Rare $\Lambda_b \rightarrow \Lambda l^+ l^- $ decay in the Bethe-Salpeter equation approach

TL;DR

This paper investigates the rare decay processes of Lambda_b baryons into Lambda baryons and lepton pairs using the Bethe-Salpeter equation, providing theoretical predictions that align with experimental data.

Contribution

The study applies the Bethe-Salpeter equation approach to calculate branching ratios of Lambda_b decays, offering new theoretical insights and parameter-dependent predictions.

Findings

Branching ratios vary with model parameters and match experimental data.

Predictions for different lepton channels are provided within specific parameter ranges.

Results demonstrate the model's consistency with observed decay rates.

Abstract

We study the rare decays $\Lambda_b \rightarrow \Lambda l^+ l^-~(l=e,\mu, \tau)$ in the Bethe-Salpeter equation approach. We find that depending on the values of parameters in our model the branching ratio $Br(\Lambda_b \rightarrow \Lambda \mu^+ \mu^-)\times 10^{6}$ varies from $0.812$ to $1.445$ when $\kappa = 0.050 \sim 0.060$ GeV$^3$ and the binding energy $E_0=-0.14$ GeV while $Br(\Lambda_b \rightarrow \Lambda \mu^+ \mu^-)\times 10^{6}$ varies from $1.051$ to $1.098$ when $\kappa = 0.055$ Gev$^3$ and the binding energy $E_0$ changes from $-0.19$ to $-0.09$ GeV. These results agree with the experimental data. In the same parameter regions, we find that the branching ratio $Br(\Lambda_b \rightarrow \Lambda e^+ e^-(\tau^+ \tau^-) )\times 10^{6}$ varies in the range $0.660-1.028$ ($0.252-0.392$) and $0.749-1.098$ ($0.286-0.489$), respectively.