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

TL;DR

The paper addresses B→ρρ decays by extending PQCD with an infrared cutoff μ_c ≈ 1 GeV to separate perturbative and nonperturbative dynamics, modeling below-μ_c effects with soft form factors and incorporating B-meson DAs from a relativistic potential model plus color-octet contributions. The leading-order calculation uses k_T-factorization and a convolution of the B and ρ distribution amplitudes with a calculable hard kernel, while corrections include NLO vertex/quark-loop/chromomagnetic penguins, plus soft and octet terms. Through a χ^2 fit to experimental data, the authors extract soft-production and color-octet parameters, finding that including soft factors and color-octet contributions improves agreement with branching fractions, CP asymmetries, and longitudinal polarization fractions, with μ_c ≈ 1 GeV yielding robust results. The approach suggests a path toward a unified description of charmless two-body B decays and helps address longstanding puzzles in related channels like ππ and Kπ, potentially enabling consistent predictions across PP, PV, and VV final states.

Abstract

In this work, we examine the observables associated with the $B\toρρ$ 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 $μ_c$, 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 $μ_c$ 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.

Figures (1)

• Figure 1: Decay diagrams contributing to the $B\to\rho\rho$ decays. Diagrams (a, b) are factorizable emission diagrams, (c, d) are nonfactorizable emission diagrams, (e, f) are nonfactorizable annihilation diagrams, and (g, h) are factorizable annihilation diagrams.