Study of B -> ππ puzzle in the standard model

Abstract

Decays of B-mesons is one of the most promising research areas to obtain information about the flavour structure of the standard model (SM) as well as to get a track of new physics (NP) path. The discrepancies among the measurements of branching ratios and CP asymmetries of B -> ππ decays (B⁺ -> <i>π⁺</i><i>π⁰</i>, B⁰ -> <i>π⁺</i><i>π^-</i> and B⁰ -> <i>π⁰</i><i>π⁰</i>) such as large direct CP asymmetry for B⁰ -> <i>π⁺</i><i>π^-</i> mode and large branching ratio for B⁰ -> <i>π⁰</i><i>π⁰</i> mode, originate the B -> ππ puzzle^1-3. According to diagrammatic approach of this b->d transition the ratio of color-suppressed amplitude (<em>C</em>) to color-allowed one (<em>T</em>) demands small ratio which is in contradiction with the SM approach^3-5. To make out the ambiguity we need to scrutinize the decays with different topological amplitudes. In this paper, the decays are studied in the SM by taking different values of C/T as constraints. We find that larger ratio of C/T is explained successfully in the SM but the lower ratio is not for which NP is needed.