mesons as probes to explore the chiral symmetry in nuclear matter z Nagoya university Quark-Hadron theory Group Daiki Suenaga　

Contents 1. Introduction I : What is the chiral symmetry ? 2. Introduction II : Chiral partner structure 3. Model and Calculation 4. Results and a summary

Contents 1. Introduction 1. Introduction I : What is the chiral symmetry ? 2. Introduction II : Chiral partner structure 3. Model and Calculation 4. Results and a summary

1. Introduction I ・Standard model - QED (Quantum electrodynamics) - the theory which can explain elementary particles - QED (Quantum electrodynamics) WS theory - weak interaction (beta decay) (perturbative) - strong interaction (origin of nuclear force) QCD (non-perturbative)

1. Introduction I ・Standard model - QED (Quantum electrodynamics) - the theory which can explain elementary particles - QED (Quantum electrodynamics) WS theory - weak interaction (beta decay) (perturbative) - strong interaction (origin of nuclear force) QCD (non-perturbative)

＝ 1. Introduction I ・The nature of QCD - We cannot solve QCD by hand ! nucleon bound state of three quarks (bound by QCD dynamics) - QCD is not perturbative in low energy region - We cannot solve QCD by hand ! ( big problem !)

× 1. Introduction I ・Problems related to QCD - Color confinement problem × Single quarks are not observable ( Why quark is so shy ? ) - Mass gap problem three quarks nucleon Nucleon mass is much larger than the sum of mass of three quark ( Why nucleon is so fat ? What did you eat ? ) - These are originated from the non-perturbative nature of QCD

1. Introduction I ・QCD vacuum - Chiral symmetry can give us a clue to - Chiral symmetry is spontaneously broken ( cf. BCS theory, higgs mechanism, etc ) - Nucleon mass is explained effectively - Pion dynamics is also explained - Chiral symmetry can give us a clue to explain the origin of mass of us

1. Introduction I Understanding of the chiral symmetry Understanding of origin of us ! I think ...

1. Introduction I ・Chiral symmetry has not well understood - For example, nucleon mass is originated from the chiral symmetry partially (parity doublet model) ? no answer... C. E. DeTar and T. Kunihiro, Phys. Rev. D 39, 2805 (1989) D. Jido, M. Oka, and A. Hosaka, Prog. Theor. Phys. 106, 873 (2001) How about consider in medium ? - Material around us is made of nuclear matter (nucleus) - We want to know about chiral symmetry in nuclear matter

1. Introduction I ・Chiral symmetry at density - Chiral condensate in the vacuum ( is order parameter )

1. Introduction I ・Chiral symmetry at density - Chiral condensate at lower density

1. Introduction I ・Chiral symmetry at density - Chiral condensate at higher density

1. Introduction I ・Chiral symmetry at density - Chiral condensate at higher density - chiral symmetry is expected to be partially restored in nuclear matter

1. Introduction I ・How can we explore the chiral in medium ? - mesons can be good probes because… quark mesons - expansion is applicable (Heavy quark spin symmetry) quarks - We can directly extract the information of chiral symmetry

Contents 1. Introduction 1. Introduction I : What is the chiral symmetry ? 2. Introduction II : Chiral partner structure 3. Model and Calculation 4. Results and a summary

2. Introduction II ・Chiral partner structure mass parity + parity - spin 1 ・ ・ spin 0 ・ ・ spin 1 spin 0

2. Introduction II ・Chiral partner structure mass parity + parity - spin 1 ・ ・ spin 0 ・ ・ spin 1 mass difference between opposite parity state comes from chiral symmetry breaking spin 0

2. Introduction II ・Chiral partner structure mass parity + parity - spin 1 ・ ・ spin 0 ・ ・ M. A. Nowak, M. Rho, and I. Zahed, PRD 48 (1993) W. A. Bardeen and C. T. Hill, PRD 49 (1994). spin 1 mass difference between opposite parity state comes from chiral symmetry breaking spin 0

2. Introduction II ・Chiral partner structure mass parity + parity - spin 1 ・ ・ spin 0 ・ ・ M. A. Nowak, M. Rho, and I. Zahed, PRD 48 (1993) W. A. Bardeen and C. T. Hill, PRD 49 (1994). spin 1 mass difference between opposite parity state comes from chiral symmetry breaking spin 0

2. Introduction II Mass of mesons in medium ? How can we observe it ? Is it possible ...?

2. Introduction II ・Decay of excited state in vacuum - Excited state mesons (parity +) can decay into the ground state mesons by emitting a pion in the vacuum mass decay ○ vacuum

2. Introduction II ・Decay of excited state in medium - Chiral symmetry is expected to be partially restored in the nuclear matter mass decay but weaken ○ vacuum in medium

× 2. Introduction II ・Decay of excited state in medium - Chiral symmetry is expected to be partially restored in the nuclear matter mass × decay × if vacuum in medium - Not only mass of mesons, but also the spectral function of them are important (especially excited state )

Contents 1. Introduction I : What is the chiral symmetry ? 2. Introduction II : Chiral partner structure 3. Model and calculation 4. Results and a summary

3. Model and calculation ・Lagrangian for heavy-light mesons - Heavy-light mesons transform as - Lagrangian is of the form where

3. Model and calculation ・Lagrangian for heavy-light mesons - Heavy-light mesons transform as - Lagrangian is of the form - corresponds to mass difference between chiral partners - we take where

3. Model and calculation ・Lagrangian in relativistic form - Heavy-light mesons are converted via and as - Lagrangian in relativistic form takes

3. Model and calculation ・How can we introduce matter effect ? - Nuclear matter is constructed by the linear sigma model with nucleon one loop with - Density dependence of is obtained from the gap equation with 2

2. Introduction II We have got Lagrangian of mesons We have constructed nuclear matter Connect them !

3. Model and calculation ・Fluctuations of in nuclear matter - Modifications of mesons are introduced as - propagator must be resummed one as where

Contents 1. Introduction I : What is the chiral symmetry ? 2. Introduction II : Chiral partner structure 3. Model and calculation 4. Results and a summary

4, Results and a summary ・Mass of mesons - Masses at several densities mass [MeV] 449 ↕ 388 ↕ 323 ↕ 229 ↕

4, Results and a summary ・Mass of mesons - Masses at several densities mass [MeV] 449 ↕ 388 ↕ 323 ↕ 229 ↕ - Mass difference gets small at higher density - Consequence of partial restoration of chiral symmetry !

4, Results and a summary ・Spectral function for mesons - Spectral function at several densities - in vacuum - results - Spectral function in vacuum - the results in several densities

4, Results and a summary ・Spectral function for mesons - Spectral function at several densities - in vacuum - results - The value of on shell mass decreases as density increases

4, Results and a summary ・Spectral function for mesons - Spectral function at several densities - in vacuum - results - decay width of gets narrowed since mass difference between and gets small

4, Results and a summary ・Spectral function for mesons - Spectral function at several densities - in vacuum - results - Landau damping due to the medium effects appears

4, Results and a summary ・Spectral function for mesons - Spectral function at several densities - in vacuum - results - Another perk can appear ?? ( threshold cusp?? )

4, Results and a summary ・Summary - We calculated the spectral function for meson in nuclear matter with partial restoration of chiral symmetry - As density increases, mass difference between and mesons gets small since chiral symmetry is partially restored - Decay width of gets narrowed - The other peak corresponds to Landau damping appears

4, Results and a summary ・How can we observe in experiments ? - Spectral function for can be observed in decay as follows ① (pair creation) nucleus

4, Results and a summary ・How can we observe in experiments ? - Spectral function for can be observed in decay as follows ① ② (medium modified) (pair creation) nucleus nucleus

4, Results and a summary ・How can we observe in experiments ? - Spectral function for can be observed in decay as follows ① ② (medium modified) (pair creation) nucleus nucleus ③ (decay in medium) nucleus

4, Results and a summary ・How can we observe in experiments ? - Spectral function for can be observed in decay as follows ① ② (medium modified) (pair creation) nucleus nucleus ③ ④ catch! (decay in medium) observe the spectral function catch! nucleus nucleus

Thank you for your attention

Back up

Back up ・Interaction among all four mesons All mesons can mix

Back up ・Subtraction and regularization