We have investigated exclusive photoproduction of light vector mesons
($\omega$, $\rho$ and $\phi$) on the nucleon at low energies. In order to
explore the questions concerning the so-called missing nucleon resonances, we
first establish the predictions from a model based on the Pomeron and meson
exchange mechanisms. We have also explored the contributions due to the
mechanisms involving $s$- and $u$-channel intermediate nucleon state. Some
discrepancies found at the energies near threshold and large scattering angles
suggest a possibility of using this reaction to identify the nucleon
resonances.Comment: 9 pages, LaTeX with sprocl.sty, 5 figures (11 eps files), Talk
  presented at the NSTAR2000 Workshop, The Physics of Excited Nucleons,
  Jefferson Lab., Newport News, Feb. 16-19, 200

Lee, T. -S. Harry

Oh, Yongseok

Titov, Alexander I.

English

arXiv

The authors have investigated exclusive photoproduction of light vector mesons ({omega}, {rho} and {phi}) on the nucleon at low energies. In order to explore the questions concerning the so-called missing nucleon resonances, they first establish the predictions from a model based on the Pomeron and meson exchange mechanisms. They have also explored the contributions due to the mechanisms involving s- and u-channel intermediate nucleon state. Some discrepancies found at the energies near threshold and large scattering angles suggest a possibility of using this reaction to identify the nucleon resonances

Oh, Y.

Titov, A. I.

Lee, T. S. H.

UNT Digital Library

. *ELECTROMAGNETIC PRODUCTION OF VECTOR MESONSAT LOW ENERGIES,Yongseok OHCenter for Theoretical Physics, Seoul National University, Seoul 151-742, KoreaandInstitute of Physics, Academia Sinica, Nankang, Taipei, Taiwan 11529, R. O. C.E-mail: ohys@phys. sinica. edu.twAlexander I. TITOVBogoliubov Laboratory of Theoretical Physics, JINR, Dubna Id 1980, RussiaE-mail: atitovt%hsunl .jinr.ruT.-S. Harry LEEPhysics Division, Argonne National Laboratory, Argonne, Illinois 6045’9, U.S.A.E-mail: lee@anph09.phy.anLgovWe have investigated exclusive photoproduction of light vector mesons (u, p and @)on the nucleon at low energies. In order to explore the questions concerning the so-called missing nucleon resonances, we first establish the predictions from a modelbased on the Pomeron and meson exchange mechanisms. We have also exploredthe contributions due to the mechanisms involving s- and u-channel intermediatenucleon state. Some discrepancies found at the energies near threshold and largescattering angles suggest a possibility of using this reaction to identify the nucleonresonances.At high energies and low momentum transfers, the exclusive electromag-netic production of vector mesons has been explained successfully by thePomeron exchange model. [1–3] However, at low energies near threshold, mesonexchange mechanisms become important, such as the x exchange in w produc-tion and the o exchange in p production. [4] Furthermore, the mechanismsinvolving intermediate nucleon and nucleon resonances (N* ), which could besuppressed at high energies, must also be included in a complete theoreticalinvestigation.To resolve the so-called “missing resonance problem”, it is essential to i-dentify the kinematic regions where the N* contributions are important. Manyof those missing nucleon resonances are predicted to have large partial widthsfor their decays into channels consisting of the nucleon and a vector meson.Therefore, one may hope to find them in vector meson electromagnetic pro-ductions. There exist some reports on the contributions from the nucleonresonances in vector meson photoproduction based on quark models [5,6] orthe Regge theory [7]. However, in order to confront the forthcoming data, it1The submitted manuscript has been createdby the University of Chicago as Operator ofArgonne National Laboratory (“Argonne”)under Contract No. W-31 -1 09-ENG-38 withthe U.S. Department of Energy. The U.S.Government retains for itself, and others act-ing on its behalf, a paid-up, nonexclusive,irrevocable worldwide license in said articleto reproduce, prepare derivative works, dis-tribute copies to the public, and perform pub-licly and display publicly, by or on behalf ofthe Government.\ —. ——:. ... ..Y (q) v (q”)z -------.!PP@) P w)(a)T vI!L__/P P P(c)Y v----------; a,ll,qP P(b)Y vP P P(d)Figure 1: Three mechanisms for vector meson (V = P,u, #) photoproduction: (a) Pomeron,(b) one-boson exchange, (c) and (d) s- and u-channel intermediate nucleon diagrams,is crucial to understand the non-resonant (background) production processeswhich could interfere strongly with the resonant production amplitudes. As astep in this direction, we have investigated the p, u and @ photoproductionsat low energies based on a model consisting of three mechanisms: Pomeronexchange, one-meson (n, q, u) exchange and the mechanism involving an in-termediate nucleon in s-channel and u-channel (called s + u nucleon-term fromnow on).Each of the considered production amplitude, as illustrated in Fig. 1, canbe written asTfi = c~(V)Mwvev(7), (1)where CK(V) and Cp(T) are the polarization vectors of the vector meson andthe photon, respectively. We first consider the Pomeron exchange depicted inFig. l(a). In this process, the incoming photon first converts into a q~ pair,which interacts with the nucleon by the Pomeron exchange before formingthe outgoing vector meson. The quark-Pomeron vertex is obtained by thePomeron-photon analogy, [1] which treats the Pomeron as a C = +1 isoscalarphoton, as suggested by a study of nonperturbative two-gluon exchanges. [8]We then have [1-3,9]m$~j 1My = i12<=@tiGp(w2 , t) Fl(t) ——(2/4fv m~–t 2p~+m$–t )x iiml(p’){ flg~” – 97’ }%(P)>where a,,~ = e2/4x, m and m’ are the spin2(2)projections of the initial andDISCLAIMERThis report was prepared as an account of work sponsoredby an agency of the United States Government. Neitherthe United States Government nor any agency thereof, norany of their employees, make any warranty, express orimplied, or assumes any legal liability or responsibility forthe accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed, orrepresents that its use would not infringe privately ownedrights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constituteor imply its endorsement, recommendation, or favoring bythe United States Government or any agency thereof. Theviews and opinions of authors expressed herein do notnecessarily state or reflect those of the United StatesGovernment or any agency thereof.DISCLAIMERPortions of this document may be illegiblein electronic imageproduced from thedocument.products. Images arebest available original,-Table 1: Coupling constants gv7n and gv7q in unit of GeV–l.final nucleons, respectively. Here we denote the four-momenta of the initialnucleon, final nucleon, incoming photon and outgoing vector meson by p, p’, qand qv, respective y. Their felicities are represented by AP, &, AT and Av. TheMandelstam variables ares = W2 = (p+ q)2, t = (p –p’)2, u = (p – gv)2. Theproton and vector meson masses are represented by mP and mv, respectively,and F1 is the isoscalar electromagnetic form factor of the nucleon,4m~ – 2.8t‘l(t) = (4m~ - t)(l - t/0.71)2 ‘The Pomeron-exchange is described by the following Regge form,(3)‘~(w2’)=(:)*p(’)-lexp{-:’a~(’)-”}(4)with W2 = (2W2 + 2m~ – m;) /4 and so = I/a&. The Pomeron trajectoryis taken to be the usual form ctP(t) = 1.08 + C@ with a~ = 0.25 GeV–2.In Eq. (2), iv is the vector meson decay constant: .fP = 5.04, ~~ = 17.05and jd = 13.13. The coupling constants /3. = ~d = 2.07 GeV–l, 6S = 1.60GeV-l and Kg = 1.1 GeV2 are chosen to reproduce the total cross section dataat high energies -ET > 10 GeV where the vector meson photoproductions arecompletely dominated by Pomeron-exchange.For the one-meson exchange diagram of Fig. 1(b), we consider scalar andpseudoscalar meson exchanges. The vector meson exchange is not allowed inthis process and the possible exchange of axial vector mesons [10] is suppressedmainly because of their heavy masses and small coupling constants.The pseudoscalar meson exchange amplitude can be obtained from theLagrangian,(5)where p = (To, q) and Au is the photon field. The coupling constants gvvn andgv~v, as given in Table 1, are obtained from the experimental partial widths[11] of the vector meson radiative decays V + yq. We use g~NN/4~ = 14.0and the SU(3) relation to obtain g~NN/gniVN =’ 0.35. To account for the effects3due to the finite hadron size at each vertex, the resulting Feynman amplitudesare regularized by the following form factors,(6)where (Am = 0.7, AV7= = 0,77) and (Aq = 1.0, AV7n = 0.9) in GeV unit. [12]The scalar (a) meson exchange was introduced in Ref. [4] to describe the pphotoproduction. This can be considered as an effective way to account for thetwo-x exchange in p production, which is expected to be significant because ofthe large branching ratio of p + r+n–-y decay. The contribution from the aexchange can be obtained from the following Lagrangian,We also regularize the resulting one-meson-exchange amplitude by the formfactors,A2 – M2 A~yoFo~N = ~2 _ ~“ ,– M:FVTU = A& – t “u(8)Following Ref. [4], we use M. = 0.5 GeV, g~NN/4~ = 8.0, A. = 1.0 GeV andAV70 = 0.9 GeV. The coupling constant gvyO is around 3.0 for reproducing thetotal cross sections of p photoproduction near threshold. We do not considerthe u-exchange in w and #Jphotoproductions, since the radiative decays ofthese two vector mesons into K+m- states are much weaker than that intosingle pion state. This could be understood by considering the current-fieldidentity. [4] (See also Ref. [12].)Finally we consider the s + u nucleon-term shown in Fig. 1(cjd). Thecorresponding amplitudes can be obtained from the following Lagrangian,(9)where the anomalous magnetic moment of the proton is KP = 1.79. The cou-pling constants are chosen to be (g~~N, KP) = (6.2, 2.0) and (gU~N, Ku) =(7.0, O), as determined in a study of TN scattering and pion photoproduc-tion. [13] In this study, we do not consider the s + u nucleon-term in # photo-production by assuming gd~~ x Odue to the OZI rule. A possible modificationdue to nonvanishing @NN coupling can be found in Ref. [12]. The form factorFv for VNN vertex is assumed to be of the form given by Ref. [141,4yp-+pp YP+PP“~‘. .,, . . . . . . . . . . . . ..lE,(GeV) E,(GcV)Figure 2: (Left figure) total cross section of p photoproduction. The dot-dashed, dashed,dot-dot-dashed, dotted and solid lines are Pomeron exchange, n exchange, u exchange, in-termediate nucleon and the sum of the amplitudes, respectively. The experimental data arefrom Refs. [15-18]. (Right figure) cross section aback with the data from Ref. [16].yp+pp1$-mE,=1.23ON . SAMl!n---- PmOm.-- *.-.,,: . . . . ;~- -....,>. — ~-+ .-..i= ,,, . . . . .~* “’2+;++””,0” +-...,. --..: . . . .-.2=!0-’” .2 m, m, Myp+ppFigure 3: Differential cross sections of p photoproduction at Ev = 1.23 and 2.8 GeV. Theexperimental data are from Refs. [18, 19]. Notations are the same as in Fig. 2.with AVNN =0.8 GeV.With the production amplitudes given above, we have explored the extentto which the existing data of vector meson photoproductions can be describedby the non-resonzmt (background) mechanisms. The p photoproduction crosssections are calculated from the amplitudes due to Pomeron, T, a exchangesand the s + u nucleon-term . In the left panel of Fig. 2 we show that thecalculated total cross sections (solid curve) agree to a very large extent, withthe data up to ET = 10 GeV. The important role of the u exchange (dot-dot-dashed curve) at energies near threshold is also shown there. The dynamicalcontent of our model can be better seen by investigating angular distributions.For example, given in the right panel of Fig. 2 is the backward integrated cross5yp+(np,:-D● B.d.md.ut..a. Smullm ---- P—-- .“—Ls56’0 $,+* t,‘\\% +. . ..--“.”... .. .. ,-, -:-,’ T --- = -.=-:-: ___‘,) -.6 ,,0E,(GF?I)yp-)ll)pnE,.14SG.V . WmIJId .::-p,-L .x—Id$,0, *%= .. ‘.:<:..- ,0” ..g ..,, -.v .. ,. . .,0- ‘ .. .. .. .. .. .. .. .,,-’0 ., ,>Ill (GA+yp+wpIdBE,.2.$*V . BN. . ..l.:2- F10’● — L~-~ ‘“” “’”,.,‘.<10-’ “i.. -.,3 .. .‘.., ----,.., . ---J.. -..,. .. .,..,0,23 &[q(GA+Figure 4: Total and differentialcross sections of w photoproduction. The experimental dataare from Refs. [15, 18, 19]. Notations are the same as in Fig. 2.sections defined by/“ &doa~aCk=zJ!2 dQ -(11)The predicted backward cross sections (solid curve) clearly overestimate theexperimental data. We find that this is caused by the dominant contributions(dotted curve) from thes + u nucleon-term . On the other hand, the calculatedcross sections will be too low if these mechanisms involving an intermediatenucleon state are not included in the calculation. Thk suggests that someother production mechanisms, which can give important contributions at largescattering angles, must be included in a more complete model. This can alsobe seen in the angular dktributions of the differential cross sections shown inFig. 3. We see that the contribution from the S+U nucleon-term (dotted curves)become dominant at large scattering angles. Therefore, precise measurementsof the differential cross sections in the backward scattering region will shedlight on the role of the intermediate nucleon states. At very low energiesnear threshold, Ev < 2 GeV, our predictions overestimate significantly thedata. This is perhaps mainly due to the neglect of the N“ excitations in ourcalculations.The u photoproduction cross sections are calculated from the Pomeron,m and q exchanges and the s + u nucleon-term. The predicted total and d-ifferential cross sections are compared with the data in Fig. 4. We see thatthe one-pion exchange (long dashed curves) dominates w photoproduction upto E7 % 6 GeV. The predicted total cross sections somewhat underestimatethe recent SAPHIR data in the IZT < 2 GeV region where the mechanismsinvolving the excitation of nucleon resonances are expected to play some roles.Similar to the case of p photoproduction, thes -t-u nucleon-term also dominates6YP+QP‘E● ----. . -m -- s.,— lad.6s~----a*. ,.,/.,,,In ‘,,’----- _,0” ~4,*,OYP+4Pto’Re,. 2.0 Ccv . Mat,---- mc-?m-- an— ad,.$ .%‘$ ‘..,.~,o.t “\\ “’”..,J‘., “’.... ..B ~.. =..:..,0-’ .:. ..<.%;...e, (G.vl ~ (GA7P*QP10’❑B,. 3.2sGeV . -.A-----10”-- =.— ml~-pI ‘.~ !0-’ ., .,..,,$ ‘.-.,, .. .., .10-’ -.. .. .‘ -’+- ~...:-~-,O”e, z, “’,III(wjFigure 5: Total and differential cross sections of@ photoproduction. The experimental dataare from Refs. [15,21,22]. Notations are the same as in Fig. 2.the cross sections at large It! region.For # photoproduction, we consider the Pomeron and pseudoscalar mesonexchanges only. We refer the calculations on the scalar meson exchanges anddirect ~ radiation arising from the non-vanishing @VN coupling to Ref. [12]and the effects of nonvanishing strangeness of the nucleon to Refs. [9, 20]. InFig. 5 we show that the predicted total and differential cross sections agree wellwith the very limited data. Contrary to the cases of p and w photoproductions,the Pomeron exchange (dash-dotted curves) gives the major contribution tothe total cross section even at energies near threshold. Thk is mainly dueto the fact that the coupling of @ to the nucleon is suppressed by the OZIrule. The contributions from m and q exchanges are also found to be small.Therefore @ photoproduction can provide a useful tool to study the nature ofthe Pomeron exchange.In summary, we have investigated the exclusive photoproduction of lightvector mesons (p, w and ~) at low energies. Our model includes the Pomeronexchange, meson (x, q, a) exchange and the s- and u-channel nucleon terms.It is found that the predicted cross sections agree with the existing data toa large extent. However, some significant discrepancies are found in the totaland differential cross sections at low energies and at large scattering angles. Itis possible that such discrepancies could be removed by extending our modelto include the effects due to the excitation of nucleon resonances. Our inves-tigation in this direction is in progress, aiming at using the new data fromcurrent experimental facilities to test various Q CD-inspired models of hadronstructure.7AcknowledgmentsWe are grateful to V. Burkert, W.-C. Chang, F. J. Klein, N. I. -Kochelev andT. Nakano for fruitful discussions and informations. Y.O. thanks the TheoryDivision of Argonne National Laboratory and the organizer of this workshopfor the warm hospitality and financial support. This work was supported inpart by KOSEF of Korea, NSC of Republic of China, Russian Foundation forBasic Research under Grant No 96-15-96426 and U.S. DOE Nuclear PhysicsDivision Contract No. W-31-109-ENG-38.References1. A. Donnachie and P. V. Landshoff, Nucl. Phys. B 244,322 (1984); NucI.Phys. B 267, 690 (1986); Phys. Lett. B 185,403 (1987).2. J.-M. Laget and R. Mendez-Galain, NUCL Phys. A 581, 397 (1995).3. M. A. Pichowsky and T.-S. H. Lee, Phys. Rev. D 56, 1644 (1997).4. B. Friman and M. Soyeur, Nucl. Phys. A 600,477 (1996).5. Q. Zhao, Z. L1 and C. Bennhold, Phys. Rev. C 58, 2393 (1998).6. Q. Zhao et al., Nucl. Phys. A 660,323 (1999).7. J. M. Laget, Saclay Report (2000), hep-ph/OO03213.8. P. V. Landshoff and O. Nachtmann, Z. Phys. C 35,405 (1987).9. A. I. Titov et al., Phys. Rev. C 58, 2429 (1998).10. N. I. Kochelev et al., Phys. Rev. D 61, 094008 (2000).11. Particle Data Group, C. Caso et uL, Eur. Phys. J. C 3, 1 (1998).12. A. I. Titov et al., Phys. Rev. C 60, 035205 (1999).13. T. Sato and T.-S. H. Lee, Phys. Rev. C 54, 2660 (1996).14. H. Haberzettl et al., Phys, Rev. C 58,40 (1998).15. The Durham RAL Databases, http: //durpdg.dur.ac. uk/hepdata.16. AHHM Collab., W. Struczinski et ai., Nucl. Phys. B 108, 45 (1976).17. ABBHHM Collab., R. Erbe et al., Phys. Rev. 175, 1669 (1968).18. SAPHIR Collab., F. J. Klein et al., TN Newslett. 14, 141(1998);F. J.Klein, Ph.D. thesis, Bonn Univ. (1996),19. J. Ballam et al., Phys. Rev. D 5, 545 (1972); Phys. Rev. D 7, 3150(1973).20. A. I. Titov, Y. Oh and S. N. Yang, Phys. Rev. Lett. 79, 1634 (1997);Y. Oh et al., Phys. Lett. B 462,23 (1999).21. H. J. Besch et al., Nucl. Phys. B 70, 257 (1974).22. H.-J. Behrend et al., Nucl. Phys. B 144, 22 (1978).8

Electromagnetic production of vector mesons at low energies

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Electromagnetic production of vector mesons at low energies

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