Predictions for the isospin-violating decays of $B_c(1P{)}^{+}\to B_c^{(\ast )+}{\pi }^0$

Abstract

In this work we study the isospin-violating decays of $B_c(1P{)}^{+}\to B_c^{(\ast )+}{\pi }^0$, which may provide additional information for the determination of the properties of the first orbital excitation states of $B_c(1P{)}^{+}$. By assuming a dual relation between the U(1) anomaly soft-gluon coupling for $B_c(1P{)}^{+}\to B_c^{(\ast )+}{\pi }^0$ and the intermediate meson loop transitions, we can quantify the isospin-violating decay effects for these four $P$-wave states. We find that the partial decay width of $B_{c0}^{\ast +}\to B_c^{+}{\pi }^0$ is about three orders of magnitude larger than that for $B_{c2}^{\ast +}\to B_c^{+}{\pi }^0$. It implies that $B_{c0}^{\ast +}$ can be established in the $B_c^{+}{\pi }^0$ decay channel as a single state. Meanwhile, the two axial-vector states $B_{c1}^{+}/B_{c1}^{\prime +}$ can be possibly identified in $B_{c1}^{+}/B_{c1}^{\prime +}\to B_c^{\ast +}{\pi }^0$ with comparable strengths. Although these isospin-violating decays turn out to be small, the theoretical predictions should be useful for guiding future experimental efforts.

12 pages and 4 figures