Non-diffractive mechanisms in the φ-meson photoproduction on nucleons

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  • 14 June 2001

    Physics Letters B 509 (2001)

    Non-diffractive mechanisms in the -meson photoproductionon nucleons

    Qiang Zhao a, B. Saghai b, J.S. Al-Khalili aa Department of Physics, University of Surrey, GU2 7XH, Guildford, UK

    b Service de Physique Nuclaire, DSM/DAPNIA, CEA/Saclay, F-91191 Gif-sur-Yvette, FranceReceived 12 February 2001; received in revised form 15 March 2001; accepted 20 March 2001

    Editor: W. Haxton


    We examine the non-diffractive mechanisms in the -meson photoproduction from threshold up to a few GeV using aneffective Lagrangian in a constituent quark model. The new data from CLAS at large angles can be consistently accounted forin terms of s- and u-channel processes. Isotopic effects arising from the reactions p p and n n, are investigatedby comparing the cross sections and polarized beam asymmetries. Our result highlights an experimental means of studyingnon-diffractive mechanisms in -meson photoproduction. 2001 Elsevier Science B.V. All rights reserved.

    PACS: 12.39.-x; 25.20.Lj; 13.60.LeKeywords: Phenomenological quark model; Photoproduction reactions; Meson production

    For a long time, the study of -meson photopro-duction has been concentrated at high energies wherethe diffractive process is the dominant source, and apomeron exchange model based on the Regge phe-nomenology explains the elastic production at smallmomentum transfers [1]. In contrast with the high en-ergy reactions, data for the photoproduction of the -meson near threshold are still very sparse, and wereavailable only for small momentum transfers [2]. Thenew data from the CLAS collaboration at JLAB [3]cover for the first time momentum transfers above 1.5(GeV/c)2 with 2.66 W 2.86 GeV, and provideimportant information about mechanisms leading tonon-diffractive processes at large angles.

    E-mail address: (Q. Zhao).

    Initiated by the possible existence of strangenessin nucleons, Henley et al. [4] showed that 1020%of strange quark admixture in the nucleon would re-sult in an ss knockout cross section compatible withthe diffractive one near threshold. More recently, ithas been shown by Titov et al. [58] using a rela-tivistic harmonic oscillator quark model that an evensmaller fraction of ss of about 5% would produce de-tectable effects in some polarization observables. InRef. [9], Williams studied the effect of an OZI evad-ing NN interaction by including the Born term withan effective NN coupling. Quite different conclu-sions were drawn from the above approaches, sincethe descriptions of the diffractive process were sig-nificantly model-dependent, and would influence notonly the fraction of a possible ss component in thenucleon, but also the OZI evading NN coupling.

    0370-2693/01/$ see front matter 2001 Elsevier Science B.V. All rights reserved.PII: S0370-2693(01) 00 43 2- 4

  • 232 Q. Zhao et al. / Physics Letters B 509 (2001) 231238

    As shown in Ref. [9], the |gNN | could have a rangeof 0.30.8, depending on the model for the diffrac-tive process. Therefore, a reliable description of thediffractive contribution, which determines what scoperemains for other non-diffractive mechanisms, is vi-tal. Near threshold, another question arising from non-diffractive -meson production is what the dominantprocess in the large angle production might be?In Ref. [10], we showed that OZI suppressed s- andu-channel contributions should be a dominant sourcefor large angle production in p p.

    Concerning the two points noted above, we studyhere, within a quark model, the non-diffractive -meson photoproduction in two isotopic channels, pp and n n, from threshold to a few GeV of A pomeron exchange model, which was deter-mined at higher energies, was then extrapolated to thelow energy limit with the same parameter. In this way,we believe the diffractive contribution has been reli-ably evaluated and should be a prerequisite for study ofnon-diffractive mechanisms in both reactions. Pion ex-change was also included but found to be small. More-over, its forward peaking character suggests that someother non-diffractive process is necessary at large an-gles. An effective qq interaction was proposed forthe s- and u-channel -meson production, which willaccount for the large angle non-diffractive contribu-tions up to W 3 GeV. In the quark model frame-work, the nucleon pole terms (Born term), as well as acomplete set of resonance contributions can be consis-tently included. Our attention will be focused on thelarge angle s- and u-channel processes in this work.We do not take into account the strangeness compo-nent, although the effective qq coupling might haveincluded effects from an OZI evading process. A com-parison with the new data from the CLAS Collabora-tion should highlight the roles played by the s- andu-channel production, and the isotopic study willprovide insight into any non-diffractive mechanism.

    The question of whether a non-diffractive processcan play a role at a few GeV of c.m. energy, is stillan open one. As pointed out by Donnachie and Land-shoff [11], contributions from two-gluon exchangesshould be small at a few GeV, and a pomeron exchangewould be enough. Laget [12] showed that a two-gluonexchange mechanism might start to play a role at large|t| with W 3 GeV. A relatively large contributionwas found from correlation processes. However, it was

    also shown that two-gluon exchange could not accountfor the increase in the cross sections at large angles.A u-channel process, which violated the s-channelhelicity conservation (SCHC), was then employed toexplain the large angle behavior. Interestingly, newlysubmitted results from the CLAS Collaboration for the electroproduction at 0.7Q2 2.2 (GeV/c)2 and2.0W 2.6 GeV suggest that some non-diffractivemechanism plays a role at large t [13]. Such resultscannot generally be explained by the SCHC pomeronexchange and the soft two-gluon-exchange model,but strongly imply that some non-perturbative processmight still compete against the progressively more im-portant perturbative QCD processes at a few GeV.To disentangle these mechanisms near threshold, oneshould start with those SCHC violated processes, inparticular, the s- and u-channel productions. Theirenergy evolution to a few GeV as well as a measur-able effect arising from their isotopic reaction shouldbe seriously considered.

    Our model consists of three processes: (i) s- andu-channel production with an effective Lagrangian;(ii) t-channel pomeron exchange; (iii) t-channel pionexchange.

    At quark level, the qq coupling is described bythe effective Lagrangian [14,15]:

    (1)Leff = (a+ ibq



    where the quark field can be u, d , or s for thelight-quark baryon system, while m represents thevector -meson field. The 3-quark baryon systemis described by the nonrelativistic constituent quarkmodel (NRCQM) in the SU(6) O(3) symmetrylimit. The vector meson is treated as an elementarypoint-like particle which couples to the constituentquark through the effective interaction. Two parame-ters, a and b, are introduced for the vector and tensorcoupling of the qq in the s- and u-channels.

    At tree level, the transition amplitude from the ef-fective Lagrangian can be expressed as the contribu-tions from the s-, u- and t-channel processes:

    (2)Mfi =Msf i +Muf i +Mtf i.In N N , Mtf i vanishes since it is proportional

    to the charge of the final state -meson. Introducingintermediate states, the s- and u-channel amplitudes

  • Q. Zhao et al. / Physics Letters B 509 (2001) 231238 233

    can be written as:

    Ms+uf i = ij

    Nf |Hm|Nj

    Nj | 1Ei + Ej he|Ni


    + ij

    Nf |he 1Ei Ej |Nj

    Nj |Hm|Ni,with

    Hm =(a + ibq



    for the quarkmeson coupling vertex, and

    (4)he =l

    elrl (1 k)eikrl , k = k


    where k and are the three-momentum and energyof the incident photon, respectively. |Nj representsthe complete set of intermediate states. In the NR-CQM, those low-lying states (n 2) have been suc-cessfully related to the resonances and can be takeninto account explicitly in the formula. Higher excitedstates can be treated as degenerate in the main quan-tum number n of the harmonic oscillator basis. A de-tailed description of this approach can be found inRefs. [14] and [15]. It should be noted that resonancesbelonging to quark model representation [70, 48] donot contribute in p p due to the Moorhouseselection rule at the electromagnetic interaction ver-tex [16]. Therefore, eight low-lying resonances willexplicitly appear in p p, while there are 16 in n n.

    The t-channel diffractive process is accounted forby the pomeron exchange model of Donnachie andLandshoff [1,17,18]. In this model, the pomeron me-diates the long range interaction between two confinedquarks, and behaves rather like a C = +1 isoscalarphoton. We summarize the vertices as follows:

    (i) Pomeronnucleon coupling:F(t)= 30f (t),

    (5)f (t)= (4M2N 2.8t)

    (4M2N t)(1 t/0.7)2,

    where 0 is the coupling of the pomeron to one lightconstituent quark; f (t) is the isoscalar nucleon elec-

    tromagnetic form factor with four-momentum trans-fer t ; the factor 3 comes from the quark-countingrule.

    (ii) Quark-meson coupling:(6)V

    (p 12q,p+ 12q

    )= fM,where f = 164.76 MeV is the decay constant ofthe -meson in e+e, which is determined bye+e = 82e e2Qf 2 /3M = 1.32 keV [19].

    A form factor 20/(20 + p2) is adopted for the

    pomeronoff-shell-quark vertex, where 0 = 1.2 GeVis the cut-off energy, and p is the four-momentum ofthe quark. The pomeron trajectory is (t) = 1 + . +t , with . = 0.08 and = 0.25 GeV2.

    The 0 exchange is introduced via the Lagrangianfor the NN coupling and coupling as

    (7)LNN =igNN 5( ),and