$S$-wave resonance contributions to the $B_{(s)}^0\to {\eta }_c(2S){\pi }^{+}{\pi }^{-}$ in the perturbative QCD factorization approach

Abstract

By employing the perturbative QCD (PQCD) factorization approach, we study the quasi-two-body $B_{(s)}^0\to {\eta }_c(2S){\pi }^{+}{\pi }^{-}$ decays, where the pion pair comes from the $S$-wave resonance $f_0(X)$. The Breit$-$Wigner formula for the $f_0(500)$ and $f_0(1500)$ resonances, and the Flatté model for the $f_0(980)$ resonance are adopted to parameterize the time-like scalar form factors in the two-pion distribution amplitudes. As a comparison, Bugg's model is also used for the wide $f_0(500)$ in this work. For decay rates, we found the following PQCD predictions: (a) $\mathcal{B}(B_s^0\to {\eta }_c(2S)f_0(X)[{\pi }^{+}{\pi }^{-}{]}_s)=\left(2.67_{-1.08}^{+1.78}\right)\times 10^{-5}$ when the contributions from $f_0(980)$ and $f_0(1500)$ are all taken into account; (b) $\mathcal{B}(B^0\to {\eta }_c(2S)f_0(500)[{\pi }^{+}{\pi }^{-}{]}_s)=\left(1.40_{-0.56}^{+0.92}\right)\times 10^{-6}$ in the Breit-Wigner model and $\left(1.53_{-0.61}^{+0.97}\right)\times 10^{-6}$ in the Bugg's model.

Comments: 7 pages, 3 figures, Some modifications. Final version to be published in Chinese Physics C