Topology change and hadron properties in cold dense matter

1. Topology change and hadron properties in cold dense matter Work inprogress with Hyun Kyu Lee and Byung-Yoon Park WCU-Hanyang Project

2. Ed. G.E. Brown & MR (February 2010)

4. “Chiral magnetic spirals” Monte Carlo simulation Observation

5. Arethere such“gems”inhadronic physics with the skyrmions originally discovered for baryons?

6. Lessons from condensed matter : “Emerging”(hidden) gauge symmetry (HLS) Senthil et al, Science 303, 1490 (2004) Neel magnet Broken spin-rotation symmetry Sigma model (skyrmion) HLS (½-skyrmion) Valence bond solid (VBS) paramagnet Broken lattice-rotation symmetry

7. Power of effective field theory Both A (Neel magnet) and B (VBS) are captured by the Nonlinear s model + Berry phase. “Spinon” =order parameter in A ≠order parameter in B While the s model describes A and B, the Berry phase plays no role in A but is crucial in B in giving the VBS order, so the phase transition does not involve the same order parameter. “Ginzburg-Landau-Wilson paradigm does not apply here.”

8. Emergent local symmetry or hls Interplay of the emergent gauge field and the Berry phase leads to HLS theory between the A phase and the B phase CP1 Skyrmions replaced by 1/2-skyrmions Skyrmion number ~

9. S. Sachdev State of ½-skyrmions (or merons)

10. Manifestation in nuclear physics Nuclear tensor forces and (a)symmetry energy Esymin compressed baryonic matter Analogy (?) to “deconfined Quantum critical phenomenon”

11. Symmetry energy Esym

12. Esym at high density is a wilderness

13. And at higher density

14. Nature: Esym at n > n0 ? Fit to FOPI/GSI data for p-/p+ ratio → “supersoft”(ESS) Xiao et al, PRL 102 (09) 062502 A: “supersoft” Ess B: all others

15. Transport model analysis using IBUU04 Z. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, PRL 102, 062502 (2009) Au+Au 400 MeV/A

16. “ESS” could be a disaster !!?? If Nature chose the “supersoft” ESS There could be NO stable neutron stars unless …!! But Nature is full of neutron stars including the Hulse-Taylor binary pulsar.

18. Avoiding the disaster If Nature chose the “supersoft” ESS There could be NO stable neutron stars unless …!! But Nature is full of neutron stars including the Hulse-Taylor binary pulsar. Drastic wayout by D.H. Wenet al, PRL 103, 211102 (09): Modify Newtonian gravity. Why not? It could be emergent (E. Verlinde, arXiv:1001.0785).

19. “Gravity doesn’t exist” The New York Times July 12, 2010

20. Avoiding the disaster If Nature chose the “supersoft” ESS There could be NO stable neutron stars unless …!! But Nature is full of neutron stars including the Hulse-Taylor binary pulsar. Drastic wayout by D.H. Wenet al, PRL 103, 211102 (09): Modify Newtonian gravity. Why not? It could be emergent (E. Verlinde, arXiv:1001.0785). But kaons will not condense, and make Bethe and Brown very unhappy

21. How to concoct the Ess Possible mechanism: medium-scaling tensor forces C. Xu & B.A. Li, arXiv:0910.4803 p, r Tensor forces cancel: Exploit medium-enhanced cancelation to describe the C14 dating by J.W. Holt et al, PRL 100, 062501 (08) Assumed scaling:

22. C14 dating “explained” J.W. Holt et al, PRL 100, 062501 (08)

23. Apply to Esym C. Xu & B.A. Li, arXiv:0910.4803 for all density (n) Fi(n)= 1-ai (n/n0) 0=a0 < a1 < a2 <a3 …<am ≈ 0.2 a0=0 a1 Esym a2 a3 am n n0

24. But half-skyrmion (or dyonic*) phase enters Drastic change Described in terms of skyrmions, baryonic matter has a “phase transition” at ndeconf > nn1/2 > n0 from a skyrmion matter to a ½-skyrmion matter *Sin, Zahed, R Ismail’s talk

25. Hls in dense matter Mimic generic features ofthe Neel-VBS (though with different physics): Nonlinear sigma model: NLs Hidden gauge invariance: Promote to gauge theory with nonabelian gauge field rm: Harada/Yamawaki HLS theory: HLS NLs model is “gauge-equivalent” to HLS

26. In nature H. Georgi, 1990 Nc→  → a ≈1 & g ~ 0 : light-quark vector mesons tend to “vector limit” (HG) or “vector manifestation” (Harada-Yamawaki) (b) V(ector)D(ominance) is violated in medium (density & temperature) xL,R decouple: L,R symmetries “restored” and xL,R and rmare the relevant degrees of freedom as in the Neel-VBS transition

27. Georgi’s “vector mode” H. Georgi, 1990 At large Nc , k  (1-a) → 0, g ~ 0 • Vector mesons (e.g., r) are light ~ 1/Nc , become degenerate with p • in the vector (or VM) limit. Cf: Weinberg’s “mended symmetry.” • Baryons as matter field are massive ~ Ncfiguring in terms of • two kindsof skyrmions Supports • A variety of light-quark phenomena, e.g. p mass difference • Heavy-light-quark phenomena, e.g., chiraldoubler • Nucleon form factor • Etc etc.

28. VD violation in nucleon form factor Iachello, Jackson & Lande, 1973 Brown, Weise, R., 1986 Bijker & Iachello, 2004 g g + (1-z/2) + (1-z/2) z Phenomenology: z ≈ 1 Cf: VD → z=2 HLS: z =

29. HLS4d “a” goes to 1: Vector dominance a la Sakurai violated in medium!!! HLS5D V = r, r’,r”, …r Holography “Core” & Cheshire Cat I. Zahed

30. Appearance of fractionized skyrmions B.Y. Park et al,1999 skyrmion half-skyrmion Simulate dense matter by putting skyrmions in FCC crystals and squeeze them: ½-skyrmions in CC appear at n1/2 Half-skyrmions skyrmions

31. Also in Hqcd: “dyonic salt” Sin, Zahed, R., Phys. Lett. B689, 23 (2010) Increasing density Instantons: FCC ½ instantons (dyons): BCC Dyons are bound by ~ 180 MeV.

32. “Phase”structure The ½-skyrmion phase at n  n1/2is characterized by i.e. “vector mode” ndeconf n1/2 Sigma model HLS model Rough estimate: n1/2 ~ (1.3 – 2) n0

33. What does the ½-skyrmion phase do to Esym ? Symmetry energy ∼ 1/Nc Collective-quantize the (neutron) skyrmion matter I. Klebanov, 1985 Isospin rotation Moment of inertia

34. Esymfrom half-skyrmion matter H.K. Lee, B.Y. Park, R. 2010

35. How to understand the cusp at in “standard”nuclear physics? n1/2 H.K. Lee, B.Y. Park, R. 2010 In-medium scaling

36. Assumptions Skyrmion number Q is conserved, a baryon can be considered as a bound pair (B ~ 100-200 MeV) of 2 half-skyrmions in the half-skyrmion phase. Half-baryons interact via exchange of pions and vector mesons, giving a meaning to “effective nuclear forces.” Quasiparticle description with effective masses and coupling constants makes sense. Scaling in density

37. Tensor forces are drastically modified in the ½-skyrmion phase “standard” nuclear physics For density n < n1/2: For density n  n1/2: , n1/2 n=0 n=n0 p+r n=2n0 Increasing tensor Decreasing tensor Above n1/2,the r tensor gets “killed,” enabling the pions (p0’s) to condense → pionic crystal in dense neutron matter ( e.g., Pandharipande and Smith 74).

38. How the ½-skyrmions act on Esym

39. ½-skyrmion vs. scaling Scaling prediction ½-skyrmion This prediction could be checked or falsified at FAIR or even RIB (e.g., KoRIA) machines

40. Application: Strange goings-on incompressed matter J.I. Kim, B.Y. Park, R. 2009 Insertanti-kaon in half-skyrmion matter Skyrmion-1/2-skyrmion background Ignore kaon back-reaction onto (half-)skyrmion matter

41. Analogy to “magnetic spirals” With spin → isospin? Chiral magnetic spirals Dzyaloshinsky-Moriya interaction Pfleiderer & Rosche, Nature, 17 June 2010

42. Anti-kaon “roaming” through ½-skyrmion matter: Wess-Zumino term How to measure isospin spirals?

43. ppnK- Exp. DBｔｈ-ex ~ 60 MeV Chiral restoration ? Relativistic effect ? Y. Akaishi 2010 n rN(0) = 9r0 1.2 fm rNav= 3r0 K- p p 1.5 fm “Challenging problem” !

44. “Mysterious” attraction in ½-skyrmion matter △B ~ 50-60 MeV DB Is this what Akaishi and Yamazaki need for dense kaonic matter ?

45. Dedonfined quantum critical? ss Hong, Zahed, R. (99) ½-skyrmions Crystal Sigma model Sigma model “superqualiton” Density n1/2 ~ (1.3-2)n0

46. Conclusion If the ½-skyrmion phase (in 4D) or the ½-instanton (or dyonic-salt) phase (in 5D) is present at a density not far above n0 , drastic effects are expected for a variety of low-temperature nuclear processes, in particular, in the EOS crucial for compact stars. So what is the real “doorway” to higher-density phase(s)?