Eur. Phys. J. C (2025) 85: 1300
https://doi.org/10.1140/epjc/s10052-025-15020-0

Regular Article - Theoretical Physics

Branching ratios and CP asymmetries of $B^0\to {\eta }_c{f}_0$ in the improved perturbative QCD formalism

¹ Department of Physics, Jiangsu Normal University, 221116, Xuzhou, China
² Department of Physics, Yantai University, 264005, Yantai, China
³ Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, 210023, Nanjing, China

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Received: 6 August 2025
Accepted: 1 November 2025
Published online: 14 November 2025

Abstract

Motivated by the idea of fragmented scalar glueball, we investigate the decays $B^0\to {\eta }_c{f}_0$ within the improved perturbative QCD (iPQCD) framework by including the known next-to-leading order corrections. Here, $B^0$ and $f_0$ denote the neutral $B_{d,s}^0$ mesons and the light scalar mesons $f_0(500,980,1370,1500)$ under the $q\overline{q}$ assignment. The CP-averaged branching ratios (BRs) and the CP asymmetries of $B^0\to {\eta }_c{f}_0$ are evaluated with the $f_0(500)[f_0(1370)]-f_0(980)[f_0(1500)]$ mixing in quark-flavor basis. For effective comparisons with the near-future measurements, we further derive the $B^0\to {\eta }_c{f}_0(\to {\pi }^{+}{\pi }^{-}/K^{+}{K}^{-})$ BRs under the narrow-width approximation. $\text{BR}(B_s^0\to {\eta }_c{f}_0(980)(\to {\pi }^{+}{\pi }^{-}))=(2.{87}_{-1.29}^{+1.38})\times {10}^{-4}$ and $\text{BR}(B_d^0\to {\eta }_c{f}_0(500)(\to {\pi }^{+}{\pi }^{-}))/\text{BR}(B_s^0\to {\eta }_c{f}_0(980)(\to {\pi }^{+}{\pi }^{-}))=({12}_{-7}^{+8})\%$ obtained in the iPQCD formalism agree with the available measurements and/or predictions within uncertainties. Large BRs of $B_s^0\to {\eta }_c{f}_0(1500)(\to {\pi }^{+}{\pi }^{-}/K^{+}{K}^{-})$ and large direct CP asymmetries of $B^0\to {\eta }_c{f}_0(1370,1500)$ are accessible in the LHCb and Belle-II experiments. The experimental tests of these iPQCD predictions would help us to understand the nature of these light scalars more deeply and provide evidences to decipher $f_0(1500)$ as a primary or fragmented scalar glueball potentially.