$H$ dibaryon and its cousins from SU(6)-constrained baryon-baryon interaction

Abstract

We constrain the $S$-wave baryon-baryon interaction using SU(6) symmetry within a nonrelativistic effective field theory. The most general leading-order Lagrangian contains two independent parameters, which we determine using physical $NN$ and lattice QCD $ΩΩ$ scattering lengths. This framework allows for parameter-free predictions in the strangeness $S=-2$ sector relevant to the $H$ dibaryon. Solving the coupled-channel scattering problem, we identify two bound states below the $ΛΛ$ threshold, one deeply bound and one shallow, along with resonances near the $ΣΣ$ and $Σ^*Σ^*$ thresholds. We demonstrate that these poles result in distinct enhancements in $ΛΛ$ invariant mass distributions, suggesting that the $H$ dibaryon exists as a multichannel bound state and providing clear signatures for experimental verification.

Figures (3)

• Figure 1: Cutoff dependence of the $\Lambda\Lambda$ scattering length $a_{\Lambda\Lambda}$ in strategy 2 with $a_{NN}$ in $^3S_1$ as input. The dot marks the $a_{\Lambda\Lambda} = 1.1$ fm at cutoff $\Lambda = 1.0$ GeV. At $\Lambda = 0.72$ GeV, $a_{\Lambda\Lambda}$ reaches the unitarity limit.
• Figure 2: Trajectories of the four dominant poles in strategy 2 with $a_{NN}$ in $^3S_1$ as input, with arrows indicating decreasing the cutoff $\Lambda$ from 2.0 GeV to 0.5 GeV. Highlighted points mark the values at $\Lambda = 1.0$ GeV. On RS $(+,+,+,+)$, the deeper bound state is shifted slightly downward to avoid overlap with the shallower one.
• Figure 3: Invariant mass distributions for the processes $\Lambda\Lambda$, $N\Xi$, $\Sigma\Sigma$, and $\Sigma^{*}\Sigma^{*}\to\Lambda\Lambda$ in strategy 2 with $a_{NN}$ in $^3S_1$, evaluated at cutoff $\Lambda = 1.0$ GeV. The vertical dashed lines indicate the four thresholds.