A model for J/psi - kaon cross section

Abstract

We calculate the cross section for the dissociation of J/psi by kaons within the framework of a meson exchange model. We find that, depending on the values of the coupling constants used, the cross section can vary from 5 mb to 30 mb at <img id="_x0000_i1026" src="../../img/revistas/bjp/v34n1a/a11img03.gif" align=absbottom>~ 5 GeV.

A model for J/y - kaon cross section

R.S. Azevedo; M. Nielsen

Instituto de Física, Universidade de São Paulo, C.P. 66318, 05389-970 São Paulo, SP, Brazil

ABSTRACT

We calculate the cross section for the dissociation of J/y by kaons within the framework of a meson exchange model. We find that, depending on the values of the coupling constants used, the cross section can vary from 5 mb to 30 mb at ~ 5 GeV.

In relativistic heavy ion collisions J/y suppression has been recognized as an important tool to identify the possible phase transition to quark-gluon plasma (QGP) [1] (for a review of data and interpretations see refs. [2,3]). Since there is no direct experimental information on J/y absorption cross sections by hadrons, several theoretical approaches have been proposed to estimate their values. In order to elaborate a theoretical description of the phenomenon, we have first to choose the relevant degrees of freedom. Some approaches were based on charm quark-antiquark dipoles interacting with the gluons of a larger (hadron target) dipole [4-6] or quark exchange between two (hadronic) bags [7,8], or QCD sum rules [9-11], whereas other works used the meson exchange mechanism [12-17]. In this case it is not easy to decide in favor of quarks or hadrons because we are dealing with charm quark bound states, which are small and massive enough to make perturbation theory meaningful, but not small enough to make non-perturbative effects negligible [9-11,18].

The meson exchange approach was applied basically to J/y – p and J/y – r cross sections, with the only exception of ref. [13] where J/y – K cross section was also estimated. However, as pointed out in ref. [14], there are some inconsistencies in the Lagrangians defined in ref. [13]. In this work we will evaluate the J/y – K cross section using a meson-exchange model as in ref. [13], but we will treat the VVV and four-point couplings in the effective Lagrangians as in ref. [14].

As in refs. [13-16] we start with the SU(4) Lagrangian for the pseudo-scalar and vector mesons. The effective Lagrangians relevant for the study of the J/y absorption by kaons are:

where we have defined the charm meson and kaon iso-doublets D º (D⁰,D⁺), D^* º (D^*0,D^*+) and K º (K⁰,K⁺).

The processes we want to study for the absorption of J/y by kaons are:

The two processes in eqs.(9) and (10) have the same cross section. Therefore, in Fig. 1 we only show the diagrams for the first process in eqs. (9) and (10).

Defining the four-momentum of the kaon, the J/y, the vector and pseudo-scalar final-state mesons respectively by p₁, p₂, p₃ and p₄, the full amplitude for the first process Ky ® D_s, without isospin factors and before summing and averaging over external spins, is given by

with

where t = (p₁ – p₃)² and u = (p₁ – p₄)².

Similarly, the full amplitude for the second process Ky ® is given by

with

We can see that the differences between these two processes are basically due to the meson exchanged. It can be shown [14] that the full amplitudes (for i = 1,2) given above satisfy current conservation: p_2n = p_3l = 0.

After averaging (summing) over initial (final) spins and including isospin factors, the cross sections for these two processes are given by

with s = (p₁ + p₂)², and

is the squared three-momentum of initial-state mesons in the center-of-momentum (c.m.) frame.

To estimate the cross sections we have first to determine the coupling constants of our effective Lagrangians. Exact SU(4) symmetry would give the following relations among the coupling constants:

For yDD, yD_sD_s, yD^*D^* and y couplings we follow refs. [12,14] and make use of the vector meson dominance model (VDM). We get

Using the above SU(4) relations we get for the other coupling constants:

and = 50.55.

The solid line in Fig. 2 shows the total cross section of J/y dissociation by kaons as a function of the initial energy . The dot-dashed line includes the contribution for both KJ/y ® D_s and J/y ® D^*

_s, while the dotted line includes the contribution for both KJ/y ® and J/y ® D. In Fig. 2 we also show, for comparison, the cross section for the process pJ/y ® D^*+D (dashed line) using the same coupling constants as in ref. [14]. We see that, considering all allowed process for the J/y dissociation by kaons, we get a cross section bigger than the pion-J/y dissociation cross section.

If instead of using the VDM to determine the couplings, we follow ref. [13] and use the experimental value of the rpp coupling constant:

we get:

In this case we get a much smaller cross section, as can be seen by the solid line in Fig. 3, where we also show (dot-dashed line) the previous result.

As can be seen by Fig. 3, the result for the cross section can vary by almost one order of magnitude, even without considering form factors in the hadronic vertices [14,16]. This gives an idea of how important it is to have a good estimate of the value of the coupling constants. In a recent work [19], the J/y – p and J/y – r cross sections were evaluated by using form factors and coupling constants estimated using QCD sum rules [20,21,22,23]. The results show that with the appropriate form factors, the total cross section can even fall for values of bigger than 4.5 GeV. In a future work we will include from factors in the hadronic vertices as well as anomalous parity interactions [16].

In summary, we have studied the cross section of J/y dissociation by kaons in a meson-exchange model that includes pseudo-scalar-pseudo-scalar-vector-meson couplings, three-vector-meson couplings, and four-point couplings. We find that these cross sections are even bigger than the J/y – p ® D^* + D dissociation cross section, and have a very strong dependence with the values of the coupling constants in the hadronic vertices. Resulting cross sections can vary between 5 mb and 30 mb for ~ 5 GeV, depending on the values of the couplings. Since these couplings are not known experimentally, it is very important to have better estimates for them.

Acknowledgments

This work was supported by CNPq and FAPESP.

References

[1] T. Matsui and H. Satz, Phys. Lett. B178, 416 (1986).

[2] R. Vogt, Phys. Reports, 310, 197 (1999).

[3] C. Gerschel and J. Huefner, Ann. Rev. Nucl. Pat. Sci., 49, 255 (1999).

[4] G. Bhanot and M.E. Peskin, Nucl. Phys. B156, 391 (1979); M.E. Peskin, Nucl. Phys. B156, 365 (1979).

[5] D. Kharzeev and H. Satz, Phys. Lett. B334, 155 (1994).

[6] S.H. Lee and Y. Oh, J. Phys. G28, 1903 (2002); Y. Oh, S. Kim, and S.H. Lee, Phys. Rev. C65, 067901 (2002).

[7] C.-Y. Wong, E.S. Swanson, and T. Barnes, Phys. Rev. C62, 045201 (2000); C65, 014903 (2001).

[8] K. Martins, D. Blaschke, and E. Quack, Phys. Rev. C51, 2723 (1995).

[9] F.S. Navarra, M. Nielsen, R.S. Marques de Carvalho, and G. Krein, Phys. Lett. B529, 87 (2002).

[10] F.O. Durães, S.H. Lee, F.S. Navarra, and M. Nielsen, Phys. Lett. B564, 97 (2003).

[11] F.O. Durães, H. Kim, S.H. Lee, F.S. Navarra, and M. Nielsen, nucl-th/0211092.

[12] S.G. Matinyan and B. Müller, Phys. Rev. C58, 2994 (1998).

[13] K.L. Haglin, Phys. Rev. C61, 031902 (2000).

[14] Z. Lin and C.M. Ko, Phys. Rev. C62, 034903 (2000).

[15] K.L. Haglin and C. Gale, Phys. Rev. C63, 065201 (2001).

[16] Y. Oh, T. Song, and S.H. Lee, Phys. Rev. C63, 034901 (2001); Y. Oh, T. Song, S.H. Lee and C.-Y. Wong, ncl-th/0205065.

[17] F.S. Navarra, M. Nielsen, and M.R. Robilotta, Phys. Rev. C64, 021901 (R) (2001).

[18] H.G. Dosch, F.S. Navarra, M. Nielsen, and M. Rueter, Phys. Lett. B466, 363 (1999).

[19] K.L. Haglin and C. Gale, hep-ph/0305174.

[20] F.S. Navarra, M. Nielsen, M.E. Bracco, M. Chiapparini, and C.L. Schat, Phys. Lett. B489, 319 (2000).

[21] F.S. Navarra, M. Nielsen, and M.E. Bracco, Phys. Rev. D65, 037502 (2002).

[22] R.D. Matheus, F.S. Navarra, M. Nielsen, and R. Rodrigues da Silva, Phys. Lett. B541, 265 (2002).

[23] M.E. Bracco, M. Chiapparini, A. Lozea, F.S. Navarra, and M. Nielsen, Phys. Lett. B521, 1 (2001).

Received on 15 August , 2003.

Publication Dates

• Publication in this collection
  11 May 2004
• Date of issue
  Mar 2004

History

• Received
  15 Aug 2003
• Accepted
  15 Aug 2003