Semileptonic decays $B/B_s \to (\eta,\etar, G)(l^+l^-,l\bar{\nu},\nu\bar{\nu})$ in the perturbative QCD approach beyond the leading order

TL;DR

This paper systematically studies semileptonic B and Bs decays involving eta, eta', and a pseudoscalar glueball using perturbative QCD, including NLO corrections, and compares different mixing schemes with experimental data.

Contribution

It incorporates next-to-leading-order corrections into pQCD calculations of form factors for these decays and compares mixing schemes, improving theoretical predictions.

Findings

NLO contributions enhance branching ratio predictions by 25%.

pQCD results align with other theoretical models.

Predictions agree across different mixing schemes.

Abstract

In this paper we make a systematic study of the semileptonic decays $B/B_s \to (\eta,\etar, G)(l^+l^-,l\bar{\nu},\nu\bar{\nu})$ by employing the perturbative QCD (pQCD) factorization approach. The next-to-leading-order (NLO) contributions to the relevant form factors are included, and the ordinary $\eta$-$\etar$ mixing scheme and the $\eta$-$\etar$-$G$ mixing scheme are considered separately, where $G$ denotes a pseudoscalar glueball. The numerical results and the phenomenological analysis indicate that (a) the NLO contributions to the relevant form factors provide 25% enhancement to the leading-order pQCD predictions for the branching ratios $Br(B^-\to \eta^{(')} l^-\bar{\nu}_l)$, leading to a good agreement between the predictions and the data; (b) for all considered decays, the pQCD results are basically consistent with those from other different theoretical models; (c) the pQCD predictions in the two considered mixing schemes agree well with each other within theoretical errors. The outcomes presented here can be tested by LHCb and forthcoming Super-$B$ experiments.