. The glueball production in $B_c$ meson decays is also investigated and the LHCb experiment may discover this channel. The sizable branching fraction in $B_c\to (\pi^+\pi^-)l^-\bar\nu$, $B_c\to (K^+K^-)l^-\bar\nu$ or $B_c\to (\pi^+\pi^-\pi^+\pi^-)l^-\bar\nu$ could be a clear signal for a scalar glueball state.Comment: 17 pages, 3 figure, revtex