A simple picture of the constituent quark as a composite system of point-like
partons is used to construct the unpolarized and polarized parton distributions
by a convolution between constituent quark momentum distributions and
constituent quark structure functions. We achieve good agreement with
experiments in the unpolarized, as well as, in the polarized case. When our
results are compared with similar calculations using non-composite constituent
quarks, the accord with the experiments of the present scheme is impressive. We
conclude that DIS data are consistent with a low energy scenario dominated by
composite constituents of the nucleon.Comment: 4 pages; latex using espcrc1.sty; 4 postscript figures; Invited talk
  at the Workshop ``Nucleon '99'', Frascati; Italy 7-9 June 1999. Submitted to
  Nuc. Phys. 

Altarelli

Ball

Bijker

Carlitz

Isgur

M. Traini

S. Scopetta

Scopetta

Traini

V. Vento

English

arXiv

A simple picture of the constituent quark as a composite system of point-like partons is used to construct the unpolarized and polarized parton distributions by a convolution between constituent quark momentum distributions and constituent quark structure functions. We achieve good agreement with experiments in the unpolarized, as well as, in the polarized case. When our results are compared with similar calculations using non-composite constituent quarks, the accord with the experiments of the present scheme is impressive. We conclude that DIS data are consistent with a low energy scenario dominated by composite constituents of the nucleon

Scopetta, Sergio

Vento Torres, Vicente

Traini, Marco

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

arXiv:hep-ph/9907440v1  21 Jul 19991Parton distributions in a constituent quark scenarioS. Scopettaa∗, V. Ventoa and M. Trainiba Departament de Fisica Teo`rica, Universitat de Vale`ncia, 46100 Burjassot (Vale`ncia),Spain; and Institut de F´ısica Corpuscular, CSICb Dipartimento di Fisica, Universita` di Trento, I-38050 Povo (Trento), Italy, and INFN,Gruppo Collegato di TrentoA simple picture of the constituent quark as a composite system of point-like partonsis used to construct the unpolarized and polarized parton distributions by a convolu-tion between constituent quark momentum distributions and constituent quark structurefunctions. We achieve good agreement with experiments in the unpolarized, as well as,in the polarized case. When our results are compared with similar calculations usingnon-composite constituent quarks, the accord with the experiments of the present schemeis impressive. We conclude that DIS data are consistent with a low energy scenariodominated by composite constituents of the nucleon.At low energies, the so called naive quark model accounts for a large number of exper-imental observations. At large energies, QCD sets the framework for an understandingof the Deep Inelastic Scattering (DIS) phenomena beyond the Parton Model. However,the perturbative approach to QCD does not provide absolute values for the observables.The description based on the Operator Product Expansion (OPE) and the QCD evo-lution requires the input of non-perturbative matrix elements. We have developed anapproach which uses model calculations for the latter ingredients at a low, hadronic, scale[1]. Moreover, in order to relate the constituent quark with the current partons of thetheory, a procedure, hereafter called ACMP, has been applied [2,3]. Within this approach,constituent quarks are effective particles made up of point-like partons (current quarks,antiquarks and gluons), interacting by a residual interaction described as in a quark model.The hadron structure functions are obtained by a convolution of the constituent quarkmodel wave function with the constituent quark structure function. This idea has beenrecently used to successfully estimate the pion structure function [4]. We summarize hereour application to the unpolarized [3] and polarized [5] DIS off the nucleon.In our picture the constituent quarks are themselves complex objects whose structurefunctions are described by a set of functions Φab that specify the number of point-likepartons of type b, which are present in the constituents of type a with fraction x of itstotal momentum [2,3]. In general a and b specify all the relevant quantum numbers of the∗Supported in part by DGICYT-PB97-1227 and TMR programme of the European Commission ERBFMRX-CT96-0082partons, i.e., flavor and spin. Let us discuss first the unpolarized case for the proton [3].The functions describing the nucleon parton distributions omitting spin degrees of free-dom are expressed in terms of the independent Φab(x) and of the constituent probabilitydistributions u0 and d0, at the hadronic scale µ20 [1], asf(x, µ20) =∫1xdzz[ u0(z, µ20)Φuf(xz, µ20) + d0(z, µ20)Φdf (xz, µ20) ] (1)where f labels the various partons, i.e., valence quarks (uv, dv), sea quarks (us, ds, s), seaantiquarks (u¯, d¯, s¯) and gluons g. The different types and functional forms of the structurefunctions for the constituent quarks are derived from three very natural assumptions [2]:i) The point-like partons are the quarks, antiquarks and gluons described by QCD; ii)Regge behavior for x→ 0 and duality ideas; iii) invariance under charge conjugation andisospin. These considerations define the following structure functions [2]Φqf (x, µ20) = Cfxaf (1− x)A−1 , (2)where f = qv, qs, g for the valence quarks, the sea and the gluons, respectively. Reggephenomenology suggests: aqv = −0.5 (ρ meson exchange) and aqs = ag = −1 (pomeronexchange). The other ingredients of the formalism, i.e., the probability distributions foreach constituent quark, are defined according to the procedure of ref. [1] and shown in [3].Our last assumption relates to the hadronic scale µ20, i.e., that at which the constituentquark structure is defined. We choose µ20= 0.34 GeV2, as defined in Ref. [1], namelyby fixing the momentum carried by the various partons. This choice of the hadronicscale determines all the parameters except one, which is fixed through the data [3]. Tocomplete the process, the above input distributions are NLO-evolved in the DIS schemeto the experimental scale, where they are compared with the data.We next generalize our previous discussion to the polarized parton distributions. Asit is explained in ref. [5], using SU(6) (spin-isospin) symmetry and other reasonablesimplifying assumptions, it can be shown that∆f(x, µ20) =∫1xdzz[ u0(z, µ20)∆Φuf (xz, µ20) + d0(z, µ20)∆Φdf (xz, µ20) ] , (3)where f labels the various partons; it means that the ACMP procedure can be extendedto the polarized case just by introducing three additional structure functions for theconstituent quarks: ∆Φqqv , ∆Φqqs and ∆Φqg. In order to determine them we add twominimal assumptions: iv) factorization: ∆Φ cannot depend upon the quark model used;v) positivity: the constraint ∆Φ ≤ Φ is saturated for x = 1. In such a way we determinecompletely the ∆Φ’s. In fact, the QCD partonic picture, Regge behavior and dualityimply that∆Φqf = ∆Cfx−∆af (1− x)∆Af−1 (4)and −12< ∆af < 0, for all f = qv, qs, g, as allowed by dominant exchange of the A1 mesontrajectory [7]. Moreover, the assumption that the positivity restriction is saturated forx = 1, in the spirit of ref. [6], implies that the Φ′s and the ∆Φ′s have the same largex behavior, and that ∆Cf = Cf , (the latter being introduced in (2)); it means that the3Figure 1. The proton F2(x,Q2), obtained by NLO-evolution to Q2 = 10 GeV2 (full),compared to the data (dots) [11]. The result which would be obtained disregardingthe constituent structure is also shown (dashed). Left (right) panel: constituent wavefunctions form ref. [9] (ref. [10]).Figure 2. Left (Right): xg1(x,Q2) for the proton (neutron) evolved at NLO toQ2 = 10 (5)GeV2, for the two extreme Regge behaviors mentioned in the text (full curves). The wavefunctions used are from ref. [10]. The data [11] are shown for comparison.partons which carry all of the momentum also carry all of the polarization. Let us stressthat the change between the polarized functions and the unpolarized ones comes onlyfrom Regge behavior; as a matter of fact, it turns out that, except for the exponent ∆afshown above, the ∆Φ’s, Eq. (4), are given by the unpolarized functions, Eq. (2). Theother ingredients, i.e., the polarized distributions for each constituent quark, are definedaccording to the procedure of ref. [1] and they are shown in ref. [5]. Finally, the partondistributions at the hadronic scale are evolved to the experimental scale by performing aNLO evolution in the AB scheme [8]. Results are shown in Figs. 1 and 2. The structurefunction F2(x,Q2), calculated by means of the obtained distributions in the DIS evolutionscheme, is shown in Fig. 1. We see that data are successfully described, the agreementbecoming impressive when compared with that obtained by similar calculations with non-composite constituents.Taking into account the almost inexistent fit of parameters, the results are surprisinglygood for both models [9,10]. In particular the momentum distribution of ref. [10] seemsto have been defined to fit the DIS data, which is not the case. In the polarized case, it is4found [5] that the constituent structure functions Eq. (4) give a good result for the proton,but they fail in reproducing the recent precise neutron data. This is to be ascribed to ournaive input for the sea and to the symmetry for the u and d quarks [5]. In particular, ithas been shown that, by redefining the sea ∆Φ, changing only one parameter so that theexperimental sea polarization is recovered, also the neutron is rather well described. Fig.2 refers to this last scenario. We have traced back the remaining disagreement with theneutron data to the symmetric treatment of u and d quarks. It can be shown that a weakbreaking of the SU(6) symmetry in the quark model used [10] and/or in the constituentquark structure functions improves considerably the agreement. The neutron is extremelysensitive to small changes in the valence structure.The procedure is also able to predict successfully several observables, such as the nucleonaxial charges [5]. It should be noticed that in this framework the spin crisis, as initiallypresented, does not arise.Since the method seems to be predictive, we are confident that it could be usefulto phenomenologically estimate unmeasured quantities, such as the transversity partondistribution h1 [13] or off-forward quantities [14], which should be measured by the nextgeneration of DIS experiments [15].Summarizing, low energy models seem to be consistent with DIS data when a structurefor the constituent is introduced. The crucial role played by the sea in the polarized case,as well as the implementation of Chiral Symmetry Breaking in our procedure, have to bemore deeply investigated. It will be the subject of future work.AcknowledgementsS.S. thanks the Organizers for the invitation and finantial support.REFERENCES1. M. Traini, V. Vento, A. Mair and A. Zambarda, Nucl. Phys. A 614 (1997) 472.2. G. Altarelli, N. Cabibbo, L. Maiani and R. Petronzio Nucl. Phys. B 69 (1974) 531.3. S. Scopetta, V. Vento and M. Traini, Phys. Lett. B 421 (1998) 64.4. G. Altarelli, S. Petrarca and F. Rapuano, Phys. Lett. B 373 (1996) 200.5. S. Scopetta, V. Vento and M. Traini, Phys. Lett. B 442 (1998) 28.6. R. Carlitz and J. Kaur, Phys. Rev. Lett. 38 (1977) 673.7. G. Altarelli, R.D. Ball, S. Forte and G. Ridolfi, Nucl. Phys. B 496 (1997) 337.8. R.D. Ball, S. Forte and G. Ridolfi, Phys. Lett. B 378 (1996) 255; G. Ridolfi, thisWorkshop.9. N. Isgur and G. Karl, Phys. Rev. D 18 (1978) 4187.10. R. Bijker, F. Iachello and A. Leviatan, Ann. Phys. 236 (1994) 69.11. EMC, Nucl. Phys. B328 (1989) 1; SMC, Phys. Rev. D 56 (1997) 5330; E154, Phys.Rev. Lett. 79 (1997) 26.12. H. L. Lai et al., Phys. Rev. D 51 (1995) 4763.13. V. Barone, this Workshop.14. A. Radyushkin, this Workshop.15. E. de Sanctis, this Workshop; T. Walcher, this Workshop.

Parton distributions in a constituent quark scenario

Crossref

Nuclear Physics A

http://dx.doi.org/10.1016/S0375-9474(00)00004-X

Parton distributions in a constituent quark scenario

Abstract

Similar works

Full text

Available Versions

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

Crossref