Observations on dA scattering at forward rapidities

We point out that the suppression in the ratio R_dAu recently observed by the BRAHMS collaboration in forward scattering is stronger than usually appreciated. This is related to the fact that at forward rapidities BRAHMS measures negatively charged hadrons and that R_dAu is defined from the ratio of dA and pp scattering cross sections. We also investigate the influence of standard shadowing on R_dAu, and the typical values of partonic momentum fractions relevant in forward scattering. We find that x_Au>0.02 dominate in the cross section.


I Introduction
The Brahms collaboration has recently presented measurements of the ratio R dAu of hadron production cross sections in dAu and pp collisions [1]. With increasing hadron rapidity, the data indicate a growing suppression of the ratio. Theoretical analyses of the data have focused on nuclear effects related to the gold nucleus, emphasizing variously the role of small x physics in the nuclear production [2], as well as of nuclear-enhanced power corrections in the dA cross section [3]. Other studies [4,5] have addressed the question of whether leading-twist shadowing could be responsible for the observed suppression.
In the present paper we hope to add valuable information that will have an impact on the present and future attempts to interpret the Brahms data, and on plans for further measurements. We base our analysis on next-to-leading order (NLO) leading-twist perturbative-QCD (pQCD) calculations of inclusive hadron production. Such calculations have enjoyed considerable success in comparisons with data from pp collisions at RHIC at √ s = 200 GeV. They yield good agreement with the Phenix data [6] for pp → π 0 X at central rapidities, and with data from Star [7] on pp → π 0 X at forward rapidities η = 3.8 and η = 3.3, the latter being essentially in the kinematic range explored by Brahms in their most forward measurements. It is appropriate to point out that there are sizable uncertainties in the NLO calculation, related to the choice of fragmentation functions and scales. However, we are confident that for the kinematics relevant for Brahms NLO pQCD does explain at least 50% of the cross section, as a conservative estimate, and hence is a viable tool for obtaining deeper insights into the production mechanism, at least for pp collisions.
The main point of our analysis can be stated very simply: the nuclear effect reported by Brahms actually appears to be substantially larger than appreciated in the studies [2,3,5].
This is related to the fact that in the very forward region, at rapidities η = 2.2 and η = 3.2, Brahms only measured negatively charged hadrons (h − ) and not the charge average (h + +h − )/2 as at the more central rapidities. In the ratio R dA the denominator refers to pp collisions, and negatively charged hadrons are expected to be produced more rarely in pp than in dA collisions, for which from isospin considerations it follows that at least π + and π − should be produced in equal numbers. This immediately implies that the ratio of dAu → h − X and pp → h − X cross sections is "intrinsically enhanced", by actually a factor of about 1.5, as we will show. The fact that Brahms nonetheless reports a suppression of the ratio is therefore truly remarkable and awaits further investigation.
We also revisit in our analysis the following questions: (i) what are the most relevant parton momentum fractions x for hadron production at Brahms, in particular at very forward rapidity η = 3.2 where the suppression of R dA is largest?
To what extent are truly small x, say, x < 10 −3 probed?
(ii) how relevant is leading-twist nuclear shadowing for the explanation of the Brahms data?
These questions have already been addressed in some detail in [5]. Our analysis extends that study by providing results within a full NLO calculation. This will generally lead to more reliable results. In addition, the enhancement effect mentioned above has of course also direct implications for estimates for R dA obtained when using leading-twist nuclear shadowing. Our calculations therefore provide an improved estimate as compared to the results of [5], where the enhancement was not taken into account. We furthermore explore more thoroughly the possible effects of leading-twist nuclear shadowing by making more extreme assumptions on the structure of screening at intermediate x, tolerated because of possible uncertainties in the connection between diffractive HERA data and gluon shadowing.
In sec. II we discuss the ranges of partonic momentum fractions mainly probed by the forward Brahms data. Section III addresses the leading-twist nuclear shadowing and its relevance in forward dA scattering. With the findings of sections II and III, we are in the position to discuss R dA in the forward region in more detail. This is done in Section IV, where we emphasize our main point related to the normalization of R dA by the pp → h − X cross section. We summarize and conclude with section V.

II Kinematics and x ranges probed in forward scattering
We consider the reaction H 1 H 2 → hX, where H 1 , H 2 are initial hadrons and h is a hadron in the final state produced at high transverse momentum p T . Since large p T ensures large momentum transfer, the cross section for the process may be written in a factorized form, where the sum is over all contributing partonic channels a+b → c+. . ., with dσ c ab the associated short-distance cross section which may be evaluated in QCD perturbation theory: The leading-order (LO) contributions dσ c,(0) ab are of order α 2 s ; the next-to-leading order (NLO) corrections are known [8] and will be included in our analysis.
In Eq. (1), f H i (x, µ) denotes the distribution function at scale µ for a parton of type i in hadron H, carrying the fraction x of the hadron's light-cone momentum. Likewise, D h c (z, µ) describes the fragmentation of produced parton c into the observed hadron h, the latter taking momentum fraction z of the parton momentum. The scale µ in Eq. (1) stands generically for the involved renormalization and factorization scales. µ should be of the order of the hard scale in the process; in the following we choose µ = p T . The dependence on µ is actually quite large even at NLO [8]; however, in this work we are mainly interested in ratios of cross sections for which the µ dependence is fairly insignificant.
The lower limits of the integrations over momentum fractions in Eq. (1) may be derived in terms of x T = 2p T / √ s and the pseudorapidity η of the produced hadron. They are given by From these equations it follows that at central rapidities η ≈ 0 the momentum fractions x 1 and x 2 can become as small as roughly p T / √ s. In forward scattering, that is, at (large) positive η, the collisions become very asymmetric. In particular, x 2 may become fairly small, whereas x 1 tends to be large. For forward kinematics at Brahms one has, typically, p T ∼ 1.5 GeV and η = 3.2. This implies that x 2 may become as small as ∼ 3.5 × 10 −4 . However, in practice it turns out that such small x 2 hardly ever contribute to the cross section: if x 2 is so small, the hadron with transverse momentum p T can only be produced if both x 1 and z are unity, where however the parton distributions f H 1 a (x 1 , µ) and the fragmentation functions D h c (z, µ) vanish. This is an immediate consequence of kinematics, as demonstrated by Eqs. (3). One can show that if the parton density f H 1 a (x 1 , µ) behaves at large 2 ) a f +a D +1 . Therefore, contributions from very small x 2 are highly suppressed.
The question, then, remains of how small x 2 really is on average for forward kinematics at RHIC. This is of course relevant for judging various explanations for the suppression of R dA seen by Brahms, in particular those relating to saturation effects in the nucleus wave function [2]. Figure 1 shows the distribution of the cross section for pp → π 0 X at √ s = 200 GeV, p T = 1.5 GeV, η = 3.2, in bins of log 10 (x 2 ). The overall normalization is unimportant of course; for definiteness we note that the sum of all entries shown in the plot yields the full NLO invariant cross section Ed 3 σ/dp 3 in pb/GeV 2 . For the calculation we have chosen the CTEQ6M [9] parton distribution functions and the fragmentation functions of Ref. [10]. One can see that the distribution peaks at x 2 > 0.01. There are several ways to estimate an average x 2 of the distribution. For example, one may define x 2 in the standard way from evaluating the integral in Eq.
(1) with an extra factor x 2 in the integrand, divided by the integral itself: where the ellipses denote the remaining factors in Eq. (1). Alternatively, one may simply determine x 2 as the median of the distribution, demanding that the area under the distribution in Fig. 1 to the left of x 2 equals that to the right. Either way, one finds an average x 2 > 0.01, typically 0.03 − 0.05 at this p T and η.
The precise shape of the distribution and the value of x 2 depend somewhat on the parton distributions (and, less so, on the fragmentation functions) chosen. We remind the reader that the distribution shown in Fig. 1 is at p T = 1.5 GeV and that we have chosen the factorization and renormalization scales to be µ = p T . This means that we are using a fairly low scale in the parton densities. At this scale, the CTEQ6 densities, in particular the gluon, are still relatively flat towards small x. In order to estimate to what extent this influences the distribution, we have calculated it for the GRV [11] parton distributions, which are steeper at this scale. The corresponding histogram in log 10 (x 2 ) is shown in Fig. 2. One can see that as expected it peaks somewhat more to the left; nevertheless there is not much quantitative change in the average x 2 . The full invariant cross section is about 15% smaller than for the CTEQ6 set. We have mentioned in the introduction that there are data from Star for the cross section for pp → π 0 X in roughly this kinematic range [7] which are in very good agreement with the NLO calculation used in Fig. 1. This supports the view that the distributions shown in Figs. 1 and 2 are realistic. not been able to identify this effect as resulting from any straightforward origin. The precise small-x behavior of the parton distributions at the rather low scales involved here plays a role (however, the effect also occurs for the steeper GRV distributions). The structure of the cross section formula in Eq. (1) itself is also partly responsible. In the lower part of Fig. 4 we show the averages as functions of rapidity for two fixed values of p T . At η = 0 one obviously starts from x 1 = x 2 ; with increasing η the two momentum fractions become very different. Toward η = cosh −1 (1/x T ) they again both tend to unity; for x 2 this happens rather late.

III Influence of leading-twist nuclear shadowing
In dA collisions, nuclear effects will alter the distribution in x 2 as well as the full cross section.
Shadowing effects at small-x 2 , x 2 < 0.05 − 0.1, will lower the cross section and will lead to yet higher average x 2 being probed. There will also be enhancements at larger x 2 , 0.05−0.1 < x 2 < 0.2, associated with yet another coherent nuclear effect, antishadowing. This will be followed by the suppression related to the EMC effect for 0.2 < x 2 < 0.8, and by the subsequent enhancement explained by the Fermi motion for x 2 > 0.8.
Since in the Brahms kinematics the average x 2 is near 0.01, the principal nuclear effect is shadowing. We investigate its role in the interpretation of the Brahms data by considering leading-twist shadowing, using the parameterization of nuclear parton distribution functions (nPDFs) derived in [12,13,14]. Unlike most other sets of nPDFs [4,15], these functions have a rather rapid and strong onset of shadowing toward small-x, so they may serve as a good tool for studying the "maximally possible" effects of leading-twist nuclear shadowing in forward dA scattering. The recent study [5] has also employed the nPDFs of [12,13,14], albeit only in the framework of a lowest order (LO) calculation.
We note that we will neglect any nuclear effects in the deuteron, for which we just use are important in our calculations, proper account of this would make the effect we will discuss in the next section even slightly bigger. Note that for heavier nuclei the convolution model contradicts the EMC effect. However here we are using it to "restore" the deuteron structure function within the procedure used to extract the neutron structure function; see [16] for an extensive discussion of nuclear effects in the deuteron parton densities.
Let us now briefly describe the approach of [12,13,14] for deriving nPDFs. Leadingtwist nuclear shadowing is obtained using Gribov's theorem [17] relating nuclear shadowing to diffraction, Collins's QCD factorization theorem for hard diffraction in DIS [18], and the QCD analysis of hard diffraction measured at HERA in terms of diffractive parton distribution functions of the proton. Operationally, the nPDFs are first derived at the initial scale Q 0 =2 GeV and for 10 −5 ≤ x ≤ 1. Standard (NLO) DGLAP evolution is then used to obtain the nPDFs for Q 2 > Q 2 0 .
Analyses of DIS by both H1 [19] and ZEUS [20] demonstrate that diffraction constitutes ≈ 10% of the total cross section in the quark-dominated channel and as much as ≈ 30% in the gluon channel. As a result, it is found in [12,13,14] that the effect of nuclear shadowing in nPDFs is large and, even more strikingly, much stronger in the gluon nPDF at small x than in the quark nPDFs.
Conservation of the baryon number and the momentum sum rule then require that the depletion of nPDFs at small values of x, x < 0.01, be accompanied by a certain enhancement at 0.05 < x < 0.2. The transition from shadowing to enhancement, and the enhancement itself, are not described by the Gribov theorem and, hence, can be only modeled. Using the available fixed-target nuclear DIS data [21] as a guide, the "standard" scenario of [12,13,14] assumes that the transition from nuclear shadowing to the enhancement takes place at x = 0.1 for quark nPDFs, and at x = 0.03 for the gluon nPDF. In the following, we will refer to this set of nPDFs as "shadowing 1". Figure 5 shows the distribution of the NLO cross section for dAu → π 0 X in log 10 (x 2 ), using shadowing 1. For comparison, we also display the previous result for pp → π 0 X of Fig. 1 [12,13,14], and a more extreme ansatz for shadowing (see text). The "spikes" in the distributions at log 10 (x 2 ) ≈ −0.8 are artifacts of the implementation of antishadowing in the nPDFs of [12,13,14]. For better comparison we have displayed the result of Fig. 1 by a solid line.
The kinematics for forward scattering at Brahms mostly corresponds to values of x 2 in the transition region between shadowing and antishadowing, where the predictions for nPDFs are rather uncertain. Therefore, in addition to the standard scenario ("shadowing 1") of nuclear shadowing, we have also explored an option for which nuclear shadowing in the gluon channel is increased by extending it up to x = 0.1, similarly to the shadowing in the quark densities. We refer to the resulting set of nPDFs as "shadowing 2". The corresponding log 10 (x 2 ) distribution of the cross section for dAu → π 0 X is also displayed in fig. 5. Compared to shadowing 1, there is only a small modification of the distribution, which will lead to a very slight further suppression of the dA cross section. It is worth emphasizing that one can hardly increase the amount of gluon shadowing at x ∼ 10 −3 since here there are constraints from J/ψ data [22]. The model of [12,13,14] gives a reasonable description of the observed suppression by a factor ∼ 2, which would be spoilt by a much stronger gluon shadowing. At the same time, as soon as the amount of gluon shadowing at x ∼ 10 −3 is fixed, the gradual decrease of shadowing with increasing x is automatic as a consequence of the decrease of the coherence length ∝ 1/m N x and of a smaller probability for diffraction. Therefore, we conclude that the standard effect of leading twist nuclear shadowing will at best be able to explain only a small fraction of the dramatic suppression of the spectra of charged hadrons at forward rapidities observed by Brahms. This statement is in line with the LO result in the revised version of [5]. Figure 5 shows the corresponding results for p T = 5 GeV. Here, larger x 2 are probed, and only slight antishadowing effects appear.
So far we have only considered π 0 production as an example. This is however not really appropriate for a comparison with the Brahms data which, at forward rapidities, are for negatively charged hadrons h − . As we will now show, for the case of h − , even in presence of the shadowing effects just discussed, the leading-twist NLO calculation predicts an enhancement, rather than a suppression, of R dA .

IV Isospin considerations for the ratio of dA and pp cross sections
We now consider the ratio R dA of single-inclusive hadron cross sections in dA and pp scattering.
The Brahms experiment has presented data [1] for R dA as a function of hadron transverse  The data points are from measurements at the ISR [23]. The curve shows the result of the NLO calculation, using the fragmentation functions of [24].
example for this is shown in Fig. 7, where we display data for the π + /π − ratio from the ISR [23] at √ s = 45 GeV. We also show the result of the NLO calculation, using the fragmentation functions of Ref. [24], which provides separate sets for negatively and positively charged pions.
[We note that there are also π + /π − data at √ s = 62 GeV [25] which lie lower and are in less impressive agreement with NLO pQCD.] As Fig. 7 shows, there is clear excess of positive pions over negative ones. In contrast, isospin considerations imply that π + and π − are produced practically equally in dAu collisions. Therefore, one expects R dA for negatively charged pions to be intrinsically enhanced, if it is normalized by the pp cross section and not, for example, by the dp one.
To go into a little more quantitative detail, we recall that at forward rapidities the partonic collisions are very asymmetric. Large contributions to the scattering come from situations in which a large-x 1 valence quark in the "projectile" (i.e., in the deuteron, or in one of the protons) hits a small-x 2 gluon in the "target" (i.e., in the gold nucleus or in the other proton). The underlying (LO) subprocess is then the quark-gluon Compton process qg → qg. For negatively charged pions one then expects that down quarks play a particularly important role in the Compton process, since both the "projectile" and the produced π − have a d valence quark. To a good approximation (see the previous section), the deuteron's d valence density is given by where we have used isospin invariance to relate the valence-d distribution in the neutron to the valence-u in the proton. Due to the up-quark excess in the proton, the distribution in Eq. (5) becomes much larger than the proton's d-valence distribution at high x, as shown in Fig. 8, resulting in an enhancement in R dA . Of course, other scattering channels will contribute as well and dilute this valence effect. In addition, Brahms does not measure only pions, but inclusive charged hadrons, h ± = π ± + K ± + (−) p + . . .. Nevertheless, when changing to charged-hadron fragmentation functions as given by [24], we find that the difference in deuteron and proton valence densities continues to play an important role in the forward production of negatively charged hadrons. This is demonstrated by Fig. 9. The solid lines show the ratio R dA at η = 0 and 1 for summed charged hadrons (h + + h − ) /2, and at η = 2.2 and 3.2 for negatively charged hadrons, exactly corresponding to the Brahms conditions. We have used the "shadowing 1" set described in the previous section. As shown in sec. II, when going from η = 0 to η = 1, the average x 2 probed slightly decreases, and shadowing effects start to become visible at the smaller p T . At η = 2.2 and η = 3.2 the x 2 become yet smaller, but since now negatively charged hadrons are measured, the valence effect discussed above outweighs any stronger shadowing, and in fact the ratio R dA strongly increases with p T because larger and larger x 1 become relevant.
For comparison we also show in Fig. 9 the results at η = 2.2 and η = 3.2 for summed charged hadrons (dashed lines). For these, the effective valence densities in the proton and deuteron are the same, and the enhancement seen for negative hadrons disappears. Shadowing effects of up to 15% are visible then, as expected from Fig. 5, and as also found in Ref. [5] where only summed charged hadrons were considered. It is remarkable that for the highest p T ∼ 3 GeV at η = 3.2 the curve for h − is enhanced by about a factor 1.5 with respect to the one for summed charges. We have used the "shadowing 1" nPDFs for the gold nucleus. The fragmentation functions are from [24]; we have found that for the case of summed charged hadrons using the set of [10] does not alter our results by more than a few per cent.
Our analysis so far has been entirely based on a NLO pQCD leading-twist calculation and the use of fragmentation functions extracted from e + e − annihilation data. We expect that even if nonperturbative phenomena are important in the kinematic regime explored by Brahms, the enhancement in R dA resulting due the different "projectiles" in the numerator and denominator will persist. Here, our reasoning is as follows: ISR data (see [26] and references therein) on π ± production at p T ∼ 1 GeV and large Feynman-x F ∼ 0.4 were found to be consistent with where u and d are typical densities for up and down valence quarks. Such spectra in x F are much harder than the ones pQCD would give, indicating the presence of a nonperturbative production mechanism. Nonetheless, the ratio of π + to π − cross sections is of a similar magnitude as the one in the perturbative regime shown in Fig. 7. Adding the fact that the yields of π + , π − , π 0 in dA scattering should be equal because of isospin, irrespective of the production mechanism, we are led to the conclusion that R dA for negatively charged hadrons should be enhanced even if nonperturbative effects dominate. Note here that nonperturbative effects in the fragmentation region are known to be consistent with the Feynman scaling. Hence if nonperturbative effects are important they should lead to about the same π + /π − ratio in pp scattering for the same x F at ISR and at RHIC.
We finally note that a potential caveat to our main finding in Fig. 9 comes from a further set of Brahms data. While we have mentioned that Brahms measures all hadrons and not just pions, we have generally assumed that pions dominate the observed hadron spectrum. However, preliminary data from Brahms [27] show that the cross section for dAu → h + X becomes significantly larger than that for dAu → h − X at p T > 1 GeV. At p T = 3 GeV, they observe about three times as many h + as h − . As we have pointed out before, isospin excludes that such an excess could be due to pions: σ(dAu → π + X) = σ(dAu → π − X), up to corrections of a few per cent related to the fact that the gold nucleus is not isoscalar. Standard sets of fragmentation functions do not predict large contributions from kaons and protons, and in the NLO calculation one ends up with σ(dAu → h + X) at most only 10% larger than σ(dAu → h − X). It is hard to conceive that proton production could lead to a large enhancement of h + over h − (that even increases with p T ) but, barring any experimental systematic problem, this appears to be the conclusion at present. If the final Brahms data continue to show this large excess, it will be a challenge to understand it in terms of a nonperturbative effect. Such an effect could, perhaps, result from coalescence of quarks from the incoming nucleon with other partons, to form a baryon. For this to work, the quarks would need to experience large transverse "kicks" and would need to lose a significant fraction of their momentum. Such a possibility could be connected to the expectations of a very strong suppression of the forward nucleon spectrum in central nucleon-nucleus collisions [28,29].

V Conclusions and outlook
We have shown that there is an intrinsic enhancement in the ratio R dAu for negatively charged hadrons, simply because of the different nature of the "projectile" (deuteron vs. proton) in the numerator and denominator of R dAu . In the light of Fig. 9

the significant suppression seen by
Brahms at η = 2.2 and η = 3.2 is even more striking than usually appreciated. The effect we have found has not been taken into account in any previous theoretical study [2,3,5] of the data, to our knowledge. We expect that future data for R dAu for summed charged hadrons in this kinematic regime will show an even stronger suppression than observed for h − , roughly by a factor 1.5. The same should happen if R pAu , rather than R dAu , were measured for h − .
Because of the effect, it is entirely impossible to explain the suppression in R dAu at forward rapidities by a conventional modification of the leading-twist parton densities in nuclei. However, even if we disregard the effect, nuclear leading-twist shadowing plays a rather unimportant role, giving at most a suppression of 15%. The reason for this is that parton momentum fractions in the gold nucleus are not very small on average even for forward kinematics, as we have shown. In other words, a large nuclear contribution originates from a range of x where nuclear effects are known to be small (or even antishadowed). This generally sets severe limitations on the ability of any initial-state small-x effects to explain the observed suppression.
We have also mentioned that the fact that Brahms observes the cross section for dAu → h + X to be significantly larger than that for dAu → h − X at p T > 1 GeV, indicates the presence of sizable nonperturbative contributions possibly related to protons. It appears likely that mechanisms responsible for an enhancement of proton production then also play a role in the observed suppression of R dAu . Nonperturbative production of pions, too, could play a role: coalescence effects involving spectator partons are likely to be strongly suppressed in p(d)A collisions as compared to the pp case [28]. This suppression is further enhanced when energies are large enough to resolve the small-x high gluon densities [29]. Such non-leading twist effects should decrease with increase of the transverse momentum of the pion, which is consistent with the trend in the data on R dAu . On the other hand, the observed excess of dAu → h + X over dAu → h − X actually increases with p T , which is quite challenging to understand. Note also that the parton energy losses that would be necessary to reproduce the Brahms effect appear to be rather large: about 10% energy loss would be needed if it occurred only in the initial state before the interaction. If one assumes that the rate of energy loss is the same in the initial and final states, a loss of about 3% is necessary. For the kinematics relevant here, the suppression is more sensitive to losses in the final state since the average z for fragmentation was found to be substantially closer to one than the averages x 1,2 in the parton densities (see Fig. 4).
To further investigate experimentally the origin of the suppression in R dAu it would be useful to perform measurements of dihadron production. Within LO kinematics, the pseudorapidities of the two hadrons are related by η 1 +η 2 = ln(x 1 /x 2 ). One may therefore single out contributions from small x 2 by demanding that both hadrons be rather forward. Fig. 10 shows this for a sample calculation. We assume that a "trigger" hadron (π 0 ) is detected with transverse momentum p T,1 = 2.5 and forward rapidity 2.5 ≤ η 1 ≤ 3.5. Let the second π 0 have 1.5 GeV ≤ p T,2 ≤ p T,1 . Without any restriction on the rapidity η 2 of the second hadron, one then obtains the higher log 10 (x 2 )-distributions in Fig. 10. As expected, these look very much like the singlehadron distributions shown in Sections II and III. If now the second hadron is also in the forward region at 1.5 ≤ η 2 ≤ 4, the lower distribution is obtained, which is entirely located at x 2 ≤ 0.01.
We also show in Fig. 10 the corresponding results for dAu collisions, using our "shadowing 1".
The shadowing effects are much more relevant for the double-forward distribution, as expected.
We note that the distributions in Fig. 10 are normalized such that they sum to the cross section dσ/dp T,1 in pb/GeV. It is evident that there is a significant decrease in rate for two forward hadrons. The results shown in Fig. 10 are only LO. The NLO corrections are expected to be sizable; they are available [30]. The two hadrons we have studied in Fig. 10 would be nearly Figure 10: LO distributions in log 10 (x 2 ) of the cross section dσ/dp T,1 for pp → π 0 π 0 X and dAu → π 0 π 0 X production at √ s = 200 GeV. The kinematic variables have been chosen as described in the text. Solid lines are for pp collisions and histograms are for dAu, using "shadowing 1". The higher-lying histograms are for the case of "arbitrary" (i.e., unconstrained) η 2 , the lower ones are for 1.5 ≤ η 2 ≤ 4.
back-to-back in azimuthal angle. Further insights into the dynamics may be gained by studying back-to-back azimuthal correlations [31,32]. We finally note that small-x 2 effects might also become more readily accessible in conceivable future pA collisions after increase of the proton energy to 250 GeV at a later stage of RHIC operations.