Semileptonic decays $$B_{c}$$ B c meson to S-wave charmonia and X(3872) within the covariant light-front approach

Abstract In this work, we investigate the semileptonic decays of $$B_{c}$$ B c meson to $$\eta _{c}(1S,2S,3S)$$ η c ( 1 S , 2 S , 3 S ) , $$\psi (1S,2S,3S)$$ ψ ( 1 S , 2 S , 3 S ) and X(3872) within the framework of covariant light-front quark model (CLFQM). We combine the helicity amplitudes via the corresponding form factors to obtain the branching ratios of the semileptonic decays $$B_{c}\rightarrow \eta _{c}(1S, 2S, 3S)\ell \nu _{\ell }$$ B c → η c ( 1 S , 2 S , 3 S ) ℓ ν ℓ , $$B_{c}\rightarrow \psi (1S, 2S, 3S))\ell \nu _{\ell }$$ B c → ψ ( 1 S , 2 S , 3 S ) ) ℓ ν ℓ and $$B_{c}\rightarrow X(3872)\ell \nu _{\ell }$$ B c → X ( 3872 ) ℓ ν ℓ , with $$\ell =e,\mu ,\tau $$ ℓ = e , μ , τ . In view of the $$R_{J/\Psi }$$ R J / Ψ anomaly released by the LHCb collaboration, it is necessary to systematically calculate the ratios $$R_X$$ R X with $$X=\psi (1S,2S,3S),\eta _c(1S,2S,3S),X(3872)$$ X = ψ ( 1 S , 2 S , 3 S ) , η c ( 1 S , 2 S , 3 S ) , X ( 3872 ) , which are helpful for checking the lepton flavor universality (LFU). We also take into account another two physical observables, the longitudinal polarization fraction $$f_{L}$$ f L and the forward–backward asymmetry $$A_{FB}$$ A FB , which can provide new clues for understanding the $$R_{J /\Psi }$$ R J / Ψ anomaly. Such theoretical predictions are necessary and interesting, and can be tested in future LHCb experiments.