<p>A crossover involving three-fermion clusters is relevant to the hadron-quark crossover, which, if occurring in a neutron star, could naturally reproduce the dense-matter equation of state recently deduced from simultaneous observations of neutron-star masses and radii. To understand the crossover mechanism, we examine the role of <i>tripling</i> fluctuations induced by the formation of three-fermion clusters. The phase-shift representation of fluctuations manifests an interplay of bound and scattering states, leading to nonmonotonic momentum distributions of baryonlike clusters and peaked sound speed at finite densities. We demonstrate them by applying our approach to a nonrelativistic system of one-dimensional three-color fermions analogous to the hadron-quark matter.</p>

Japan

Hiroyuki Tajima

Kei Iida

Toru Kojo

Haozhao Liang

Tripling Fluctuations and Peaked Sound Speed in Fermionic Matter

We investigate the phase structure and the equation of state (EoS) for dense two-color QCD (QC2D) at low temperature (T = 40 MeV, 324 lattice) for the purpose of extending our previous works [1, 2] at T = 80 MeV (164 lattice). Indeed, a rich phase structure below the pseudo-critical temperature T  c  as a function of quark chemical potential μ has been revealed, but finite volume effects in a high-density regime sometimes cause a wrong understanding. Therefore, it is important to investigate the temperature dependence down to zero temperature with large-volume simulations. By performing 324 simulations, we obtain essentially similar results to the previous ones, but we are now allowed to get a fine understanding of the phase structure via the temperature dependence. Most importantly, we find that the hadronic-matter phase, which is composed of thermally excited hadrons, shrinks with decreasing temperature and that the diquark condensate scales as ⟨qq⟩ ∝ μ 2 in the BCS phase, a property missing at T = 80 MeV. From careful analyses, furthermore, we confirm a tentative conclusion that the topological susceptibility is independent of μ. We also show the temperature dependence of the pressure, internal energy, and sound velocity as a function of μ. The pressure increases around the hadronic-superfluid phase transition more rapidly at the lower temperature, while the temperature dependence of the sound velocity is invisible. Breaking of the conformal bound is also confirmed thanks to the smaller statistical error.

Etsuko Itou

Kotaro Murakami

Daiki Suenaga

Lattice study on finite density QC2D towards zero temperature

We investigate theoretically a nonrelativistic trace anomaly and its impact on the low-temperature equation of state in spatially one-dimensional three-component fermionic systems with a three-body interaction, which exhibit a nontrivial three-body crossover from a bound trimer gas to dense fermionic matter with increasing density. By applying the <math><mi>G</mi></math>-matrix approach to the three-body interaction, we obtain the analytical expression for the ground-state equation of state relevant to the high-density degenerate regime and thereby address how the three-body contact or, equivalently, the trace anomaly emerges. The analytical results are compared with the recent quantum Monte Carlo data. Our study of the trace anomaly and the sound speed could have some relevance to the physics of hadron-quark crossover in compact stars.

Nonrelativistic trace anomaly and equation of state in dense fermionic matter

We construct an extended version of the linear sigma model in such a way as to describe spin-1 hadrons as well as spin-0 hadrons in two-color QCD (<math><mrow><msub><mrow><mi>QC</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>D</mi></mrow></math>) by respecting the Pauli-Gürsey <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><mo>)</mo></math> symmetry. Within a mean-field approximation, we therefrom examine a mass spectrum of the spin-1 hadrons at finite quark chemical potential (<math><msub><mi>μ</mi><mi>q</mi></msub></math>) and zero temperature. Not only mean fields of scalar mesons and scalar-diquark baryons but also of vector mesons and vector-diquark baryons are incorporated. As a result, we find that, unless all of those four types of mean fields are taken into account, neither lattice result for the critical <math><msub><mi>μ</mi><mi>q</mi></msub></math> that corresponds to the onset of baryon superfluidity nor for <math><msub><mi>μ</mi><mi>q</mi></msub></math> dependence of the pion mass can be reproduced. We also find that a slight suppression of the <math><mi>ρ</mi></math> meson mass in the superfluid phase, which was suggested by the lattice simulation, is reproduced by subtle mixing effects between spin-0 and spin-1 hadrons. Moreover, we demonstrate the emergence of an axial-vector condensed phase and possibly of a vector condensed phase by identifying the values of <math><msub><mi>μ</mi><mi>q</mi></msub></math> at which the corresponding hadron masses vanish. The possible presence of isotriplet <math><msup><mn>1</mn><mo>−</mo></msup></math> diquarks that may be denoted by a tensor-type quark bilinear field is also discussed.

Mass spectrum of spin-one hadrons in dense two-color QCD: Novel predictions by extended linear sigma model

We show that the strong spin-triplet neutron-proton interaction causes polaronic protons to occur in neutron matter at subnuclear densities and nonzero temperatures. As the neutron density increases, proton spectra exhibit a smooth crossover from a bare impurity to a repulsive polaron branch; this branch coexists with an attractive polaron branch. With the neutron density increased further, the attractive polarons become stable with respect to deuteron formation. For two adjacent protons, we find that the polaron effects and the neutron-mediated attraction are sufficient to induce a bound diproton, which leads possibly to diproton formation in the neutron skin region of neutron-rich nuclei in laboratories as well as in neutron stars.

Hajime Moriya

Wataru Horiuchi

Eiji Nakano

Polaronic proton and diproton clustering in neutron-rich matter

We formulate a method for calculating the hadron-hadron scattering amplitudes at nonzero chemical potential (μ) in the hadronic phase at zero temperature, where the baryon number symmetry remains to be violated. Although it is widely believed that the physical quantities do not change even if we turn on a small μ at zero temperature, the shape of correlation functions for a single hadron depends on μ. Then, the dispersion relation of the single hadron is modified to E(p, μ) =   <math> <msqrt> <mrow> <msup> <mi>p</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>m</mi> <mn>2</mn> </msup> </mrow> </msqrt> </math>  $$ \sqrt{{\textbf{p}}^2+{m}^2} $$  – μn  O . Here, m and n  O  denote the hadron mass at μ = 0 and the quantum number, respectively. From this relation, it is possible that the effective mass of the hadron depends on μ. We extend the HAL QCD method at μ = 0 to the case of μ ≠ 0, which allows us to extract the scattering phase shifts via the interaction potential. We have found that the interaction potential can depend on μ only through the effective mass while the scattering phase shifts, obtained by solving the Schrödinger equation with the interaction potential, are independent of μ. We also numerically analyze the S-wave scatterings of two pions with isospin I = 2 and two scalar diquarks within the framework of QC2D at nonzero quark chemical potential. While the lattice is not exactly set to zero temperature, the μ-independence can be observed. Furthermore, we improve the results for the S-wave scatterings of two hadrons obtained above by taking the μ-independence for granted. Thanks to the asymmetric property of the correlation functions for diquarks at μ ≠ 0, we can access a long-τ regime and can reduce the systematic error coming from inelastic contributions.

Chemical potential (in)dependence of hadron scatterings in the hadronic phase of QCD-like theories and its applications

We investigate modifications of hadron masses at finite quark chemical potential in two-flavor and two-color QCD, data of which are available from lattice simulations, within a linear sigma model based on approximate Pauli-Gursey <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><mo>)</mo></math> symmetry. The model describes not only ground-state scalar diquarks and pseudoscalar mesons but also the excited pseudoscalar diquarks and scalar mesons; each ground-state diquark (meson) has the corresponding excited diquark (hadron) with opposite parity as a chiral partner. Effects of chiral symmetry breaking and diquark condensates are incorporated by a mean-field treatment. We show that various mixings among the hadrons, which are triggered by the breakdown of baryon number conservation in the superfluid phase, lead to a rich hadron mass spectrum. We discuss the influence of <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>A</mi></msub></math> anomaly on the density dependence of the mass spectrum and also manifestations of the chiral partner structures as the density increases in the superfluid phase. The predicted hadron masses are expected to provide future lattice simulations with useful information on such symmetry properties in dense two-color QCD.

Probing the hadron mass spectrum in dense two-color QCD with the linear sigma model

We propose an interpolating equation of state that satisfies phenomenologically established boundary conditions in two extreme regimes at high temperature and low baryon density and at low temperature and high baryon density. We confirm that the hadron resonance gas model with the Carnahan-Starling excluded volume effect can reasonably fit the empirical equation of state at high density up to several times the normal nuclear density. We identify the onsets of strange particles and quantify the strangeness contents in dense matter. We finally discuss the finite temperature effects and estimate the thermal index <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>th</mi></mrow></msub></math> as a function of the baryon density, which should be a crucial input for the core-collapse supernova and the binary neutron star merger simulations.

Yuki Fujimoto

Kenji Fukushima

Yoshimasa Hidaka

Taiwan

Atsuki Hiraguchi

Equation of state of neutron star matter and its warm extension with an interacting hadron resonance gas

Abstract We obtain the equation of state (EoS) for two-color quantum chromodynamics (QCD) at low temperature and high density from the lattice Monte Carlo simulation. We find that the velocity of sound exceeds the relativistic limit () after BEC-BCS (Bose-Einstein condensation–Bardeen–Cooper–Schrieffer) crossover in the superfluid phase. Such an excess of the sound velocity is previously unknown from any lattice calculations for QCD-like theories. This finding might have a possible relevance to the EoS of neutron star matter revealed by recent measurements of neutron star masses and radii.

Velocity of sound beyond the high-density relativistic limit from lattice simulation of dense two-color QCD

Abstract We determine the scale-setting function and the pseudocritical temperature on the lattice in  two-color quantum chromodynamics (QCD) using the Iwasaki gauge and Wilson fermion actions. Although two-color QCD does not correspond to the real world, it is very useful as a good testing ground for three-color QCD. The scale-setting function gives the relative lattice spacings of simulations performed at different values of the bare coupling. It is a necessary tool for taking the continuum limit. First, we measure the meson spectra for various combinations of () and find a line of constant physics in the – plane. Next, we determine the scale-setting function via  scale in the gradient flow method. Furthermore, we estimate the pseudocritical temperature at zero chemical potential from the chiral susceptibility. Combining these results, we can discuss the QCD phase diagram in which both axes are given by dimensionless quantities, namely the temperature normalized by the pseudocritical temperature on the lattice and the chemical potential normalized by the pseudoscalar meson mass. This makes it easy to compare among several lattice studies, and also makes it possible to compare theoretical analyses and lattice studies in the continuum limit.