Are scalar mesons visible in B+- --> pi+pi-pi+- decays?

TL;DR

This paper investigates the role of scalar mesons in B+- --> pi+pi-pi+- decays using a QCD-based model that incorporates scalar and vector pion form factors constrained by experimental data, revealing the significance of scalar contributions.

Contribution

It provides a unified, unitary model of scalar meson contributions in B decays, incorporating multiple resonances through pion scalar form factors constrained by experimental data.

Findings

Scalar mesons significantly influence decay distributions.

Helicity angle asymmetry attributed to broad f0(600) meson.

Absence of f0(980) signal explained by scalar form factor dip.

Abstract

Two pion effective mass and helicity angle distributions in the charged B-meson decays into three charged pions are studied. The weak decay amplitudes are calculated in the framework of the QCD factorization approximation. The strong interactions between the pairs of pions are taken into account using scalar and vector pion form factors. The scalar form factors are constrained by data on pion-pion, kaon-antikaon and four pion production incorporated into a multichannel model of the coupled amplitudes. The vector form factor is obtained from the Belle Collaboration analysis of the tau- --> pi- pi0 nu_{tau} decays. The theoretical distributions of the dipion effective masses are compared with the corresponding results of the recent Dalitz plot analysis of B+- --> pi+pi-pi+- decays performed by the BABAR Collaboration. We find that the S-wave dipion amplitude, although much smaller than the P-wave amplitude, plays an important role even in the rho(770) mass range. We show that the helicity angle distribution is strongly asymmetric in the rho- meson range. This effect can be attributed to the broad f0(600)(or sigma) meson. The fact that the signal of the B+- --> f0(980) pi+- decay has not been found in the experimental analysis can be easily explained in our model since the relevant B decay amplitude is proportional to the scalar form factor which has a dip at the f0(980) mass. We obtain a unified unitary description of the contribution of the three scalar resonances f0(600), f0(980) and f0(1400) in terms of the pion non-strange scalar form factor.