Predictions for the isospin-violating decays of $B_{c}(1P)^{+}\to B_{c}^{(*)+}π^{0}$

TL;DR

This work analyzes isospin-violating decays $B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0}$ to probe the first orbital excitations of the $B_c$ system. It employs an effective Lagrangian approach tied to a duality between the $U(1)$ anomaly-induced soft-gluon coupling and intermediate meson loop transitions, with couplings fixed via the $^{3}P_{0}$ model. The main finding is that $\Gamma(B_{c0}^{*+}\to B_{c}^{+}\pi^{0})$ is about $10^{3}$ times larger than $\Gamma(B_{c2}^{*+}\to B_{c}^{+}\pi^{0})$, while the axial-vector states $B_{c1}^{+}$ and $B_{c1}'^{+}$ yield comparable widths in $B_{c1}^{(\prime)+}\to B_{c}^{*+}\pi^{0}$. Although the isospin-violating decays are small, these predictions offer valuable guidance for future experiments to establish and distinguish the four $P$-wave $B_c$ states.

Abstract

In this work we study the isospin-violating decays of $B_{c}(1P)^{+}\to B_{c}^{(*)+}π^{0}$, 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 $B_{c}(1P)^{+}\to B_{c}^{(*)+}π^{0}$ 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 $B_{c0}^{*+}\to B_{c}^{+}π^{0}$ is about three orders of magnitude larger than that for $B_{c2}^{*+}\to B_{c}^{+}π^{0}$. It implies that $B_{c0}^{*+}$ can be established in the $B_{c}^{+}π^{0}$ decay channel as a single state. Meanwhile, the two axial-vector states $B_{c1}^{+}/B_{c1}'^{+}$ can be possibly identified in $B_{c1}^{+}/B_{c1}'^{+}\to B_{c}^{*+}π^{0}$ with comparable strengths. Although these isospin-violating decays turn out to be small, the theoretical predictions should be useful for guiding future experimental efforts.

Figures (4)

• Figure 1: Schematic diagrams of the decay $B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0}$ via intermediate meson loops without $\eta-\pi^{0}$ mixing, where $\mathcal{B}=(B^{+},B^{0})$ and $\mathcal{D}=(D^{0},D^{+})$. (a)--(h) illustrate different intermediate meson loops.
• Figure 2: Schematic diagrams of the decay $B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0}$ via intermediate meson loops and $\eta-\pi^{0}$ mixing, where $\mathcal{B}=(B^{+},B^{0},B_{s}^{0})$ and $\mathcal{D}=(D^{0},D^{+},D_{s}^{+})$. (a)--(h) illustrate different intermediate meson loops.
• Figure 3: The partial decay width of $B_{c}(1P)^{+}\to B_{c}^{(*)+}\pi^{0}$ as a function of the cutoff parameter $\alpha$.
• Figure 4: Dependence of the contributions from different loop diagrams to $g_{B_{c}(1P)^{+}B_{c}^{(*)+}\pi^{0}}$ on the cutoff parameter $\alpha$. (a)$-$(d) correspond to different $B_{c}(1P)^{+}$ states.