Predictions for p + Pb at 4.4A TeV to test initial state nuclear shadowing at the Large Hadron Collider. G. G. Barnaf¨oldi,1 J. Barrette,2 M. Gyulassy,3,1 P. Levai,1 and V. Topor Pop2 1WIGNER RCP, Institute for Particle and Nuclear Physics P.O.Box 49, Budapest, 1525, Hungary 2 2McGill University, Montreal, H3A 2T8, Canada 1 0 3Columbia University, New York, N.Y. 10027, USA 2 n (Dated: January 23, 2012) a J Abstract 3 2 Collinear factorized perturbative QCD model predictions are compared for p+Pb at 4.4A TeV ] h to test nuclear shadowing of parton distribution at the Large Hadron Collider (LHC). The nuclear t - cl modification factor (NMF), RpPb(y = 0,pT < 20 GeV/c) = dnpPb/(Ncoll(b)dnpp), is computed u n with electron-nucleus (e+A) global fit with different nuclear shadow distributions and compared [ to fixed Q2 shadow ansatz used in Monte Carlo Heavy Ion Jet Interacting Generator (HIJING) 2 v 6 type models. Due to rapid DGLAP reduction of shadowing with increasing Q2 used in e+A global 4 6 fit, our results confirm that no significant initial state suppressionis expected (R (p ) = 1 0.1) pPb T 3 ± . in the p range 5 to 20 GeV/c. In contrast, the fixed Q2 shadowing models assumed in HIJING 1 T 1 1 type models predict in the above pT range a sizable suppression, RpPb(pT) = 0.6 0.7 at mid- − 1 : pseudorapidity that is similar to the color glass condensate (CGC) model predictions. For central v i X (N = 12) p + Pb collisions and at forward pseudorapidity (η = 6) the HIJING type models coll r a predict smaller values of nuclear modification factors (R (p )) than in minimum bias events at pPb T mid-pseudorapidity (η = 0). Observation of R (p = 5 20 GeV/c) < 0.6 for minimum bias pPb T − ∼ p+A collisions would pose a serious difficulty for separating initial from final state interactions in Pb+Pb collisions at LHC energies. PACS numbers: 12.38.Mh, 24.85.+p,25.75.-q, 24.10Lx 1 I. INTRODUCTION In this paper we compare predictions for moderate p < 20 GeV/c observables in p+Pb T reactions at 4.4A TeV at the Large Hadron Collider (LHC), that will help to discriminate between models of initial conditions assumed in Pb+Pb collisions at 2.76A TeV. The possi- bility that the first data on p+Pb may be taken soon, with a potential high physics payoff motivates this paper. All models details are extensively discussed in the literature and we focus only on the updated nuclear modification factor, R (η,p ,b) = dn /(N (b)dn ), pPb T pPb coll pp predictionstestablewithashort4.4ATeVrun. Inminimum bias(MB)andcentral (0 20%) − p+Pb collisions the average number of binary nucleon-nucleon (NN) interactions (with an inelastic cross section σin 65 mb) is NMB 7 and NCen 12 respectively. NN ≈ coll ≈ coll ≈ This control experiment has long been anticipated to play a decisive role in helping to deconvolute initial and final state interaction effects in Pb+Pb reactions at the LHC. The d + Au control experiment at 0.2A TeV played a similar critical role for Au+Au at the Relativistic Heavy Ion Collider (RHIC) in 2004 [1, 2]. The importance of p+Pb was also emphasized in the 2007 Last Call for LHC compilation of predictions [3] and many other works [4–10]. The open problem after the first very successful LHC heavy ion run in 2010 [11] remains how to deconvolute nuclear modification effects due to initial state and final state effects. Without a clear calibration of the magnitude of initial state suppression of the incident nuclear partonic flux it is not possible to draw firm conclusions about the properties of the quark gluon plasma (QGP) phase of matter produced at the LHC. At RHIC the same prob- lemwasresolved atmid-rapidity bytheobservationofnoappreciable nuclear modificationin d+Au control experiments in 2003 [1, 2] (see also Figure 3 below). An approximately factor of four suppression of moderate p mid-rapidity pions observed in Au+Au at RHIC could T then be interpreted as due to final state jet energy loss in a high opacity QGP produced in central Au+Au collisions at RHIC. At the LHC the initial flux is much more uncertain than at RHIC because of the higher density ofpartons atanorder of magnitude smaller fractionalmomenta x = 2p /√s < 10−3. T At high initial densities all models predict a breakdown of additivity of the nuclear parton distribution functions (nPDF). The magnitude of the breakdown however varies greatly in the literature in both collinear factorized approaches and k factorized parton saturation T 2 model approaches [3–5, 7–10]. Therefore, even a rough first experimental constraint from p+Pbinteractions would have highimpact onthe development ofnuclear collision modeling. II. NUCLEAR SHADOWING AND JET QUENCHING AT LHC ENERGIES Nuclear shadowing of quark and gluon nPDFs at large x > 0.01 and moderate Q2 is well constrained from e + A and lower energy p + A data. Global fit parametrizations of the nuclear parton distribution functions (nPDF) are available [5, 8, 9]. DGLAP evolution [12] to higher Q2 predicts a rapid reduction of shadowing effects and therefore only modest modifications of R (p ) = 1 0.1 for p > 5 GeV/c have been predicted [9, 10, 13]. As pPb T T ± emphasized in [10], any observed significant modification from unity would be inconsistent with most current nPDFs and therefore pose a severe challenge to conventional collinear factorized QCD approximation to high-p processes not only in p+Pb but even more so in T Pb+Pb collisions. We continue here to investigate this central thesis. AtRHICthereisclearevidence athighrapidities, wheresmall fractionalpartonmomenta x 10−3 similar to central p + Pb are probed, that binary collision scaling of collinear ∼ factorization breaks down. Color Glass Condensate (CGC) k factorization models have T been developed to explain these deviations [14, 15] and nearly identical R 0.7 0.1 pA ≈ ± nuclear modifications factors were predicted in Ref. [14] (KKT04) for forward rapidities at RHIC and mid-rapidity at the LHC. However, collinear factorized approaches with DGLAP evolved nPDF appear to provide an alternate explanation of forward single inclusive yields at RHIC [5, 8]. At LHC energies we can differentiate between these explanations because the collinear factorized approach predicts only small nuclear modification for mid-rapidity pions (see Fig. 3 below), while at RHIC energies it predicts large modifications, as CGC does, for forward produced pions. The much higher energy range at the LHC also opens the kinematic window on small x physics that can be explored in p+A collisions at mid-rapidity. Some CGC models [16, 17] predict a suppression with R (η = 0,p 10GeV/c) 0.5 with strong dependence on pPb T ≈ ≈ the initial evolution conditions. Such small values of R would imply that nearly all pPb nuclear suppression observed in NMF R in Pb+Pb collisions, previously attributed to PbPb jet quenching in the final state, could instead be due to nonlinear initial state parton flux suppression. 3 Due to a factor of two increase in the final parton densities at the LHC, jet quenching is expected to produce higher suppression than at RHIC energies. Actually, the observed Pb+Pb suppression of pions at the LHC energy was surprisingly weaker than expected from RHIC constrained analysis extrapolated to the LHC [18]. Thus, from the perturbative final state interaction point of view there appears to be no room for initial state suppression. Therefore, a measurement of R at mid-rapidity significantly less than unity would con- pPb tradict not only perturbative QCD (pQCD) models of the initial state nPDF evolution but also theory of the final state perturbative opacity series of jet energy loss. Since strong coupling AdS/CFT holography [19] predicts even stronger final state suppression effects, an observation in p+Pb of significant deviations from unity would then call into question the validity of holographic interpretations of RHIC and LHC A+ A results, including the applicability of minimal viscous hydrodynamics to apparent perfect fluidity. At sufficiently high energies and virtualities, QCD factorization theorems guarantee that jet observables can be calculated in perturbation theory. The open question is at what scale does factorization break down for nuclear processes. CGC theory [14–17, 20–28] has a saturation natural scale Q (x,A) that in principle provides the answer when Q >> Λ . s s QCD However, nuclear jet observables up to LHC energies are sensitive to details of large x > 0.01 < as well as small A = 1 “corona” nucleon distributions for which Q 1 GeV. s ∼ Monte Carlo models as HIJING1.0 [29], HIJING2.0 [30] and HIJING/BB¯2.0 [31] have been developed to study hadron productions in p+p, p+A and A+A collisions. They are es- sentially two-component models, which describe the production of hard parton jets and the soft interaction between nucleon remnants. The hard jets production is calculated employ- ing collinear factorized multiple minijet within pQCD. A cut-off scale p in the transverse 0 momentum of the final jet production has to be introduced below which (p < p ) the T 0 interaction is considered nonperturbative and is characterized by a finite soft parton cross section σ . Jet cross section, depend on the parton distribution functions (PDFs) that are soft parametrized from a global fit to data [30]. Nucleons remnants interact via soft gluon exchanges described by the string models [33, 34] and constrained from lower energy e + e,e + p,p + p data. The produced hard jet pairs and the two excited remnants are treated as independent strings, which fragments to resonances that decay to final hadrons. Longitudinal beam jet string fragmentations strongly depend on the values used for string tensions that control quark-anti-quark (qq¯) 4 anddiquark-anti-diquark (qqqq) paircreationratesandstrangeness suppression factors(γ ). s In the HIJING1.0 and HIJING2.0 models a constant (vacuum value) for the effective value of string tension is used, κ = 1.0 GeV/fm. At high initial energy density the novel nuclear 0 physics is due to the possibility of multiple longitudinal flux tube overlapping leading to strong longitudinal color field (SCF) effects. Strong Color Field (SCF) effects are modeled in HIJING/BB¯2.0 by varying the effective string tensions value. SCF also modify the frag- mentation processes resulting in an increase of (strange)baryons which play an important role in the description of the baryon/meson anomaly. In order to describe p+p and central Pb + Pb collisions data at the LHC we have shown that an energy and mass dependence of the mean value of the string tension should be taken into account [31]. Moreover, to better describe the baryon/meson anomaly seen in data a specific implementation of JJ¯ loops, has to be introduced. For a detailed discussion see Ref. [31]. Similar result can be obtained by including extra diquark-antidiquark pair production channels from strong coherent fields formed in heavy ion collisions [32]. All HIJING type models implement nuclear effects such as nuclear modification of the partons distribution functions, i.e., shadowing and jet quenching via a medium induced parton splitting process (collisional energy loss is neglected) [29]. In the HIJING1.0 and HIJING/BB¯2.0 models Duke-Owen (DO) parametrization of PDFs [35] is used to calculate the jet production cross section with p > p . In both models using a constant cut-off T 0 p = 2 GeV/c and a soft parton cross section σ = 54 mb fit the experimental p + p 0 soft data. However, for A+ A collisions in HIJING/BB¯2.0 model we introduced an energy and mass dependence of the cut-off parameter, p (s,A) [31] at RHIC and at the LHC energies, in 0 order not to violate the geometrical limit for the total number of minijets per unit transverse area. In HIJING2.0 [30] model that is also a modified version of HIJING1.0 [29] the Gluck- Reya-Vogt (GRV) parametrization of PDFs [36] is implemented. The gluon distributions in this different parametrization are much higher than the DO parametrization at small x. In addition, an energy-dependent cut-off p (s) and σ (s) are also assumed in order to better 0 soft describe the Pb + Pb collisions data at the LHC. One of the main uncertainty in calculating charged particle multiplicity density in Pb + Pb collisions is the nuclear modification of parton distribution functions, especially gluon distributions at small x. In HIJING type models one assume that the parton distributions per nucleon in a nucleus (with atomic number A and charge number Z), f (x,Q2), are a/A 5 factorizableintopartondistributionsinanucleon(f )andtheparton(a)shadowing factor a/N (S ), a/A f (x,Q2) = S (x,Q2)f (x,Q2) (1) a/A a/A a/N The impact parameter dependence is implemented through the parameter s , a 5 b2 s (b) = s 1 (2) a a3 (cid:18) − R2 (cid:19) A where R = 1.12A1/3 is the nuclear radius. A In HIJING/BB¯2.0 the shadowing factor for gluon and quark are assumed to be equal (S (x,Q2) = S (x,Q2)) and are similar with those used in HIJING1.0 [29]. They were g/A q/A selected in order to fit the centrality dependence of the central charged particle multiplicity density attheLHC.Incontrast, inHIJING2.0amuch strongerimpactparameterdependence of the gluon (s = 0.22 0.23) and quark (s = 0.1) shadowing factor is used in order to g q − fit the LHC data. Due to this stronger gluon shadowing the jet quenching effect has to be neglected [30]. Note, all HIJING type models assume a scale-independent form of shadowing parametrization (fixed Q2). This approximation could breakdown at very large scale due to dominance of gluon emission dictated by the DGLAP [12] evolution equation. At Q = 2.0 and 4.3 GeV/c, which are typical scales for mini-jet production at RHIC and LHC respectively, it was shown that the gluon shadowing varies approximately by 13% in EPS09 parametrizations [6]. III. COMPARATIVE STUDY OF MODEL PREDICTIONS Figure 1 shows HIJING/BB¯2.0 predictions of the global observables dN /dη and R (η) ch pPb = (dNch )/dη)/(N dNch/dη) characteristics of minimum bias p + Pb collisions at 4.4A pPb coll pp TeV. The predictions for p+p are also shown. Minijet cutoff and string tension parameters p = 3.1 GeV/c and κ = 2.9 GeV/fm for p+Pb are determined from fits to p+p and A+A 0 systematics from RHIC to the LHC (see Ref. [31] for details). Note, these calculations assume no jet quenching. The absolute normalization of dN /dη is however sensitive to the low p < 2 GeV/c non- ch T perturbative hadronization dynamics that is performed via LUND [33] string JETSET [34] fragmentationasconstrained fromlower energy e+e,e+p,p+p data. The default HIJING1.0 parametrization of the fixed Q2 = 2 GeV2 shadow function leads to substantial reduction 0 6 40 2 ) hd 35 p+Pb, YS (with shadow) h(1.75 YS (b = 0-9 fm) /ch p+Pb, NS (no shadow) Pb NS (b = 0-9 fm) dN 30 pp Rp1.5 Ncoll = 6.4 25 1.25 20 1 15 0.75 10 0.5 5 0.25 0 0 -10 -5 0 5 10 -10 -5 0 5 10 h h pseudorapidity, pseudorapidity, FIG. 1: (Color online) (a) HIJING/BB¯2.0 predictions of charged particles pseudorapidity distri- bution (dN /dη) for minimum bias (MB) p+Pb collisions at 4.4A TeV. Solid YS curve includes ch fixed Q2 shadowing functions from HIJING1.0 [29], while the dashed NS curve has no shadowing. (b) Ratio R (η) calculated assuming N (MB) = 6.4 pPb coll (solid histograms) of the global multiplicity at the LHC. It is important to emphasize that theno shadowing results (dashed curves) aresubstantially reduced inHIJING/BB¯2.0 relative to no shadowing prediction with default HIJING/1.0 from Ref. [29], because both the default minijet cut-off p = 2 GeV/c and the default vacuum string tension κ = 1 GeV/fm (used 0 0 in HIJING1.0) are generalized to vary monotonically with centre of mass (cm) energy per nucleon √s and atomic number, A. As discussed in [31], systematics of p+p and Pb+Pb multiparticle production from RHIC to the LHC are used to fix the energy (√s) and the A dependence. Thus the cut-off parameter p (s,A) = 0.416 √s0.191 A0.128 GeV/c and the 0 mean value of the string tension κ(s,A) = κ (s/s0)0.06 A0.167 GeV/fm. The above formulae 0 lead to p = 3.1 GeV/c and κ = 2.9 GeV/fm at 4.4A TeV for p+Pb collisions. For p+p 0 collisions at 4.4TeVwe use aconstant cut-offparameter p = 2 GeV/candastring tension 0pp value of κ = 2.7 GeV/fm. pp Note, even in the case of no shadowing shown in Fig. 1, the increase to p = 3.1 GeV/c 0 from p = 2 GeV/c (value used in p+p at 4.4 TeV) causes a significant reduction by a factor 0 of roughly two of the minijet cross section and hence final pion multiplicity. This reduction 7 of minijet production also is required to fit the low charged particle multiplicity growth in A+A collisions from RHIC to LHC (a factor of 2.2) [37]. ] 2 c 2 -V 10 R p+Pb, YS (b = 0-9 fm) YS, N = 6.4 e pPb coll G 1 p+Pb, NS (b = 0-9 fm) NS, N = 6.4 [ -1 pp coll 10 -2 hd T10 1 p -3 d 10 / -4 h c10 N -5 2 10 CGC - rcBK d ) -6 EKS99 T10 p -7 |h| < KKT04 |h| < 0.8 0.8 10 HIJING2.0 p2 -8 -1 / 10 10 1 ( 0 5 10 15 20 0 5 10 15 20 p [GeV/c] p [GeV/c] T T FIG.2: (Coloronline)(a)Minimumbiastransversemomentumdistributionsatmid-pseudorapidity η < 0.8 predicted by HIJING/BB¯2.0 with (solid histogram) and without (dashed histogram) | | HIJING1.0 shadowing functions [29]. The results for p+p collisions at 4.4 TeV (dotted histogram) are also included. (b) The mid-pseudorapidity nuclear modification factor of charged hadrons R from HIJING/BB¯2.0 model. The solid and thin dashed histograms have the same meaning pPb as in part (a). They are compared to pQCD leading order (LO) predictions (dash dotted) [13] using HIJING2.0 shadowing functions [30], and to DGLAP Q2 evolved nPDF, EKS99 (dotted) [4]. Predictions of CGC model (thick dashed) [14] (KKT04) and CGC - rcBK model (thick solid) from Ref. [27] are also included. We interpret this as additional phenomenological evidence for gluon saturation physics not encoded in leading twist shadow functions. The p > 5 GeV/c minijets tails are un- T affected but the bulk low p < 5 GeV/c multiplicity distribution is sensitive to this extra T energy (√s) and A dependence of the minijet shower suppression effect. It is difficult to relatep tosaturationscale Q directly, because inHIJINGhadronizationproceeds through 0 sat longitudinal field string fragmentation. The energy (√s) and A dependence of the string tension value arises from strong color field (color rope) effects not considered in CGC phe- 8 nomenologythatassumes k factorizedgluonfusionhadronization. HIJINGhadronizationof T minijets is not via independent fragmentation functions as in PYTHIA [34], but via string fragmentation with gluon minijets represented as kinks in the strings. The interplay be- tween longitudinal string fragmentation dynamics and minijets is a nonperturbative feature of HIJING type models. The approximate triangular (or trapezoidal) rapidity asymmetry seen in the ratio R (η) sloping downwards from the nuclear beam fragmentation region at pPb negative pseudorapidity η < 5 toward 1/N in the proton fragmentation region (η > 5) coll − is a basic Glauber geometric effect first explained in Refs. [38, 39] and realized via string fragmentation in HIJING. In Fig. 2 are displayed the predicted transverse spectra and nuclear modification factor for charged hadrons at mid-pseudorapidity, η < 0.8. Including shadowing reduces R pPb | | from unity to about 0.7 in the interesting 5 to 10 GeV/c region close to the prediction of Color Glass Condensate model [14] (KKT04). A similar nuclear modification factor is found [13] using leading order (LO) pQCD collinear factorization with HIJING2.0 parameterization of shadowing functions [40], GRV parton distribution functions (nPDF) from Ref. [36], and hadron fragmentation functions from Ref. [41]. In stark contrast to the three curves near 0.7 0.1 from completely different dynami- ± cal modeling the standard DGLAP evolved global e+A fit nPDF (dotted curve labelled EKS99 [4]) predicts near unity for transverse momenta above 5 GeV/c. The no shadowing HIJING/BB¯2.0 values (NS, thin dashed histogram) goes to unity above 5 GeV/c, but the nonperturbative string hadronizationpullstheintercept atp = 0nearto 1/2asconstrained T by the global triangular enhanced form of dN /dη relative to dN /dη shown in Fig. 1b. pPb pp Note, that the model BGK77 from Refs. [38, 39] also predicts R (y,p = 0) = 1 at the pA T nuclear target rapidity and 1/N (b) at the proton projectile rapidity. coll However, a recent new version of the CGC-rcBK model [27] predicts essentially no shad- owing/saturation effects at η = 0 in contrast to both CGC-KKT04 [14] and CGC-rcBK model from Ref. [16]. The absence of shadowing at midrapidity in the CGC-rcBK [27] model is due to a phenomenological extra anomalous dimension γ, introduced to modify color dipole cross section σ (r) (r2)γ. This significantly steepens the pp transverse dipole ∝ momentum distribution relative to the quadratic form σ (r) r2 used in CGC model dipole ∝ (MV) [42] as required to reproduce LHC pp data. Recently, posible extra A dependence of this extra anomalous dimension has been proposed [28]. It would be very surprising indeed 9 if future p + Pb data would show no evidence of shadowing with a R 1.0 at η = 0 pPb ≈ mid-pseudorapidity which could then be ascribed either to (i) rapid DGLAP Q2 evolution of shadowing in EKS09 [6] parametrization or to (ii) accidental cancellation of deep satura- tion effects due to an anomalous short distance behavior of the dipole cross section in CGC modeling. FIG. 3: (Color online) Predictions updated at 4.4A TeV of Refs. [13] results for central 0 20% − (b < 3.5 fm) p+ Pb at mid-rapidity. The original predictions at 0.2A TeV for d+ Au are also included. Compared are the results obtained with fixed Q2 shadowing functions HIJING2.0 [30] with (b-dep) and without (b-indep) impact parameter dependence. Predictions with DGLAP Q2 evolved shadowing functions from Ref. [4] (EKS99) and Ref. [5] (EPS08) are also shown. The data are from PHENIX Collaboration [43]. What is significant about higher p deviations from unity is that the nuclear modification T factor in central A+A collisions is related to the minimum bias p+A by simple Glauber geometric considerations, that can be expressed as 10