Mass modifica+on of hadrons associated with par+al chiral symmetry restora+on Masayasu Harada (Nagoya University) ＠ The 34 th Reimei Workshop “Physics of Heavy- Ion Collisions at J-PARC” (August 8, 2016) Based on discussions with • Hiroyuki Sako, Yusuke Takeda, Yong-Liang Ma, Youngman Kim, See also • M. Harada, Y.L. Ma, D. Suenaga, Y. Takeda, in prepara+on. • Y. Motohiro, Y.Kim, M.Harada, Phys. Rev. C 92, 025201 (2015) 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 1
Introduc)on 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 2
of Hadrons ? Origin of Mass of Us = One of the Interes)ng problems of QCD 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 3
Chiral Invariant Mass of Baryons ? • Parity doublet model for light baryons – In [C.DeTar, T.Kunihiro, PRD39, 2805 (1989)], N*(1535) is regarded as the chiral partner to the N(939) having the chiral invariant mass. – In [D.Jido, T.Hatsuda, T.Kunihiro, PRL84, 3252 (2000)], Δ (1700) is regarded as the chiral partner to Δ (1232). m B = m 0 B + m qq spontaneous chiral symmetry breaking chiral invariant mass • How much mass of nucleon or Δ is from the spontaneous chiral symmetry breaking ? • What is the value of the chiral invariant mass ? 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 4
Phase diagram of Quark-Gluon system high Early Universe temperature • Chiral Symmetry Restra)on • Deconfinement of Quarks 1 trillion kelvin • Spontaneous Chiral Symmetry Breaking • Confinement of Quarks Neutron Star High density 100 million ton/cm 3 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 5
Important for understanding the spontaneous chiral symmetry breaking chiral symmetric phase chiral symmetry broken phase at high T and/or density at vacuum qq ≠ 0 (chiral condensate) qq = 0 • The spontaneous chiral symmetry breaking is expected to generate a part of hadron masses. • It causes mass difference between chiral partners. • Changing T and/or density will cause some change of hadron masses. 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 6
In [Y. Motohiro, Y.Kim, M.Harada, Phys. Rev. C 92, 025201 (2015)], we studied nuclear maher using a parity doublet model, and showed some rela+ons between the chiral invariant mass of nucleon and the phase structure. We also presented a density dependence of the nucleon mass, which changes reflec+ng the par+al chiral symmetry restora+on. What happens to the mass of Delta baryon ? 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 7
Change of Delta at RHIC ? STAR: arXiv:nucl-ex/040301 In-medium spectral funcion of Δ by Hees-Rapp, PLB606, 59 (2005) These show that medium effects push up the Δ mass at high temperature. • What happens at high density ? • What is the rela+on to the par+al chiral symemtry restora+on ? 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 8
• In this talk, I will show a preliminary study of the mass of Δ baryon at high density, based on a parity doublet structure. Outline 1. Introduc+on 2. Nuclear maher from a parity doublet model 3. Density dependence of effec+ve mass of Delta baryon 4. Summary 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 9
2. Nuclear maher from a parity doublet model Y. Motohiro, Y.Kim, M.Harada, Phys. Rev. C 92, 025201 (2015) 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 10
Parity Doublet model C.DeTar, T.Kunihiro, PRD39, 2805 (1989) D.Jido, M.Oka, A.Hosaka, PTP106, 873 (2001) • An excited nucleon with negative parity such as N*(1535) is regarded as the chiral partner to the N(939) which has the positive parity. • These nucleons have a chiral invariant mass in addition to the mass generated by the spontaneous chiral symmetry breaking. • In this model, the origin of our mass is not only the chiral symmetry breaking. 2016/08/8 11 Physics of Heavy-Ion Collisions at J-PARC
Determina+on of the parameters at vacuum • Masses of parity eigenstates • Determina+on of parameters at vacuum (D.Jido et al., PTP106, 873 (2001)) – Inputs : m + = 939 MeV, m - = 1535 MeV, σ 0 = f π = 93 MeV, and g π N+N- = 0.7 obtained from Γ N*→ π N = 75 MeV. – Outputs : m 0 = 270 MeV , g 1 = 9.8 , g 2 = 16 . • Global fit in an extended model (S.Gallas et al., PRD82, 014004 (2010) ) shows m 0 = 460 +- 136 MeV. 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 12
Laqce analysis • The result in [G. Aarts, C. Allton, S. Hands, B. Jaeger, C. Praki, and J. I.Skullerud, Phys. Rev. D 92, 014503 (2015)] and [L.Y.Glozman, C.B.Lang, M. Schrock, Phys. Rev. D86, 014507 (2012)] seems to show the existence of large chiral invariant mass. G. Aarts et al., PRD92 G.Aarts et al., PRD92 Y.L. Glozman et al., PRD86 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 13
Nuclear maher in parity doublet models • A parity doublet model including D.Zschiesche et al., PRC75, 055202 (2007) omega meson with 4-point interac+on is used in a Walecka-type mean field analysis. – Large value of m 0 is needed to reproduce the incompressibility. • Rho meson is further included with 4-point interac+on. V.Dexheimer et al., – m 0 > 800 MeV is needed to have 100 < PRC77, 025803 (2008) K < 400 MeV • Different values of m 0 are preferred at vacuum and in medium ? – We construct a model with a 6-point interac+on of sigma, but without 4- point interac+on for vector mesons. – We obtain K = 240 MeV for m 0 > 500 MeV. 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 14
Inputs from medium property • We calculate the thermodynamic poten+al in the nuclear medium in our model, using the mean field approxima+on. • Then, we determine 4 parameters from the following physical inputs for a given value of the chiral invariant mass m 0 (500 ≦ m 0 ≦ 900 MeV). – Nuclear satura+on density – Binding energy at normal nuclear density – Incompressibility = 240 MeV – Symmetry energy : E sym ( ρ 0 ) = 31 MeV 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 15
Binding Energy, Pressure, Mean fields m 0 = 500 MeV Pressure Binding Energy 70 30 � n / � B =0.5 m 0 =500[MeV] 60 � n / � B =1 25 � n / � B =0.5 � n / � B =0.6 50 � n / � B =0.7 20 E/A-m p [MeV] 40 � n / � B =0.8 � n / � B =0.9 P[MeV] 30 15 � n / � B =1.0 20 10 10 5 0 0 -10 -20 -5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 0.05 0.1 0.15 0.2 � B [fm -3 ] ρ B (fm 3 ) � [fm -3 ] ρ B (fm 3 ) h ω i = g ω NN (MeV) 〈 σ 〉 (MeV) ρ B m 2 ω 90 m 0 = 500 MeV m 0 = 500, 700 MeV 30 20 50 m 0 = 700 MeV 10 ρ B / ρ 0 ρ B / ρ 0 0 1 2 0 1 2 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 16
Effec+ve masses of nucleons • In this talk, I define effec+ve masses of nucleons by including effects of exchanging the sigma and omega mesons in the mean field approxima+on, following our recent work [M.Harada, Y.L.Ma, D.Suenaga, Y.Takeda, in prepara+on]. N N σ ω N N = 1 q � m (e ff ) ( g 1 + g 2 ) 2 h σ i 2 + 4 m 2 0 ⌥ ( g 2 � g 1 ) h σ i + g ω NN h ω i (nucleon) ± 2 q � = 1 m (e ff ) ( g 1 + g 2 ) 2 h σ i 2 + 4 m 2 0 ⌥ ( g 2 � g 1 ) h σ i � g ω NN h ω i (anti-nucleon) ± 2 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 17
Density dependence of effec+ve masses = 1 q � m (e ff ) ( g 1 + g 2 ) 2 h σ i 2 + 4 m 2 0 ⌥ ( g 2 � g 1 ) h σ i + g ω NN h ω i (nucleon) ± 2 = 1 q � m (e ff ) ( g 1 + g 2 ) 2 h σ i 2 + 4 m 2 0 ⌥ ( g 2 � g 1 ) h σ i � g ω NN h ω i (anti-nucleon) ± 2 m 0 = 700 MeV Masses (MeV) 3000 1500 m N ( − ) + m N ( − ) m N ( − ) m N ( − ) 1000 m N (+) + m N (+) m N (+) 1500 500 m N (+) 0 1 2 0 1 2 ρ B / ρ 0 ρ B / ρ 0 • Sum of masses of nucleon and an+-nucleon decreases toward m 0 reflec+ng the par+al chiral symmetry restora+on. • Studying effec+ve masses will give a clue for m 0 . 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 18
3. Density dependence of effec+ve mass of Delta baryon 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 19
Chiral Partner Structure of Delta D.Jido, T.Hatsuda, T.Kunihiro, PRL84, 3252 (2000) D.Jido, M.Oka, A.Hosaka, PTP106, 873 (2001) • Δ (1232) and Δ (1700) are regarded as chiral partners. q g 2 ) 2 h σ i 2 + m 2 m ∆ ± = (¯ g 1 + ¯ 0 ∆ ⌥ (¯ g 1 � ¯ g 2 ) h σ i • I use masses of Δ (1232) and Δ (1700) as inputs. • m 0 Δ must lie m 0 Δ ≦ 1460 MeV. • In the following analysis, I use m 0 Δ = 1400, 700 MeV as typical examples. 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 20
Density dependence of effec+ve masses q g 2 ) 2 h σ i 2 + m 2 m ∆ ± = (¯ g 1 + ¯ 0 ∆ ⌥ (¯ g 1 � ¯ g 2 ) h σ i + g ω ∆∆ h ω i ( ∆ ) q g 2 ) 2 h σ i 2 + m 2 m ∆ ± = (¯ g 1 + ¯ 0 ∆ ⌥ (¯ g 1 � ¯ g 2 ) h σ i � g ω ∆∆ h ω i (anti- ∆ ) I use g ω ∆∆ = g ω NN = 5 . 4 as a typical example. m 0 Δ = 700 MeV Masses (MeV) m 0 Δ = 1400 MeV ∆ ( − ) 1600 1600 ∆ ( − ) 1200 1200 ∆ (+) 800 800 ∆ (+) ρ B / ρ 0 0 1 2 ρ B / ρ 0 0 1 2 Increasing or decreasing of Δ (+) baryon mass only is not enough for measuring the chiral symmetry restora+on. 2016/08/8 Physics of Heavy-Ion Collisions at J-PARC 21
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