Statistical repulsion on hyperons in two-color dense QCD

TL;DR

This work investigates hyperon onset in dense QC$_2$D by introducing a heavy-quark doublet to mimic strangeness, enabling sign-problem-free lattice studies. The authors develop an effective field theory with light quarks, light diquarks, heavy quarks, and light-heavy hyperon-like diquarks, and compute a renormalized effective potential in a mean-field framework. They show that light-quark loops generate an effective repulsion for hyperons, delaying their appearance and mitigating potential EOS softening, with the onset controlled by the renormalized quadratic coefficient $(C_2^Y)_R$ of the hyperon fields. The delay is amplified by larger heavy-quark coupling $g_Y$ and heavier vacuum hyperon mass $m_Y^{\rm vac}$, suggesting a fundamental mechanism—statistical repulsion from quark saturation—for suppressing hyperon-induced instabilities in dense matter. The results also provide a bridge to three-color QCD via the quark-saturation picture and set the stage for future EOS calculations beyond hyperon onset.

Abstract

We investigate the onset of hyperons in baryonic (diquark) matter in two-color QCD (QC$_2$D) by introducing heavy quark doublets that emulate strange quarks. An even number of flavors is required to avoid the sign problem in lattice Monte Carlo simulations. To explore QC$_2$D matter containing both light and heavy quarks, we construct a model in which quarks interact with light-light, light-heavy (hyperonic), and heavy-heavy diquarks via Yukawa couplings. As the quark chemical potential increases, the light diquarks condense first and form baryonic matter, and this onset density can be understood in hadronic terms. In contrast, the onset density of hyperons is substantially higher than that estimated from the hadronic sector of the model. This shift reflects an effective repulsion among baryons induced by the pre-occupied light quarks. The Pauli blocking of light quarks suppresses the attractive diquark correlations responsible, in vacuum, for making hyperons lighter than the sum of the constituent light and heavy quark masses. Implications for three-color QCD are also briefly discussed.

Figures (6)

• Figure 1: The evolution of $(M_q, \Delta)$ as functions of $\mu$. The onset of diquark condensate is $\mu = m_\pi/2$. The $\Delta$ at tree level grows as $\Delta \sim \mu$, while inclusion of the quark coupling tempers the growth, resulting $\Delta \sim M_0$. $M_q$ and $M_q^{\rm tree}$ largely overlap and the difference is not visible.
• Figure 2: The baryon density $n_B$ as functions of $\mu$ for the one-loop, tree, and ChPT cases. We take $n_0 = 0.16\,{\rm fm}^{-3}$ as a unit.
• Figure 3: The squared sound speed $c_s^2 = \mathrm{d} P/\mathrm{d} \varepsilon$ as functions of $\mu$ for the one-loop, tree, and ChPT cases. The conformal limit $1/3$ is also plotted for eye-guide.
• Figure 4: The density evolution of the coefficient $C_2^Y$ for the quadratic term of $Y_{u,d}$. When $C_2^Y$ becomes negative, the hyperon fields condense. At tree level the hyperon condensates emerge at $\mu = m_Y^{\rm vac} /2$ or $\mu_B = m_Y^{\rm vac}$. After including the coupling $g_Y$ between quark and heavy-light diquark, the onset chemical potential is shifted to a higher value for a greater $g_Y$.
• Figure 5: The density evolution of $C_2^Y$ for the vacuum hyperon mass, $m_Y^{\rm vac} = 200, 300, 400$, and 500 MeV, with $g_Y/g=0.75$. The dashed lines are the results for $g_Y=0$. For a larger $m_Y^{\rm vac}$, more quark states are occupied so that the statistical repulsion sets in before $Y$ condenses.