Mass modifica+on of hadrons associated with par+al chiral symmetry - - PowerPoint PPT Presentation

Mass modifica+on of hadrons associated with par+al chiral symmetry restora+on

Masayasu Harada (Nagoya University) ＠The 34th 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)

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Introduc)on

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Origin of Mass

?

• f Hadrons
• f Us

One of the Interes)ng problems of QCD

=

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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).

4

• How much mass of nucleon or Δ is from the

spontaneous chiral symmetry breaking ?

• What is the value of the chiral invariant mass ?

mB = m0B +m qq

chiral invariant mass spontaneous chiral symmetry breaking

2016/08/8 Physics of Heavy-Ion Collisions at J-PARC

Phase diagram of Quark-Gluon system

High density

Neutron Star

high temperature 1 trillion kelvin 100 million ton/cm3

• Spontaneous Chiral Symmetry Breaking
• Confinement of Quarks
• Chiral Symmetry Restra)on
• Deconfinement of Quarks

Early Universe

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Important for understanding the spontaneous chiral symmetry breaking

chiral symmetry broken phase at vacuum chiral symmetric phase at high T and/or density

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.

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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.

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What happens to the mass of Delta baryon ?

Change of Delta at RHIC ?

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STAR: arXiv:nucl-ex/040301

These show that medium effects push up the Δ mass at high temperature.

In-medium spectral funcion of Δ by Hees-Rapp, PLB606, 59 (2005)

• What happens at high density ?
• What is the rela+on to the par+al chiral symemtry

restora+on ?

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• 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

• 2. Nuclear maher from a parity

doublet model

• Y. Motohiro, Y.Kim, M.Harada, Phys. Rev. C 92, 025201 (2015)

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Parity Doublet model

• 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
• nly the chiral symmetry breaking.

C.DeTar, T.Kunihiro, PRD39, 2805 (1989) D.Jido, M.Oka, A.Hosaka, PTP106, 873 (2001)

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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, σ0 = fπ = 93 MeV, and gπN+N- = 0.7 obtained from ΓN*→πN = 75 MeV. – Outputs : m0 = 270 MeV , g1 = 9.8 , g2 = 16 .

• Global fit in an extended model (S.Gallas et al.,

PRD82, 014004 (2010) ) shows m0 = 460 +- 136 MeV.

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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.

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G.Aarts et al., PRD92

• G. Aarts et al., PRD92

Y.L. Glozman et al., PRD86

Nuclear maher in parity doublet models

• A parity doublet model including
• mega meson with 4-point

interac+on is used in a Walecka-type mean field analysis.

– Large value of m0 is needed to reproduce the incompressibility.

• Rho meson is further included with

4-point interac+on.

– m0 > 800 MeV is needed to have 100 < K < 400 MeV

• Different values of m0 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 m0 > 500 MeV.

14

D.Zschiesche et al., PRC75, 055202 (2007) V.Dexheimer et al., PRC77, 025803 (2008)

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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 m0 (500 ≦ m0 ≦ 900 MeV).

– Nuclear satura+on density – Binding energy at normal nuclear density – Incompressibility – Symmetry energy : Esym(ρ0) = 31 MeV

15

= 240 MeV

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1 2 50 90

Binding Energy, Pressure, Mean fields

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m0 = 500 MeV

• 20
• 10

10 20 30 40 50 60 70 0.05 0.1 0.15 0.2 0.25 0.3 0.35 E/A-mp[MeV] B[fm-3] n/B=0.5 n/B=1

• 5

5 10 15 20 25 30 0.05 0.1 0.15 0.2 P[MeV] [fm-3] m0=500[MeV] n/B=0.5 n/B=0.6 n/B=0.7 n/B=0.8 n/B=0.9 n/B=1.0

Binding Energy Pressure

ρB (fm3) ρB (fm3)

〈σ〉 (MeV)

ρB/ρ0 ρB/ρ0

m0 = 500 MeV m0 = 700 MeV

hωi = gωNN m2

ω

ρB (MeV)

1 2 10 20 30

m0 = 500, 700 MeV

Effec+ve masses of nucleons

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• 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 N N ω

m(eff)

±

= 1 2 q (g1 + g2)2hσi2 + 4m2

0 ⌥ (g2 g1)hσi

• + gωNNhωi

(nucleon) m(eff)

±

= 1 2 q (g1 + g2)2hσi2 + 4m2

0 ⌥ (g2 g1)hσi

• gωNNhωi

(anti-nucleon)

1 2 1500 3000

Density dependence of effec+ve masses

• Sum of masses of nucleon and an+-nucleon decreases

toward m0 reflec+ng the par+al chiral symmetry restora+on.

• Studying effec+ve masses will give a clue for m0.

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m0 = 700 MeV mN(−) mN(−) mN(+) mN(+)

mN(−) + mN(−)

mN(+) + mN(+) m(eff)

±

= 1 2 q (g1 + g2)2hσi2 + 4m2

0 ⌥ (g2 g1)hσi

• + gωNNhωi

(nucleon) m(eff)

±

= 1 2 q (g1 + g2)2hσi2 + 4m2

0 ⌥ (g2 g1)hσi

• gωNNhωi

(anti-nucleon) ρB/ρ0 ρB/ρ0 Masses (MeV) 1 2 500 1000 1500

• 3. Density dependence of

effec+ve mass of Delta baryon

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Chiral Partner Structure of Delta

• Δ(1232) and Δ(1700) are regarded as chiral partners.

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D.Jido, T.Hatsuda, T.Kunihiro, PRL84, 3252 (2000) D.Jido, M.Oka, A.Hosaka, PTP106, 873 (2001)

• I use masses of Δ(1232) and Δ(1700) as inputs.
• m0Δ must lie m0Δ ≦ 1460 MeV.
• In the following analysis, I use m0Δ = 1400, 700

MeV as typical examples.

m∆± = q (¯ g1 + ¯ g2)2hσi2 + m2

0∆ ⌥ (¯

g1 ¯ g2)hσi

Density dependence of effec+ve masses

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Masses (MeV)

m0Δ = 700 MeV

∆(−) ∆(−) ∆(+) ∆(+)

I use gω∆∆ = gωNN = 5.4 as a typical example.

Increasing or decreasing of Δ(+) baryon mass only is not enough for measuring the chiral symmetry restora+on.

ρB/ρ0

m0Δ = 1400 MeV

ρB/ρ0 m∆± = q (¯ g1 + ¯ g2)2hσi2 + m2

0∆ ⌥ (¯

g1 ¯ g2)hσi + gω∆∆ hωi (∆) m∆± = q (¯ g1 + ¯ g2)2hσi2 + m2

0∆ ⌥ (¯

g1 ¯ g2)hσi gω∆∆ hωi (anti-∆)

1 2 1200 800 1600 1 2 1200 800 1600

1 2 1500 2000 2500

Par+al chiral symmetry restora+on

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ρB/ρ0 ρB/ρ0

1 2 500

∆(−) − ∆(+) (MeV)

• Studying the mass difference of chiral partners gives a clue for

par+al chiral symmetry restora+on, independently of the value

• f m0Δ.
• Taking sum of par+cle and an+-par+cle will give a clue for

chiral invariant mass.

m0Δ = 700, 1400 MeV m0Δ = 1400 MeV

∆(+) + ∆(+) (MeV)

m0Δ = 700 MeV

m∆± = q (¯ g1 + ¯ g2)2hσi2 + m2

0∆ ⌥ (¯

g1 ¯ g2)hσi + gω∆∆ hωi (∆) m∆± = q (¯ g1 + ¯ g2)2hσi2 + m2

0∆ ⌥ (¯

g1 ¯ g2)hσi gω∆∆ hωi (anti-∆)

４．Summary

• We studied density dependence of

Delta baryon masses from the mean field contribu+ons of sigma and

• mega mesons.
• Increasing or decreasing of Δ(+)

baryon mass only is not enough for measuring the chiral symmetry restora+on.

• Studying the mass difference of

chiral partners gives a clue for par+al chiral symmetry restora+on, independently of the value of m0Δ.

• Taking sum of par+cle and an+-

par+cle will give a clue for the chiral invariant mass m0D.

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1 2 1200 800 1600 1 2 1200 800 1600

m0Δ = 700 MeV m0Δ = 1400 MeV

1 2 500

m0Δ = 700, 1400 MeV

1 2 1500 2000 2500

m0Δ = 1400 MeV m0Δ = 700 MeV

Discussions

• For more realis+c study of Δ mass in maher, we should

check the effect of π-N loop, which is needed to study the in-medium spectral func+on.

• There seems s+ll a difference of the es+mated value of

the chiral invariant mass of nucleon between the one at vacuum and the one in the maher.

• The analysis in the 3-flavor parity doublet model shows

that the chiral partner of the posi+ve parity nucleon, N(939), is not N*(1535), but a mixture of N*(1440), N*(1535), N*(1650), … [H.Nishihara and M.Harada,

• Phys. Rev. D92, 054022 (2015), and work in

prepara+on.]

• It is interes+ng to include 2 parity doublets for nucleon

into a model.

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