Different approaches to the Roper resonance are reviewed, revealing the multiple facet of this state and the need for some crucial experiments.Dajemo pregled nekoliko mogućih tumačenja Roperove rezonancije, te ukazujemo na složenost tog stanja, kao i na potrebu za novim mjerenjima

Golli, Bojan

Rosina, Mitja

English

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ISSN1330–0016CODEN FIZBE7THE ROPER RESONANCE REVISITEDMITJA ROSINAa,b and BOJAN GOLLIc,baFaculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia,bJožef Stefan Institute, Jamova 39, P.O. Box 3000, 1001 Ljubljana, SloveniaE-mail address: Mitja.Rosina@ijs.sicFaculty of Education, University of Ljubljana, Ljubljana, SloveniaE-mail address: Bojan.Golli@ijs.siReceived 12 September 2003; Accepted 26 April 2004Online 10 October 2004Different approaches to the Roper resonance are reviewed, revealing the multiplefacet of this state and the need for some crucial experiments.PACS numbers: 14.20.Gk UDC 539.12.1Keywords: Roper resonance, electroexcitation amplitudes, non-relativistic quark model1. IntroductionThe first excited state of the nucleon, the Roper resonance, seems to be a com-plicated object, characterized by its relatively low energy and by a rather peculiarbehaviour of electroexcitation amplitudes, in particular the sign at Q2 = 0, whichcannot be reproduced in the framework of the non-relativistic quark model. Severalmodels have been suggested to explain these features. On one hand, the predictionsfor the amplitudes are not yet conclusive, and on the other hand, theQ2-dependenceof the electroproduction is poorly measured. Therefore, it would be very importantto perform new measurements in order to distinguish different models. We shallconfront three classes of models:• The constituent quark model• The breathing model• Explicit non-quark degrees of freedomFIZIKA B 13 (2004) 1, 217–222 217rosina and golli: the roper resonance revisited2. The constituent quark modelThe dynamics in the three-quark Hilbert space has to mimic non-quark degreesof freedom by a corresponding effective quark-quark interaction. The Graz group [1]has shown, that one can get the Roper resonance lower than the negative parityexcited states with a pion exchange interaction (while the one-gluon exchange in-teraction gives Roper resonance above negative parity states). It is still not knownwhether the Graz interaction is also sufficient to reproduce the amplitudes. If theyuse correct relativistic boosts, they get good elastic electromagnetic form factors.For inelastic processes (such as the electroexcitation of the Roper resonance) theyhave still many open questions regarding relativity, two-body currents, spin-orbitand tensor forces and vector meson exchanges; their work is in progress.The importance of a correct relativistic treatment in CQM calculations of theEM amplitudes has been stressed by [2 – 4] yielding the correct sign at the pho-ton point. In all of these approaches, the change of the amplitudes sign aroundQ2 ∼ 0.2–0.5 (GeV/c)2 is predicted – a feature that is absent in other approachesdiscussed below. This behaviour may therefore represent a crucial test of the modelwhen more precise measurements will be available.3. The breathing modelThe explanation that the Roper state is a breathing mode seems physically plau-sible, but in addition to the three quarks also the chiral field (pions, sigmas) andthe confining field (the chromodielectric bag or glueball field) should breathe. Ob-viously, with more degrees of freedom, the “inertial parameter” increases, loweringthe vibration frequency.A convenient relativistic model for the breathing mode is the chiral chromodi-electric model with the Lagrangian [5]:L = iψ̄γµ∂µψ +gχψ̄(σ̂ + iτ · π̂γ5)ψ + Lσ,π + Lχ , (1)whereLχ =12∂µχ̂ ∂µχ̂− 12M2 χ̂2 , Lσ,π =12∂µσ̂∂µσ̂ +12∂µπ̂ · ∂µπ̂ −U(π̂2 + σ̂2) , (2)and U is the usual Mexican hat potential.A non-chiral version of this model has been used to describe coupled vibrationsof valence quarks and the background chromodielectric field in the framework ofthe RPA [6]. The energy of the lowest excitation turned out to be 40 % lower thanthe pure 1s–2s excitations. A similar result was obtained by Guichon [7], using theMIT bag model and considering the Roper resonance as a collective vibration ofvalence quarks and the bag.The inclusion of chiral mesons, in particular the σ-meson which accounts forthe (ππ)I=0s−wave N decay, can further decrease the energy of the Roper resonance.The Ljubljana/Coimbra group [8, 9] has described the Roper resonance as a super-218 FIZIKA B 13 (2004) 1, 217–222rosina and golli: the roper resonance revisitedposition of quark excitations coupled to the “breathing” chromodielectric field (seeFig. 1) and the lowest vibrational mode of the σ-field on top of the ground stateΨRoper =c1√1 − c2((1s)2(2s) − c(1s)3)+ c2â†σ (1s)3.0,0 0,5 1,0 1,5 2,0012345678910 quark density meson potentialNucleonfm-1r / fm0,0 0,5 1,0 1,5 2,0012345678910 quark density meson potentialRoperfm-1r / fmFig. 1. The baryon densities (solid lines) and the effective potentials (dashed lines)generated by the self-consistently determined π, σ and χ fields in the nucleonand the Roper. One can see the broader density distribution and softer effectivepotential in the case of Roper.FIZIKA B 13 (2004) 1, 217–222 219rosina and golli: the roper resonance revisitedFor a sufficiently low mass of the σ-meson, the inclusion of the σ vibration canlower the energy of the Roper resonance. Furthermore, since the photon is notcoupled to this mode, the electroproduction amplitudes are reduced compared tothose calculated from the quarks alone.The important role of the σ-meson has been also found by Kukulin and collab-orators [10, 11]. Here the σ-meson is coupled to the (1s)1(1p)2 quark configurationrather than to the (1s)2(2s)1.The presence of σ-meson vibrations is consistent with the recent phase shiftanalysis by Krehl et al. [12] who found that the resonant behaviour in the P11channel can be explained solely through the coupling to the σ-N channel, withoutassuming any internal (i.e. quark) radial excitation of the nucleon. In our view,radial excitations of quarks are needed in order to explain relatively large electro-production amplitudes, which would indicate that the σ-N channel couples to allnucleon 12+excitations rather than to the Roper resonance alone.4. Explicit non-quark degrees of freedomThe “hybrids” (the non-quark degrees of freedom) can be incorporated, togetherwith mesonic degrees of freedom, in a superpositionΨRoper = cqqqψqqq + cqqqπψqqqπ + cqqqσψqqqσ + cqqqGψqqqG + cqqqgψqqqg + . . . ,with an obvious notation (G = glueball, g = gluon). Several authors estimatedit [12 – 14] and their suggestions are still inconclusive. Experiment is called for to“determine” the expansion coefficients c.Krehl et al. [12] coupled the πN, σN, π∆ and ηN channels for the phase shifts,showing the importance of the σ excitation, as mentioned before. Li et al. [13]consider the Roper resonance as a qqqg hybrid with the glue field excited; then thetransverse helicity amplitude decreases rapidly with Q2, while the longitudinal onevanishes. Carlson et al. [14] also argue that the Roper resonance might be a qqqghybrid characterized with the suppression of the transverse electroproduction; thetransverse-to-longitudinal ratio is proposed as a good diagnostics.5. The meson-nucleon-Roper couplingThe virtual Roper state can play an important role in three-body nuclear forcesin a process in which tree nucleons N1, N2 and N3 exchange mesons in the followingway:N1 → N1 + π, N2 + π → N∗ → N2 + σ, N3 + σ → N3 .Therefore, the knowledge of the gπNN∗ and gσNN∗ couplings is of interest. They canbe deduced from partial width of the Roper resonance decays, but this experimentalinput is still very rough. For Γ = 350 ± 100 MeV and branching ratios 60 – 70%220 FIZIKA B 13 (2004) 1, 217–222rosina and golli: the roper resonance revisited(5 – 10%) for the Nπ (Nσ) channel, it follows g2πNN∗/4π = 3.4±1.2 and g2σNN∗/4π =0.34 ± 0.21. The latter value is too uncertain to decide whether the cancellationbetween the σ and ω exchange will lead to an attractive or repulsive contributionto nuclear forces.An alternative analysis using the photoproduction of ρ or ω has been proposedby Madeleine Soyeur [15]:[(γ → ω)+p−−−−−−−−−−−−→(π0 − exchange) ρ0+N∗+] + [(γ → ρ0)+p−−−−−−−−−−−−→(σ − exchange) ρ0+N∗+] ,and analogously for ω. While the photoproduction of ρ is sensitive to gπNN∗ , thephotoproduction of ω is sensitive to gσNN∗ . Accurate measurements are recom-mended.6. ConclusionWhile several models can explain the low excitation energy of the Roper reso-nance, they do differ in their predictions regarding the sign, magnitude, transverse-to-longitudinal ratio and σ-to-ω branching ratio of electroproduction amplitudes.Accurate experiments are called for to resolve these issues as well as the Q2-dependence of the amplitudes.References[1] L. Ya. Glozman, W. Plessas, K. Varga and R. F. Wagenbrunn, Phys. Rev. D 58 (1998)094030.[2] S. Capstick, Phys. Rev. D 46 (1992) 2864; S. Capstick and B. D. Keister, Phys. Rev.D 51 (1995) 3598.[3] F. Cardarelli, E. Pace, G. Salmè and S. Simula, Phys. Lett. B 397 (1997) 13.[4] F. Cano and P. González, Phys. Lett. B 431 (1998) 270.[5] M. C. Birse, Prog. Part. Nucl. Phys. 25 (1990) 1; T. Neuber, M. Fiolhais, K. Goekeand J. N. Urbano, Nucl. Phys. A 560 (1993) 909.[6] W. Broniowski, T. D. Cohen and M. K. Banerjee, Phys. Lett. B 187 (1987) 229.[7] P. A. M. Guichon, Phys. Lett. B 163 (1985) 221; Phys. Lett. B 164 (1985) 361.[8] P. Alberto, M. Fiolhais, B. Golli and J. Marques, Phys. Lett. B 523 (2001) 273.[9] B. Golli, P. Alberto and M. Fiolhais, Bled Workshops in Physics 2 1 (2001) 38; acces-sible also at http://www-f1.ijs.si/BledPub/.[10] V. I. Kukulin, Proc. 18th Eur. Conf. on Few-Body Problems in Physics, Bled, Slovenia,September 8–14, 2002, eds. R. Krivec et al., Few-Body Systems Suppl. 14 (2003) 71.[11] V. I. Kukulin, I. T. Obukhovsky, V. N. Pomerantsev and A. Faessler, Phys. Atom.Nucl. 64 (2001) 1667; J. Phys. G. 27 (2001) 1851.[12] O. Krehl, C. Hanhart, S. Krewald and J. Speth, Phys. Rev. C 62 (2000) 025207.[13] Zhenping Li, Volker Burkert and Zhujun Li, Phys. Rev. D 46 (1992) 70.FIZIKA B 13 (2004) 1, 217–222 221rosina and golli: the roper resonance revisited[14] C. E. Carlson and N. C. Mukhopadhyay, Phys. Rev. Lett. 67 (1991) 3745.[15] M. Soyeur, Nucl. Phys. A 671 (2000) 532.RAZMATRANJE ROPEROVE REZONANCIJEDajemo pregled nekoliko mogućih tumačenja Roperove rezonancije, te ukazujemona složenost tog stanja, kao i na potrebu za novim mjerenjima.222 FIZIKA B 13 (2004) 1, 217–222

Razmatranje Roperove rezonancije

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