Contributions of interference and non-interference components to CP asymmetries in heavy meson decays

Abstract

In multi-body decays of heavy mesons, conventional CP asymmetry observables obtained by integrating over the full phase space are insensitive to the higher-order wave expansion contributions in the decay amplitude squared, and consequently fail to retain information on interference effects among different resonances. To overcome this limitation, one can introduce a phase-space partitioning scheme based on the zeros of Legendre polynomials, supplemented by a sign-function weighting procedure. On such a basis, two observables are defined, namely an asymmetry observable $\mathcal{A}_{\pm}^{\mathrm{asy},l}$, and the corresponding CP asymmetry $\mathcal{A}_{\mathrm{CP}}^{\mathrm{asy},l}$. We further separate the observables into interference and non-interference parts and analyze their respective roles. As an application, the decay channel $B^\pm\rightarrow\pi^\pm\pi^+\pi^-$ are analyzed in the region near the $\rho^0(1450)$ resonance. Using the LHCb data, the results show that odd-$l$ schemes are particularly effective in isolating interference contributions, while even-$l$ schemes are more sensitive to non-interference terms. This new assignment scheme has the potential to be extended to other decay processes, thus enriching the available physical observables.