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

TL;DR

This work addresses how to probe the nature of light scalar mesons, including the fragmented scalar glueball hypothesis, by computing branching ratios and CP asymmetries of $B^0 \to \eta_c f_0$ decays in the improved perturbative QCD (iPQCD) framework with NLO corrections. The authors model the $f_0$ states in a two-quark flavor basis with mixing angles $\varphi$ and $\varphi'$ and derive CP-averaged BRs and CP asymmetries for $B_d^0$ and $B_s^0$ decays, including quasi-two-body results under the narrow-width approximation. They find sizable BRs for $B_s^0 \to \eta_c f_0(980)(\to \pi^+\pi^-)$ and $B_s^0 \to \eta_c f_0(1500)(\to \pi^+\pi^-/K^+K^-)$ and sizable direct CP asymmetries in $B^0 \to \eta_c f_0(1370,1500)$, making these modes accessible at LHCb and Belle-II. The clean ratios constructed to cancel hadronic uncertainties can constrain the mixing angles and SU(3) flavor-breaking effects, with potential to distinguish $f_0(1500)$ as a primary vs fragmented scalar glueball and to advance understanding of light-scalar QCD dynamics.

Abstract

Motivated by the idea of fragmented scalar glueball, we investigate the decays $B^0 \to η_c f_0$ 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 $B^0 \to η_c f_0$ 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 $B^0 \to η_c f_0 (\to π^+ π^-/K^+ K^-)$ BRs under the narrow-width approximation. ${\rm BR}(B_s^0 \to η_c f_0(980) (\to π^+ π^-))= (2.87^{+1.38}_{-1.29}) \times 10^{-4}$ and ${\rm BR}(B_d^0 \to η_c f_0(500)(\to π^+π^-))/{\rm BR}(B_s^0 \to η_c f_0(980)(\to π^+π^-)) = (12^{+8}_{-7})\%$ obtained in the iPQCD formalism agree with the available measurements and/or predictions within uncertainties. Large BRs of $B_s^0 \to η_c f_0(1500) (\to π^+ π^-/K^+ K^-)$ and large direct CP asymmetries of $B^0 \to η_c f_0(1370, 1500)$ 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.

Figures (6)

• Figure 1: (Color online) Leading quark-level Feynman diagrams of $B^0 \to \eta_c f_0$
• Figure 2: Typical Feynman diagrams contributing to the $B^{0} \to \eta_c f_0$ decays in the PQCD approach at leading order.
• Figure 3: Vertex corrections to the $B^{0} \to \eta_c f_0$ decays.
• Figure 4: (Color online) Dependence of ${\rm BR}(B^{0} \to \eta_c f_{0}(980) (\to \pi^+\pi^-/K^+K^-))$ on $\varphi \in [-90^\circ, 90^\circ]$ in the iPQCD formalism: solid (dotted) line corresponds to $B^{0} \to \eta_c f_{0}(980) (\to \pi^+\pi^-) [B^0 \to \eta_c f_0(980) (\to K^+ K^-)]$.
• Figure 5: (Color online) Dependence of ${\rm BR}(B_d^{0} \to \eta_c f_{0}(1500) (\to \pi^+\pi^-/K^+K^-))$ on $\varphi^\prime \in [0^\circ, 180^\circ]$ in the iPQCD formalism: solid (dashed) line corresponds to $B_{d}^{0} \to \eta_c f_{0}(1500) (\to \pi^+ \pi^-) [B_{d}^{0} \to \eta_c f_{0}(1500) (\to K^+K^-)]$ with left (right) panel in $S1 (S2)$.