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Parity Doublet Model in Heavy-Ion Collisions

Youngman Kim

(CENS, IBS)

The 8th International Workshop on Nuclear Dynamics in Heavy-ion Reactions (IWND2026)

August 21-25, Taiyuan, China

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김영만 (金永晩)

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  • Chiral symmetry

wikipedia

However, no L, R nucleons

V-L=A

V+L=V

No parity partner

  • Chiral symmetry breaking

Reminders

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  • Chiral symmetry

: vector transform

: axial-vector transform

Pauli matrix

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Origin of nucleon mass?

Can nuclear matter, HICs and nuclei do anything for this?

Nucleon mass (in the chiral limit) in the linear sigma model

Quark-antiquark condensate: non-perturbative gluon interactions are included.

(SSB, ChiSB)

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A BCS-like trial ground state --> true vacuum contains chiral (quark-antiquark) condensates in free space [Finger & Mandula, NPB 199, 168 (1982)]

In dense nuclear matter, chiral condensates will be reduced as low energy phase space is already occupied by the fermions in Fermi sea.

E

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  • Parity doublet model (in dense matter)

  • Candidate of a chiral invariant mass

  • PDM in HIC with the DJBUU code

  • Summary

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Parity doublet model in dense matter

Introduce two nucleon fields that transform in a mirror way under chiral transformations:

c.f. Naïve assignment:

Mirror assignment

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The state N+ is the nucleon N(938). while N- is its parity partner conventionally identified with N(1500).

“Linear sigma model with parity doubling,” C. E. DeTar and T. Kunihiro, Phys. Rev. D 39, 2805 (1989)

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D. Zschiesche, L. Tolos, Jurgen Schaffner-Bielich, Robert D. Pisarski, Phys. Rev. C75 (2007) 055202

Cold, dense nuclear matter in a SU(2) parity doublet model

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Y. Motohiro, M. Harada, YK, Erratum: Phys.Rev. C95 (2017) 059903

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To fix the parameters in our model with a given m0

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Delta matter (for HIC at a few hundreds MeV) in a parity doublet model (within MFA)

Yusuke Takeda, YK, Masayasu Harada, Phys. Rev. C97 (2018) 065202

* In symmetric matter, Delta enters into matter at (1-4) times the saturation density.

The stable Δ-nucleon matter is realized around 4 times the saturation density, and the phase transition from nuclear matter to Δ-nucleon matter is of first order in the wide parameter region.

* In asymmetric matter, the phase transition from the nuclear matter to the stable Δ-nucleon matter can be of the second order for most parameter region. The onset density is smaller than that in symmetric matter.

* In symmetric dense matter, larger chiral invariant nucleon mass tends to lower the transition density to the stable N-Δ phase.

* Partial restoration of chiral symmetry is enhanced by Delta matter.

🡪 a transport code (DJBUU)

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A candidate of the chiral invariant mass?

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We put a constituent quark in a (simple) Copenhagen vacuum!

Igor A. Mazur, YK, Masayasu Harada, Hyun Kyu Lee, Int. J. Mod. Phys. E 32 (2023) 2350060

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m ~ ChiSB

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Igor A. Mazur, YK, Masayasu Harada, Hyun Kyu Lee, Int. J. Mod. Phys. E 32 (2023) 2350060

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Projectile

Target

PDM in HIC: further constraints on the value of the chiral invariant mass?

Initialization

Propagation

Collisions

Clustering

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DJBUU

DaeJeon Boltzmann-Uehling-Uhlenbeck (DJBUU) code

The primary version of DJBUU was written when Sangyong Jeon from McGill University was visiting RISP (Rare Isotope Science Project) of IBS (Institute for Basic Science) in Korea.

Myungkuk Kim, Sangyong Jeon, Y.-M. Kim, YK, Phys. Rev. C 101 (2020) 064614, H.

Wolter, …, Kyungil Kim, YK, … et al

Prog. Part. Nucl. Phys. 125 (2022) 103962

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DJBUU with surface term (2025~)

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preliminary

preliminary

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preliminary

preliminary

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Myungkuk Kim, Sangyong Jeon, Young-Min Kim, YK, and Chang-Hwan Lee, Phys. Rev. C 101 (2020)  064614.

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Pion production in an extended parity doublet model, Jia Zhou, Kyungil Kim, Sangyong Jeon, Jun Xu and YK,

Symmetry 17 (2025) 12, 2155

How about pion production?

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  • Nuclear matter saturation properties: m0~ (500-800) MeV

  • HIC: m0~ (500-800) MeV

  • Nuclear structures and neutron star properties: m0~ 700 MeV

  • To focus more on chiral symmetry: DJBUU+ChNM model with MFA and beyond MFA - Jia Zhou (Tongji Univ) et al

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Summary