Abstract
The description of the \( \eta\) and \( \eta^{{\prime}}_{}\) mesons in the Dyson-Schwinger approach has relied on the Witten-Veneziano relation. The present paper explores the consequences of using instead its generalization recently proposed by Shore. On the examples of three different model interactions, we find that irrespective of the concrete model dynamics, our Dyson-Schwinger approach is phenomenologically more successful in conjunction with the standard Witten-Veneziano relation than with the proposed generalization valid in all orders in the 1/N c expansion.
Similar content being viewed by others
References
For example, see refs. Alkofer:2000wg,Roberts:2000hi,Roberts:2000aa,Holl:2006ni,Fischer:2006ub for recent reviews and references on various applications of the DS approach.
R. Alkofer, L. von Smekal, Phys. Rep. 353, 281 (2001).
C.D. Roberts, arXiv:nucl-th/0007054.
C.D. Roberts, S.M. Schmidt, Prog. Part. Nucl. Phys. 45, S1 (2000).
A. Höll, C.D. Roberts, S.V. Wright, arXiv:nucl-th/0601071.
C.S. Fischer, J. Phys. G 32, R253 (2006).
D. Klabučar, D. Kekez, Phys. Rev. D 58, 096003 (1998).
D. Kekez, D. Klabučar, M.D. Scadron, J. Phys. G 26, 1335 (2000).
P. Jain, H.J. Munczek, Phys. Rev. D 48, 5403 (1993).
D. Kekez, D. Klabučar, Phys. Rev. D 73, 036002 (2006).
D. Kekez, D. Klabučar, Phys. Rev. D 71, 014004 (2005).
D. Horvatić, D. Blaschke, D. Klabučar, A.E. Radzhabov, Phys. Part. Nucl. 39, 1033 (2008).
D. Horvatić, D. Klabučar, A.E. Radzhabov, Phys. Rev. D 76, 096009 (2007)
D. Blaschke, G. Burau, Y.L. Kalinovsky, P. Maris, P.C. Tandy, Int. J. Mod. Phys. A 16, 2267 (2001).
D. Kekez, B. Bistrović, D. Klabučar, Int. J. Mod. Phys. A 14, 161 (1999).
B. Bistrović, D. Klabučar, Phys. Lett. B 478, 127 (2000)
R. Alkofer, C.D. Roberts, Phys. Lett. B 369, 101 (1996).
D. Kekez, D. Klabučar, Phys. Rev. D 65, 057901 (2002).
O. Lakhina, P. Bicudo, arXiv:0708.0984.
M.S. Bhagwat, L. Chang, Y.X. Liu, C.D. Roberts, P.C. Tandy, Phys. Rev. C 76, 045203 (2007).
E. Witten, Nucl. Phys. B 156, 269 (1979).
G. Veneziano, Nucl. Phys. B 159, 213 (1979).
G.M. Shore, Nucl. Phys. B 744, 34 (2006).
G.M. Shore, Lect. Notes Phys. 737, 235 (2008).
D. Blaschke, D. Horvatić, D. Klabučar, A.E. Radzhabov, hep-ph/0703188, in Proceedings of the Mini-Workshop Progress in Quark Models, Bled, Slovenia, 2006, edited by B. Golli, M. Rosina, S. Širca (DMFA - založništvo, Ljubljana, 2006) p. 20.
B. Alles, M. D’Elia, A. Di Giacomo, Nucl. Phys. B 494, 281 (1997).
D. Blaschke, H.P. Pavel, V.N. Pervushin, G. Ropke, M.K. Volkov, Phys. Lett. B 397, 129 (1997).
Th. Feldmann, Int. J. Mod. Phys. A 15, 159 (2000).
Th. Feldmann, P. Kroll, B. Stech, Phys. Rev. D 58, 114006 (1998).
B. Lucini, M. Teper, U. Wenger, Nucl. Phys. B 715, 461 (2005).
L. Del Debbio, L. Giusti, C. Pica, Phys. Rev. Lett. 94, 032003 (2005).
B. Alles, M. D’Elia, A. Di Giacomo, Phys. Rev. D 71, 034503 (2005).
J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985).
H. Leutwyler, Nucl. Phys. Proc. Suppl. 64, 223 (1998).
R. Kaiser, H. Leutwyler, hep-ph/9806336, in Proceedings of the Workshop Nonperturbative Methods in Quantum Field Theory, Adelaide, Australia, 1998, edited by A.W. Schreiber, A.G. Williams, A.W. Thomas (World Scientific, Singapore, 1998).
J. Schechter, A. Subbaraman, H. Weigel, Phys. Rev. D 48, 339 (1993).
Th. Feldmann, P. Kroll, B. Stech, Phys. Lett. B 449, 339 (1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
V. Vento
Rights and permissions
About this article
Cite this article
Horvatić, D., Blaschke, D., Kalinovsky, Y. et al. \( \eta\) and \( \eta{^\prime}\) mesons in the Dyson-Schwinger approach using a generalization of the Witten-Veneziano relation. Eur. Phys. J. A 38, 257–264 (2008). https://doi.org/10.1140/epja/i2008-10670-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epja/i2008-10670-x