Abstract
On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of S-wave and P-wave charmonium states. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving S- and Pwave mesons are taken into account. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy \( \sqrt s \) up to the second order. Relativistic corrections to the quark bound state wave functions in the rest frame are considered by means of the Breit-like potential. It turns out that the examined effects change essentially the nonrelativistic results of the cross section for the considered reactions at the center-of-mass energy \( \sqrt s \) = 10.6 GeV.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. Abe et al., Phys. Rev. D 70, 071102 (2004).
B. Aubert et al., Phys. Rev. D 72, 031101 (2005).
E. Braaten and J. Lee, Phys. Rev. D 67, 054007 (2003); Phys. Rev. D 72, 099901(E) (2005).
K.-Y. Liu, Z.-G. He, and K.-T. Chao, Phys. Lett. B 557, 45 (2003).
K. Hagiwara, E. Kou, and C.-F. Qiao, Phys. Lett. B 570, 39 (2003).
G. T. Bodwin, J. Lee, and E. Braaten, Phys. Rev. Lett. 90, 162001 (2003).
S. J. Brodsky, A. S. Goldhaber, and J. Lee, Phys. Rev. Lett. 91, 112001 (2003).
K.-Y. Liu, Z.-G. He, and K.-T. Chao, Phys. Rev. D 77, 014002 (2008).
J.P. Ma and Z.G. Si, Phys. Rev.D 70, 074007 (2004).
A. E. Bondar and V. L. Chernyak, Phys. Lett. B 612, 215 (2005).
V. V. Braguta, A. K. Likhoded, and A. V. Luchinsky, Phys. Rev. D 72, 074019 (2005).
Y.-J. Zhang, Y.-J. Gao, and K.-T. Chao, Phys. Rev. Lett. 96, 092001 (2006).
G. T. Bodwin, D. Kang, and J. Lee, Phys. Rev. D 74, 114028 (2006).
D. Ebert and A. P. Martynenko, Phys. Rev. D 74, 054008 (2006).
H.-M. Choi and Ch.-R. Ji, Phys. Rev. D 76, 094010 (2007).
Z.-G. He, Y. Fan, and K.-T. Chao, Phys. Rev. D 75, 074011 (2007).
A. V. Berezhnoy, Phys. At. Nucl. 71, 1803 (2008).
G. T. Bodwin, J. Lee, and Ch. Yu, Phys. Rev. D 77, 094018 (2008).
D. Ebert, R. N. Faustov, V. O. Galkin, and A. P. Martynenko, Phys. Lett. B 672, 264 (2009).
A. P. Martynenko, Phys. Rev. D 72, 074022 (2005).
D. Ebert, R. N. Faustov, V. O. Galkin, and A. P. Martynenko, Phys. Rev. D 70, 014018 (2004).
G. T. Bodwin and A. Petrelli, Phys. Rev.D 66, 094011 (2002).
S. J. Brodsky and J. R. Primack, Ann. Phys. (N.Y.) 52, 315 (1969).
R. N. Faustov, Ann. Phys. (N.Y.) 78, 176 (1973).
G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev. D 51, 1125 (1995).
J. H. Kuhn, J. Kaplan, and El J. O. Safiani, Nucl. Phys. B 157, 125 (1979).
J. A. M. Vermaseren, math-ph/0010025.
E. N. Elekina and A. P. Martynenko, Phys. Rev. D 81, 054006 (2010), arXiv: 0910.0394 [hep-ph].
N. Brambilla, A. Pineda, J. Soto, and A. Vairo, Rev. Mod. Phys. 77, 1423 (2005).
B. A. Kniehl, A. A. Penin, V. A. Smirnov, and M. Steinhauser, Nucl. Phys. B 635, 357 (2002).
K. Melnikov and A. Yelkhovsky, Phys. Rev. D 59, 114009 (1999).
P. Falkensteiner, H. Grosse, F. Schöberl, and P. Hertel, Comput. Phys. Commun. 34, 287 (1985).
V. V. Braguta, A. K. Likhoded, and A. V. Luchinsky, Phys. Lett. B 635, 299 (2006).
Y.-J. Zhang, Y.-Q. Ma, and K.-T. Chao, Phys. Rev. D 78, 054006 (2008).
D. Ebert, R. N. Faustov, and V. O. Galkin, Phys. Rev. D 67, 014027 (2003).
Author information
Authors and Affiliations
Corresponding author
Additional information
The text was submitted by the authors in English.
Rights and permissions
About this article
Cite this article
Elekina, E.N., Martynenko, A.P. Double S- and P-wave charmonium production in e + e − annihilation. Phys. Atom. Nuclei 74, 130–138 (2011). https://doi.org/10.1134/S1063778811010169
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063778811010169