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The chiral condensate describes the density ofcondensed quark-antiquark pairs in the QCDground state. A nonvanishing value of thecondensate signals the spontaneous breaking ofchiral symmetry, which in the limit of masslessquarks is an exact symmetry of the QCDLagrangian. Strong interactions govern thedynamics of protons and neutrons. Analyzingthe density and temperature dependence of thechiral condensate in nuclear matter can revealthe presence of novel phase transitions.

Background Results

Conclusions

Increasing temperature (up to 100 MeV)strongly reduces the chiral condensate, whichindicates a fast approach to chiral symmetry athigh temperatures. Nuclear correlations athigher density (up to around 0.2 fm-3) hinderthe restoration of chiral symmetry. Theanalysis of the different contributions showsthat the dominant contribution is thenoninteracting term.

References

1. C. Wellenhofer et al., “Nuclear thermodynamics from chiral low-momentum interactions”, Phys. Rev. C 89 (2014) 064009.

2. T. Krüger et al., “The chiral condensate in neutron matter”, Phys. Lett. B 726 (2013) 412.

3. S. Fiorilla et. al., “Nuclear thermodynamics and the in-medium chiral condensate”, Phys. Lett. B 714 (2012) 251.

KeighleyRockcliffe¹²,JeremyHolt²1.DepartmentofPhysicsandAstronomy,RensselaerPolytechnicInstitute,Troy,NY12180

2.CyclotronInstitute,TexasA&MUniversity,CollegeStation,TX77843

Analyzingchiralcondensatedependenceontemperatureanddensity

Motivation

We want to understand the nature of thedensest observable matter in the universe,neutron stars. Astrophysical observations givelimited insight into the composition oftheir innermost cores. By analyzing thethermodynamic properties of the chiralcondensate in hot neutron matter we hope toshed light on the existence of novel phases inthese dense astrophysical objects.

Method

Chiral effective field theory is used to studythe behavior of the scalar quark condensatewith changing temperature and density ofneutron matter. Two-body and three-bodychiral nuclear forces were employed to find thefree energy and its dependence on the pionmass at moderate temperatures and densities.

Figure 1. Anillustrationofthedifferentperturbativecontributionstotheneutronmatterfreeenergy.¹

Figure 2. Condensate ratio as a function of neutron matter density.

Figure 4. Condensate ratio as a function of neutron matter density at different temperatures.

Figure 3. Condensate ratio plotted by Krüger et. al.², as a function of neutron matter density to be compared to Figure 2.

Figure 5. Condensate ratio calculated with just the Omega0 contribution.

Figure 6. Change in the condensate ratio calculated with just the Omega1 contribution.

Figure 7. Change in the condensate ratio calculated with just the Omega2 contribution.

Equations

Acknowledgments

Texas A&M UniversityDOE grant: PHY-1263281NSF grant: DE-FG03-93ER40773

Free Energy Equation based on many-body kernel contributions.³

Chiral condensate ratio for zero temperature.²

Pion mass derivative of the one-body contribution.³

Partition-like function of momentum.³