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
(8)L0 = eNg
Then the amplitude for the 0 exchange can be de-rived in the NRCQM. The commonly used couplings,g2NN/4 = 14, g2 = 0.143, are adopted. A signexists between the two pion exchange amplitudes forp p and n n, i.e., gpp = gnn, due tothe isospin symmetry.
In the pion exchange, the only parameter =300 MeV comes from the quark model form factore(qk)2/62 given by the spatial integral over thenucleon wavefunctions. The meson exchange hasnot been included due to its even smaller contributioncompared to the pion exchange. A recent study showed that the gNN coupling could be as smallas 1.1, which means that exchange can be neglectedsafely in -meson production.
A criticism of the application of a NRCQM to W 3 GeV is that relativistic effects become important dueto the high momentum transfer between the incomingphoton and the constituent quarks. In principle, oneneeds a relativistic version of the quark model totake into account the time axis. However, a self-consistent relativistic quark model is not available yet.On the other hand, the NRCQM has made impressivesuccess in hadron spectroscopy as well as most photo-excitation helicity amplitudes for baryons . In
234 Q. Zhao et al. / Physics Letters B 509 (2001) 231238
our approach, uncertainties arising from NRCQMsshortcoming can be regarded as being efficiently takeninto account in two ways: (i) The masses as well astotal decay widths of those low-lying resonances comefrom the experimental output. Therefore, one neednot fit the baryon spectroscopy. (ii) A Lorentz boostfactor for each momentum in the spatial integrals isemployed to take into account the Lorentz contractioneffects up to W 3 GeV. In fact, it shows that energyevolution of those s- and u-channel terms is veryimportant in relating a pomeron exchange model to theeffective Lagrangian model.
In the range of the CLAS measurements, the value|t| = 2 (GeV/c)2 corresponds to a scattering angleof 90 in the c.m. system. For larger valuesof |t|, the cross section will reflect features from anon-diffractive mechanism, which in our model is de-scribed by the s- and u-channel -meson production.The energy evolution as well as the large angle crosssections provide a direct constraint on the parame-ters in our model. A numerical fit of the old data at E = 2.0 GeV and the new ones  at 3.6 GeVgives a = 0.241 0.105 and b = 0.458 0.091,which are consistent with previous work . Qual-itatively, the ratio of parameter a for the - and-meson (see Ref. ) can be related to the ratiogNN/gNN , namely, gNN/gNN = a()/a(). InRef. , a()= 2.5 accounted for the differentialand total cross sections reasonably. In Ref. , thebest value a() = 2.72 was derived. It shows thata()/a() = 0.096 0.087 covers a range veryclose to the value determined by SU(3) symmetry, i.e.,gNN/gNN = tan 3.7 = 0.065, where the angle3.7 is the deviation from the ideal mixing .This feature is strongly related to the effective quarkvector-meson coupling and quark model phenomenol-ogy which perhaps need to be seriously considered infuture investigation. In this work, we just treat the cou-plings as parameters and leave them determined bythe data. The signs of the parameters reflect the rela-tive phases between the pomeron exchange terms andthe s- and u-channel transition amplitudes. We assumethat the quarkphoton vertices and quark-mesonvertices in both the pomeron exchange and s- and u-channel processes have the same signs, even thoughthe quark flavors are different. Then we leave the rela-tive phases determined by the signs of the parameters.The sign for pion exchange is fixed by Eqs. (7) and (8).
Fig. 1. Differential cross section for p p at E = 3.6 GeV.The dot-dashed, dashed, and solid curves denote the pion exchange,pomeron plus pion, and full model calculations, respectively, whilethe dotted curve represents full model calculation excluding theu-channel contribution. Data come from  (dot),  (square), and (diamond).
In Fig. 1, the differential cross section is calcu-lated at E = 3.6 GeV for p p. The dot-dashed and dotted curves denote the results for ex-clusive pion exchange and pion plus pomeron ex-change, respectively. Clearly, the pomeron exchangeis the dominant mechanism at small momentum trans-fers. It can be seen that above |t| = 2 (GeV/c)2,the pomeron plus pion exchange cannot reproducethe flattened feature of the cross section. With thes- and u-channel contributions taken into account,the full model calculation is presented by the solidcurve. It is also found that the u-channel has a rel-atively stronger contribution to the cross sectionsabove the resonance energy region. Meanwhile, theu-channel nucleon pole term is dominant over otheru-channel contributions. This feature is in agreementwith the findings of Ref. . The dotted curve de-notes the result excluding the u-channel from con-tributing. It should be noted that the s- and u-channelcontributions might be slightly over-estimated sincethe small two-gluon-exchange contributions are over-looked here.
Q. Zhao et al. / Physics Letters B 509 (2001) 231238 235
Next, we show that an isotopic -meson photopro-duction on the neutron will be able to provide us withinformation about the large angle -meson productionmechanism.
The qq coupling in n n can be described inthe same way as in p p. But the isospin degreeso...