Recent progress on nuclear physics from Skyrme model Yong-Liang Ma Jilin University In Collaboration with: M. Harada, B. R. He H. K. Lee, Y. Oh, B. Y. Park, M. Rho, D. Suenaga, G.-S Yang

2014/10/31Dense One of the biggest challenges in particle physics Where the nucleon mass from? In reality Mass generated through Higgs mechanism DIFFICULT be accessed from fundamental QCD

2014/10/31Dense Dense matter provides a environment for exploring the origin of mass and mechanism of chiral symmetry breaking. However: Difficult to explore from fundmental QCD; Nonperturbative region of QCD, sign problem in Lattice. Any approach, effective model level or effective theory level, is valuable. The SKYRME MODEL is such a model in which Single baryon, baryonic matter and medium modified hadron properties can be unifiedly described. It’s a natural framework to investigate the mechanism/charactors of Chiral symmetry restoration, origin of nucleon mass, nucleon force, relevant EoMs of compact stars, etc.

2014/10/31Dense Skyrme Model Construction Five dimensional models from gauge/gravity duality Chiral effective theory of mesons, e.g., ChPT Pure phenomenological model, e.g., BPS

CONTENTS I.Introduction II.Skyrme model from chiral effective theories III.Dilaton Effect: Chiral restoration and vector manifestation. IV.A Pure phenomenological model: (near)BPS Skyrme model V.Summary and discussions Dense

I. Introduction Dense

Baryons are toplogical solitons in a nonlinear theory of pions Dense Witten’s large Nc argument on baryon Arising of hQCD

Skyrme model: results Adkins, Nappi, Witten, NPB 228 (1983). Jackson, Rho, PRL 51 (1983). Adkins, Nappi, Witten, NPB 233 (1984). Dense

1960, T. H. R. Skyrme Two skyrmions Dense

y z x y z 0 x z x y Dense Skyrmion matter from crystal  Originally: I. Klebaov, Nucl. Phys. B262(1985) CC  Kugler & Shtrikman, PLB208 (1988) 491; PRD40 (1989) /10/31 Widely used in condense matter physics

2014/10/31Dense

Dense Hadron properties in medium /10/31

Dense To describe nature, extension or modification is necessary.  O(1) Correction?  More resonance effect?  Puer phenomenological model based on chiral symmetry?  ……

Meson spectrum: Going up ∞ tower π χ ρ,ωρ,ω χ Dense … 14 Nuclear force  Vector meson: Essential for tensor force Sum of one-pion exchange and one-rho exchange  Light scalar meson: Attractive nucleon interaction  Omega meson,  … 2014/10/31 II. Skyrme model from chiral effective theories

Early attempts to include vector mesons Dense Ｐｈｅｎｏｍｅｎｏｌｏｇｉｃａｌ ｍｏｄｅｌ Ｍａｓｓｉｖｅ Ｙａｎｇ－Ｍｉｌｌｓ Ｔｈｅｏｒｙ : Syracuse group Hidden Local symmetry approach: Nagoya Group (Chiral EFT)

2014/10/31Dense

Drawbacks in the previous works 1.From physics, more D.O.F should be included. 2.Higher order terms, such as O(p 4 ) terms, are at O(N c ) like O(p 2 ); should be considered. 3.More complicated form of the Lagrangian. 4.Uncontrollable large number of low energy constants. Hinders systematical study of baryonic matter. Dense Thanks to the AdS/CFT correspondence, all the above defects can be overcome from holographic QCD models. 2014/10/31

Vector meson effect from chiral effective theory YM, Y. Oh, G.S. Yang, M. Harada, H. K. Lee, B.Y. Park, M. Rho, Phys.Rev. D86 (2012) YM, G.S. Yang, Y. Oh, M. Harada, Phys.Rev. D87 (2013) parameters! Difficult to fix them phenomenologically! Dense

HLS from hQCD models Dense

 The  meson reduces the soliton mass from 922 MeV in the HLS(  ) to 834 MeV in the HLS(  ;  ) but  meson increases the soliton mass to 1184 MeV. This is contrast to the naive expectation that including more vector mesons would decrease the soliton mass.  The  meson interacts with the other mesons through the hWZ terms  the importance of the hWZ terms in Skyrme phenomenology.  The role of the vector mesons can also be verified by comparing the soliton wave functions  All these behaviors can be found in the Skyrmion radii. No parameter dependence. Dense

Dense Baryonic matter YM, M. Harada, H. Y. Lee, Y. Oh, B. Y. Park, M. Rho, Phys.Rev. D88 (2013) 1,

Introduce external gauge field by gauge the chiral symmetry and meson fluctuations by substitution: In-medium modification of pion decay constant Dense

Dense Consider: 2014/10/31 In-medium modification of pion decay constant

Dense

In-medium modification of the baryon properties Dense

Dense III. Dilaton effect: Chiral Restoration and Vector Manifestation We are using an effective theory of QCD in terms the macroscopic degrees freedom, i.e., hadrons. This effective theory should match to QCD at some scale where the chiral symmetry is restored. However  the chiral symmetry breaking and scale symmetry link to each other and chiral symmetry breaking could be triggered by scale symmetry breaking. Frenud-Nambu Theorem, 1968  Attractive force between nucleons.  Large skyrmion mass, supressed by dilaton. YM, M. Harada, H. Y. Lee, Y. Oh, B. Y. Park, M. Rho, Phys. Rev.D. (2014) VM: Harada & yamawaki, PRL86(2001) /10/31

Dense Scale invariant HLS and lessons /10/31 Implement HLS by dilaton  :

Dense Dilaton implimented Scale invariant HLS In medium modified hadron properties Chiral symmetry does not restored, VM does not appear! Why! 2014/10/31

Dense Screening effect Modified Lagr. Chiral symmetry is restored, VM does appear! /10/31

Dense Chiral invariant mass Parameterization of the in- medium modified hadron properties: /10/31

Dense Further progresses 1.Local chiral symmetry breaking (dense effect): Qualitatively, independent of the density.

2014/10/31Dense

2014/10/31Dense Further progresses 2. Local chiral symmetry breaking (resonance effect): π, ρ, ωπ, ρ π, ρ, ω, χ

2014/10/31Dense 3. Relation to the chiral density wave: e.g., Achim Heinz, Francesco Giacosa, and Dirk H. Rischke, How to translating the density dependence of quark condensate to the chemical dependence of CDW? In progress!

2014/10/31Dense Simplification of the model from HLS Hans Bethe’s working philosophy: (in doing the very complicated supernova explosion simulation) that anything less than ½ is set to zero and anything greater than ½ is set to 1. How to understand this simplification physically? Working in progress.

2014/10/31Dense Simplification of the model from HLS How to understand this simplification physically? Working in progress.

2014/10/31Dense Heavy-light meson in medium We studied the mass spectrum of heavy-light mesons to probe the structure of the spin-isospin correlation in the nuclear medium, which is expected to occur in the skyrmion crystal or the chiral density wave phase. D. Suenaga, B. R. He, YM, M. Harada, Phys.Rev. C89 (2014) ; Mass spitting of the heavy-light mesons with chiral partner structure, in progress!

V. Summary and Discussion Dense

Dense Skyrme Model Construction Five dimensional models from gauge/gravity duality Chiral effective theory of mesons, e.g., ChPT Pure phenomenological model, e.g., BPS Integrate out heavier modes What is the relation?

“When you use quantum field theory to study low-energy phenomena, then according to the folk theorem, you're not really making any assumption that could be wrong, unless of course Lorentz invariance or quantum mechanics or cluster decomposition is wrong, provided you don't say specifically what the Lagrangian is. As long as you let it be the most general possible Lagrangian consistent with the symmetries of the theory, you're simply writing down the most general theory you could possibly write down.... “ “What is quantum field theory, and what did we think it is?” hep-th/ Final Remark: Weinberg ‘folk theorem’ “F-proof”: It’s hard to see how it can go wrong! 2014/10/31Dense