Statistical repulsion on hyperons in two-color dense QCD

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.

💡 Research Summary

The paper tackles the long‑standing hyperon puzzle – the premature appearance of hyperons in dense nuclear matter that softens the equation of state (EOS) below the two‑solar‑mass neutron‑star constraint – by studying a two‑color version of QCD (QC₂D) where first‑principles lattice simulations are feasible. To emulate strange quarks without re‑introducing the sign problem, the authors introduce a heavy quark doublet (Q_u, Q_d) with degenerate masses around 500 MeV. This guarantees a positive fermion determinant while providing “strange‑like” degrees of freedom.

An effective low‑energy model is built that contains three kinds of diquarks: light‑light (D), heavy‑heavy (D_Q) and light‑heavy (Y_i). All diquarks couple to their constituent quarks through Yukawa interactions. The light sector is described by a linear sigma model with Pauli‑Gürsey symmetry, ensuring that the light‑light diquark is degenerate with the pion. When the quark chemical potential μ reaches μ = m_π/2, the light‑light diquark condenses, forming a Bose‑Einstein condensate (BEC) that smoothly evolves into a BCS‑type paired state as μ grows. In this regime the light quarks already occupy a Fermi sea.

Hyperons are represented by the light‑heavy diquarks Y_u ∼ u Q_d and Y_d ∼ d Q_u. In vacuum the attractive diquark correlation makes their mass m_Y roughly the sum of a light and a heavy constituent, i.e. comparable to the kaon mass. However, once the light quarks are saturated in the diquark condensate, the formation of a new light‑heavy diquark requires an additional light quark state that is already blocked by Pauli exclusion. This “statistical repulsion” raises the effective energy cost of creating a hyperon.

The authors compute the one‑loop effective potential including the fermion loop, renormalize the theory with counterterms (choosing λ_Q and λ_Y to vanish in vacuum), and extract the self‑energy Π_Y for the hyperon fields. The sign of the quadratic term in the hyperon sector determines the critical chemical potential μ_c^Y. Their analysis shows that Π_Y becomes positive only at a chemical potential significantly larger than the naive threshold μ_B = m_Y (where μ_B = 2μ). Numerically, the hyperon onset is shifted from a density of order 1.5 n₀ (the density where light diquarks condense) to roughly 3–4 n₀, indicating a strong suppression.

The paper argues that this mechanism is independent of phenomenological Y‑N or Y‑N‑N repulsive forces; it originates purely from quark‑level statistics. The authors discuss how a similar effect should be present in three‑color QCD, where dense quark matter inevitably fills the u and d Fermi seas, thereby blocking the quark content of hyperons and delaying their appearance. This provides a microscopic justification for a stiff EOS at several times nuclear saturation density without invoking large many‑body hyperonic forces.

Finally, the work emphasizes that QC₂D offers a unique testing ground: lattice simulations can be performed without a sign problem, allowing future quantitative checks of the statistical repulsion picture. Limitations such as neglecting heavy‑heavy diquark condensation and treating quartic couplings only as medium‑induced are acknowledged, and extensions to include multiple hyperon species and direct comparison with lattice data are proposed.

In summary, the study presents a concrete, quark‑based explanation for hyperon suppression in dense matter, demonstrates it within a renormalizable two‑color model, and suggests that statistical repulsion may be a key ingredient in resolving the hyperon puzzle for realistic neutron‑star interiors.