Study of Β → ππ puzzle in the Standard model

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 Β → ππ decays (Β⁺ → π⁺π⁰, Β⁰ → π⁺π^-, Β⁰ → π⁰π⁰), such as large direct CP asymmetry for Β⁰ → π⁺π^-, mode and large branching ratio for Β⁰ → π⁰π⁰ mode, originate the Β → ππ puzzle. According to diagrammatic approach of this b → d transition the ratio of color-suppressed amplitude (C) to color-allowed one (T) demands small ratio which is in contradiction with the SM approach. 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. (author)