Fock space expansion of sigma meson in leading-N(c)

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Elsevier Science Bv
Google Scholar
Research Projects
Organizational Units
Journal Issue
We examine the leading-N(c) behavior of the masses and transition matrix elements of some low-lying, few particle configurations in QCD. A truncation of the Fock space produces an effective, symmetric Hamiltonian that we diagonalize. The lowest eigenvalue is identified as the sigma meson if the Hamiltonian is chosen to represent the scalar sector. As an application, the coefficients of the (c) powers are then fit to two-loop Unitarized SU(2) Chiral Perturbation Theory results for the sigma mass and width as a function of the number of colors, and we show that those results can be accommodated using the QCD N(c) dependence previously derived for matrix elements, without the need for unnatural parameters or fine tunings. Finally, we show a very preliminary good quality fit, estimating the proportion of tetraquark/molecule-like (dominant), q (q) over bar like (subdominant) and exotic-like (marginal) configurations in the sigma.
Copyright © 2010 Elsevier B.V. All rights reserved. We thank S. Narison for the invitation to the inspiring 2010 edition of this conference, and interesting discussions with R. Jaffe, J. A. Oller. Work supported by grants FPA2008-00592, FIS2008-01323, FIS2006-03438 (MICINN), U.Complutense/Banco Santander grant PR34/07-15875 BSCH and UCMBSCH GR58/08 910309 and the EU-Research Infrastructure Integrating Activity “Study of Strongly Interacting Matter” (HadronPhysics2, Grant 227431) under the EU 7th Framework Programme. High Energy Physics International Conference on Quantum Chromodynamics (15. 2010. Montpellier, Francia)
Unesco subjects
[1] M. H. Johnson and E. Teller, Phys. Rev. 98 (1955) 783. [2] R. Kaminski, G. Mennessier and S. Narison, Phys. Lett. B 680 (2009) 148 G. Mennessier, S. Narison and X. G. Wang, Phys. Lett. B 688 (2010) 59 [3] R. Garcia-Martin, R. Kaminski and J. R. Pelaez, Int. J. Mod. Phys. A 24 (2009) 590 F. J. Yndurain, R. Garcia-Martin and J. R. Pelaez, Phys. Rev. D 76 (2007) 074034 [4] I. Caprini, G. Colangelo and H. Leutwyler, Phys. Rev. Lett. 96 (2006) 132001 [5] A. H. Fariborz, R. Jora and J. Schechter, Phys. Rev. D 79 (2009) 074014 D. Black, Nucl. Phys. Proc. Suppl. 186 (2009) 275; E. van Beveren, D. V. Bugg, F. Kleefeld and G. Rupp, Phys. Lett. B 641 (2006) 265 [6] A. P. Szczepaniak and E. S. Swanson, Phys. Rev. D 65 (2002) 025012 [7] J. M. Torres-Rincon and F. J. Llanes-Estrada, Phys. Rev. Lett. 105 (2010) 022003 [8] M. G. Rocha, F. J. Llanes-Estrada, D. Schutte and S. V. Chavez, Eur. J. Phys. A 44 (2010) 411 [9] A. Dobado, M. J. Herrero and T. N. Truong, Phys. Lett. B 235 (1990) 134. [10] A. Dobado and J. R. Pelaez, Phys. Rev. D 56 (1997) 3057 [11] A. Gomez Nicola, J. R. Pelaez and G. Rios, Phys. Rev. D 77 (2008) 056006 [12] J. R. Pelaez, Phys. Rev. Lett. 92 (2004) 102001 [13] J. R. Pelaez and G. Rios, Phys. Rev. Lett. 97 (2006) 242002 [14] J. Gasser and H. Leutwyler, Nucl. Phys. B 250, 465 (1985). [15] S. Peris and E. de Rafael, Phys. Lett. B 348, 539 (1995). [16] J. R. de Elvira, J. R. Pelaez, M. R. Pennington and D. J.Wilson, arXiv:1001.2746 [hep-ph]. [17] H. Feshbach, Ann. Phys. 19, 287-313 (1962). [18] J. R. Pelaez, arXiv:hep-ph/0509284. J. R. Pelaez and G. Rios, arXiv:0905.4689 [hep-ph]. J. Nieves and E.. Ruiz Arriola, Phys. Rev. D 80 (2009) 045023. J. R. Pelaez, J. Nebreda and G. Rios, arXiv:1007.3461 [hep-ph]. [19] A. Hosaka, presentation at the workshop “QCD from the bound states perspective”, Trento, 2-6 Aug. 2010.