Publication: Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory
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2011-04-11
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Amer Physical Soc
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We calculate the pion-pion elastic scattering phase shifts for pion masses from the chiral limit to values of interest for lattice studies. At low energies, we use the standard Chiral Perturbation Theory expressions to one and two loops. In addition, we study the phase shifts' mass dependence in the resonance region by means of dispersion theory in the form of unitarized Chiral Perturbation Theory and the inverse amplitude method. We pay particular attention to the case when resonances are close to threshold, illustrating the different behavior between scalar and vector resonances. We also provide the estimation of uncertainties, which are dominated by those of the O[p^(6)] chiral parameters.
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©2011 American Physical Society.
We thank J. Dudek for lattice results and detailed explanations. Our work was partially supported by the Spanish Ministerio de Educación y Ciencia research Contract Nos.: FPA2007-29115-E, FPA2008-00592 and FIS2006-03438, and U. Complutense/Banco Santander Grant Nos. PR34/07-15875-BSCH and UCM-BSCH GR58/08 910309. 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 the European Union.
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[1] M. H. Johnson and E. Teller, Phys. Rev. 98, 783 (1955).
[2] K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010).
[3] G. Colangelo, J. Gasser, and H. Leutwyler, Phys. Rev. Lett. 86, 5008 (2001).
[4] C. W. Bernard et al., Phys. Rev. D 64, 054506 (2001).
[5] Ph. Boucaud et al. (ETM Collaboration), Phys. Lett. B 650, 304 (2007).
[6] C. Allton et al. (RBC and UKQCD Collaborations), Phys. Rev. D 76, 014504 (2007).
[7] C. R. Allton et al., Phys. Lett. B 628, 125 (2005).
[8] M. Gockeler et al. (QCDSF Collaboration), Proc. Sci., LAT2008 (2008) 136;J. Noaki et al., Proc. Sci., LAT2008 (2008) 107 [arXiv:0810.1360].
[9] S. R. Beane et al., Phys. Rev. D 77, 014505 (2008).
[10] X. Feng, K. Jansen, and D. B. Renner, Phys. Lett. B 684, 268 (2010).
[11] J. Bulava, K. J. Juge, C. J. Morningstar, M. J. Peardon, and C. H. Wong, Proc. Sci., LAT2009 (2009) 097 [arXiv:0911.2044]; C. Morningstar et al., in HADRON 2009: Proceedings of the XIII International Conference on Hadron Spectroscopy, edited by Volker Crede, Paul Eugenio, and A. Ostrovidov, AIP Conf. Proc. No. 1257 (AIP, New York, 2010).
[12] J. J. Dudek, R. G. Edwards, M. J. Peardon, D. G. Richards, and C. E. Thomas, arXiv:1011.6352.
[13] K. Sasaki and N. Ishizuka, Phys. Rev. D 78, 014511 (2008).
[14] J. Gasser and H. Leutwyler, Ann. Phys. (N.Y.) 158, 142 (1984).
[15] T. N. Truong, Phys. Rev. Lett. 61, 2526 (1988); 67, 2260 (1991); A. Dobado et al., Phys. Lett. B 235, 134 (1990).
[16] A. Dobado and J. R. Pela´ez, Phys. Rev. D 47, 4883 (1993); 56, 3057 (1997).
[17] A. Gomez Nicola, J. R. Pela´ez, and G. Rı´os, Phys. Rev. D 77, 056006 (2008).
[18] C. Hanhart, J. R. Pela´ez, and G. Rı´os, Phys. Rev. Lett. 100, 152001 (2008).
[19] J. F. Donoghue, Phys. Rev. C 74, 024002 (2006); T. Damour and J. F. Donoghue, Phys. Rev. D 78, 014014 (2008).
[20] J. Nebreda and J. R. Pela´ez, Phys. Rev. D 81, 054035 (2010).
[21] J. R. Peláez and G. Rı´os, Phys. Rev. D 82, 114002 (2010).
[22] P. C. Bruns and U.-G. Meißner, Eur. Phys. J. C 40, 97 (2005).
[23] S. Weinberg, Physica A (Amsterdam) 96, 327 (1979).
[24] G. Colangelo, J. Gasser, and H. Leutwyler, Nucl. Phys. B603, 125 (2001).
[25] G. Colangelo et al., arXiv:1011.4408.
[26] G. Colangelo and S. Durr, Eur. Phys. J. C 33, 543 (2004).
[27] J. Bijnens, G. Colangelo, G. Ecker, J. Gasser, and M. E. Sainio, Nucl. Phys.B508, 263 (1997); B517, 639(E) (1998).
[28] J. Bijnens, Prog. Part. Nucl. Phys. 58, 521 (2007).
[29] P. Buettiker, S. Descotes-Genon, and B. Moussallam, Eur. Phys. J. C 33, 409 (2004); S. Descotes-Genon and B. Moussallam, Eur. Phys. J. C 48, 553 (2006).
[30] G. Amoros, J. Bijnens, and P. Talavera, Nucl. Phys. B602, 87 (2001).
[31] L. Girlanda, M. Knecht, B. Moussallam, and J. Stern, Phys. Lett. B 409, 461 (1997).
[32] J. Gasser and U. G. Meissner, Phys. Lett. B 258, 219 (1991).
[33] G. Grayer et al., Nucl. Phys. B75, 189 (1974); L. Rosselet et al., Phys. Rev. D 15, 574 (1977); S. Pislak et al. (BNLE865 Collaboration), Phys. Rev. Lett. 87, 221801 (2001); J. R. Batley et al. (NA48/2 Collaboration), Eur. Phys. J. C 54, 411 (2008); W. Hoogland et al., Nucl. Phys. B126, 109 (1977); M. J. Losty et al., Nucl. Phys. B69, 185 (1974); N. B. Durusoy et al., Phys. Lett. B 45, 517 (1973); S. D. Protopopescu et al., Phys. Rev. D 7, 1279 (1973); P. Estabrooks and A. D. Martin, Nucl. Phys. B79, 301 (1974); B. Hyams et al., Nucl. Phys. B64, 134 (1973); D. H. Cohen et al., Phys. Rev. D 7, 661 (1973).
[34] R. Garcia-Martín, R. Kamiński, J. R. Peláez, J. R. de Elvira, and F. J. Ynduraín, Phys. Rev. D 83, 074004 (2011).
[35] J. Nebreda, G. Ríos, J. R. Peláez, and F. J. Ynduraín (work in progress).
[36] P. C. Bruns and U. G. Meissner, Eur. Phys. J. C 40, 97 (2005).
[37] G. Ecker, J. Gasser, H. Leutwyler, A. Pich, and E. de Rafael, Phys. Lett. B 223, 425 (1989).
[38] F. Von Hippel and C. Quigg, Phys. Rev. D 5, 624 (1972); H. Becker et al. (CERN-Munich Collaboration), Nucl. Phys. B150, 301 (1979); V. Chabaud et al. (CERNCracow-Munich Collaboration), Nucl. Phys. B223, 1 (1983); R. Kaminski, L. Lesniak, and K. Rybicki, Z. Phys. C 74 79 (1997); S. Kopp et al. (CLEO Collaboration), Phys. Rev. D 63, 092001 (2001).
[39] J. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics (Wiley, New York, 1952), p. 361.
[40] M. A. B. Beg and A. Zepeda, Phys. Rev. D 6, 2912 (1972).
[41] M. K. Volkov and V. N. Pervushin, Nuovo Cimento Soc. Ital. Fis. A 27, 277 (1975).
[42] J. Nieves, M. Pavon Valderrama, and E. Ruiz Arriola, Phys. Rev. D 65, 036002 (2002).
[43] A. Dobado and J. R. Pelaez, Phys. Rev. D 65, 077502 (2002).
[44] A. Gomez Nicola and J. R. Peláez, Phys. Rev. D 65, 054009 (2002); J. R. Peláez, Mod. Phys. Lett. A 19, 2879 (2004).
[45] J. R. Peláez, AIP Conf. Proc. 892, 72 (2007); H. Leutwyler, AIP Conf. Proc. 1030, 46 (2008).
[46] N. Levinson, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 25, 9 (1949); R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hilll, New York, 1966).