Branching fraction, $CP$ asymmetry, and polarization in $B\toρρ$ decays with the modified perturbative QCD approach

Abstract: In this work, we examine the observables associated with the $B\to\rho\rho$ decays, including branching fractions, $CP$ asymmetry parameters, and longitudinal polarization fractions in the perturbative QCD (PQCD) approach with a few improvements. The essential distinction between this study and previous works lies in the introduction of an infrared cutoff at the critical scale $\mu_c$, which is approximately at the scale of $1\;\text{GeV}$. The contributions above the critical scale are calculated using the PQCD approach, consistent with earlier studies, while the contributions below the scale $\mu_c$ are regarded as nonperturbative and represented by some soft form factors. In addition, the distribution amplitude of the $B$ meson, derived from the relativistic potential model, and the contributions from the color-octet quark-antiquark components are also taken into account. With these modifications, we find that the theoretical results agree well with the experimental measurements for most observables, the introduction of the infrared cutoff enhances the reliability of the perturbation calculations, and the color-octet contributions play a key role in explaining the experimental data.