Relativistic calculations of $R(D^{(*)})$, $R(D^{(*)}_s)$, $R(\eta_c)$ and $R(J/\psi)$

TL;DR

This paper calculates key ratios of semileptonic B meson decays within the Standard Model using a relativistic Bethe-Salpeter approach, addressing discrepancies with experimental data and emphasizing relativistic form factor corrections.

Contribution

It provides improved Standard Model predictions for various $R$ ratios using relativistic corrections, aligning with experimental results and other models.

Findings

Predicted ratios are consistent with experimental data.

Relativistic corrections significantly impact form factor calculations.

Provides decay rates and form factors at zero recoil.

Abstract

Recently, the deviation of the ratios $R(D)$, $R(D^{*})$ and $R(J/\psi)$ have been found between experimental data and the Standard Model predictions, which may be the hint of New Physics. In this work, we calculate these ratios within the Standard Model by using the improved instantaneous Bethe-Salpeter method. The emphasis is pad to the relativistic correction of the form factors. The results are $R(D)=0.312 ^{+0.006}_{-0.007}$, $R(D^*)= 0.249^{+0.001}_{-0.002}$, $R(D_s)=0.320 ^{+0.009}_{-0.009}$, $R(D^*_s)=0.251 ^{+0.002}_{-0.003}$, $R(\eta_c)=0.384 ^{+0.032}_{-0.042}$, and $R(J/\psi)=0.267 ^{+0.009}_{-0.011}$, which are consistent with predictions of other models and the experimental data. The semileptonic decay rates and corresponding form factors at zero recoil are also given.