1. Q UARK M ATTER WITH C HIRALITY I MBALANCE Marco Ruggieri ( マルコ ルジエーリ ) ) 京都大学基礎物理学研究所 京都市, 2011 年 4 月 21 日

2. C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM Sophie Bushwick, http://www.bnl.gov/today/story.asp?ITEM_NO=1870

3. C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM Sophie Bushwick, http://www.bnl.gov/today/story.asp?ITEM_NO=1870 Critical Endpoint (CP) First order and crossover lines intersect at CP Asakawa and Yazaki, Nucl.Phys. A504 (1989) 668-684

4. C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM Sophie Bushwick, http://www.bnl.gov/today/story.asp?ITEM_NO=1870 Critical Endpoint (CP) First order and crossover lines intersect at CP It might exist in QCD Fodor and Katz, JHEP03(2002)014 Asakawa and Yazaki, Nucl.Phys. A504 (1989) 668-684 For a review see de Forcrand in PoS LAT2009 (2009) 010

5. C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM Fodor and Katz, JHEP03(2002)014 C. R. Allton et al., Phys. Rev. D71 (2005) 054508 Gavai and Gupta, Phys. Rev. D78 (2008) 114503 De Forcrand and Philipsen, Nucl. Phys. B642 (2002) 290 P. De Forcrand et al., arXiv:0911.5682 S. Eijiri, Phys. Rev. D78 (2008) 074507 A. Ohnishi et al., Pos LAT2010 (2010) 202 Lattice K. Fukushima et al., Phys. Rev. D80 (2009) 054012 Bowman and Kapusta, Phys. Rev. C79 (2009) 015202 Zhang and Kunihiro, Phys. Rev. D80 (2009) 290 A. Ohnishi et al., arXiv:1102.3753 M. A. Stephanov, PoS LAT2006 (2006) 024 Abuki et al., Phys. Rev. D81 (2010) 125010 Basler and Buballa, Phys. Rev. D82 (2010) 094004 Model Calculations Ueda’s Poster

6. C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM Sophie Bushwick, http://www.bnl.gov/today/story.asp?ITEM_NO=1870 Critical Endpoint (CP) First order and crossover lines intersect at CP Nowadays, it has been hard to detect CP by means of Lattice simulations with Nc=3, because of the sign problem. Idea for detection: Continue CP to another critical point, which can be detected on the Lattice Asakawa and Yazaki, Nucl.Phys. A504 (1989) 668-684 For a review see de Forcrand in PoS LAT2009 (2009) 010

7. M APPING THE C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM M.R., arXiv:1103.6186 Chiral Chemical Potential conjugated to chiral density: N5=nR - nL Baryon Chemical Potential conjugated to baryon density

8. M APPING THE C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM M.R., arXiv:1103.6186 Chiral Chemical Potential conjugated to chiral density: N5=nR - nL Baryon Chemical Potential conjugated to baryon density In QGP context, to mimic chirality change induced by instantons and strong sphalerons in Quark-Gluon-Plasma: K. Fukushima et al, Phys.Rev. D78 (2008) 074033 K. Fukushima, R. Gatto and M. R., Phys.Rev. D81 (2010) 114031 M Chernodub and A. Nedelin, arXiv:1102.0188 [hep-ph] References

9. M APPING THE C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM M.R., arXiv:1103.6186 Chiral Chemical Potential conjugated to chiral density: N5=nR - nL Baryon Chemical Potential conjugated to baryon density In several non-QGP contexts: L. D. McLerran et al, Phys.Rev. D43 (1991) 2027 Nielsen and Ninomiya, Phys.Lett. B130 (1983) 389 A. N. Sisakian et al, hep-th/9806047 M. Joyce et al., Phys.Rev. D53 (1996) 2958 References

10. M APPING THE C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM M.R., arXiv:1103.6186 Chiral Chemical Potential conjugated to chiral density: N5=nR - nL Baryon Chemical Potential conjugated to baryon density Not affected by the sign problem, see for a nice explanation: K. Fukushima et al, Phys.Rev. D78 (2008) 074033 Remark 1 Grand Canonical Ensembles with a chiral chemical potential can be simulated on the Lattice with Nc=3.

11. M APPING THE C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM M.R., arXiv:1103.6186 Chiral Chemical Potential conjugated to chiral density: N5=nR - nL Baryon Chemical Potential conjugated to baryon density Not affected by the sign problem, see for a nice explanation: K. Fukushima et al, Phys.Rev. D78 (2008) 074033 Remark 1 Grand Canonical Ensembles with a chiral chemical potential can be simulated on the Lattice with Nc=3. We are aware that m 5 is not a true chemical potential: chiral condensate mixes L and R components, thus making N5 a non-conserved quantity. Remark 2

12. M APPING THE C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM M.R., arXiv:1103.6186 Chiral Chemical Potential conjugated to chiral density: N5=nR - nL Baryon Chemical Potential conjugated to baryon density W5: World with m =0 and finite m 5: Find a Critical Endpoint: CP5 W: World with m 5=0 and finite m : Find a Critical Endpoint: CP continuation Possibility of continuation is proved in the article I introduce two worlds:

13. M APPING CP M.R., arXiv:1103.6186 W5 Phase Diagram obtained within the P-NJL model: K. Fukushima, Phys.Lett. B591 (2004) 277-284 W. Weise et al., Phys.Rev. D73 (2006) 014019 M. Yahiro et al., Phys.Rev. D82 (2010) 076003 Polyakov Loop: collective field sensitive to confinement See also: K. Kondo, Phys.Rev. D82 (2010) 065024 M. Frasca, IJMPE18 (2009) 693 N-J-L, Phys.Rev.122:345-358,1961. )

14. M APPING THE C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM M.R., arXiv:1103.6186 W5 Capable to capture the EoS of full QCD at zero and imaginary chemical potential M. Yahiro et al., arXiv:1104.2394 [hep-ph]

15. M APPING THE C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM M.R., arXiv:1103.6186 W5 Chiral Condensate Polyakov Loop Deconfinement and c S Restoration are entangled for any value of m 5 This is different from what is found at real chemical potential, see: M. Yahiro et al., arXiv:1104.2394 [hep-ph]

16. M APPING THE C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM M.R., arXiv:1103.6186 W5 M Chernodub and A. Nedelin, arXiv:1102.0188 [hep-ph] K. Fukushima, R. Gatto and M. R., Phys.Rev. D81 (2010) 114031 Qualitative agreement with previous studies

17. M APPING THE C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM M.R., arXiv:1103.6186 CP CP5 W5 W Evolution 2D projection CP5 is not an accident, but CP viewed by strongly interacting matter in W5. Its detection (?) can be interpreted as a signature of the real world CP.

18. M APPING THE C RITICAL E NDPOINT OF THE QCD P HASE D IAGRAM M.R., arXiv:1103.6186 P-NJL result Interesting theoretical question: How do the above ratios change when Nc is larger? CP CP5 W5 W Use the model to estimate: Evolution 2D projection

19. C ONCLUSIONS AND O UTLOOK Phase Structure of Quark Matter (QM) with m5 similar to that of QM of our Universe QM with m5 can be simulated on Lattice (no sign problem) Critical Endpoint (CP) of QCD is continued to a new Critical Endpoint, CP5 Detection of CP5, if found on the Lattice, can be interpreted as a signature of CP Mapping inhomogeneous phases Study the Nc dependence of the mapping coordinates Kamikado’s Poster

20. T HANK Y OU Non pentirti di ciò che hai fatto, se quando l'hai fato eri felice (Do not regret the things you did, if when you did them you were happy)