Form Factors for $B_c^*\to η_c+lν_l$ at NLO in QCD

Abstract

We present the Non-Relativistic QCD (NRQCD) calculations at the next-to-leading order (NLO) of $α_s$ for $B_c^*\to η_c$ vector, axial-vector, tensor and axial-tensor form factors, and obtain complete analytical expressions for the form factors, along with their asymptotic forms in the hierarchical heavy quark limit. Our results show that the NLO corrections are both sizable and well-behaved in the low squared transfer momentum $(q^2)$ region. Using the NRQCD + lattice + $z$-series method, we further provide theoretical predictions for $B_c^*\to η_c$ form factors across the full physical $q^2$ range. Based on these predicted form factors, we finally compute the decay widths and branching fractions for the semileptonic decays $B_c^*\to η_c+l{ν_l}$.

Figures (14)

• Figure 1: Tree and one-loop sample Feynman diagrams contributing to the form factors, where the circled cross symbol "$\oplus$" denotes a certain heavy flavor-changing current vertex.
• Figure 2: The renormalization scale $\mu$ dependence of the normalized form factor $\hat{V}(\mu)=V(\mu){(m_b/10)^3}/({\Psi_{B_c^*}(0) \Psi_{\eta_c}(0)})$ at LO, asymptotic NLO and complete NLO at the maximum recoil point $q^2=0$.
• Figure 3: The same as in Fig. \ref{['fig:Vmu']}, but for $\hat{A}_0(\mu)$.
• Figure 4: The same as in Fig. \ref{['fig:Vmu']}, but for $\hat{A}_1(\mu)$.
• Figure 5: The same as in Fig. \ref{['fig:Vmu']}, but for $\hat{A}_2(\mu)$.