1. mesons as probes to explore the chiral symmetry in nuclear matterz
Nagoya university
Quark-Hadron theory Group
Daiki Suenaga　

2. 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. 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

4. 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)

5. 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)

6. ＝ 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 !)

7. × 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

8. 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

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

10. 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

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

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

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

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

15. 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

16. 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

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

18. 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

19. 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

20. 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

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

22. 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

23. 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

24. × 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 )

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

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

27. 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

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

29. 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

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

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

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

33. 4, Results and a summary ・Mass of mesons - Masses at several densities
mass [MeV]
449 ↕
388 ↕
323 ↕
229 ↕

34. 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 !

35. 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

36. 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

37. 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

38. 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

39. 4, Results and a summary ・Spectral function for mesons
- Spectral function at several densities
- in vacuum
- results
- Another perk can appear ??
( threshold cusp?? )

40. 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

41. 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

42. 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

43. 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

44. 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

45. Thank you for
your attention

46. Back up

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

48. Back up
・Subtraction and regularization