General Analysis of $B$ Meson Decay into Two Fermions

Abstract

We study how to measure the current structure of the process that $B$ meson decays into two unstable fermions ${\bar{f}}_a$ and $f_b$ in model independent way. We use the momentum distributions of subsequent decay products affected by ${\bar{f}}_a{f}_b$ spin correlation. We have found the following: (1) We can extract the absolute values of two effective coupling constants from the opening angle between the particles decayed from ${\bar{f}}_a$ and $f_b$ (2) We can extract the real part of the interference from the energy distribution of one of the decayed particles from ${\bar{f}}_a$ or $f_b$. (3) No new information can be obtained from the energy distribution of two decayed particles from ${\bar{f}}_a$ and $f_b$. (4) The imaginary part of interference is extracted from the azimuthal angle asymmetry of final-state decay products. (5) If only one of two fermions is unstable, we can extract the real part of interference from each of the energy distribution and opening angle distribution. We show several simple examples.

Comments: 27 pages, 20 figures