Exclusive glueball production in high energy nucleus-nucleus collisions
aa r X i v : . [ h e p - ph ] D ec Exclusive glueball production in high energy nucleus-nucleus collisions
M. V. T. Machado and M. L. L. da Silva High Energy Physics Phenomenology Group, GFPAE IF-UFRGSCaixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil Centro de Ciˆencias Fisicas e Matem´aticas. Departamento de Fisica - UFSCBairro Trindade. Caixa Postal 476. CEP 88040-970. Florianopolis. SC. Brazil
The cross sections for the glueball candidates production in quasi-real photon-photon collisionsand on central diffraction processes, i.e. double Pomeron exchange, in heavy ion interactions atRHIC and LHC are computed. The rates for these distinct production channels are compared andthey may be a fruitful approach to the investigation of glueballs.
PACS numbers: 25.75.Cj;19.39.-x;12.38.-t;12.39.Mk;14.40.Cs
I. INTRODUCTION
The gluon self-coupling in QCD opens the possibility ofexisting bound states of pure gauge fields known as glue-balls. Glueballs ( G ) are predicted by several theoreticalformalisms and by lattice calculations. For a comprehen-sive review on the current status of theoretical and ex-perimental aspects of glueball studies we quote Ref. [1]and Ref. [2], respectively. Many mesons have stood up asgood candidates for the lightest glueball in the spectrumand in particular the scalar sector ( J P C = 0 ++ ) seemspromising. The mesons f (1500) and the f (1710) havebeen considered the principal candidates for the scalarglueball[3, 4]. However, in this mass region the glue-ball state will mix strongly with nearby q ¯ q states [4, 5].More recently, the BES collaboration observed a new res-onance called X (1835) [6]. It is an important candidatefor glueball and the nature of meson X (1835) has severalinterpretations. One of them consider it a pseudo-scalarglueball ( J P C = 0 − + ) as first suggested in Ref. [7] andafterwards in [8].Recently, the clean topologies of exclusive particle pro-duction in electromagnetic interactions hadron-hadronand nucleus-nucleus collisions mediated by colorless ex-changes such the QCD Pomeron or two photons haveattracted an increasing interest [9]. The cross sectionsfor these processes are smaller than the correspondentinclusive production channels, which it is compensatedby a more favorable signal/background relation. Experi-mentally, exclusive events are identified by large rapiditygaps on both sides of the produced central system andthe survival of both initial state particles scattered atvery forward angles with respect to the beam.Here, we will focus on exclusive glueball productionin two-photon and Pomeron-Pomeron interactions in co-herent nucleus-nucleus collisions at high energy colliders(RHIC and LHC). In these cases, the photon flux scalesas the square charge of the beam, Z , and then the cor-responding cross section is highly enhanced by a factor ∝ Z ≈ for gold or lead nuclei. A competing chan-nel, which produces similar final state configuration, isthe central diffraction (CD) process. Such a reaction ismodeled in general by two-Pomeron interaction. Exper- imentally, the separation of these channels is somewhatdifficult and from theoretical point of view the Pomeron-Pomeron are subject to large uncertainties at collider en-ergies. One goal of present work is to compare the crosssections for these two channels in the production of glue-ball candidates. This paper is organized as follows: innext section we present the main expressions for crosssection calculation of two-photon and Pomeron-Pomeronprocesses and in last section we shown the numerical re-sults and discussions. II. CROSS SECTION CALCULATION
Let us start with the glueball production in photon-photon scattering at coherent heavy ion collisions usingthe Weizs¨acker - Williams approximation (EPA approxi-mation). In such an approach, the cross section for a twoquasi-real photon process to produce a glueball state, G ,at center-of-mass energy W γγ factorises into the productof the elementary cross section for γγ → G convolutedwith the equivalent photon spectra from the colliding ions[9]: σ γγ ( AA → A + G + A ) = Z dk k dk k dn γ dk dn γ dk σ ( γγ → G ) , (1)where k , are the photon energies and dn/dk is thephoton flux at the energy k emmited by the hadron A .The photon energies determine the center-of-mass energy W γγ = √ k k and the rapidity Y of the produced sys-tem. Namely, one has k , = ( W γγ /
2) exp( ± Y ) and Y =(1 /
2) ln ( k /k ). In addition, √ s NN is the center-of-massenergy of the ion-ion system and the Lorentz relativisticfactor is given by γ L = √ s NN / (2 m N ). In particular, inthe numerical calculations we use √ s NN = 0 . .
5) TeVand γ L = 109 (2930) for RHIC (LHC).In the EPA approximation, the flux of equivalent pho-tons from a relativistic particle of charge Z is determinedfrom the Fourier transform of its electromagnetic field.For an extended charge with electromagnetic form fac-tor, F A ( Q ), the energy spectrum can be computed as, dn γ/A ( x ) dk = α Z π A ( x ) x Z Q − Q Q | F A ( Q ) | dQ , (2)where x = k/E is the fraction of the beam energy carriedby the photon and A ( x ) = 1 − x +(1 / x ). Moreover, α =1 /
137 and Q is the four-momentum transfer squaredfrom the charge, with Q ≈ ( xm N ) / (1 − x ).The glueball production in two-photon fusion can becalculated using the narrow resonance approximation[10]: σ ( γγ → G ) = (2 J + 1) 8 π M G Γ( G → γγ ) δ (cid:0) W γγ − M G (cid:1) , (3)where Γ( G → γγ ) is the partial two-photon decay widthof G , M G is the glueball mass and J is the spin of thestate G . Here, we compute the production rates forthe mesons f (1500), f (1710) and X (1835) [11], respec-tively. The reason is due to they have been mentioned aspossible glueball candidates by phenomenologists [1, 2].Some important comments are in order. The predic-tions for the two-photon component are in practice some-what difficult as the branching ratios have not been mea-sured. To compute numerical values for the meson (glue-ball) cross section in two-photon reactions estimates forthe two-photon decay widths are needed. The determi-nation of them depend upon whether the meson state is apure quarkonium, pure gluonic or a mixed hybrid state.For a pure quarkonium state the width can be related(at leading order) to the two-gluon width, Γ( q ¯ q → gg ).Namely, Γ( q ¯ q → γγ ) ≃ D c e q ( α/α s ) Γ( q ¯ q → gg ), where D c = 9 / e q is the relevant quarkcharge. One can estimate the two-gluon width from thetotal width for the meson state and the theoretical expec-tation that the q ¯ q → gg branching ratio is of order α s [12]. In case of a pure gluonic state, the two-photon widthcan be computed using a nonrelativistic gluon bound-state model as performed for instance in Ref. [13]. There,the unknown parameters as the digluon wavefunction, orits first/second derivative at the origin, are determinedby using measured values of Γ( J/ψ → Gγ ).Now, we compute estimates for the two-photon widthsassuming pure q ¯ q and pure gluonic resonances, respec-tively. For the first case, as discussed above, we takeΓ( R → γγ ) = e q (3 α ) Γ tot ( R ) /
2. Using the ParticleData Group (PDG) average values for the total widthone gets Γ( f (1500) → γγ ) ≃ . f (1710) → γγ ) ≃ . X (1835) → γγ ) ≃ . µ b, 3.4(216) µ b and1.1(84) µ b at RHIC(LHC). If we are conservative, onecan consider the experimental upper bounds for the two-photon widths of f (1500) and f (1710). This proceduregives an upper limit of the cross section for those reso-nances in peripheral collisions. The ALEPH experiment For pure glueball resonance, G , the branching ratio is Br ( G → gg ) ≃
1, whereas mixing states will give intermediate values ofbranching ratio. [3] studied the γγ production of those glueball candi-dates via their decay to π + π − and the following limits were determined: Γ( f (1500) → γγ ) ≤ .
08 keV andΓ( f (1710) → γγ ) ≤ .
25 keV. Using those limits thecorresponding cross sections are of order 0.95 mb (20 µ b)for f (1500) and 11.5 mb (180 µ b) for f (1710) at LHC(RHIC) energies. We quote Ref. [14] for a comparisonof our results with a wide class of theoretical models andexotic QCD states in the meson production in photon-photon process.For a pure glueball resonance we follow [13], adaptedfor the candidates considered here. Namely, assumingthe f resonances as states with J = L = 0 then Eq.(54) of Ref. [13] has been used, where we take thePDG values for the radiative J/ψ decays in the fol-lowing channels: ψ → γf (1500) → γππ and ψ → γf (1710) → γK ¯ K . Assuming the X (1835) resonanceto be a state with J = 0 and L = S = 1 we relay onEq. (35) of [13] and use the PDG value for the de-cay channel ψ → γX (1835) → γπ + π − η ′ . Putting alltogether, the estimates for the two-photon width for apure glueball resonance are Γ( f (1500) → γγ ) ≃ .
77 eV,Γ( f (1710) → γγ ) ≃ .
03 eV and Γ( X (1835) → γγ ) ≃ .
021 keV. Notice that for the X (1835) a larger widthis predicted [8], being of order 1.1 keV. The widths areabout three orders of magnitude smaller that for pure q ¯ q states. Therefore, as the two-photon cross section scalesas (2 J + 1)Γ ( R → γγ ), Eq. (3), one can consider the ex-perimental feasibility of using peripheral heavy-ion colli-sions to determine the nature of the resonances discussedabove. The values for the corresponding widths and cor-responding cross sections estimates are shown in TableI. Now, we address the Pomeron-Pomeron channel. Inparticular, we focus on the central diffraction (doublePomeron exchange, DPE) in nucleus-nucleus interac-tions. As a starting point we compute the DPE proton-proton cross section making use of the Bialas-Landshoff[15, 16] approach. We believe that this non-perturbativeapproach is a reasonable choice due to the light massof glueballs candidates considered in present calcula-tion. For a perturbative QCD guided calculation wequote the recent work in Ref. [17], where the exclu-sive scalar f (1500) meson production is carefully inves-tigated. Here, we are particularly interested in the exclu-sive and central inclusive (central inelastic) DPE produc-tion of glueball states. In the exclusive DPE event thecentral object G is produced alone, separated from theoutgoing hadrons by rapidity gaps, pp → p + gap + G +gap+ p . In the central inclusive DPE event an additionalradiation accompanying the central object is allowed. Inapproach we are going to use, Pomeron exchange corre- Here, we consider the ALEPH limits Γ( γγ → f (1500)) · Br ( f (1500) → π + π − ) < .
31 keV, Γ( γγ → f (1710)) · Br ( f (1710) → π + π − ) < .
55 keV and taking the branchingratios 0 . ± .
07 and 0 . ± .
016 [3], respectively sponds to the exchange of a pair of non-perturbative glu-ons which takes place between a pair of colliding quarks.For DPE central inclusive G production we can neglectthe additional gap spoiling effect, so-called Sudakov ef-fect. The scattering matrix is given by, M = M (cid:18) ss (cid:19) α ( t ) − (cid:18) ss (cid:19) α ( t ) − F ( t ) F ( t ) × exp ( β ( t + t )) S gap (cid:0) √ s (cid:1) . (4)Here M is the amplitude in the forward scattering limit( t = t = 0). The standard Pomeron Regge trajectoryis given by α ( t ) = 1 + ǫ + α ′ t with ǫ ≈ . , α ′ = 0 . − . The momenta of incoming (outgoing) protonsare labeled by p and p ( k and k ), whereas the glue-ball momentum is denoted by P . Thus, we can define thefollowing quantities appearing in Eq. (4): s = ( p + p ) , s = ( k + P ) , s = ( k + P ) , t = ( p − k ) , t = ( p − k ) . The nucleon form-factor is given by F p ( t ) = exp( bt ) with b = 2 GeV − . The phenomenolog-ical factor exp ( β ( t + t )) with β = 1 GeV − takes intoaccount the effect of the momentum transfer dependenceof the non-perturbative gluon propagator. The factor S gap takes the gap survival effect into account i.e. theprobability ( S ) of the gaps not to be populated bysecondaries produced in the soft rescattering. For ourpurpose here, we will consider S = 0 .
032 at √ s = 5 . and S = 0 .
15 at √ s = 200 GeV (RHIC). In particular, for RHIC we haveused an estimation using a simple one-channel eikonalmodel for the survival probability [18], whereas for theLHC energy we follows Ref. [19] that considers a two-channel eikonal model that embodies pion-loop insertionsin the pomeron trajectory, diffractive dissociation andrescattering effects. We quote Ref. [20] for a detailedcomparison between the two approaches and further dis-cussions on model dependence of inputs and considera-tion of multi-channel calculations.Following the calculation presented in Ref. [16] we find M for colliding hadrons, M = 32 α D Z d ~κ p λ V Jλν p ν exp( − ~κ /τ ) , (5)where κ is the transverse momentum carried by each ofthe three gluons. V Jλν is the gg → G J vertex dependingon the polarization J of the G J glueball meson state.For the cases considered here, J = 0, one obtains thefollowing result [16, 21]: p λ V λν p ν = s ~κ M G A, (6) It is obtained using a parametric interpolation formula for theKMR survival probability factor [19] in the form S = a/ [ b +ln( p s/s )] with a = 0 . b = − .
988 and s = 1 GeV . Thisformula interpolates between CD survival probabilities of 4 . . where A is expressed by the mass M G and the widthΓ( gg → G ) of the glueball meson through the relation: A = 8 πM G Γ( gg → G ) . (7)For obtaining the two-gluon decays widths the followingrelation is used, Γ ( G → gg ) = Br ( G → gg ) Γ tot ( G ).At this point, some discussion is in order. The two-gluonwidth depends on the branching fraction of the resonance R to gluons, Br ( G → gg ) and its knowledge would givequantitative information on the glueball content of a par-ticular resonance. As discussed before, it is a theoreti-cal expectation [12] that Br ( R ( q ¯ q ) → gg ) = O ( α s ) ≃ . − . R ( G ) → gg ) ≃
1. Here, we willbe conservative and assume the resonance to be a pureglueball. This fact translates into an upper bound forthe exclusive DPE production as the cross section scaleswith Γ ( R → gg ). Following Ref. [22], the two-gluonwidth can be computed from the resonance branchingfraction in J/ψ radiative decay, Br ( ψ → γ G ). For thecandidates of interest here one obtains:Br ( G (0 ++ ) → gg ) = 8 π ( π − Br [ ψ → γ G (0 ++ )] c R x | H J ( x ) | Γ tot M ψ M G , Br ( G (0 − + ) → gg ) = 8 π ( π − Br [ ψ → γ G (0 − + )] c R x | H J ( x ) | Γ tot M ψ M G , where the function H J (( x ) is determined in the non-relativistic quark model (NRQM) (see appendix of Ref.[22]) and c R is a numerical constant ( C R = 1 , / , / J P C = 0 − + , ++ , ++ , respectively). The massesof J/ψ and of resonance are M ψ and M G , respectively,and x = 1 − ( M G /M ψ ). Based on equations above,in Ref. [22] the following values for the branchingfractions for scalar glueballs candidates are obtained:Br [ f (1500)] = 0 . ± .
11, Br [ f (1710)] = 0 . ± . X the situation is less clear due tosmall information on its decaying channels in radiative J/ψ decays. The authors in [22] have a prediction for η resonance which gives Br [ η (1410)] = 0 . ± .
2. Asthe branching fraction scales as 1 /M G in this theoreti-cal model, an educated guess for the X branching frac-tion would be Br [ X (1835)] = ( M η /M X ) · Br [ η (1410)] =0 . ± .
15. In the numerical calculations we set thelimit case Br [ X (1835)] = 1 and notice that the branch-ing would be about 30 % smaller. The values for Γ gg usedin our calculations are summarized in Table II. A conse-quence on the small deviation for the branching fractionin pure q ¯ q and glueball resonance is the difficulty in test-ing their nature using the exclusive diffractive data. Anoption would be to obtain for instance the differentialcross section on angular distributions and then comparethe predictions for each composition (pure q ¯ q , mixingstate and pure glueball).In addition, we use the parameters τ = 1 GeV and D G τ = 30 GeV − [16] where G is the scale of theprocess independent non-perturbative quark gluon cou-pling. An indirect determination of unknown parameter Glueball Candidate Γ γγ [eV] RHIC [nb] LHC [ µ b] f (1500) 0.77 14-9.3 0.7-1.3 f (1710) 7.03 60-43 3.8-8.6 X (1835) 0.021 0.11-0.09 0.01-0.02TABLE I: Cross sections for pure glueball candidates pro-duction through photon-photon fusion in electromagneticnucleus-nucleus collisions at RHIC and LHC energies. α = G / π has been found in Ref. [23] using experi-mental data for central inclusive dijet production crosssection at Tevatron. Namely, it has been found the con-straint S ( √ s = 2 TeV) /α = 0 .
6, where S is thegap survival probability factor (absorption factor). Con-sidering the KMR [19] value S = 0 .
045 for CD pro-cesses at Tevatron energy, one obtains α = 0 . T ( κ, µ ) [24] inside the loop integral over ~κ . TheSudakov factor T ( κ, µ ) is the survival probability that agluon with transverse momentum κ remains untouchedin the evolution up to the hard scale µ = M G /
2. Thefunction T ( κ, µ ) is given by [24]: T ( κ, µ ) = exp − Z µ ~κ α s (cid:16) ~k (cid:17) π d~k ~k × Z − δ " zP gg ( z ) + X q P qg ( z ) dz ! , (8)where δ = (cid:12)(cid:12)(cid:12) ~k (cid:12)(cid:12)(cid:12) / ( µ + (cid:12)(cid:12)(cid:12) ~k (cid:12)(cid:12)(cid:12) ), P gg ( z ) and P qg ( z ) are theDGLAP spitting functions. In next section we willdiscuss the effect of introducing the Sudakov factor inthe estimation of exclusive production in the Pomeron-Pomeron channel.In order to calculate the AA cross section the pro-cedure presented in Ref. [25] is considered, where thecentral diffraction and single diffraction cross sectionsin nucleus-nucleus collisions are computed using the so-called criterion C (we quote Ref. [25] for further de-tails). Using the profile function for two colliding nuclei, T AB = R d ¯ b T A (¯ b ) T B ( b − ¯ b ), the final expression for CDcross section in AA collisions is given by [25]: σ CD AA = A Z d b T AA ( b ) exp (cid:2) − A σ inpp T AA ( b ) (cid:3) σ CD pp . (9)where σ inpp and σ CD pp = S × σ CD pp ( √ s ) are the inelasticand CD cross sections in proton-proton case, respectively.Using Woods-Saxon nuclear densities and consideringthe inelastic cross section σ inpp = 73 (49) mb for LHC(RHIC) energy, √ s AA = 5 . .
2) TeV, we compute the
Glueball Γ gg [MeV] RHIC [mb] LHC [mb] f (1500) 69.8 0 . ± .
21 (inc.) 0 . ± .
51 (inc.)0 . ± .
14 (exc.) 0 . ± .
32 (exc.) f (1710) 70.2 0 . ± .
26 (inc.) 0 . ± .
52 (inc.)0 . ± .
16 (exc.) 0 . ± .
31 (exc.) X (1835) 70.27 0 . ± .
24 (inc.) 0 . ± .
50 (inc.)0 . ± .
14 (exc.) 0 . ± .
29 (exc.)TABLE II: Cross sections for inclusive (inc.) and exclusive(exc.) glueball production in double Pomeron exchange pro-cess for RHIC and LHC energies.
CD cross section for nuclear collisions. The values for theinelastic cross section are obtained from DPMJET [26],where the scattering amplitude is parameterized using σ tot , ρ and elastic slope (these parameters are taken as fit-ted by the PHOJET model [27]). We notice that for LHCenergy the effective atomic number dependence is propor-tional to A / , which means that the nuclear CD crosssection is only one order of magnitude larger than thenucleon-nucleon cross section. For completeness, we givethe values of the DPE cross sections for the proton-protoncase used in Eq. (9): σ CD pp (RHIC) = 0 . , . , . σ CD pp (LHC) = 0 . , . , .
83 mb for f (1500), f (1710) and X (1835), respectively.In next section we compare the two production chan-nels and investigate the main theoretical uncertainties.We provide estimates of cross sections and event ratesfor both processes for RHIC and LHC energies at theheavy ion mode. III. RESULTS AND DISCUSSIONS
In what follows the numerical results for the two-photon and Pomeron-Pomeron processes are presentedand discussed. In Table I the cross sections for glueballproduction in photon-photon fusion at RHIC and LHCenergies are shown. For RHIC we have considered thenominal center of mass energy of 200 GeV for gold-goldcollisions and for LHC we take the planned nominal en-ergy of 5500 GeV in lead-lead collisions. The first valuecorresponds to the cross section obtained using a non-factorizable photon flux (Cahn-Jackson) [28] and the sec-ond one refers to the factorizable flux as shown in Eqs.(1-2). The deviation is sizable for RHIC and LHC. Thecross sections are sufficiently large for experimental mea-surement. The event rates can be obtained using thebeam luminosity [9]: for LHC one has L PbPb = 5 · cm − s − , which produces the following number of events.One has 3 . · , 2 · and 4 for f (1500), f (1710) and X (1835), respectively, in the nominal LHC running timewith ions of 10 s (one month). The event rates canbe enhanced in a pPb mode, where the nominal beamluminosity is increased three order of magnitude com-pared to the PbPb mode. The present calculation canbe compared to previous studies on glueball productionin heavy ion collisions [29, 30]. In general, the numericalresults are similar to those computations and the maindeviation comes from the distinct estimates for the two-photon decays widths. A direct comparison can be donefor the f (1710) case, where in Ref. [30] one gets 48nb for RHIC and 2.3 µ b for LHC (using cut on impactparameter b > R A and using Γ γγ ≃ AA crosssection as a function of the resonance mass at the LHCenergy. This makes simple the computation of event ratesprovided the specific meson state and its two-photon de-cay width. Using the Cahn-Jackson photon flux, weobtain in the interval 400 ≤ M R ≤ σ upc ( AA → R J + AA )(2 J + 1) Γ( R J → γγ ) = σ M βR M R / , (10)where σ = 4 . β = − . γγ and M R are the decay width and the resonance mass in unitsof GeV, respectively. Several authors have argued fora low lying scalar glueball, with mass between 500 and1200 MeV [1, 2], depending on the proponents. The pa-rameterization above allows to obtain estimates startingfrom a modeling for the two-photon width.In Table II the results for Pomeron-Pomeron produc-tion of glueball is presented. The estimates are shown forthe inclusive (inc.) and exclusive (exc.) double Pomeronexchange as discussed in previous section. Namely, forthe inclusive production the Sudakov survival factor isnot included (glueball is produced in association withPomeron remnants) whereas for the exclusive case it istaken into account. In order to estimate the model de-pendence in the CD cross section, we have changed thesoft Pomeron parameters in order to be consistent withthe semi-hard Pomeron values considered in the DESY-HERA fits to diffractive deep inelastic scattering (DDIS).For instance, taking FIT A of the H1 Coll. [31] parame-terization for the diffractive structure function F D (3)2 onehas ǫ = 0 . α ′ = 0 .
06 and b = 2 .
75 GeV − . Such achange enhances the cross section by a factor 3 for PbPbcollisions at the LHC. In Table II, the cross sections arepresented taking into account such a theoretical errorband. Lower bound corresponds to soft Pomeron param-eters and upper bound stands for the semihard Pomeronones. For RHIC energy, the Pomeron-Pomeron contribu-tion seems to be bigger than the photon-photon channelin a large extent. On the other hand, at the LHC they arecompetitive. However, the Pomeron contribution can beeasily separated from photon channel by imposing a cuton the impact parameter of collision. After imposing thiskinematic cut ( b > R A ) the Pomeron contribution is re-duced as they are dominated by small impact parametercontributions.The present result is difficult to be compared directlyto previous studies on Refs. [29, 30]. Those author did not include survival probability gap on their calculationsand the theoretical approaches for Pomeron-Pomeron in-teraction are distinct. For instance, in Ref. [29] the IP IP → G cross section is obtained using the Pomeron-quark coupling like a isoscalar photon, which allows toobtain the DPE cross section from the two-photon one.On the other hand, in Ref. [30], only the inclusive doublePomeron production is considered. Following that study,we can perform a closer comparison. The cross sectionsare computed there with inelastic scattering effects us-ing the Glauber approximation (in Table 3 of Ref. [30],see σ AA elastic), which is similar to procedure presentedhere. After including gap survival probability factor onegets for the f (1710) meson the values 1.23 (3.04) mbfor RHIC (LHC), which is not so far from our resultspresented for inclusive production in Table II.Finally, it is important to discuss the uncertainties onthe current calculations and the experimental feasibil-ity of detecting glueballs candidates. The main uncer-tainty here is the model dependence on obtaining thetwo-photon and the two-gluon widths for a pure glue-ball meson. For the two-photon width we considereda nonrelativistic gluon bound-state model of Ref. [13],which it could be a debatable issue and it is far frombeing optimal. There are more modern approaches as re-viewed in Ref. [2], but this is out of the scope of presentwork. For the two-gluon widths, we obtained them fromthe quarkonium width based on a non relativistic bound-state calculation [22]. This type of matrix elements havebeen discussed in Refs. [32] giving rise to an effect ofchiral suppression. We did not discuss the implicationof those findings in present calculation. Concerning theexperimental detection, the advantage of the exclusiveprocesses discussed here is clear: glueballs are probablybeing produced with a high cross section in inelastic col-lisions (in pp or AA reactions) but when the multiplicityis high the combinatorial background is overwhelming.In exclusive production there is no combinatorial back-ground. In the ultraperipheral two-photon production ofglueballs, the final state configuration is clear: nuclei re-main intact after collision and a double large rapidity gapbetween them is present (glueball is centrally producedwith a low p T transverse momenta spectrum). This typeof measurement is already done at RHIC for photopro-duction of vector mesons and exclusive dilepton produc-tion with a signal identification well understood [33]. Thesituation for DPE glueball production is similar, with the p T spectrum being broader than the processes initiatedby two-photons. Thus, a transverse momentum cut (andalso impact parameter of collision) could separate the twochannels (for a review on these issues we quote Ref. [34]). Acknowledgments
The authors thank Curtis A. Meyer, Nikolai Kochelev,Pedro Bicudo and Dimiter Hadjimichef for com-ments/suggestions. One of us (MVTM) acknowledgesthe Aristotle University of Thessaloniki and the organiz-ers of the
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