Abstract
We calculate several diagonal and non-diagonal fluctuations of conserved charges in a system of \(2+1+1\) quark flavors with physical masses, on a lattice with size \(48^3\times 12\). Higher order fluctuations at \(\mu _B=0\) are obtained as derivatives of the lower order ones, simulated at imaginary chemical potential. From these correlations and fluctuations we construct ratios of net-baryon number cumulants as functions of temperature and chemical potential, which satisfy the experimental conditions of strangeness neutrality and proton/baryon ratio. Our results qualitatively explain the behavior of the measured cumulant ratios by the STAR collaboration. We explain the obtained simulation results with a simple model, and find consistent behaviour with a scenario with no nearby critical end point in the QCD phase diagram.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Y. Aoki, G. Endrodi, Z. Fodor, S. Katz, K. Szabo, Nature 443, 675 (2006). https://doi.org/10.1038/nature05120
Y. Aoki, Z. Fodor, S. Katz, K. Szabo, Phys. Lett. B 643, 46 (2006). https://doi.org/10.1016/j.physletb.2006.10.021
Y. Aoki, S. Borsanyi, S. Durr, Z. Fodor, S.D. Katz et al., JHEP 0906, 088 (2009). https://doi.org/10.1088/1126-6708/2009/06/088
S. Borsanyi et al., JHEP 1009, 073 (2010). https://doi.org/10.1007/JHEP09(2010)073
T. Bhattacharya, M.I. Buchoff, N.H. Christ, H.T. Ding, R. Gupta et al., “QCD Phase Transition with Chiral Quarks and Physical Quark Masses,” Phys. Rev. Lett. 113(8), 082001 (2014). https://doi.org/10.1103/PhysRevLett.113.082001
A. Bazavov, T. Bhattacharya, M. Cheng, C. DeTar, H. Ding et al., Phys. Rev. D 85, 054503 (2012). https://doi.org/10.1103/PhysRevD.85.054503
C. Allton, S. Ejiri, S. Hands, O. Kaczmarek, F. Karsch et al., Phys. Rev. D 66, 074507 (2002). https://doi.org/10.1103/PhysRevD.66.074507
C. Allton, M. Doring, S. Ejiri, S. Hands, O. Kaczmarek et al., Phys. Rev. D 71, 054508 (2005). https://doi.org/10.1103/PhysRevD.71.054508
R.V. Gavai, S. Gupta, Phys. Rev. D 78, 114503 (2008). https://doi.org/10.1103/PhysRevD.78.114503
S. Basak et al., PoS LATTICE2008, 171 (2008)
O. Kaczmarek, F. Karsch, E. Laermann, C. Miao, S. Mukherjee et al., Phys. Rev. D 83, 014504 (2011). https://doi.org/10.1103/PhysRevD.83.014504
Z. Fodor, S. Katz, Phys. Lett. B 534, 87 (2002). https://doi.org/10.1016/S0370-2693(02)01583-6
P. de Forcrand, O. Philipsen, Nucl. Phys. B 642, 290 (2002). https://doi.org/10.1016/S0550-3213(02)00626-0
M. D’Elia, M.P. Lombardo, Phys. Rev. D 67, 014505 (2003). https://doi.org/10.1103/PhysRevD.67.014505
Z. Fodor, S. Katz, JHEP 0203, 014 (2002). https://doi.org/10.1088/1126-6708/2002/03/014
Z. Fodor, S. Katz, JHEP 0404, 050 (2004). https://doi.org/10.1088/1126-6708/2004/04/050
C. Bonati, M. D’Elia, F. Negro, F. Sanfilippo, K. Zambello, Phys. Rev. D 98(5), 054510 (2018). https://doi.org/10.1103/PhysRevD.98.054510
F. Karsch, Central Eur. J. Phys. 10, 1234 (2012). https://doi.org/10.2478/s11534-012-0074-3
A. Bazavov, H. Ding, P. Hegde, O. Kaczmarek, F. Karsch et al., Phys. Rev. Lett. 109, 192302 (2012). https://doi.org/10.1103/PhysRevLett.109.192302
S. Borsanyi, Z. Fodor, S. Katz, S. Krieg, C. Ratti et al., Phys. Rev. Lett. 111, 062005 (2013). https://doi.org/10.1103/PhysRevLett.111.062005
S. Borsanyi, Z. Fodor, S. Katz, S. Krieg, C. Ratti et al., Phys. Rev. Lett. 113, 052301 (2014). https://doi.org/10.1103/PhysRevLett.113.052301
C. Ratti, “Lattice QCD and heavy ion collisions: a review of recent progress,” Rept. Prog. Phys. 81(8), 084301 (2018). https://doi.org/10.1088/1361-6633/aabb97
A. Bazavov, et al., “Skewness and kurtosis of net baryon-number distributions at small values of the baryon chemical potential,” Phys. Rev. D. 96(7), 074510 (2017). https://doi.org/10.1103/PhysRevD.96.074510
M.A. Stephanov, K. Rajagopal, E.V. Shuryak, Phys. Rev. D 60, 114028 (1999). https://doi.org/10.1103/PhysRevD.60.114028
M. Cheng, N. Christ, S. Datta, J. van der Heide, C. Jung et al., Phys. Rev. D 77, 014511 (2008). https://doi.org/10.1103/PhysRevD.77.014511
J. Gunther, R. Bellwied, S. Borsanyi, Z. Fodor, S.D. Katz, A. Pasztor, C. Ratti, EPJ Web Conf. 137, 07008 (2017). https://doi.org/10.1051/epjconf/201713707008
M. D’Elia, G. Gagliardi, F. Sanfilippo, Phys. Rev. D 95(9), 094503 (2017). https://doi.org/10.1103/PhysRevD.95.094503
R. Bellwied, S. Borsanyi, Z. Fodor, S.D. Katz, A. Pasztor, C. Ratti, K.K. Szabo, Phys. Rev. D 92(11), 114505 (2015). https://doi.org/10.1103/PhysRevD.92.114505
A. Roberge, N. Weiss, Nucl. Phys. B 275, 734 (1986). https://doi.org/10.1016/0550-3213(86)90582-1
V. Vovchenko, A. Pasztor, Z. Fodor, S.D. Katz, H. Stoecker, Phys. Lett. B 775, 71 (2017). https://doi.org/10.1016/j.physletb.2017.10.042
J.I. Kapusta, C. Gale, Finite-Temperature Field Theory, 2nd edn. (Cambridge University Press, Cambridge, 2006). https://doi.org/10.1017/CBO9780511535130. Cambridge Books Online
A. Vuorinen, Phys. Rev. D 67, 074032 (2003). https://doi.org/10.1103/PhysRevD.67.074032
C. McNeile, C. Davies, E. Follana, K. Hornbostel, G. Lepage, Phys. Rev. D 82, 034512 (2010). https://doi.org/10.1103/PhysRevD.82.034512
H. Akaike, IEEE Trans. Autom. Control 19, 716 (1974)
B. Friman, F. Karsch, K. Redlich, V. Skokov, Eur. Phys. J. C71, 1694 (2011). https://doi.org/10.1140/epjc/s10052-011-1694-2
P. Cea, L. Cosmai, A. Papa, Phys. Rev. D 93(1), 014507 (2016). https://doi.org/10.1103/PhysRevD.93.014507
X. Luo, PoS CPOD2014, 019 (2014)
J. Thäder, “Higher Moments of Net-Particle Multiplicity Distributions,” Nucl. Phys. A. 956, 320 (2016). https://doi.org/10.1016/j.nuclphysa.2016.02.047
A. Andronic, P. Braun-Munzinger, J. Stachel, Nucl. Phys. A 772, 167 (2006). https://doi.org/10.1016/j.nuclphysa.2006.03.012
S. Borsanyi, Z. Fodor, J.N. Guenther, S.K. Katz, K.K. Szabo, A. Pasztor, I. Portillo, C. Ratti, JHEP 10, 205 (2018). https://doi.org/10.1007/JHEP10(2018)205
JUQUEEN: IBM Blue Gene/Q Supercomputer System at the Jülich Supercomputing Centre. Technical Report 1 A1, Jülich Supercomputing Centre (2015). https://doi.org/10.17815/jlsrf-1-18
Acknowledgements
This project was funded by the DFG grant SFB/TR55. This work was supported by the Hungarian National Research, Development and Innovation Office, NKFIH grants KKP126769 and K113034. An award of computer time was provided by the INCITE program. This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer JUQUEEN [41] at Jülich Supercomputing Centre (JSC) as well as on HAZELHEN at HLRS Stuttgart, Germany. This material is based upon work supported by the National Science Foundation under grants no. PHY-1654219 and OAC-1531814 and by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, within the framework of the Beam Energy Scan Theory (BEST) Topical Collaboration. C.R. also acknowledges the support from the Center of Advanced Computing and Data Systems at the University of Houston. Financial Support by the German Ministry of Research and Education (Grant 05P18PXFCA) is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Borsanyi, S. et al. (2019). The QCD Phase Diagram from the Lattice. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering ' 18. Springer, Cham. https://doi.org/10.1007/978-3-030-13325-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-13325-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-13324-5
Online ISBN: 978-3-030-13325-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)