Scalar susceptibilities and four-quark condensates in the meson gas within chiral perturbation theory

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We analyze the properties of four-quark condensates and scalar susceptibilities in the meson gas, within finite temperature chiral perturbation theory (ChPT). The breaking of the factorization hypothesis does not allow for a finite four-quark condensate and its use as an order parameter, except in the chiral limit. This is rigorously obtained within ChPT and is therefore a model-independent result. Factorization only holds formally in the large N-c limit and breaks up at finite temperature even in the chiral limit. Nevertheless, the factorization breaking terms are precisely those needed to yield a finite scalar susceptibility, deeply connected to chiral symmetry restoration. Actually, we provide the full result for the SU(3) quark condensate to next-to-next-to- leading order in ChPT, thus extending previous results to include kaon and eta interactions. This allows us to check the effect of those corrections compared to previous approaches and the uncertainties due to low-energy constants. We provide a detailed analysis of scalar susceptibilities in the SU(3) meson gas, including a comparison between the pure ChPT approach and the virial expansion, where the unitarization of pion scattering is crucial to achieve a more reliable prediction. Through the analysis of the interactions within this approach, we have found that the role of the sigma resonance is largely canceled with the scalar isospin two-channel interaction, leaving the rho(770) as the main contribution. Special attention is paid to the evolution towards chiral restoration, as well as to the comparison with recent lattice analysis. DOI: 10.1103/PhysRevD.87.016001
© 2013 American Physical Society. This work was partially supported by the Spanish Research Contracts No. FIS2008- 01323 and No. FPA201127853-C02-02. We acknowledge the support of the European Community-Research Infrastructure Integrating Activity "Study of Strongly Interacting Matter'' (acronym HadronPhysics2, Grant Agreement No. 227431) under the Seventh Framework Programme of EU.
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[1] R. D. Pisarski and F. Wilczek, Phys. Rev. D 29, 338 (1984). [2] C. Bernard, T. Burch, C. DeTar, J. Osborn, S. Gottlieb, E. Gregory, D. Toussaint, U. Heller, and R. Sugar (MILC Collaboration), Phys. Rev. D 71, 034504 (2005). [3] Y. Aoki, Z. Fodor, S. D. Katz, and K. K. Szabo, Phys. Lett. B 643, 46 (2006). [4] Y. Aoki, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, Nature (London) 443, 675 (2006). [5] M. Cheng et al., Phys. Rev. D 81, 054504 (2010). [6] Y. Aoki, S. Borsanyi, S. Durr, Z. Fodor, S. D. Katz, S. Krieg, and K. K. Szabo, J. High Energy Phys. 06 (2009) 088. [7] S. Ejiri, F. Karsch, E. Laermann, C. Miao, S. Mukherjee, P. Petreczky, C. Schmidt, W. Soeldner, and W. Unger, Phys. Rev. D 80, 094505 (2009). [8] S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo (Wuppertal-Budapest Collaboration), J. High Energy Phys. 09 (2010) 073. [9] F. Karsch, K. Redlich, and A. Tawfik, Eur. Phys. J. C 29, 549 (2003). [10] P. Huovinen and P. Petreczky, Nucl. Phys. A837, 26 (2010). [11] A. Andronic, P. Braun-Munzinger, and J. Stachel, Nucl. Phys. A772, 167 (2006). [12] A. Andronic, P. Braun-Munzinger, and J. Stachel, Phys. Lett. B 673, 142 (2009); 678, 516(E) (2009). [13] A. Andronic, P. Braun-Munzinger, J. Stachel, and M. Winn, Phys. Lett. B 718, 80 (2012). [14] S. Weinberg, Physica (Amsterdam) 96, 327 (1979). [15] J. Gasser and H. Leutwyler, Ann. Phys. (N.Y.) 158, 142 (1984). [16] J. Gasser and H. Leutwyler, Nucl. Phys. B250, 465 (1985). [17] J. Gasser and H. Leutwyler, Phys. Lett. B 184, 83 (1987). [18] P. Gerber and H. Leutwyler, Nucl. Phys. B321, 387 (1989). [19] T. N. Truong, Phys. Rev. Lett. 61, 2526 (1988); A. Dobado, M. J. Herrero, and T. N. Truong, Phys. Lett. B 235, 134 (1990). [20] A. Dobado and J. R. Pelaez, Phys. Rev. D 47, 4883 (1993); 56, 3057 (1997). [21] A. Gomez Nicola, J. R. Pelaez, and G. Rios, Phys. Rev. D 77, 056006 (2008). [22] A. Dobado, A. Gómez Nicola, F. J. Llanes-Estrada, and J. R. Pelaez, Phys. Rev. C 66, 055201 (2002). [23] D. Fernandez-Fraile, A. Gomez Nicola, and E. T. Herruzo, Phys. Rev. D 76, 085020 (2007). [24] D. Cabrera, D. Fernández-Fraile, and A. Gómez Nicola, Eur. Phys. J. C 61, 879 (2009). [25] D. Fernández-Fraile and A. Gómez Nicola, Eur. Phys. J. C 62, 37 (2009). [26] R. Dashen, S.-K. Ma, and H. J. Bernstein, Phys. Rev. 187, 345 (1969). [27] G. M. Welke, R. Venugopalan, and M. Prakash, Phys. Lett. B 245, 137 (1990); V. L. Eletsky, J. I. Kapusta, and R. Venugopalan, Phys. Rev. D 48, 4398 (1993). [28] A. Nyffeler, Z. Phys. C 60, 159 (1993). [29] A. Dobado and J. R. Pelaez, Phys. Rev. D 59, 034004 (1998). [30] R. Venugopalan and M. Prakash, Nucl. Phys. A546, 718 (1992). [31] J. R. Pelaez, Phys. Rev. D 66, 096007 (2002). [32] A. Gómez Nicola, J. R. Peláez, and J. Ruiz de Elvira, Phys. Rev. D 82, 074012 (2010). [33] C. Hanhart, J. R. Pelaez, and G. Rios, Phys. Rev. Lett. 100, 152001 (2008); J. R. Pelaez and G. Rios, Phys. Rev. D 82, 114002 (2010). [34] J. Nebreda and J. R. Pelaez, Phys. Rev. D 81, 054035 (2010). [35] J. Nebreda, J. R. Pelaez, and G. Rios, Phys. Rev. D 83, 094011 (2011). [36] J. Bijnens, G. Colangelo, and G. Ecker, J. High Energy Phys. 02 (1999) 020. [37] M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B147, 385 (1979). [38] S. Narison and R. Tarrach, Phys. Lett. 125B, 217 (1983). [39] C. A. Domínguez and K. Schilcher, J. High Energy Phys. 01 (2007) 093. [40] G. Leibbrandt, Rev. Mod. Phys. 47, 849 (1975). [41] V. L. Eletsky, Phys. Lett. B 299, 111 (1993). [42] S. Leupold, Phys. Lett. B 616, 203 (2005). [43] S. Leupold, J. Phys. G 32, 2199 (2006). [44] M. B. Johnson and L. S. Kisslinger, Phys. Rev. D 61, 074014 (2000). [45] A. V. Smilga and J. J. M. Verbaarschot, Phys. Rev. D 54, 1087 (1996). [46] A. Gomez Nicola and R. Torres Andres, Phys. Rev. D 83, 076005 (2011). [47] G. Amorós, J. Bijnens, and P. Talavera, Nucl. Phys. B602, 87 (2001). [48] G. Ecker, J. Gasser, A. Pich, and E. de Rafael, Nucl. Phys. B321, 311 (1989). [49] J. Bijnens and I. Jemos, Nucl. Phys. B854, 631 (2012). [50] J. Bordes, C. A. Domínguez, P. Moodley, J. Penarrocha, and K. Schilcher, J. High Energy Phys. 10 (2012) 102. [51] R. Garcia Martin and J. R. Pelaez, Phys. Rev. D 74, 096003 (2006). [52] G. Chanfray, M. Ericson, and J. Wambach, Phys. Lett. B 388, 673 (1996). [53] G. Colangelo, J. Gasser, and H. Leutwyler, Nucl. Phys. B603, 125 (2001). [54] R. García-Martin, R. Kaminski, J. R. Peláez, J. Ruiz de Elvira, and F. J. Yndurain, Phys. Rev. D 83, 074004 (2011). [55] A. Gómez Nicola and J. R. Peláez, Phys. Rev. D 65, 054009 (2002). [56] J. Bijnens and K. Ghorbani, Phys. Lett. B 636, 51 (2006).