Marco Ruggieri 2011 4 21 QUARK MATTER WITH

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 QUARK MATTER WITH CHIRALITY IMBALANCE

CRITICAL ENDPOINT OF THE QCD PHASE DIAGRAM Sophie Bushwick, http: //www. bnl. gov/today/story. asp? ITEM_NO=1870

CRITICAL ENDPOINT OF THE QCD PHASE Asakawa and Yazaki, Nucl. Phys. A 504 (1989) 668 -684 DIAGRAM Critical Endpoint (CP) First order and crossover lines intersect at CP Sophie Bushwick, http: //www. bnl. gov/today/story. asp? ITEM_NO=1870

CRITICAL ENDPOINT OF THE QCD PHASE Asakawa and Yazaki, Nucl. Phys. A 504 (1989) 668 -684 DIAGRAM Critical Endpoint (CP) First order and crossover lines intersect at CP It might exist in QCD Sophie Bushwick, http: //www. bnl. gov/today/story. asp? ITEM_NO=1870 Fodor and Katz, JHEP 03(2002)014 For a review see de Forcrand in Po. S LAT 2009 (2009) 010

CRITICAL ENDPOINT OF THE QCD PHASE DIAGRAM Lattice Fodor and Katz, JHEP 03(2002)014 C. R. Allton et al. , Phys. Rev. D 71 (2005) 054508 Gavai and Gupta, Phys. Rev. D 78 (2008) 114503 De Forcrand Philipsen, Nucl. Phys. B 642 (2002) 290 P. De Forcrand et al. , ar. Xiv: 0911. 5682 S. Eijiri, Phys. Rev. D 78 (2008) 074507 A. Ohnishi et al. , Pos LAT 2010 (2010) 202 Model Calculations K. Fukushima et al. , Phys. Rev. D 80 (2009) 054012 Bowman and Kapusta, Phys. Rev. C 79 (2009) 015202 Zhang and Kunihiro, Phys. Rev. D 80 (2009) 290 Ueda’s Poster A. Ohnishi et al. , ar. Xiv: 1102. 3753 M. A. Stephanov, Po. S LAT 2006 (2006) 024 Abuki et al. , Phys. Rev. D 81 (2010) 125010 Basler and Buballa, Phys. Rev. D 82 (2010) 094004

CRITICAL ENDPOINT OF THE QCD PHASE Asakawa and Yazaki, Nucl. Phys. A 504 (1989) 668 -684 DIAGRAM 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 Sophie Bushwick, http: //www. bnl. gov/today/story. asp? ITEM_NO=1870 For a review see de Forcrand in Po. S LAT 2009 (2009) 010

M. R. , ar. Xiv: 1103. 6186 MAPPING THE CRITICAL ENDPOINT OF THE Baryon Chemical Potential QCD PHASE DIAGRAM conjugated to baryon density Chiral Chemical Potential conjugated to chiral density: N 5=n. R - n. L

M. R. , ar. Xiv: 1103. 6186 MAPPING THE CRITICAL ENDPOINT OF THE Baryon Chemical Potential QCD PHASE DIAGRAM conjugated to baryon density References Chiral Chemical Potential conjugated to chiral density: N 5=n. R - n. L In QGP context, to mimic chirality change induced by instantons and strong sphalerons in Quark-Gluon-Plasma: K. Fukushima et al, Phys. Rev. D 78 (2008) 074033 K. Fukushima, R. Gatto and M. R. , Phys. Rev. D 81 (2010) 114031 M Chernodub and A. Nedelin, ar. Xiv: 1102. 0188 [hep-ph]

M. R. , ar. Xiv: 1103. 6186 MAPPING THE CRITICAL ENDPOINT OF THE Baryon Chemical Potential QCD PHASE DIAGRAM conjugated to baryon density References Chiral Chemical Potential conjugated to chiral density: N 5=n. R - n. L In several non-QGP contexts: L. D. Mc. Lerran et al, Phys. Rev. D 43 (1991) 2027 Nielsen and Ninomiya, Phys. Lett. B 130 (1983) 389 A. N. Sisakian et al, hep-th/9806047 M. Joyce et al. , Phys. Rev. D 53 (1996) 2958

M. R. , ar. Xiv: 1103. 6186 MAPPING THE CRITICAL ENDPOINT OF THE Baryon Chemical Potential QCD PHASE DIAGRAM conjugated to baryon density Remark 1 Chiral Chemical Potential conjugated to chiral density: N 5=n. R - n. L Not affected by the sign problem, see for a nice explanation: K. Fukushima et al, Phys. Rev. D 78 (2008) 074033 Grand Canonical Ensembles with a chiral chemical potential can be simulated on the Lattice with Nc=3.

M. R. , ar. Xiv: 1103. 6186 MAPPING THE CRITICAL ENDPOINT OF THE Baryon Chemical Potential QCD PHASE DIAGRAM conjugated to baryon density Remark 1 Chiral Chemical Potential conjugated to chiral density: N 5=n. R - n. L Not affected by the sign problem, see for a nice explanation: K. Fukushima et al, Phys. Rev. D 78 (2008) 074033 Grand Canonical Ensembles with a chiral chemical potential can be simulated on the Lattice with Nc=3. Remark 2 We are aware that m 5 is not a true chemical potential: chiral condensate mixes L and R components, thus making N 5 a non-conserved quantity.

M. R. , ar. Xiv: 1103. 6186 MAPPING THE CRITICAL ENDPOINT OF THE Baryon Chemical Potential QCD PHASE DIAGRAM conjugated to baryon density I introduce two worlds: Chiral Chemical Potential conjugated to chiral density: N 5=n. R - n. L W 5: W: World with m=0 and finite m 5: World with m 5=0 and finite m: Find a Critical Endpoint: CP 5 continuation Find a Critical Endpoint: CP Possibility of continuation is proved in the article

M. R. , ar. Xiv: 1103. 6186 MAPPING CP N-J-L, Phys. Rev. 122: 345 -358, 1961. ) W 5 Polyakov Loop: collective field sensitive to confinement Phase Diagram obtained within the P-NJL model: K. Fukushima, Phys. Lett. B 591 (2004) 277 -284 W. Weise et al. , Phys. Rev. D 73 (2006) 014019 M. Yahiro et al. , Phys. Rev. D 82 (2010) 076003 See also: K. Kondo, Phys. Rev. D 82 (2010) 065024 M. Frasca, IJMPE 18 (2009) 693

M. R. , ar. Xiv: 1103. 6186 MAPPING THE CRITICAL ENDPOINT OF THE QCD PHASE DIAGRAM W 5 Capable to capture the Eo. S of full QCD at zero and imaginary chemical potential M. Yahiro et al. , ar. Xiv: 1104. 2394 [hep-ph]

M. R. , ar. Xiv: 1103. 6186 MAPPING THE CRITICAL ENDPOINT OF THE QCD PHASE DIAGRAM Chiral Condensate W 5 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. , ar. Xiv: 1104. 2394 [hep-ph]

M. R. , ar. Xiv: 1103. 6186 MAPPING THE CRITICAL ENDPOINT OF THE M Chernodub and A. Nedelin, QCD PHASE DIAGRAM ar. Xiv: 1102. 0188 [hep-ph] W 5 Qualitative agreement with previous studies K. Fukushima, R. Gatto and M. R. , Phys. Rev. D 81 (2010) 114031

M. R. , ar. Xiv: 1103. 6186 MAPPING THE CRITICAL ENDPOINT OF THE QCD PHASE DIAGRAM Evolution W 5 CP W CP 5 is not an accident, but CP viewed by strongly interacting matter in W 5. Its detection (? ) can be interpreted as a signature of the real world CP. 2 D projection

M. R. , ar. Xiv: 1103. 6186 MAPPING THE CRITICAL ENDPOINT OF THE QCD PHASE DIAGRAM Evolution W 5 CP W Use the model to estimate: P-NJL result Interesting theoretical question: How do the above ratios change when Nc is larger? 2 D projection

CONCLUSIONS AND OUTLOOK Phase Structure of Quark Matter (QM) with m 5 similar to that of QM of our Universe QM with m 5 can be simulated on Lattice (no sign problem) Critical Endpoint (CP) of QCD is continued to a new Critical Endpoint, CP 5 Detection of CP 5, if found on the Lattice, can be interpreted as a signature of CP Mapping inhomogeneous phases Kamikado’s Poster Study the Nc dependence of the mapping coordinates

THANK YOU 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)