Finite-volume analysis of the $H$-dibaryon including left-hand-cut effects

Abstract

We implement the finite-volume $N/D$ representation to study two-baryon interactions from lattice QCD data. We include the left-hand cut induced by one-pion exchange in this formalism, and study the $H$-dibaryon at the SU(3)${}_{\text{F}}$-symmetric point, with a pion mass around $417$ MeV. The $N/D$ formalism is then compared to the Lüscher quantization condition, used to describe the same system via effective-range expansions. The results show a mild but statistically significant effect produced by the inclusion of the left-hand cut, especially on the binding energy of the $H$-dibaryon.

12 pages, 3 figures, and Supplemental Material (5 pages, 5 figures)