14 June 2001
Physics Letters B 509 (2001) 231238www.elsevier.nl/locate/npe
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 . 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 . Thenew data from the CLAS collaboration at JLAB 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: firstname.lastname@example.org. (Q. Zhao).
Initiated by the possible existence of strangenessin nucleons, Henley et al.  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.  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. , 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. , 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. , 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 c.m.energy. 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 , contributions from two-gluon exchangesshould be small at a few GeV, and a pomeron exchangewould be enough. Laget  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 . 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
Nj | 1Ei + Ej he|Ni
Nf |he 1Ei Ej |Nj
Hm =(a + ibq
for the quarkmeson coupling vertex, and
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.  and . 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 . 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 .
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