Exclusive photoproduction of J/psi and psi(2S) states in pp and AA collisions at the LHC
aa r X i v : . [ h e p - e x ] O c t Exclusive photoproduction of
J/ψ and ψ (2 S ) statesin pp and AA collisions at the LHC Magno V. T. Machado
High Energy Physics Phenomenology Group, GFPAE IF-UFRGSCaixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
In this contribution we report on the investigations of the exclusive production of
J/ψ and ψ (2 S ) states in proton-proton and nucleus-nucleus reactions at the LHC using thetheoretical framework of light-cone dipole formalism. The exclusive vector meson photoproduction has being investigated both experimentally andtheoretically in recent years as it allows to test perturbative Quantum Chromodynamics. Thequarkonium masses, m V , give a perturbative scale for the problem even in the photoproductionlimit. An important feature of these processes at the high energy regime is the possibility toinvestigate the Pomeron exchange. For this energy domain hadrons and photons can be con-sidered as color dipoles in the mixed light cone representation, where their transverse size canbe considered frozen during the interaction. Therefore, the scattering process is characterizedby the color dipole cross section describing the interaction of those color dipoles with the nu-cleon/nucleus target. Here, we summarize the results presented in Refs. [1] where the exclusiveproduction of J/ψ and the radially excited ψ (2 S ) mesons were studied in pp and AA colli-sions in the LHC energy range. The theoretical framework considered is the light-cone dipoleformalism, where the c ¯ c fluctuation (color dipole) of the incoming quasi-real photon interactswith the nucleon or nucleus target via the dipole cross section and the result is projected in thewavefunction of the observed hadron. At high energies, the transition of the regime describedby the linear dynamics of emissions chain to a new regime where the physical process of re-combination of partons becomes important is expected. It is characterized by the limitation onthe maximum phase-space parton density that can be reached in the hadron wavefunction, theso-called parton saturation phenomenon. The transition is set by saturation scale Q sat ∝ x λ ,which is enhanced in the nuclear case. The predictions for ψ (2 S ) are somewhat new as mostpart of predictions in literature concern only to the ψ (1 S ) state. The exclusive meson photoproduction in hadron-hadron collisions can be factorized in termsof the equivalent flux of photons of the hadron projectile and photon-target production crosssection [2]. The photon energy spectrum, dN pγ /dω , which depends on the photon energy ω , iswell known [2]. The rapidity distribution y for charmonium photoproduction in pp collisionsan be written down as, dσdy ( pp → p ⊗ ψ ⊗ p ) = S (cid:20) ω dN pγ dω σ ( γp → ψ ( nS ) + p ) + ( y → − y ) (cid:21) . (1)The produced state with mass m V has rapidity y ≃ ln(2 ω/m V ) and the square of the γp centre-of-mass energy is given by W γp ≃ ω √ s . The absorptive corrections due to spectatorinteractions between the two hadrons are represented by the factor S gap . The photon-Pomeroninteraction will be described within the light-cone dipole frame, where thee probing projectilefluctuates into a quark-antiquark pair with transverse separation r (and momentum fraction z )long after the interaction, which then scatters off the hadron. The cross section for exclusivephotoproduction of charmonia off a nucleon target is given by, σ ( γp → ψ ( nS ) + p ) = 116 πB V (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)X h, ¯ h Z dz d r Ψ γh, ¯ h σ dip ( x, r ) Ψ V ∗ h, ¯ h (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (2)where Ψ γ and Ψ V are the light-cone wavefunction of the photon and of the vector meson,respectively. The Bjorken variable is denoted by x , the dipole cross section by σ dip ( x, r ) andthe diffractive slope parameter by B V . Here, we consider the energy dependence of the slopeusing the Regge motivated expression (see [1] for details). Similarly, the rapidity distribution y in nucleus-nucleus collisions has the same factorized form, dσdy ( AA → A ⊗ ψ ( nS ) ⊗ Y ) = " ω dN Aγ dω σ ( γA → ψ ( nS ) + Y ) + ( y → − y ) , (3)where the photon flux in nucleus is denoted by dN Aγ /dω and Y = A (coherent case) or Y = A ∗ (incoherent case). The exclusive photoproduction off nuclei for coherent and incoherentprocesses can be simply computed in high energies where the large coherence length l c ≫ R A is fairly valid. the expressions for both cases are given by [3], σ ( γA → ψ ( nS ) + A ) = Z d b |h Ψ V | − exp (cid:20) − R G σ dip ( x, r ) T A ( b ) (cid:21) | Ψ γ i| ,σ ( γA → ψ ( nS ) + A ∗ ) = 116 π B V ( s ) Z d b T A ( b ) |h Ψ V | R G σ dip ( x, r ) exp (cid:20) − R G σ dip ( x, r ) T A ( b ) (cid:21) | Ψ γ i| , where T A ( b ) = R dzρ A ( b, z ) is the nuclear thickness function. In the numerical evaluations,we have considered the boosted gaussian wavefunction and the phenomenological saturationmodel proposed in Ref. [4] (CGC model) which encodes the main properties of the saturationapproaches. The nuclear ratio for the gluon density is denoted by R G ( x, Q = m V / pp collisions at the forward region 2 . < η ± < . x variabledown to x ≈ × − . We assume for the absorption factor the average value S = 0 . σ ( pp → p + J/ψ + p ) × Br = 698 pb for rapidity between 2 and 4.5. In terms ofmuon pseudorapidities we get σ pp → J/ψ ( → µ + µ − ) (2 . < η µ ± < .
5) = 298 pb. This is in goodagreement to the experimental result 307 ±
42 pb [5]. For the ψ (2 S ) mesons it is obtained σ ( pp → p + ψ (2 S ) + p ) × Br = 18 pb for rapidities 2 . < y < .
5. Accordingly, we now predict σ pp → ψ (2 S )( → µ + µ − ) (2 . < η µ ± < .
5) = 7 . . ± . y d σ / d y [ m b ] ALICE dataR G = 1R G = Model 1R G = Model 2 LHC 2.76 TeVPb+Pb−>Pb+Pb+J/ ψ −4 −2 0 2 4 y −2 −1 d σ i n c / d y [ m b ] ψ (1S) ψ (2S) ALICE data
LHC 2.76 TeVPb+Pb−>Pb+Pb * + ψ (nS) Figure 1: The rapidity distribution of coherent (left panel) and incoherent (right panel) ψ (1S,2S)photoproduction at √ s = 2 .
76 TeV in PbPb collisions at the LHC (see text).performed predictions for the next LHC runs in pp mode. We have found dσ J/ψ dy = 6 . ψ (2 S ) state theextrapolation gives dσ ψ (2 S ) dy = 1 . ψ (1 S ) state, using distinct scenarios for the nuclear gluon shadowing. The dot-dashedcurve represents the result using R G = 1. It overestimates the ALICE data [6] on the backward(forward) and mainly in central rapidities. The situation is improved if we consider nuclearshadowing renormalising the dipole cross section. The reason is that the gluon density in nucleiat small Bjorken x is expected to be suppressed compared to a free nucleon due to interferences.For R G , we have considered the theoretical evaluation of Ref. [7]. As a prediction at centralrapidity, one obtains dσdy ( y = 0) = 4 . , .
68 and 2 .
27 mb for calculation using R G = 1, Model1 (strong shadowing) and Model 2 (weak shadowing), respectively. In Fig. 1 (right panel) ispresented the incoherent cross section for both ψ (1 S ) and ψ (2) states with R G = 1. This work was partially financed by the Brazilian funding agency CNPq and by the French-Brazilian scientific cooperation project CAPES-COFECUB 744/12.
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