Determination of SU(2) chiral perturbation theory low energy constants from a precise description of pion-pion scattering threshold parameters
| dc.contributor.author | Nebreda Manjón, Jenifer | |
| dc.contributor.author | Peláez Sagredo, José Ramón | |
| dc.contributor.author | Ríos, G. | |
| dc.date.accessioned | 2023-06-19T14:57:13Z | |
| dc.date.available | 2023-06-19T14:57:13Z | |
| dc.date.issued | 2013-09-03 | |
| dc.description | ©2013 American Physical Society. J. R. P. thanks the late F. J. Ynduráin for many discussions about the possibility to carry out this project after completing [13]. J. Nebreda acknowledges funding by the German Academic Exchange Service (DAAD) and the Fundación Ramón Areces. G. R. acknowledges partial support by the EU Integrated Infrastructure Initiative HadronPhysics3 Project under Grant No. 283286 and by DFG (CRC 16, ‘‘Subnuclear Structure of Matter’’ and CRC 110, ‘‘Symmetries and the Emergence of Structure in QCD’’). We also thank B. Kubis and U.-G. Meißner for their reading of the manuscript and their valuable suggestions and corrections, Z. H. Guo and H. Q. Zheng for clarifying the use of their axiomatic bounds, and B. Ananthanarayan for kindly helping us with the existing sum rules for c parameters. This work is partly supported by DGICYT Contracts No. FPA2011-27853-C02-02 and No. FPA2010-17806, and the EU Integrated Infrastructure Initiative Hadron Physics Project under Contract No. RII3-CT-2004-506078. | |
| dc.description.abstract | We determine the values of the one- and two-loop low energy constants appearing in the SU(2) Chiral Perturbation Theory calculation of pion-pion scattering. For this we use a recent and precise sum rule determination of some scattering lengths and slopes that appear in the effective range expansion. In addition we provide sum rules for these coefficients up to third order in the expansion. Our results when using only the scattering lengths and slopes of the S, P, D, and F waves are consistent with previous determinations but seem to require higher order contributions if they are to accommodate the third order coefficients of the effective range expansion. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Unión Europea. FP7 | |
| dc.description.sponsorship | Ministerio de Economía y Competitividad (MINECO) | |
| dc.description.sponsorship | German Academic Exchange Service (DAAD) | |
| dc.description.sponsorship | Fundación Ramón Areces | |
| dc.description.sponsorship | DFG (CRC 16 and CRC 110) | |
| dc.description.sponsorship | DGICYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/33867 | |
| dc.identifier.doi | 10.1103/PhysRevD.88.054001 | |
| dc.identifier.issn | 1550-7998 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1103/PhysRevD.88.054001 | |
| dc.identifier.relatedurl | http://journals.aps.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/34933 | |
| dc.issue.number | 5 | |
| dc.journal.title | Physical review D | |
| dc.language.iso | eng | |
| dc.publisher | Amer Physical Soc | |
| dc.relation.projectID | HADRONPHYSICS (283286) | |
| dc.relation.projectID | FPA2011-27853-C02-02 | |
| dc.relation.projectID | FPA2010-17806 | |
| dc.relation.projectID | Hadron Physics Project (RII3-CT-2004-506078) | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Isospin breaking | |
| dc.subject.keyword | Partial waves | |
| dc.subject.keyword | Form-factors | |
| dc.subject.keyword | Sum-rules | |
| dc.subject.keyword | Constraints | |
| dc.subject.keyword | Amplitudes | |
| dc.subject.keyword | Qcd | |
| dc.subject.keyword | Lagrangians | |
| dc.subject.keyword | Equation | |
| dc.subject.keyword | Symmetry | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Determination of SU(2) chiral perturbation theory low energy constants from a precise description of pion-pion scattering threshold parameters | |
| dc.type | journal article | |
| dc.volume.number | 88 | |
| dcterms.references | [1] S. Weinberg, Physica (Amsterdam) 96A, 327 (1979). [2] J. Gasser and H. Leutwyler, Ann. Phys. (N.Y.) 158, 142 (1984). [3] M. Knecht, B. Moussallam, J. Stern, and N. H. Fuchs, Nucl. Phys. B457, 513 (1995). [4] J. Bijnens, G. Colangelo, G. Ecker, J. Gasser, and M. E. Sainio, Phys. Lett. B 374, 210 (1996); Nucl. Phys. B508, 263 (1997); B517, 639(E) (1998). [5] G. Colangelo, S. Durr, A. Juttner, L. Lellouch, H. Leutwyler, V. Lubicz, S. Necco, C. T. Sachrajda et al., Eur. Phys. J. C 71, 1695 (2011). [6] D. Espriu, E. de Rafael, and J. Taron, Nucl. Phys. B345, 22 (1990); F. J. Llanes-Estrada and P. de A. Bicudo, Phys. Rev. D 68, 094014 (2003). [7] G. Ecker, J. Gasser, A. Pich, and E. de Rafael, Nucl. Phys. B321, 311 (1989); J. F. Donoghue, C. Ramirez, and G. Valencia, Phys. Rev. D 39, 1947 (1989). [8] J. Gasser and H. Leutwyler, Nucl. Phys. B250, 465 (1985). [9] G. Amoros, J. Bijnens, and P. Talavera, Nucl. Phys. B585, 293 (2000); B598, 665(E) (2001). [10] C. Riggenbach, J. Gasser, J. F. Donoghue, and B. R. Holstein, Phys. Rev. D 43, 127 (1991). [11] G. Colangelo, J. Gasser, and H. Leutwyler, Nucl. Phys. B603, 125 (2001). [12] J. Bijnens and I. Jemos, Nucl. Phys. B854, 631 (2012). [13] R. Garcia-Martin, R. Kaminski, J. R. Pelaez, J. Ruiz de Elvira, and F. J. Yndurain, Phys. Rev. D 83, 074004 (2011). [14] J. R. Batley et al. (NA48-2 Collaboration), Eur. Phys. J. C 70, 635 (2010). [15] S. R. Beane, E. Chang, W. Detmold, H. W. Lin, T. C. Luu, K. Orginos, A. Parreño, M. J. Savage, A. Torok, and A. Walker-Loud (NPLQCD Collaboration), Phys. Rev. D 85, 034505 (2012). [16] G. Wanders, Helv. Phys. Acta 39, 228 (1966). [17] M. G. Olsson, Phys. Rev. 162, 1338 (1967). [18] J. L. Basdevant, J. C. Le Guillou, and H. Navelet, Nuovo Cimento Soc. Ital. Fis. 7A, 363 (1972). [19] B. Ananthanarayan, D. Toublan, and G. Wanders, Phys. Rev. D 53, 2362 (1996). [20] B. Ananthanarayan and P. Buttiker, Phys. Rev. D 54, 1125 (1996). [21] B. Ananthanarayan and P. Buettiker, Phys. Lett. B 415, 402 (1997). [22] G. Wanders, Helv. Phys. Acta 70, 287 (1997). [23] G. Wanders, Phys. Rev. D 56, 4328 (1997). [24] B. Ananthanarayan, G. Colangelo, J. Gasser, and H. Leutwyler, Phys. Rep. 353, 207 (2001). [25] B. Ananthanarayan and P. Buettiker, Eur. Phys. J. C 19, 517 (2001). [26] F. P. Palou and F. J. Yndurain, Nuovo Cimento Soc. Ital. Fis. 19A, 245 (1974). [27] F. J. Yndurain, arXiv:hep-ph/0212282. [28] R. Froissart, in Proceedings of the La Jolla Conference on Elementary Particles, 1961 (unpublished); V. N. Gribov, Zh. Eksp. Teor. Fiz. 41, 1962 (1961) [Sov. Phys. JETP 14, 1395 (1962)]. [29] F. J. Yndurain, Rev. Mod. Phys. 44, 645 (1972). [30] B. Ananthanarayan, D. Toublan, and G. Wanders, Phys. Rev. D 51, 1093 (1995); A. V. Manohar and V. Mateu, Phys. Rev. D 77, 094019 (2008); V. Mateu, Phys. Rev. D 77, 094020 (2008). [31] P. Dita, Phys. Rev. D 59, 094007 (1999). [32] Z.-H. Guo, O. Zhang, and H. Q. Zheng, AIP Conf. Proc. 1343, 259 (2011). [33] S. M. Roy, Phys. Lett. 36B, 353 (1971). [34] G. Mahoux, S. M. Roy, and G. Wanders, Nucl. Phys. B70, 297 (1974). [35] J. R. Pelaez and F. J. Yndurain, Phys. Rev. D 69, 114001 (2004). [36] I. Caprini, G. Colangelo, and H. Leutwyler, Eur. Phys. J. C 72, 1860 (2012). [37] R. Kaminski, J. R. Pelaez, and F. J. Yndurain, Phys. Rev. D 77, 054015 (2008). [38] J. R. Pelaez and F. J. Yndurain, Phys. Rev. D 71, 074016 (2005). [39] J. Gasser, Proc. Sci., KAON (2008) 033 [arXiv:0710.3048]; G. Colangelo, J. Gasser, and A. Rusetsky, Eur. Phys. J. C 59, 777 (2008). [40] V. Cuplov and A. Nehme, arXiv:hep-ph/0311274; A. Nehme, Eur. Phys. J. C 40, 367 (2005); Phys. Rev. D 69, 094012 (2004). [41] M. Knecht and R. Urech, Nucl. Phys. B519, 329 (1998); S. Descotes-Genon and M. Knecht, Eur. Phys. J. C 72, 1962 (2012). [42] We have weighted each fit by the square of its X^2/d:o:f., whereas the uncertainty is obtained by adding in quadrature the averaged statistical uncertainty to the maximum difference between the resulting central value and the central value of each fit. [43] A. Bazavov et al. (MILC Collaboration), Proc. Sci., CD09 (2009) 007 [arXiv:0910.2966]. [44] A. Bazavov, C. Bernard, C. DeTar, X. Du, W. Freeman, S. Gottlieb, U. M. Heller, J. E. Hetrick et al., Proc. Sci., LATTICE2010 (2010) 083 [arXiv:1011.1792]. [45] Y. Aoki et al. (RBC and UKQCD Collaborations), Phys. Rev. D 83, 074508 (2011). [46] H. Fukaya, S. Aoki, S. Hashimoto, T. Kaneko, J. Noaki, T. Onogi, and N. Yamada (JLQCD Collaboration), Phys. Rev. Lett. 104, 122002 (2010); 105, 159901(E) (2010). [47] For the constraints obtained within SU(3) ChPT we have used the conversion between SU(3) and SU(2) LECs given in [8]. [48] We give the fit results in terms of r~_i defined as r~_i =(4π)^4 r_i, which have a size of order one. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 70900239-cb8b-49f3-931f-9dc6a8b7d8d5 | |
| relation.isAuthorOfPublication.latestForDiscovery | 70900239-cb8b-49f3-931f-9dc6a8b7d8d5 |
Download
Original bundle
1 - 1 of 1
