Different Nuclear Dependence of J / ψ and ψ ′ Production in p - A and A - p Collisions ∗

While presently available p-A data observe that the nuclear dependence of J/ψ and ψ production is the same within errors, we show that different nuclear dependence of J/ψ and ψ production in the kinematic region uncovered by the present p-A data can be predicted based on two different nuclear absorption scenarios. It is found that the predicted production ratio σ(ψ)/σ(J/ψ) at positive xF in A-p collisions is mainly determined by nuclear absorption, and hence allows direct experimental test of nuclear absorption scenarios. 12.38.Mh, 13.85.-t, 25.75.+r Typeset using REVTEX Partly supported by the National Natural Science Foundation of China E-mail: [email protected], Telefax: (086)-010-2562586 1 Quarkonium production in experiments with a proton-beam incident on a nucleus target, i.e. p-A collisions, has attracted much attention in recent years in connection with J/ψ suppressions in high energy heavy-ion collisions [1–4]. Actually it is a good place to check the hadronic absorption models which attribute the observed J/ψ suppressions in nucleus-nucleus collisions to the absorption of J/ψ through its interactions with hadronic environment instead of the formation of quark-gluon plasma (QGP). In particular, the experimental observations [5,6] that the J/ψ and ψ production has the same nuclear dependence in p-A collisions put a strict constraint on various absorption models. However, it has been realized that all present experiments for the production of J/ψ and ψ in p-A collisions studied only J/ψ or ψ which is fast in the lab system or has positive Feynman xF . In fact, in the kinematic region not yet probed by present p-A experiments, i.e. the negative xF region, different nuclear dependence of J/ψ and ψ ′ production can be predicted based on different scenarios of absorption by target nucleons, which will be shown in this work. One of these scenarios, the “traditional” nuclear absorption model (we shall refer to it as Scenario-I throughout this work), has been established in the literature [7–10] to account for the effects of absorption by nucleons in the following way: while the cc̄ pair (pre-meson), produced as a colour singlet and of small spatial size, is expanding gradually to its bound state size, it can be dissociated by nucleons through an interaction cross section depending on the size of the cc̄ pair. Very recently another scenario (Scenario-II) [11], stemming from the most recent theoretical progress made in hadronic production of quarkonium states, has been proposed to explain the observed charmonium suppression in hadron-nucleus and nucleus-nucleus collisions. This scenario considers charmonium production through the intermediate next-to-leading Fock space state consisting of a colour octet cc̄ pair and a soft gluon. The interaction between this composite state and nucleons can lead to charmonium suppression. In this work we shall show how these two different absorption scenarios could accommodate present p-A data and yet predict different nuclear dependence of J/ψ and ψ production in p-A collisions at negative xF . At negative xF in p-A collisions the mechanisms of charmonium production such as 2 nuclear shadowing [12–14] and intrinsic charm [15,10] are expected to be unimportant and will be neglected in our work. Initial state energy loss effects [16] may lead to an increase of charmonium production in the negative xF region, which gives an opposite trend to the experimental data. Furthermore, the usual EMC effects [17] can be important at negative xF [18]. The initial state energy loss and EMC effects are not included in our study and their effects will be discussed later. Our previous work [19] showed that xF -dependent comover contributions, as well as the nuclear absorptions, are essential for a comparison between theories and experimental data at small xF . We shall include only the effects of absorption by target nucleons and comovers in our study of J/ψ and ψ production in p-A collisions at negative xF . In fact, recent results on open charm production near xF=0 [20] suggested that absorptions may be the dominant cause of the charmonium suppression in p-A collisions at negative xF . We shall show in this work that although the individual J/ψ and ψ production at negative xF in p-A collisions predicted by the two different absorption scenarios may depend on the choice of parameters in comover contributions, the ratio of the two production cross sections σ(J/ψ)/σ(ψ) is insensitive to comover contributions, and therefore the prediction of the ratio may allow an experimental test of nuclear absorption scenarios. However, a study of charmonium production at negative xF (corresponding to the case of charmonium moving slow in the rest frame of target nucleus) is essentially impossible in an experiment of proton-beam incident on a nucleus target (p-A collisions). An alternative is the experiment of a heavy ion beam incident on a hydrogen or deuterium target [18,21], which we shall call A-p collisions. In A-p collisions the produced charmonia are moving fast in the lab system and thus the relevant measurements are more readily. In this work we have also calculated and compared the predictions of the mentioned two absorption scenarios for J/ψ and ψ production in A-p collisions at CERN-SPS energy. In Scenario-I for p-A collisions the produced charmonium states (J/ψ or ψ) or cc̄ pairs (pre-mesons) can been dissociated by nucleons in the target nucleus into open-charm pairs (DD̄), which leads to suppressions of charmonium production. However, the formation of 3 charmonium bound state requires finite proper time, and this formation time will suffer a Lorentz delay in the lab system. In the kinematic region reached by present experiments, the produced cc̄ pair is moving fast in the lab system and may have been outside the target nucleus before it forms a physical charmonium bound state due to the Lorentz delay of the formation time in the lab system. Therefore, present experimental data show that the J/ψ and ψ productions have the same nuclear dependence in p-A collisions, although the radii of the J/ψ and ψ bound states differ by almost a factor of two in potential models [22]. According to this picture, those cc̄ pairs which are slow in the lab system will have enough time to form the charmonium bound states (J/ψ or ψ, etc.) inside the target nucleus, and thus the interaction of fully formed bound states J/ψ and ψ with the surrounding target nucleons may lead to different nuclear dependence for J/ψ and ψ production through the nuclear absorption depending on the final-state size, as we shall see below by explicit calculations. Including only the effects of absorption by nucleons and comovers, the xF -dependent cross section for quarkonium production in p-A collisions is dσ dxF = A dσ dxF ∫