Effect of meson cloud on the jet nuclear modification factor in pA collisions
aa r X i v : . [ nu c l - t h ] D ec Effect of meson cloud on the jet nuclear modification factor in pA collisions B.G. Zakharov L.D. Landau Institute for Theoretical Physics, GSP-1, 117940, Kosygina Str. 2, 117334 Moscow, Russia (Dated: October 2, 2018)We study the effect of the nucleon meson cloud on centrality dependence of the jet nuclearmodification factor R pA . We find that the meson-baryon Fock components may lead to a noticeabledeviation of R pA from unity. Our results for R pA show the same tendency as that observed byATLAS in p + P b collisions at √ s = 5 .
02 TeV. The meson cloud suppresses the central jet eventsand enhances the peripheral jet events. But quantitatively the effect is somewhat smaller than inthe data.
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I. INTRODUCTION
Factorization of hard and soft process [1] suggests that in the cross section of hard reactions the soft physics can beaccumulated in parton distribution functions (PDFs) of colliding particles. However, the factorization theorems donot forbid the existence of correlations between hard and soft final particles. The correlations of this type have beenobserved in recent measurements by ATLAS [2] of the centrality dependence of the jet nuclear modification factor R pA for p + P b collisions at √ s = 5 .
02 TeV. The R pA for jet production is defined as R pA = dN jetpA /dp T dyN coll dN jetpA /dp T dy , (1)where N jetpA and N jetpp are the jet yields in pA and pp collisions, and N coll is the number of the binary collisions. In [2]it has been observed that the jet nuclear modification factor R pP b in the broad (minimum bias) 0 −
90% centralityregion is close to unity. However, it is not the case for narrow centrality bins. For high p T the R pP b has been foundto be suppressed in central events ( R pP b <
1) and to be enhanced in peripheral events ( R pP b < y > R pP b in the centralevents might arise from the final state interaction effects in the small-size quark-gluon plasma, if it is formed in pP b collisions [3]. However, the fact the minimum bias jet R pP b observed in [2] is approximately consistent with unity,says that the potential effect of the plasma mini-fireball is small (or it is well compensated by the medium effects in pp collisions [4] due to modification of the denominator of (1) [3]). In [5] it was proposed that the ATLAS data [2]can be explained by the initial state correlations of the hard and soft partons in the wave function of the projectileproton. The mechanism of [5] assumes that in the presence of an energetic parton (which is necessary for a hardprocess to occur) the number of soft partons in the projectile is suppressed. Then, assuming that the multiplicityof soft particles produced in the underlying events (UEs) with jet production is proportional to the number of softpartons in the projectile proton, it leads naturally to correlation of the jet R pA with the multiplicity/centrality ofthe UEs. In the recent more sophisticated analyses [6, 7] this parton level mechanism has been addressed withinthe Monte-Carlo generators PYTHIA and HIJING. But only a very crude agreement with the ATLAS data [2] hasbeen attained. However, of course, similarly to [5], the analyses [6, 7] are of a qualitative nature. Because, dueto the nonperturbative physics of the UE, it impossible to obtain robust predictions for the multiplicity/centralitydependence of R pA within the parton level schemes.The purpose of the present work is to study the effect of the meson-baryon Fock components in the proton on thejet nuclear modification factor. It is known that the total weight of the meson-baryon Fock states in the fast physicalnucleon may be as large as ∼
40% [8]. The meson cloud of the proton plays an important role in the flavor dependenceof nucleon PDFs in deep inelastic scattering (DIS), and is probably responsible for the violation of the Gottfried sumrule [8]. The emergence of the centrality dependence of R pA in the scenario with the meson cloud is conceptuallyvery similar to the partonic mechanism of [5]. In this scenario the hard process selects in the projectile proton wavefunction fluctuations with a reduced fraction of the meson-baryon states (as compared to the soft interactions). Itresults in suppression of the UE multiplicity in jet production at high p T , that should lead to centrality dependenceof R pA due to difference in the centrality categorization for minimum bias (soft) events and jet events. In the presentanalysis we simulate the UE activity in jet events within the Monte-Carlo Glauber (MCG) wounded nucleon modelwith the meson cloud developed in [9, 10]. We find that a considerable part of the centrality dependence of the jetnuclear modification factor measured by ATLAS [2] may be explained by the meson-baryon Fock components of theproton. II. THEORETICAL FRAMEWORK
Our treatment of the meson-baryon components is similar to that in previous analyses of the meson cloud effects inDIS based on the infinite momentum frame (IMF) picture [8, 11–13]. In this picture the physical nucleon IMF wavefunction reads | N phys i = p W N | N i + X MB Z dxd k Ψ MB ( x, k ) | M B i , (2)where N , B , and M denote the bare baryon and meson states, x is the meson fractional longitudinal momentum, k is the tranverse meson momentum, Ψ MB is the M B probability amplitude, W N = 1 − W MB is the weight of theone-body Fock state in the physical nucleon, and W MB = X MB Z dxd k | Ψ MB ( x, k ) | (3)is the total weight of the M B
Fock components. The proton PDF for a parton i , D i/p , corresponding to the Fockstate decomposition (2), can be written as [8] D i/p ( x, Q ) = W N ˜ D i/p ( x, Q ) + Z x dyy ˜ D i/M ( x/y, Q ) f M/p ( y ) + Z x dyy ˜ D i/B ( x/y, Q ) f B/p ( y ) . (4)Here ˜ D i/M and ˜ D i/B are the PDFs for the bare particles, and f M,B/p are the p → M, B splitting functions given by f M/N ( x ) = Z d k | Ψ MB ( x, k ) | , (5) f B/N ( x ) = Z d k | Ψ MB (1 − x, k ) | . (6)The analyses of the meson effects in DIS [8, 11–13] show that in the Fock state decomposition (2) it is enoughto include πN , π ∆, ρN and ρ ∆ two-body systems. The total weight of these states in the physical nucleon isabout 40% [8] with the dominating contribution from the πN states. For simplicity, we neglect the difference in thePDFs generated by the above four two-body states, and treat them as one effective πN state with normalization W MB = 0 .
4. This is a reasonable assumption, because the ∆ and ρ PDFs should be close to that for N and π .Following the analyses of DIS [8, 13] we evaluated the f π/p splitting function using the ordinary γ pion-nucleonvertex with the dipole formfactor F = (cid:18) Λ + m N Λ + M πN ( x, k ) (cid:19) (7)with Λ = 1 . M πN is the invariant mass of the πN state in the IMF.We write the jet cross section ( σ ( p T , y ) = dσ/dp T dy ) as a sum σ ( p T , y ) = σ N ( p T , y ) + σ MB ( p T , y ) , (8)where the first term on the right-hand-side of (8) corresponds to the one-body contribution to the proton PDFs fromthe first term in (4), and the second term describes the effect from the last two terms in (4) due to the two-body Fockcomponents. In jet events the dynamics of the UEs in pA collisions depends crucially on the relative contribution ofthe σ N and σ MB to the total jet cross section, because it controls the probabilities of the N and M B states in thehard process given by W jN ( p T , y ) = σ N ( p T , y ) σ N ( p T , y ) + σ MB ( p T , y ) , (9) W jMB ( p T , y ) = σ MB ( p T , y ) σ N ( p T , y ) + σ MB ( p T , y ) . (10)In our model in jet events soft interaction of the projectile proton and the nucleus with the probability W jN occurs as N + A collision and with the probability W jMB as M B + A collision.As usual, we define the minimum bias centrality c through the theoretical charged multiplicity distribution P [14] c ( N ch ) = ∞ X N = N ch P ( N ) . (11)Here N ch is the theoretical charged multiplicity in the pseudorapidity window used for the centrality categorization(as in [9, 10] we use the pseudorapidity region | η | < . R pA arises due to the fact that the shapes of the charged multiplicity distributions for the minimumbias soft events (used in the centrality selection) and for the jet events are different. For a given centrality class { c } N coll can be written as [15] N coll ( { c } ) = σ NNin σ pAin Z d b T ( b ) P s ( { c } , b ) , (12)where P s is the probability that multiplicity of the UE belongs to the centrality class { c } and T is the impact parameterprobability distribution of the binary collisions. In the approximation of zero interaction radius T is reduced to thenuclear profile function T A ( b ) = R dzρ A ( b , z ) ( ρ A is the nuclear density). In our two-component model P s can bewritten as P s ( { c } , b ) = W N P N ( { c } , b ) + W MB P MB ( { c } , b ) , (13)where P N,MB ( { c } , b ) are the centrality probabilities for the N + A and M B + A collisions. In calculation of thenumerator of (1) the probability that in a jet event the multiplicity for the UE belongs to the centrality class { c } (wedenote it P j ) can be written via W jN and W jMB as P j ( { c } , b, p T , y ) = W jN ( p T , y ) P N ( { c } , b ) + W jMB ( p T , y ) P MB ( { c } , b ) . (14)In terms of the probabilities (13), (14) the theoretical R pA can be written as R pA ( { c } , p T , y ) = R ( p T , y ) R d b T ( b ) P j ( { c } , b, p T , y ) R d b T ( b ) P s ( { c } , b ) . (15)Here the factor R account for modification of the hard cross section due to the nuclear modification of the PDFs ofbound nucleons (in nucleus). For the whole centrality range { c } = (0 , P j,s = 1 and R pA is simply reduced to R . III. NUMERICAL RESULTS AND DISCUSSION
In Fig. 1 we show f M/p splitting function used in (4) obtained with γ pion-nucleon vertex for the dipole formfactor(7). One can see that the meson spectrum is strongly peaked near x ∼ .
3. For the bare meson PDFs in (4) we use theLO parametrization of the pion PDFs of [17]. For the bare nucleon PDFs we use the LO CTEQ6 [16] parametrizations.For the PDF momentum scale Q for pion we use the hard parton transverse momentum p T . In our model, due to thepresence of the M B component, the transverse mean-square radius of the bare proton becomes smaller by a factor of a ≈ .
88. To account for a possible decrease of the range of the DGLAP evolution due to a bigger initial momentumscale we take Q = ap T for the bare nucleon PDFs. However, the choice Q = p T gives practically same results. For thenucleons in a lead nucleus we use the LO CTEQ6 [16] PDFs with the EKS98 [18] nuclear corrections. The hard crosssections have been calculated using the LO pQCD formula. To simulate the higher order effects for the virtualityscale in α s we take the value cQ with c = 0 .
265 as in the PYTHIA event generator [19]. This gives a fairly gooddescription of the p T -dependence of the inclusive jet cross section obtained in [2].We have computed the numerator and denominator of (15) by sampling pA collisions within the MCG model withmeson cloud developed in [9, 10]. The interested reader is referred to those papers for details of our MCG scheme.In Fig. 2 we compare our results with the ATLAS data [2]. To illustrate the effect of the nuclear modification ofthe nucleon PDFs, in Fig. 2 we present the results obtained with and without the EKS98 correction factor R in(15). From Fig. 2 one sees that the effect of the meson cloud on the R pA shows qualitatively the same tendency asthat observed by ATLAS [2]. The M B component suppresses the central jet events and enhances the peripheral jet x f M / p ( x ) FIG. 1: f M/p splitting function normalized to W MB = 0 . x -distribution for the πN Fock component. p T [GeV] R p P b FIG. 2: R pPb versus p T for p + P b collisions at √ s = 5 .
02 TeV for 0-10% (upper), 20-30% (middle), 60 −
90% (lower) centralityclasses. The solid curves show our results with the EKS98 correction factor R in (15), and the dashed ones without R . Datapoints are from ATLAS [2]. events. Similarly to the ATLAS data the effect is more pronounced at y >
0. However, quantitatively the effect issomewhat smaller than in the data. It is possible that a better agreement with the ATLAS data [2] can be obtained byaccounting for the correlations between hard and soft partons in the bare constituents in the projectile proton, due tothe mechanism discussed in [5–7]. We postpone this for future work. Also, it is possible that the meson effects in theproton PDFs can be enhanced due to the nonperturbative quark-gluon-pion anomalous chromomagnetic interactionrelated to the instantons discussed recently in [20].
Acknowledgments
I thank N.I. Kochelev for discussion of the results of [20]. This work is supported in part by the grant RFBR15-02-00668-a.
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