Branching ratios and CP asymmetries of $B^0 \to \eta_c f_0$ in the improved perturbative QCD formalism

TL;DR

This paper calculates branching ratios and CP asymmetries for $B^0 o ext{eta}_c f_0$ decays using improved perturbative QCD, providing predictions that can test the nature of scalar mesons and glueballs in upcoming experiments.

Contribution

It offers the first detailed predictions of $B^0 o ext{eta}_c f_0$ decay observables within the improved pQCD framework including NLO corrections, considering scalar meson mixing and glueball hypotheses.

Findings

Predicted branching ratio for $B_s^0 o ext{eta}_c f_0(980)$ matches existing data.

Large branching ratios and CP asymmetries are accessible at LHCb and Belle-II.

Results support the scalar meson mixing and glueball interpretations.

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 $q\bar q$ 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. ${\rm BR}(B_s^0 \to \eta_c f_0(980) (\to \pi^+ \pi^-))= (2.87^{+1.38}_{-1.29}) \times 10^{-4}$ and ${\rm BR}(B_d^0 \to \eta_c f_0(500)(\to \pi^+\pi^-))/{\rm BR}(B_s^0 \to \eta_c f_0(980)(\to \pi^+\pi^-)) = (12^{+8}_{-7})\%$ 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.