New $CP$ sum rules from exact $U$-spin degeneracy

Abstract

We propose a new class of $CP$ sum rules in the $U$-spin limit, based on the observation that the weak phase in the Standard Model can be removed in the degenerate limit $m_d=m_s$. Unlike previous $U$-spin analyses formulated at the amplitude level, our sum rules are expressed directly in terms of decay widths. They apply to matched partial waves, spin observables, and angular moments and include nonpairwise cases beyond the usual single-insertion $d\leftrightarrow s$ relation.