The $η^\prime N$ interaction from the $η^\prime p$ correlation function

TL;DR

This work addresses the poorly known eta' N interaction by computing the eta' p femtoscopy correlation function within a coupled-channel Bethe-Salpeter framework that includes K0 Sigma+, K+ Sigma0, K+ Lambda, eta p, and eta' p channels and eta-eta' mixing. By varying a single parameter alpha that controls the strength of the singlet coupling, the authors explore predictions for the eta' p scattering length a_{eta' p} and the resulting correlation function C_{eta' p}(p) under a finite-range source with radius R=1 fm. They find strong sensitivity of C_{eta' p}(p) to a_{eta' p}, with larger enhancements for attractive interactions, while inelastic channel effects are small (less than about 10%), and the elastic channel dominates. Measuring C_{eta' p} can thus constrain both the real and imaginary parts of a_{eta' p}, informing the eta' N interaction and the possible existence of eta' bound states in nuclear matter, with implications for in-medium eta' properties and the U_A(1) anomaly at finite density.

Abstract

We evaluate for the first time the $η^\prime p$ femtoscopic correlation function to study the $η^\prime N$ interaction. We find it extremely sensitive to the value of the $η^\prime p$ scattering length, for which at present there exists only very limited information, not even knowing its sign. The measurement of this correlation function would provide much valuable information on the $η^\prime N$ interaction, which could then also be used to settle the issue of possible $η^\prime$ nucleus bound states, an issue attracting much attention in the nuclear physics community.

Figures (3)

• Figure 1: The $\eta^\prime p$ correlation function for the different values of the potential parameter $\alpha$ in Eq. \ref{['eq:Pot_alpha']}. The solid lines indicate the results calculated with $q_\text{max} = 630$ MeV, and the shaded bands show the results for $q_\text{max} = 637 \pm 72$ MeV.
• Figure 2: The $\eta^\prime p$ correlation functions for the elastic $\eta^\prime p$ channel $C^\text{el}_{\eta^\prime p}$ (dashed lines), and for the full coupled channels $C_{\eta^\prime p}$ (solid lines). The results indicated by the solid lines here are identical to those in Fig. \ref{['fig:1']} for $\alpha=-0.50$, $-0.25$, $0.00$, respectively.
• Figure 3: The $\eta^\prime p$ correlation functions for the different transitions to the $\eta^\prime p$ channel with the potential parameter $\alpha=-0.50$. The result labeled as $\eta^\prime p$ is identical to the elastic $\eta^\prime p$ channel $C^\text{el}_{\eta^\prime p}$ in Fig. \ref{['fig:2']}. For each inelastic channel, the production weight of $\omega^{\text{prod}}_{i}=10$ is taken into account.