Four-body decays B(s) → (Kπ)S/P(Kπ)S/P in the perturbative QCD approach

Abstract

A bstract We investigate the four-body decays B ( s ) → ( Kπ ) S/P ( Kπ ) S/P in the Kπ -pair invariant mass region around the K * (892) resonance in the perturbative QCD (PQCD) approach, where ( Kπ ) S/P denotes a S - or P -wave Kπ configuration. The contributions from the P -wave resonance K * (892) and from possible S -wave components are included into the parametrization of the Kπ two-meson distribution amplitudes, which are the non-perturbative inputs in this formalism. We calculate the branching ratio for each resonance and observe sizable S -wave contributions to the B s modes, well consistent with recently available LHCb data. We also deduce the polarization fractions for the $$ {K}^{\ast }{\overline{K}}^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:msup> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> final states, and compare our predictions to those in previous PQCD analyses of the corresponding two-body B → $$ {K}^{\ast }{\overline{K}}^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>K</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:msup> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>∗</mml:mo> </mml:msup> </mml:math> decays. The polarization puzzle associated with the two U -spin related channels B 0 → $$ {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>K</mml:mi> <mml:mrow> <mml:mo>∗</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mrow> <mml:mo>∗</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msup> </mml:math> and $$ {B}_s^0\to {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>K</mml:mi> <mml:mrow> <mml:mo>∗</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mover> <mml:mi>K</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mrow> <mml:mo>∗</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:msup> </mml:math> still exists. In addition to direct CP asymmetries, triple-product asymmetries and S -wave induced direct CP asymmetries originating from the interference among various helicity amplitudes, are presented. It is shown that true triple-product asymmetries are rather small, while direct CP asymmetries and S -wave-induced direct CP asymmetries are significant in some decays. Our results will be subject to stringent tests with precise data from B factories in the near future.

Topics & Concepts