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Nonperturbative effects in the proton sea

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NONPERTURBATIVE EFFECTS IN THE PROTON SEA W.SCH ¨AFER,J.SPETH Institut f¨u r Kernphysik,Forschungszentrum J¨u lich D-52425J¨u lich,Germany E-mail:Wo.Schaefer@fz-juelich.de We revisit the evaluation of the pionic mechanism of the ˉu ?ˉd -asymmetry in the proton structure function.Our analysis is based on the unitarity relation between contributions of di?erent mechanisms to the inclusive particle production and the total photoabsorption cross-section (i.e.the proton structure function).We rean-alyze the role of isovector reggeons in inclusive production of nucleons and Delta isobars in hadronic reactions.A rather large contribution of reggeon-exchange in-duced production of Delta isobars is found.This leaves much less room for the pion-exchange induced mechanism of ?production and provides a constraint on the πN ?form factor.The production of leading pions in proton-proton collisions puts additional constraints on the πNN vertex form factors.All these constraints are used then to estimate the pion content of the nucleon and allow to calculate parameter-free the x -dependence of ˉd ?ˉu .We discuss the violation of the Got-tfried Sum Rule and ˉd -ˉu asymmetry and compare to the one obtained from the E866experiment at Fermilab.1Introduction Since the discovery of the Gottfried sum rule violation 1there has been a long ongoing discussion on the ˉd ?ˉu asymmetry in the nucleon sea.Considerable atttraction has been received recently by the E866experiment at Fermilab 2,which provided the ?rst detailed measurement of the Bjorken–x dependence of the ˉd ?ˉu –asymmetry from the comparison of pp and pd Drell–Yan production.Their striking ?nding is that the asymmetry tends to vanish at x ~0.3.The strong observed asymmetry has no explanation in terms of the purely pQCD dynamics,and thus it gives important hints on the impact of the non-perturbative proton structure on the generation of the nucleons’s sea quark

content.Following the early work of Sullivan 3,a natural dynamical explana-tion emerges within the framework of the isovector meson cloud model of the nucleon (for a recent review see 4).Here a special role is played by the pion,and it is intuitively appealing to account for the nonperturbative meson/baryon structure of the proton,by including the pion as the nonperturbative parton in the light cone wave function of the interacting nucleon:

|N phys =|N bare +|Nπ +|?π +....(1)Here the pion,that is contained in the Nπ,?π–Fock states can emerge as the target in the deep inelastic γ?N photoabsorption process,while the spectator

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baryonic constituent N,?appears in the ?nal state,separated from the rem-nants of the γ?π–interaction by a rapidity gap and carrying a large fraction z of the incoming proton’s lightcone momentum.Hence,inclusive production of baryons,like γ?p →Xn is naturally described in terms of the pionic ’partons’in the nucleon.But precisely the same dynamics is supposed to be at work,if we swap the virtual photon against the proton projectile.This opens the possibility to use a large body of experimental knowledge on inclusive parti-cle production in hadronic reactions to constrain the meson/baryon dynamics relevant for deep inelastic scattering.In the following we shall demonstrate,that if one accounts consistently for the

so–derived constraints,a satisfactory description of the Fermilab data emerges 5.

a)b)c)p,γ?p,γ??

Nonperturbative effects in the proton sea

Nonperturbative effects in the proton sea

Nonperturbative effects in the proton sea

Figure 1:The mechanisms for inclusive production of forward neutrons.a)pion exchange,b)background from (reggeized)ρ,a 2exchanges,c)neutrons originating from the decay of an intermediate ?–resonance.

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Inclusive production of baryons and mesons in hadronic reactions 2.1Production of forward neutrons and ?–isobars

Following the above described strategy,we ?rst turn to the description of the forward neutron production in pp collisions.We take into account three pro-duction mechanisms:the dominant pion exchange,the background contribu-tion from the isovector exchanges ρ,a 2,and,?nally,the production of neutrons from the decay of an intermediate ?–resonance (see ?g 1).In addition,we have to account for the distortion of the incoming proton waves,employing standard methods of the generalized eikonal approximation 6.Following the reasoning in 6,we apply the absorptive corrections only in the pp scattering,they can be neglected in the γ?p –case.It is important to notice,that the phase space

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of the forward neutrons includes the kinematical boundary z~1,which cor-responds to a large Regge parameter s/M2X?1,where M2X is the invariant mass squared of the inclusive system X.Hence the proper formalization of the ρ–exchange mechanism should be a Regge treatment7.

In the Regge formulation,the contribution to the inclusive cross section from the pion exchange mechanism has the form:

z dσ(p→n)

16π2

(?t)

contribution (see ?g 3.).

Nonperturbative effects in the proton sea

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z E d σ/d 3p , m b /G e V 2Figure 2:Invariant cross section for the reaction pp →nX at p LAB =24GeV/c.The experimental data are taken from 9.The long dashed curve shows the contribution from the pion exchange;the dotted curve is the ρ,a 2-exchange contribution,and the dashed curve shows the contribution from the two step process p →?→n .In additionally we present the sum of the two background contributions as the dot-dashed line.Finally the solid curve represents the sum of all components.

2.2Constraints from forward pion production

The good description of the forward baryon production can make us con?dent,that we have found a proper description of the πN,π?–fock states in the region where the baryon carries a large momentum fraction z ~0.6÷1.However we should be aware,that the forward baryon production data do not put any constraint on the region z ~<0.6;in such a kinematical region we cannot expect the meson/Reggeon exchanges to be the dominant reaction mechanisms.On the other hand,in the Fock–state picture a baryon carrying a small momentum fraction z B ?1is accompanied by the meson carrying large z M =1?z B ~1.Hence,the natural place to check the consistency of the Fock–state parameters is the production of forward,z π~1,pions.The important message from the experimental data (?g.4)is:there are no pions carrying large momentum fractions 0.6~

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Nonperturbative effects in the proton sea

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z d σ/ d z , m b Figure 3:Di?erential cross section dσ/dz for the reaction pp →?++X at p LAB =400GeV/c.The dashed curve is the contribution from pion-exchange;the dotted curve shows the ρ,a 2contribution.Shown by the solid curve is the sum of the two.Experimental data are taken from 10(open circles),and 11(?lled circles).

above leads to the middle solid curve in ?g.4.Incidentally,the dotted line on ?g.4shows the result of a previously emloyed formfactor 12that also did a reasonable job on forward neutrons,but does not respect the pion production data.

3Regge mechanisms vs.Fock–state picture

In the introduction we stressed the relevance of the pion as the nonperturba-tive parton in the light–cone wave function of the interacting proton.Here the question arises what kind of Fock–state should then be associated with the ρ,a 2-Reggeon exchange production mechanisms,if any?In other words,know-ing the reaction mechanisms that populate several inclusive channels,what can we say about their impact on the total cross section?We remind,that one of the ?rm predictions of Regge theory is a very speci?c phase of the amplitudes.While the inclusive cross section is calculated from the modulus of the ampli-tude squared,|A |2,it is the product of two amplitudes,A ·A ,that enters the evaluation of the total cross section.The result may be summarized by gener-alized AGK cutting rules 5,13:for the purely real pion exchange amplitude,this implies that inelastic interactions of the projectile with the pions in the target hadrons enhances the total cross section,whereas the ρ,a 2–exchanges,which have a phase ~(1+i ),happen to give a vanishing contribution to the total cross section.Hence,it does not make any sense,to identify the Reggeon ex-

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Nonperturbative effects in the proton sea

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z z d σ/d z , m b

Figure 4:Di?erential cross section zdσ/dz (pp →π0X )at p LAB =400GeV/c.The data are taken from 10.The dotted curve shows a prediction of the model 12.The solid curves were calculated with a ’Gaussian’form factor F πNN (t )=exp(? R 2G

(t ?m 2π) 2).The curves in the ?gure correspond to R 2G =1.0,1.5,and 2.0GeV ?2(from top to bottom).The dashed curves were calculated with an exponential form factor F πNN (t )=exp(R 2E (t ?m 2π)).The

curves in the ?gure are for R 2E =1.0,1.5,and 2.0GeV

?2(from top to bottom).change mechanism in inlusive reactions in terms of a meson/baryon–Fock state of the proton.We want to point out that there is no mystery connected with such a di?erent impact of the phases on di?erent observables.For instance in the inclusivex pp →pX ,di?ractive channels (imaginary amplitude)dominate for z ~1,and it is well known that the opening of di?ractive channels comes along with the absorptive correction to the total cross section,which is negative 13.

4The ˉd ?ˉu asymmetry from pions in the nucleon

Following our reasoning above,we include the πN ,π?–Fock states only.They lead to a contribution to the total γ?p –cross section –i.e.the quark/antiquark–distributions in the proton given by

?πq (x,Q 2)=

1x

dz πσπp tot d 3 p ,(4)

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and similarly for theπ?–Fock state.Besides the Fock–state parameters de-termined in our analysis above,we need as an input the quark distributions in the pion.Notice,that for the calculation ofˉd(x)?ˉu(x)only the pion’s valence distributions enter.These are reasonably well constrained down to x~0.2from the Drell–Yan experiments,for de?niteness we take the GRV–parametrization14.We obtain a total multiplicity of pions in the proton asso-ciated with theπN–state of nπN~0.21÷0.28and of nπ?~0.03?nπN for theπ?–contribution.This translates to a Gottfried sum of0.21~0.2owes to the fact that we have no contributions from hard zπ~>0.5pions in the nucleon. 5Summary

Our reanalysis of the pionic contribution to theˉd?ˉu–asymmetry has been based on a uni?ed treatment of the inclusive production of leading nucleons,?’s and pions in hadronic high energy collisions.We paid special attention to the background contributions in the leading baryon production,and clari?ed the relation of Reggeon–exchange mechanisms and the Fock–state picture of the interacting nucleon.Severe constraints on our parameters were found to arise from the forward pion data.A good agreement with the recent E866data onˉd?ˉu was found.

Finally we want to point at another spin–o?of our analysis:namely one may use the pions in the nucleon as targets in deep inelastic scattering and hence obtain information on its structure function at small x,unexplored by the Drell-Yan experiments15.Our?ndings for the relevant background contri-butions show that this task is well feasible.

Acknowledgments

We wish to thank C.Carlson and A.Radyushkin for invitation.W.S.is in-debted to INT/JLab for the?nancial support.

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d (x )-u (x )__

Nonperturbative effects in the proton sea

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0.80Figure 5:Flavour asymmetry ˉd (x )?ˉu (x )at Q 2=54GeV 2.Experimental data are from

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