Neutral pion decay in Dense Skyrmion Matter

1. KPS2005(LENS) October 20, 2005 Neutral pion decayin Dense Skyrmion Matter B.-Y. Park(Chungnam Nat’l Univ.) A. Kalloniatis(Univ. of Adelaide)

2. Non-linear s Model Pion dynamics Higher order derivative terms & baryonic degrees of freedom

3. Skyrme’s Old Idea U(x) : mapping fromR3-{ }=S3toSU(2)=S3 8 topological soliton R ~ 1 f m M ~ 1.5 GeV 1960, T. H. R. Skyrme baryon ?

4. static soliton config. fluctuating pions Unified approach to pion-baryon system

5. Skyrmion Crystal

6. Pion in the dense baryonic matter? classical ground state config. static soliton config. fluctuating pions

7. Basic Idea

8. e.g. effective mass H.-J. Lee, B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl. Phys. A (2003)

9. Skyrme Model(mp=0) \ Pion fluctuation in rB=0 space Vacuum : U=1

10. pdynamics(r=0) \ Skyrmion matter Pion fluctuations on top of the skyrmion matter + p-skyrmion matter interactions

11. pdynamics(r=0) \

12. pdynamics(r=0) \

13. pdynamics(r=0) \ In-Medium pion decay constant ? In-Medium pion mass ?

14. pion effective mass H.-J. Lee, B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl. Phys. A (2003)

15. e.g.#2 pion velocity H.-J. Lee, B.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A (2004)

16. pdynamics(r=0) Pion-BG interactions 0th-order propagator \

17. S = …. + +

18. S S S = + Pion propagator in medium + + Pion velocity in medium

19. Pion velocity in medium H.-J. Lee, B.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A (2004)

20. p0 -> ggin Dense Skyrmion Matter A. Kalloniatis, B.-Y. Park, PRD71, 034010 (2005)

21. U(1) gauged Skyrme Model with Gauging U(1) symmetry under with

22. U(1) gauged Skyrme Model Gauging U(1) symmetry under with Gauged Wess-Zumino-Witten term

23. Pion fluctuation in rB=0 space Vacuum : U=1

25. Pion fluctuation in rB=0 space Skyrmion matter : U0 \ s(x) Gab(x) C(U0) D(U0) F(U0)

27. Effective quantities

28. p0 -> gg in medium

29. p0 -> nnin Dense Skyrmion Matter A. Kalloniatis, C. Janathan, B.-Y. Park, PRD71,114001 (2005)

30. Gauging Skyrme Model Electroweak vector fields with

31. & WZW term

32. & Leptonic part

33. p0 -> nn possible? n Z n Z Z p0 p0 _ _ n n Z Impossible for massless neutrinos

34. In medium? n Z p0 _ n In-medium modified “effective” vertex Again impossible for massless neutrinos

35. In medium? n Z p0 _ n possible if the background potential provide momentum

36. In medium? _ n A. Kalloniatis, C. Janathan, B.-Y. Park, PRD71, 114001 (2005) n Z p0 In-medium modification of the pion propagator Lorentz symmetry break down possible !

37. 10-4 ~ 10-3

38. Future Work n g p0 _ g n

39. Pion in the dense baryonic matter? classical ground state config. fluctuating pions