Mixing effects of $\eta -{\eta }^{\prime }$ in ${\Lambda }_b\to \Lambda {\eta }^{{(}^{\prime })}$ decays

Abstract

We perform a thorough analysis of the $\eta -{\eta }^{\prime }$ mixing effects on the ${\Lambda }_b\to \Lambda {\eta }^{{(}^{\prime })}$ decays based on the perturbative QCD (PQCD) factorization approach. Branching ratios, up-down and direct $CP$ asymmetries are computed by considering four popular mixing schemes, such as $\eta -{\eta }^{\prime }$, $\eta -{\eta }^{\prime }-{\eta }_c$, $\eta -{\eta }^{\prime }-G$, and $\eta -{\eta }^{\prime }-G-{\eta }_c$ mixing formalism, where $G$ represents the physical pseudoscalar gluball. The PQCD predictions with the four mixing schemes does not change much for the $\eta$ channel but changes significantly for the ${\eta }^{\prime }$ one. In particular, the value of $\mathcal{B}({\Lambda }_b\to \Lambda {\eta }^{{}^{\prime }})$ in the $\eta -{\eta }^{\prime }-G-{\eta }_c$ mixing scheme exceeds the present experimental bound by a factor of 2, indicates the related mixing angles may be overestimated. Because of the distinctive patterns of interference between $S$-wave and $P$-wave amplitudes, the predicted up-down asymmetries for the two modes differ significantly. The obvious discrepancies among different theoretical analyses should be clarified in the future. The direct $CP$ violations are predicted to be at the level of a few percent mainly due to the tree contributions of the strange and nonstrange amplitudes suffer from the color suppression and CKM suppression. Finally, as a byproduct, we investigate the ${\Lambda }_b\to \Lambda {\eta }_c$ process, which has a large branching ratio of order $10^{-4}$, promising to be measured by the LHCb experiment. Our findings are useful for constraining the mixing parameters, comprehending the ${\eta }^{{(}^{\prime })}$ configurations, and instructing experimental measurements.

arXiv comment19 pages,1 figure,7 tables, updated to match published version

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