Non-resonant Four-body Decay of B→D^- π^+ π^+ π^-

We have calculated the branching ratio of the non-resonant B→D^- π^+ π^+ π^- four body decay using a simple model based on the framework of the naïve factorization approach where one can ommit the nonfactorization effects. In naive factorization approach, according to the Feynman diagram, there are only two tree diagrams for this decay mode. In the first diagram, the matrix element of decay mode is factorized into a B→D form factor multiplied by a ۳π decay constant and in the second diagram, the matrix element is factorized into a B→Dπ form factor multiplied by a ۲π decay constant, According to the rest mass of the particles, we assume that in the rest frame of B meson, the D meson remains stationary, so we obtain the value (۳.۴۷±۰.۱۴)×۱۰^(-۳) for the branching ratio of the B→D^- π^+ π^+ π^- decay mode in naive factorization approach, while the experimental results is (۳.۹±۱.۹)×۱۰^(-۳).