Direct Photon Production in Proton-Nucleus and Nucleus-Nucleus Collisions

Direct Photon Production in Proton-Nucleus and Nucleus-Nucleus Collisions

J. Cepila J. Nemchik Czech Technical University in Prague, FNSPE, Břehová 7, 11519 Prague, Czech Republic Institute of Experimental Physics SAS, Watsonova 47, 04001 Košice, Slovakia

Prompt photons produced in a hard reaction are not accompanied with any final state interaction, either energy loss or absorption. Therefore, besides the Cronin enhancement at medium transverse momenta and small isotopic corrections at larger , one should not expect any nuclear effects. However, data from PHENIX experiment exhibits a significant large- suppression in central and collisions that cannot be accompanied by coherent phenomena. We demonstrate that such an unexpected result is subject to the energy sharing problem near the kinematic limit and is universally induced by multiple initial state interactions. We describe production of photons in the color dipole approach and find a good agreement with available data in collisions. Besides explanation of large- nuclear suppression at RHIC we present for the first time predictions for expected nuclear effects also in the LHC energy range at different rapidities. We include and analyze also a contribution of gluon shadowing as a leading twist shadowing correction modifying nuclear effects at small and medium .

direct photons, nuclear suppression, gluon shadowing
13.85.Qk, 24.85.+p, 25.75.-q, 25.75.Cj

If a particle with mass and transverse momentum is produced in a hard reaction then the corresponding values of Bjorken variable in the beam and the target are . Thus, forward rapidity region allows to study already at RHIC coherence phenomena (shadowing), which are expected to suppress particle yields.

Observed suppression at large at RHIC [1] should be interpreted carefully. Similar suppression is observed for any reaction studied so far at any energy. Namely, all fixed target experiments have too low energy for the onset of coherence effects. The rise of suppression with shows the same pattern as observed at RHIC.

This universality of suppression favors another mechanism which was proposed in [2] and is based on energy conservation effects in initial state parton rescatterings. As a result the effective projectile parton distribution correlates with the nuclear target [2, 3] and can be expressed in term of the suppression factor, [2],


where is the nuclear thickness function defined at impact parameter , mb [2] and the normalization factor is fixed by the Gottfried sum rule.

In this paper we study a production of direct photons on nuclear targets. Photons produced in a hard reaction have no final state interactions and so no nuclear effects are expected at large . However, we show that large- photons are universally suppressed by energy deficit in multiple interactions Eq. (1) since the kinematic limit can be approached increasing at fixed . We study also a rise of this suppression with in the RHIC and LHC kinematic regions.


The process of direct photon production in the target rest frame can be treated as radiation of a real photon by a projectile quark. The distribution of photon bremsstrahlung in quark-nucleon interactions reads [4]:


where , and the light-cone (LC) wave functions of the projectile fluctuation are presented in [4]. Feynman variable is given as and in the target rest frame . For the dipole cross section in Eq. (2) we used GBW [5] parametrization. The hadron cross section is given convolving the parton cross section, Eq. (2), with the corresponding parton distribution functions (PDFs) and [4],


where is the fractional quark charge, PDFs and are used with the lowest order parametrization from [6] at the scale .

Assuming production of direct photons on nuclear targets the onset of coherence effets is controlled by the coherence length, , where and is the energy and mass of the projectile quark. The fraction of the proton momentum carried by the quark is related to as .

The condition for the onset of shadowing is a long coherence length (LCL), , where is the nuclear radius. Then the color dipole approach allows to incorporate shadowing effects via a simple eikonalization of [7], i.e. replacing in Eq. (2) by . This LCL limit can be safely used in calculations of nuclear effects in the RHIC and LHC energy regions especially at forward rapidities. Here higher Fock components containing gluons lead to additional corrections, called gluon shadowing (GS). The corresponding suppression factor [8] was included in calculations replacing by in the above expression for .

Figure 1: (Left) Invariant cross section for direct photon production in collisions at as a function of vs. data from PHENIX experiment [9]. (Right) Ratio of the cross sections in to collisions at  GeV vs. preliminary data from PHENIX experiment [10].
Figure 2: Ratio of the cross sections in to collisions at  GeV and at different fixed values of 0, 1, 2 and 3. Dotted lines represent calculations without corrections for energy conservation and GS. Dashed lines additionally include corrections for energy deficit Eq. (1) and solid lines also GS.

We start with production of direct photons in collisions. The left panel of Fig. 1 shows model calculations based on Eq. (3) using GRV98 PDFs [6] and demonstrates so a reasonable agreement with data from PHENIX experiment [9]. Another test of the model is a comparison with PHENIX data [10] obtained in collisions as is depicted in the right panel of Fig. 1. Besides isotopic effects giving a value at large , we predict also an additional suppression coming from corrections for energy conservation Eq. (1).

Since one can approach the kinematic limit increasing we present predictions for nuclear effects at several fixed as dependence of the nuclear modification factor at RHIC energy depicted in Fig. 2 and at LHC energy depicted in Fig. 3. All these Figs. clearly demonstrate a dominance of GS at small and medium and energy conservation effects Eq. (1) at large . Both effects rise rapidly with . Note that unexpected large- suppression violating so QCD factorization can be tested in the future by the new data from RHIC and LHC experiments especially at forward rapidities.

Figure 3: The same as Fig. 2 but for the ratio at  TeV and at fixed 0, 2, 3 & 4.

The same mechanism allows to explain also large- suppression of photons produced in collisions at the energies 200 and 62 GeV in accordance with data from PHENIX experiment [11]. Corresponding results can be found in [3]. Large error bars of the data do not allow to provide a definite confirmation for the predicted suppression.


Using the color dipole approach we study production of direct photons in collisions on nuclear targets. We demonstrate that at fixed rapidities effects of coherence (GS) dominate at small and medium whereas corrections for energy conservation Eq. (1) are important at larger . Both effects cause a suppression and rise rapidly with rapidity.

First we test this approach in the RHIC kinematic region demonstrating a good agreement with PHENIX data in and collisons at mid rapidities (see Fig. 1).

Then we present predictions for behavior of nuclear effects at different fixed rapidities in the RHIC and LHC kinematic regions. Since photons have no final state interactions, no suppression is expected at large . However, we specify for the first time the kinematic regions at RHIC and LHC where one can expect and study in the future a rather strong -suppression, which is caused by energy sharing problem Eq. (1).

The same mechanism explains well also a strong suppression at large observed in collisions at RHIC in accordance with data from PHENIX experiment.

This work was supported by the Slovak Funding Agency, Grant 2/0092/10 and by Grants VZ MŠMT 6840770039 and LC 07048 (Ministry of Education of the Czech Rep.).


  • [1] I. Arsene et al., [BRAHMS Collaboration], Phys. Rev. Lett. 93, 242303 (2004); Hongyan Yang et al., J. Phys. G34, S619 (2007).
  • [2] B.Z. Kopeliovich et al., Phys. Rev. C72, 054606 (2005); J. Nemchik et al., Phys. Rev. C78, 025213 (2008).
  • [3] B.Z. Kopeliovich and J. Nemchik, J. Phys. G38, 043101 (2011); arXiv:1009.1162[hep-ph].
  • [4] B.Z. Kopeliovich, A. Schäfer and A.V. Tarasov, Phys. Rev. C59, 1609 (1999).
  • [5] H. Kowalski, L. Motyka and G. Watt, Phys. Rev. D74, 074016 (2006).
  • [6] M. Gluck, E. Reya and A. Vogt, [GRV98], Eur. Phys. J. C5, 461 (1998).
  • [7] A.B. Zamolodchikov, B.Z. Kopeliovich and L.I. Lapidus, Sov. Phys. JETP Lett. 33, 595 (1981).
  • [8] B.Z. Kopeliovich, J. Nemchik, A. Schäfer and A. Tarasov, Phys. Rev. C65, 035201 (2002).
  • [9] S.S. Adler et al., [PHENIX Collaboration], Phys. Rev. Lett. 98, 012002 (2007).
  • [10] D. Peressounko et al., [PHENIX Collaboration], Nucl. Phys. A783, 577 (2007).
  • [11] T. Isobe et al., [PHENIX Collaboration], J. Phys. G34, S1015 (2007); T. Sakaguchi et al., [PHENIX Collaboration], Nucl. Phys. A805, 355 (2008).
Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
Add comment
Loading ...
This is a comment super asjknd jkasnjk adsnkj
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test description