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

###### Abstract

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 .

###### keywords:

direct photons, nuclear suppression, gluon shadowing###### Pacs:

13.85.Qk, 24.85.+p, 25.75.-q, 25.75.CjIf 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],

(1) |

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]:

(2) |

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],

(3) |

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 .

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.

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.

## References

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