CP-odd window into long distance dynamics in rare semileptonic $B$ decays

Abstract

We consider the combined measurements of CP-averaged decay rates and direct CP asymmetries of $B^\pm\to K^\pm \ell^+ \ell^-$ and $B^\pm\to \pi^\pm \ell^+ \ell^-$ to probe (non-local) four-quark operator matrix element contributions to rare semileptonic B meson decays. We also explore how their effects could be in principle disentangled from possible local new physics effects using $U$-spin relations. To this end, we construct a ratio of CP-odd decay rate differences which are exactly predicted within the standard model in the $U$-spin limit, while the leading $U$-spin breaking effects can also be systematically calculated. Our results motivate binned measurements of the direct CP asymmetry in $B^\pm\to \pi^\pm \ell^+ \ell^-$ as well as dedicated theoretical estimates of $U$-spin breaking both in local form factors as well as in four-quark matrix elements.