Deeply bound dibaryon $d^{\ast }(2380)$ from meson-exchange saturation $\Delta \Delta$ effective field theory

Abstract

We propose an RG-improved effective-field-theory framework for the deeply bound dibaryon $d^{\ast }(2380)$, a $\Delta \Delta$ bound state in the $(J,I)=(3,0)$ ${}^7{S}_3$ channel. Its binding momentum $\gamma \simeq 320$ MeV gives $\gamma /m_{\pi }\simeq 2.3$, indicating the need to re-organize the short-range dynamics beyond a formal pionless EFT. We match the large-$N_c$-constrained pionless contact potential to a meson-exchange-saturated contact interaction in which the $\sigma ,\rho ,\omega$ dynamics are integrated out at the hadronic scale $m_V$, yielding the controlled expansion parameter $\gamma /m_V\simeq 0.42$. Normalizing the contact coupling to the deuteron and substituting the phenomenological CD-Bonn couplings gives $B_{\Delta \Delta }\simeq 96$ MeV. The $\simeq 14\%$ discrepancy from $B_{\exp }=84$ MeV is of the natural size of $\mathcal{O}(1/N_c^2)\simeq 11\%$ corrections to the $NN$ potential, confirming compatibility with a controlled EFT expansion organized around the finite-range hadronic scale. As a result, the observed $d^{\ast }(2380)$ pole emerges from the virtual state to bound state by using the EFT re-organization in this work.

7 pages, 2 tables