Decays of $B$ Mesons to Two Light Pseudoscalars

Abstract

The decays $B\to PP$, where $P$ denotes a pseudoscalar meson, are analyzed, with emphasis on charmless final states. Numerous triangle relations for amplitudes hold within SU(3) symmetry, relating (for example) the decays $B^{+}\to {\pi }^{+}{\pi }^0,{\pi }^0{K}^{+}$, and ${\pi }^{+}{K}^0$. Such relations can improve the possibilities for early detection of $CP$-violating asymmetries. Within the context of a graphical analysis of decays, relations are analyzed among SU(3) amplitudes which hold if some graphs are neglected. One application is that measurements of the rates for the above three $B^{+}$ decays and their charge-conjugates can be used to determine a weak CKM phase. With measurements of the remaining rates for $B$ decays to $\pi \pi ,\pi K$, and $K\bar{K}$, one can obtain two CKM phases and several differences of strong phase shifts.

Comments: 6 figures available from the authors upon request. 28 pages, TECHNION-PH-94-8