Nuclear Suppresion at Large x

Nuclear suppression at large x Czech Technical University in Prague, FNSPE, Břehová 7, 11519 Prague, Czech Republic & Institute of Experimental Physics SAS, Watsonova 47, 04001 Košice, Slovakia E-mail: [email protected] Michal Šumbera∗ Nuclear Physics Institute ASCR, 25068 Řež/Prague, Czech Republic E-mail: [email protected] We discuss a common feature of all known reactions on nuclear targets - a significant suppression of the relative production yields at large x. Interpretation of this effect based on energy conservation restrictions in initial state parton multiple interactions in nuclear matter is presented. We describe several applications of this interpretation using the light-cone dipole approach-based calculations. We demonstrate that the same mechanism of large-x suppression is important also at lower energies where coherent nuclear effects are not expected. This allows to exclude from the interpretation of observed phenomena the models based on the Color Glass Condensate. PACS: 13.85.Lg, 13.60.Le High-pT physics at LHC -09 February 4-7, 2009 Prague, Czech Republic ∗ Speaker. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ PoS(High-pT physics09)042 Jan Nemchik Michal Šumbera Nuclear suppression at large x 1. Introduction 2 PoS(High-pT physics09)042 The main aim of the recent measurements of high-pT hadrons produced in the beam fragmentation region in the deuteron-nucleus collisions at the Relativistic Heavy Ion Collider (RHIC) is to reach the smallest values of Bjorken x in the nucleus. This allows to observe the coherence effects which should usually lead to nuclear suppression. Such a suppression of high-pT hadrons has been indeed found by the BRAHMS [1, 2] and STAR [3] Collaborations. Natural interpretation of the observed suppression based on the coherence effects was performed in [4] within a model based on color glass condensate (CGC). However, such an approach misses a global applicability for any energy and leads to problems with explanation of nuclear suppression at lower energies and for different reactions. For example, a similar suppression like at RHIC was measured also at much lower energy in p + Pb collisions at SPS corresponding to c.m.s. √ energy s = 17.3 GeV where no effects of coherence are possible. The observed rise of the nuclear suppression with Feynman xF by the NA49 Collaboration [5] is in accord with the same pattern seen in the RHIC energy range. The same pattern of increasing suppression with xF is also demonstrated by the E772 experiment at Fermilab [6] for the Drell-Yan (DY) process. Quite strong and universal nuclear suppression at large xF is also confirmed by the collection of data from [7] for production of different species of particles in p + A collisions. These examples and another reactions treated in ref. [8] confirm our expectation that this common feature should be attributed to all know reactions on nuclear targets. This allows to expect naturally that the same mechanism should cause the observed suppression at large xF independently of the energy and type of the reaction. Such a common mechanism of nuclear suppression was proposed in refs. [8, 9, 10] (see also [11, 12]). It is not related to coherence and can be applied to any reaction at forward rapidities and at any energy. Then the large-xF nuclear suppression can be treated, alternatively, as a Sudakov suppression, a consequence of a reduced survival probability for large rapidity gap (LRG) processes in nuclei, an enhanced resolution of higher Fock states by nuclei, or an effective energy loss that rises linearly with energy. It was also demonstrated in [8] that the nuclear suppression at large xF caused by the initial state multiple interactions is a leading twist effect leading to breakdown of QCD factorization. Natural interpretation of suppression comes from energy conservation restrictions. Projectile parton propagating through a nucleus experiences multiple interactions. As a result it losses gradually energy leading at large xF to a reduction of the probability to give a major fraction of the initial energy to one particle produced on a nucleus compared to a proton target. For this reason, the nuclear ratio should be suppressed below one at large xF . Such an interpretation based on the energy conservation leads also to xF scaling of the nuclear suppression as was analyzed in [10]. Besides, as an another consequence of energy conservation restrictions, observed nuclear ef√ fects occur also at midrapidities [13], i.e. at large xT = 2 pT / s, where pT is transverse momentum of the produced particles. In spite of the Cronin effect at moderate pT , the main consequence of QCD factorization is that the nuclear ratio should approach one at large pT . However, initial state multiple interactions and energy sharing lead to a suppression pattern similar to that occurring at large xF . Thus, at large xT the nuclear ratio should fall below one. Moreover, we predict also xT -scaling of this effect similarly to xF -scaling at forward rapidities. Michal Šumbera Nuclear suppression at large x The onset of nuclear suppression at midrapidities at large xT manifests itself also through data on production of neutral pions in d + Au collisions measured by the PHENIX Collaboration [13]. The same Collaboration [14] also demonstrated a strong nuclear effects at large pT for direct photon production in Au + Au collisions. In this paper using a novel mechanism from refs. [8, 9] based on energy conservation in initial state multiple interactions we analyze and quantify the nuclear suppression at large xF and large xT for a variety of processes occurring in p(d) + A and A + B collisions: • high-pT hadron production at forward rapidities in p(d)+A collisions, • production of hadrons at SPS energies vs. NA49 data, • Drell-Yan production at Fermilab energy at large xF , • high-pT hadron production at midrapidities, • direct photon production at large pT in Au+Au collisions. 2. Survival probability of large rapidity gaps Energy conservation restrictions lead to a feature common to all reactions; namely, when the final particle is produced with xF → 1 (xT → 1), insufficient energy is left to produce anything else. In another words, gluon radiation during propagation of the projectile hadron or its debris is forbidden by energy conservation. As a class, such events are usually called LRG processes. If a large-xF particle is produced, the rapidity interval to be kept empty is ∆y = − ln(1 − xF ). Assuming as usual an uncorrelated Poisson distribution for radiated gluons, the Sudakov suppression factor, i.e. the probability to have a rapidity gap ∆y, becomes S(∆y) = e−hnG (∆y)i , (2.1) where nG (∆y) is the mean number of gluons that would be radiated within ∆y if energy conservation were not an issue. The mean number hnG (∆y)i of gluons radiated in the rapidity interval ∆y is related to the height of the plateau in the gluon spectrum, hnG (∆y)i = ∆y dnG /dy. Then, the Sudakov factor acquires the simple form, S(xF ) = (1 − xF )dnG /dy . The height of the gluon plateau was estimated in ref. [15] as, ! mρ2 dnG 3αs . ln = dy π Λ2QCD (2.2) (2.3) For further calculations we take αs = 0.4 (see discussion in ref. [8]), which gives with high accuracy dnG /dy = 1, i.e. the Sudakov factor, S(xF ) = 1 − xF . 3 (2.4) PoS(High-pT physics09)042 • production of leading hadrons with small pT , Michal Šumbera Nuclear suppression at large x One can formulate nuclear suppression at xF → 1 (xT → 1) as a survival probability of the LRG in multiple interactions with the nucleus. Every additional inelastic interaction contributes an extra suppression factor S(xF ). The probability of an n-fold inelastic collision is related to the Glauber model coefficients via the Abramovsky-Gribov-Kancheli (AGK) cutting rules [16]. Then the survival probability at impact parameter b reads, h i A 1 h in hA WLRG (b) = exp −σinhN TA (b) ∑ σinhN TA (b) S(xF )n−1 , n=1 n! (2.5) 3. Production of leading hadrons with small pT The left panel of Fig. 1 shows the collection of data from [7] for production of different species of particles in p + A collisions exhibiting quite a strong and universal suppression at large xF . Moreover, these data covering the laboratory energy range from 70 to 400 GeV demonstrate with a reasonable accuracy the xF scaling of nuclear effects. Relating the observed suppression to the dynamics discussed in the previous section, the nuclear effects can be calculated using Eq. (2.5) summing over the number of collisions and integrating over the impact parameter. Then, the nucleus-to-nucleon ratio normalized to the number of nucleon A reads Z o n 1 d 2 b e−σe f f TA (b) e(1−xF )σe f f TA (b) − 1 . (3.1) RA/N (xF ) = (1 − xF ) σe f f A In the Glauber model σe f f = σinNN . However, Gribov’s inelastic shadowing corrections substantially reduce σe f f [17, 18]. To compare with data, the nuclear effects are parametrized as RA/N ∝ Aα , where the exponent α varies with A. We used A = 40, for which the Gribov corrections evaluated in [18] lead to σe f f ∼ 20 mb. Then a simple expression Eq. (3.1) explains the observed xF scaling and describes rather well the data. 4. High-pT hadron production at forward rapidities Assuming large values of hadron transverse momenta, the cross section of hadron production in d + A (p + p) collisions is given by a convolution of the distribution function for the projectile valence quark with the quark scattering cross section and the fragmentation function, d2σ = 2 d pT d η ∑ q Z1 dz fq/d(p) (x1 , q2T ) zmin d 2 σ [qA(p)] d 2 qT d η qT =pT /z Dh/q (z) , z2 (4.1) qT η where x1 = √ e is the light-cone momentum fraction of the projectile taken away by the quark. s The quark distribution functions in the nucleon have the form using the lowest order parametrization of Gluck, Reya and Vogt [19]. We used proper fragmentation functions using parametrization from [20]. 4 PoS(High-pT physics09)042 where TA (b) is the nuclear thickness function. Michal Šumbera Rd+Au(pT) Nuclear suppression at large x 1.2 BRAHMS data h- 1 STAR data π0 0.8 η = 3.2 0.6 η = 4.0 0.2 Rd = 0.3 fm Rd = 0.2 fm 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 pT (GeV) Figure 1: (Left) Exponent describing the A dependence (∝ Aα ) of the nucleus-to-proton ratio for production of different hadrons as a function of xF . (Right) Ratio of negative hadron and neutral pion production rates in d − Au and pp collisions as function of pT at pseudorapidity η = 3.2 and η = 4.0 vs. data from the BRAHMS [1] and STAR Collaborations [3], respectively. The cross section of quark scattering on the target d σ [qA(p)]/d 2 qT d η in Eq. (3.1) is calculated in the light-cone dipole approach [21, 22]. In our calculations, we separate the contributions characterized by different initial transverse momenta and sum over different mechanisms of highpT production. Details can be found in [8]. Interaction with a nuclear target does not obey factorization, since the effective projectile quark distribution correlates with the target. The main source of suppression at large pT concerns initial state multiple interactions in nuclear matter leading to energy conservation restrictions valid at any energy. The quark distribution in the nucleus can be then evaluated performing summation over multiple interactions and using the probability of an n-fold inelastic collision related to the Glauber model coefficients with Gribov’s corrections via AGK cutting rules [16]. It has the following form: A (x1 , q2T , b) = fq/N ∞ n (x1 , q2T ) , ∑ vn (b) fq/N (4.2) n=0 where the coefficients vn are dependent on nuclear impact parameter b,  n σe f f TA (b) vn (b) =  n+1 . 1 + σe f f TA (b) 2 (r ) / σ (r ) has been evaluated in [8]. Here the effective cross section σe f f = σq̄q T q̄q T 5 (4.3) PoS(High-pT physics09)042 0.4 Michal Šumbera Nuclear suppression at large x n (x , q2 ) in Eq. (4.2) are also given by the GRV The valence quark distribution functions fq/N 1 T parametrization [19] but contain extra suppression factors, S(x1 )n = (1 − x1 )n (2.4), corresponding to an n-fold inelastic collision, n fq/N (x1 , q2T ) = Cn fq/N (x1 , q2T ) S(x1 )n , (4.4) Rp+Pb Rd+Au(pT) 1.2 η = 3.2, s1/2 = 200 GeV η = 2.8, s1/2 = 130 GeV 1 η = 2.1, s 1/2 NA49 data 1 π π- + = 62.4 GeV 0.8 0.8 xF = 0.025 0.6 0.6 π0 0.4 0.4 0 xF = 0.375 0.2 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 pT (GeV) pT (GeV) √ Figure 2: (Left) Theoretical predictions for an approximate exp(η )/ s- scaling of the ratio Rd+Au (pT ) for π 0 production rates in d − Au and pp collisions. (Right) Ratio, R p+Pb (pT ), for π ± production rates in p − Pb and pp collisions as a function of pT at two fixed values of Feynman xF = 0.025 and 0.375 vs. the NA49 data [5]. Energy conservation restrictions in multiple parton rescatterings should lead also to xF scaling of nuclear effects [8, 9, 10] since a corresponding parton energy loss is proportional to initial energy. We expect approximately the same effect of nuclear suppression at different energies and pseudorapidities corresponding to the same values of xF . Such a behavior is demonstrated in the left panel of Fig. 2, where we present pT dependence of nuclear attenuation factor Rd+Au (pT ) for 6 PoS(High-pT physics09)042 where the normalization factors Cn are fixed by the Gottfried sum rule. In 2004 the BRAHMS Collaboration [1] found a substantial nuclear suppression for high-pT negative hadrons produced at pseudorapidity η = 3.2. Two years later, the STAR Collaboration [3] has observed even stronger suppression for neutral pions at η = 4.0 as one sees from the right panel of Fig. 1. Because the data cover rather small x2 ∼ 10−3 , the interpretation of such a suppression has been tempted to be a result of saturation [23, 24] or the CGC [25], expected in some models [4]. However, as a demonstration of an alternative interpretation of a strong onset of nuclear effects at large η , the right panel of Fig. 1 clearly shows a good agreement of our model based on energy conservation with corresponding data. Much stronger nuclear effects at η = 4 can be simply explained by the stronger energy conservation restrictions leading to much smaller survival probability of LRG in multiple quark interactions at larger η -values [8, 10]. Michal Šumbera Nuclear suppression at large x π 0 production in the RHIC kinematic range at different c.m.s. energies and η keeping the same value of xF . 5. Nuclear suppression at small energy vs. NA49 data 6. Drell-Yan production at large xF 1.2 RW/D(x1) RW/D(x1) The DY reaction is also known to be considerably suppressed at large xF (x1 ) [27] as one can see from Fig. 3. The origin of this suppression does not follow from the effects of coherence or shadowing since the corresponding data was obtained by the E772 Collaboration [6] at Fermilab at rather low energy of 800 GeV in the lab. frame. E772 data for DY 1.1 1 E772 data for DY 1.1 1 0.9 0.9 0.8 0.8 6 < M < 7 GeV 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 7 < M < 8 GeV 0.7 GBW with charm GBW KST 0.6 0.5 1.2 GBW with charm GBW KST 0.6 0.5 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x1 x1 Figure 3: Normalized ratio of Drell-Yan cross sections on Tungsten and Deuterium as a function of x1 for two different intervals of the dilepton effective mass. Solid, dashed and dotted curves correspond to different parametrizations of the dipole cross section: KST [33], GBW [34] without and with inclusion of charm quark [35], respectively. Treating the DY process in the rest frame of the nucleus this process looks like radiation of a heavy photon/dilepton by a valence quark [28]. The coherence length in this case is related to the ¯ and reads [28, 27], mean lifetime of a fluctuation q → qll lc = 2Eq α (1 − α ) 1 (1 − α ) M 2 = , mN x2 (1 − α ) M 2 + m2q α 2 + p2T (1 − α ) M 2 + α 2 m2q + p2T 7 (6.1) PoS(High-pT physics09)042 The main attribute of a novel mechanism of nuclear suppression at forward rapidities proposed in [8] is its applicability and validity at any energy. The right panel of Fig. 2 clearly manifests that the pion production in p + Pb collisions at SPS at low energy of 158 GeV in lab. frame exhibits the same pattern of nuclear suppression as that in the RHIC kinematic range. Such a suppression and its rise with xF can not be explained within CGC picture whose validity is confined to the region of x1 < 0.01 hardly accessible at SPS. The model predictions for nuclear suppression have been performed employing the dipole formalism for calculation of nuclear broadening using the standard convolution expression based on QCD factorization from [26]. Initial state multiple interactions leading to breakdown of QCD factorization are included as described in sect. 4 and presented also in [8]. One can see a reasonable agreement of our calculations with NA49 data [5]. Michal Šumbera Nuclear suppression at large x 7. High-pT hadron production at midrapidities Another consequence of energy conservation restrictions in multiple parton rescatterings is √ that nuclear effects should occur also at midrapidities, i.e. at large xT = 2 pT / s. However, the corresponding values of pT should be high enough to keep variable xT on the same level as Feynman xF at forward rapidities. Such an expectation is confirmed by the recent data from the PHENIX Collaboration [13] showing an evidence for nuclear suppression at large pT > 8 ÷ 10 GeV (see the left panel of Fig. 4). At η = 0 the small-pT region is dominated by production and fragmentation of gluons. On the other hand, the region of very large pT is dominated by production and fragmentation of valence quarks. Consequently, any value of the hadron transverse momentum differs only in the relative contributions of valence quarks and gluons. In comparison with reactions at forward rapidities (large xF ) where mostly valence quarks dominate, here one should include also gluons in our calculations. Details can be found in ref. [26]. Correspondingly, the cross section for hadron production, Eq. (4.1), is extended also for gluons with corresponding distribution function, parton scattering cross section and the fragmentation function. Including multiple parton rescatterings, the gluon distribution in the nucleus is given by the same formula as for quarks (see Eq. (4.2), except σe f f in Eq. (4.2), which should be multiplied by the Casimir factor 9/4. If the effects of energy conservation in multiple parton rescatterings are not taken into account the pT dependence of Rd+Au (pT ) is described by the thin dashed line. One can see from the left panel of Fig. 4 that our calculations at moderate pT are not in a bad agreement with data and a small suppression at large pT is given by the isospin effects. After inclusion of energy sharing in multiple parton rescatterings the model predictions presented by the thin solid line underestimate the data at moderate pT . However, at larger pT quite a strong onset of nuclear effects is not in disagreement with corresponding experimental points. 8 PoS(High-pT physics09)042 where M is the effective mass of the dilepton; ~pT and α are the transverse momentum and the fraction of the light-cone momentum of the quark carried by the dilepton; and Eq = xq s/2mN and mq are the energy and mass of the projectile valence quark. The fraction of the proton momentum xq carried by the valence quark in this reference frame is not equal to x1 , but α xq = x1 . At large x1 → 1, also α → 1, i.e. the coherence length Eq. (6.1) vanishes in this limit, no shadowing is possible and nuclear suppression can not be explained by the CGC based models. Alternative interpretation of nuclear suppression at large x1 is based again on energy conservation restrictions in multiple quark rescatterings using results discussed above in sect. 2 (see also [8, 9, 10]). Model calculations have been performed using expressions for the production cross sections in the color dipole approach [29, 30]. For the differential cross section for the photon radiation in a quark-nucleus collision we adopt [31] the light-cone Green function formalism [32] which naturally incorporates effects of quantum coherence. Fig. 3 shows our calculations for several parametrizations of the dipole cross section: KST [33], GBW [34] without and with inclusion of charm quark [35]. The difference between corresponding curves can be treated as a measure of the theoretical uncertainty. Model predictions are in a reasonable agreement with data from the E772 experiment [6]. Michal Šumbera 1.2 π 0 1.1 1 RAu+Au(pT) Rd+Au(pT) Nuclear suppression at large x 1.4 PHENIX data 1.2 1 0.8 0.6 0.9 0.4 without EMC effect and multiple rescatterings with EMC effect without EMC effect 0.2 η=0 0.7 0 0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 4 6 8 10 12 14 16 18 20 pT (GeV) pT (GeV) Figure 4: (Left) Nuclear attenuation factor Rd+Au (pT ) as a function of pT for production of π 0 mesons at √ s = 200 GeV and η = 0 vs. data from PHENIX Collaboration [13]. (Right) Nuclear modification factor for direct photon production in Au − Au collisions as a function of pT . Calculations in the RHIC energy range at midrapidities are most complicated since this is the transition region between the regimes of long (small pT ) and short (large pT ) coherence lengths. Instead of too complicated rigorous light-cone Green function formalism [36, 37, 38, 39] we preset corrections for finite coherence length using the linear interpolation performed by means of the so-called nuclear longitudinal form factor [26]. Such a situation is described by the thick solid and dashed lines reflecting the cases with and without inclusion of energy conservation in multiple parton rescatterings, respectively. It brings the model predictions to a better agreement with data at moderate pT . Finally we would like to emphasize again that nuclear suppression at large pT > 10 GeV observed by the PHENIX experiment [13] can not be explained as a result of CGC because data cover rather large x2 ∼ 0.05 − 0.1 where no effects of quantum coherence are possible. The minimum bias data from the PHENIX Collaboration [13] (see the left panel of Fig. 4) are not very precise and do not allow to make a definite conclusion about the onset of nuclear effects at large pT > ∼ 8 ÷ 10 GeV. However, the same data distributed over different centralities in spite of large error bars demonstrate more decisively that the nuclear suppression Rd+Au < 1 at pT > ∼ 9 ÷ 10 GeV for centrality 0 − 20%. This gives a crucial signal to expect a suppression also for minimum bias events even according to worst scenario when more peripheral collisions do not contribute to overall nuclear suppression (i.e. Rd+Au → 1 at centralities > ∼ 20%). More precise data at midrapidities and large pT are needed in the RHIC energy range for a clear manifestation of breakdown of QCD factorization, R p+Au < 1. 8. Direct photon production in Au+Au collisions Data from the PHENIX Collaboration [14] represent another demonstration of a strong suppression in production of direct photons in Au + Au collisions. Expressions for production cross sections have been derived employing the dipole formalism [32, 29, 30, 22, 40]. Model predictions 9 PoS(High-pT physics09)042 0.8 Michal Šumbera Nuclear suppression at large x for the ratio RAu+Au as a function of pT are compared with the PHENIX data [14] in the right panel of Fig. 4. If energy conservation restrictions in initial state multiple parton interactions are not taken into account the model calculations depicted by the dash-dotted line overestimate the data at large pT > ∼ 13 GeV. The onset of isospin effects gives a value RAu+Au → 0.8 in accord with our calculations. Inclusion of the energy conservation in multiple parton rescatterings leads to stronger nuclear effects at large pT as it is demonstrated by the dashed line. It brings a better agreement of the model with data. Finally, the solid line additionally includes also a small correction for the EMC effect [41]. In this paper we analyze a significant nuclear suppression at forward rapidities (large xF ) and at midrapidities (large xT ) for variety of processes. The new results are the following : • QCD factorization fails at the kinematic limits, xF → 1, xT → 1. Nuclear targets cause a suppression of partons with x → 1, due to energy sharing problems. • Suppression of high-pT hadrons at large forward rapidity observed by the BRAHMS and STAR Collaborations is well explained by the energy conservation restrictions in multiple parton rescatterings. • We predict xF (xT ) scaling of nuclear effects, i.e. the same suppression at different energies and rapidities corresponding to the same value of xF (xT ). • The same formalism explains well the nuclear suppression and its rise with xF at low energy of 158 GeV in the lab. frame in accord with NA49 data [5]. • Suppression of Drell-Yan pairs at large xF observed by E772 Collaboration [6] is again well explained by the same mechanism based on the energy sharing problems in initial state interactions. • As a consequence of energy conservation restrictions in multiple parton rescatterings we √ predict that nuclear effects occur also at midrapidities, i.e. at large xT = 2 pT / s. Model calculations describe well the PHENIX data [13] for production of high-pT hadrons at η = 0. • With the same input we find a strong nuclear suppression for the large- pT direct photon production in Au + Au collisions in a good agreement with the PHENIX data [14]. • Study of nuclear effects at small energies and at midrapidities is very important because at large pT the data cover rather large x2 ∼ 0.05 − 0.1, where no effects of coherence are possible. It allows to exclude the saturation models or the models based on CGC from interpretation of observed nuclear suppression. Acknowledgments: This work was supported in part by the Grant Agency of the Czech Republic, Grant 202/07/0079, by the Slovak Funding Agency, Grant 2/7058/27 and by Grants VZ MSM 6840770039 and LC 07048 (Ministry of Education of the Czech Republic). 10 PoS(High-pT physics09)042 9. Summary and conclusions Michal Šumbera Nuclear suppression at large x References [1] BRAHMS Collaboration, I. Arsene et al., Phys. 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