Abstract
We study the semileptonic decay of the $B_c (0^-)$ to charmonia through the bottom-to-charm-quark electroweak current in the framework of basis light-front quantization. Explicitly, we calculate the weak transition form factors for processes of $B_c$ decaying into $\eta_c$ or $J/\psi$ based on the corresponding initial and final valence light-front wave functions both obtained from the basis light-front quantization. We also present the corresponding differential decay width and branching ratios, as well as the branching ratios for decays into the $\eta_c'$ and the $\psi'$. We observe unphysical frame dependence of the calculated form factors, which is attributed to only including the valence light-front wave functions. Based on the analysis of current component, we propose a preferred set of frames to calculate these form factors.
Highlights
Precise measurement of elements Vq1q2 in the CabibboKobayashi-Maskawa (CKM) matrix is crucial to the electroweak theory
The decay process Bc → ηclνl In basis light-front quantization (BLFQ), we employ an effective Hamiltonian which consists of a 2D harmonic oscillator (HO) transverse confinement, a longitudinal confinement, and an effective one-gluon-exchange potential [28,29]
We investigated the semileptonic decay form factors, differential decay width, and the branching ratios of the Bc meson to the pseudoscalar state ηc and vector state J=ψ with the BLFQ approach
Summary
Precise measurement of elements Vq1q2 in the CabibboKobayashi-Maskawa (CKM) matrix is crucial to the electroweak theory. Recent experiments observed anomalies in the decays of B → DðÃÞτνand Bc → J=ψτν [2,3,4,5,6,7,8], which could indicate the existence of physics beyond the standard model These processes have been studied in nonrelativistic quantum chromodynamics (QCD) [9,10], covariant light-front quark model [11], QCD sum rules [12], and various other theoretical approaches [13,14,15,16,17]. Semileptonic decay form factors is timelike, whereas in the light-front approach the traditional choice of the DrellYan frame only allows for spacelike momentum transfer.
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