How elastic unitarity governs resonance peaks and residue phases

Abstract

Imposing elastic unitarity on resonant amplitudes yields a geometric rule connecting the reaction threshold, S-matrix pole, and Breit-Wigner peak. Validated across six orders of magnitude in energy, from ${}^5\text{He}$ to the Higgs boson, this rule predicts currently unknown residue phases: $-44(12{)}^{\circ }$ for ${}^5\mathrm{He}$, $-24(7{)}^{\circ }$ for $\Sigma (1385{)}^{+}$, and $-7(13{)}^{\circ }$ for $\Xi (1530{)}^0$. By inverting this formalism, we determine the ${\rm Y}(4S)$ pole from its empirical peak to be $10575(1)-i8.3(13)$ MeV, with a $-52(6{)}^{\circ }$ phase.

5 pages, 2 figures, and 1 table