Bled Workshops in Physics Vol. 17, No. 1 p. 44 A Proceedings of the Mini-Workshop Quarks, Hadrons, Matter Bled, Slovenia, July 3 - 10, 2016 Puzzles in eta photoproduction: the 1685 MeV narrow peak* B. Gollia'c and S. Sircab'c a Faculty of Education, University of Ljubljana, 1000 Ljubljana, Slovenia bFaculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia c and Jozef Stefan Institute, 1000 Ljubljana, Slovenia Abstract. We claim that a narrow peak in the cross section near 1685 MeV in the yn —> nn channel can be explained through a peculiar radial behaviour of the p-wave quark states with j = 1/2 and j = 3/2 in the low lying S11 resonances and the opening of the KZ threshold rather than by an exotic resonance. We explain the mechanism of its formation in the framework of a coupled channel formalism which incorporates quasi-bound quarkmodel states corresponding to the two low lying resonances in the S11 partial wave. A relation to the Single Quark Transition Model is pointed out. 1 Motivation In this contribution we discuss a possible quark-model explanation for a narrow structure at W « 1685 MeV in the yn —» nn reaction observed by the GRAAL Collaboration [1] which, however, turned out to be absent in the np channel. Az-imov et al. [2] were the first to discuss the possibility that the structure could belong to a partner of the 0+ pentaquark in the exotic antidecouplet of baryons. More conventional explanations have attributed the peak to the threshold effect of the KZ channel [3], interference of the nearby S n, Pn and P13 resonances [4], constructive and destructive interference of the two lowest S n resonances in the nn and np channels, respectively, as anticipated in the framework of the Giessen model [5,6] as well as in the Bonn-Gatchina analysis [7,8]. In the framework of the constituent-quark model coupled to the pseudoscalar meson octet the (non)appearance of the peak was related to different EM multipoles (at the quark level) responsible for excitation in either of the two channels [9]. 2 The coupled channel approach In our recent paper [10] we have systematically analysed the partial waves with sizable contributions to the nN, KA and KZ decay channels using a SU(3) extended version of the Cloudy Bag Model (CBM) [11] which includes also the p and œ mesons1. We have found that the main contribution to n photoproduction * Talk delivered by B. Golli 1 The method has been described in detail in our previous papers [12-16] where we have analysed the scattering and electro-production amplitudes in different partial waves. Puzzles in eta photoproduction ... 45 at low and intermediate energies comes from the S11 partial wave. In this contribution we therefore concentrate on the S11 partial wave in which the considered phenomenon is most clearly visible. In our approach the main contribution to n production in the S11 partial wave stems from the resonant part of the electroproduction amplitude which can be cast in the form MN yn = J^^ -¿T- <^r|Vy|Vn> TnN nN , (1) where TnNnN is the T-matrix element pertinent to the nN —» nN channel, Vy describes the interaction of the photon with the electromagnetic current and £ is the spin-isospin factor depending on the considered multipole and the spin and isospin of the outgoing hadrons. Here |¥R> = c (W)|N(1535)> + c2(W)|N(1650)> with |N(1535)> = cos-&|70,28, J = 1> - sin#|70,48, J = 2> , |N(1650)> = sin #|70,28, J = 1> + cos #|70,48, J = 2 > and Ct(W) are W-dependent coefficients determined in the coupled-channel calculation for scattering. The strong T^NnN amplitude is obtained in a coupled channel calculation with ten channels involving n, p, n and K mesons. The most important channels are shown in Fig. 1. The behaviour of the amplitudes is dominated by the N (1535) and N (1650) resonances as well as the nN, KA and KI thresholds. In the 1100 1200 1300 1400 1500 1600 1700 1800 1100 1200 1300 1400 1500 1600 1700 1800 W [MeV] W [MeV] Fig. 1. The real and imaginary parts of the scattering T matrix for the dominant nN, nA, nN, KA and KZ channels in the Sn partial wave. The corresponding thin curve denote the 2014-2 solution of the Bonn-Gatchina group [17] for the nN channel.. The data points for the elastic channel are from the SAID partial-wave analysis [18]. present calculation we put the mixing angle 0 to the popular value of 30° and assume that all meson-quark coupling constants are fixed at their quark-model 46 B. Golli and S. Sirca values dictated by the SU(3) symmetry. While the real part of the elastic amplitude is well reproduced, the imaginary part is rather strongly underestimated in the region of the second resonance which can be to some extent attributed to too strong couplings in the nA, KA and KI channels. This discrepancy should be taken into account when assessing the quality of the photoproduction amplitudes in the following. 3 The n photoproduction amplitudes The electromagnetic amplitude in (1) in the S11 partial wave is dominated by the photon-quark coupling while the coupling to the pion cloud turns out to be small. The spin doublet and quadruplet states involve quarks excited to the p orbit with either j = 2 or j = | [19]: |482 > = 1|(ls)2(1p3/2)1) + ^8|(ls)2(1pl/2)1) , (2) |28 2 > =- 2 |(1s)2(1p3/2)1> + ^-K1s)2(1pi/2)1> + ^l(1s)2(1pi/211) ' , (3) where the last two components with p1/2 correspond to coupling the two s-quarks to spin 1 and 0, respectively; the flavour (isospin) part is not written explicitly. The quark part of the dominant E0+ transition operator can be cast in the form i=1 drjq • A?1 = IM12 ](i)+ M 32 J(i) [1 + 2 To(i)] , l ¿1j l 2 2 j where M1 = V 3 M 3 = V 3 dr r2 dr r2 (4) jo(qr) 3v? (r)us(r) + u? (r)vs (r) - ^(qrK (r)vs(r) , (5) . V 2 2 / 2 J -jo(qr)u13 (r)vs (r) + 2j2(qr) (ui (r)vs(r)- 3v? (r)us(r)U (6) The quark transition operator is defined through (ljmj|lLj^|2ms> = Clm LM. 2 s Evaluating (4) between the resonant states and the nucleon we notice that for the proton, the isoscalar part of the charge operator exactly cancels the isovector part in the case of the first two components in (2) and (3). This is a general property known as the Moorhouse selection rule [20] and follows from the fact that the flavour part in these two components corresponds to the mixed symmetric state $M,S. The proton therefore receives no contribution from the 1s —» 1p3/2 transition. This is not the case with the neutron which receives contributions from all components in (2) and (3). The quark in the 1p3/2 orbit has a distinctly different radial behaviour from that in the 1p1/2 orbit, which is reflected in a different q-and W-behaviour of the amplitudes (5) and (6). The E0+ amplitudes are shown in Fig. 2 for the proton and the neutron in the region of the KI threshold. Our results do show a (bump-like) structure in the yn Puzzles in eta photoproduction ... 47 channel, which is absent in the yp channel, though its strength in the imaginary part is lower compared to the Bonn-Gatchina 2014-2 analysis (which fits well the experimental cross-section). A moderate rise of the neutron real amplitude below the KI threshold is clearly a consequence of the contribution from the j = 3/2 orbit, while the cusp-like drop in the amplitudes is due to the KI threshold. This \yp ^ nP ImE0+ , m°d/e21 vertex \ \ \ j =3/2 \ \ — 1 x BoGA 1580 1600 1620 1640 1660 1680 1700 1720 W [MeV] 1580 1600 1620 1640 1660 1680 1700 1720 W [MeV] 1580 1600 1620 1640 1660 1680 1700 1720 W [MeV] Yn ^ nn ReE0+ ________ ____ model j = 1/2 -■-■ j = 3/2 ........... -1xBoGA - - v ---- -------- 1580 1600 1620 1640 1660 1680 1700 1720 W [MeV] Fig. 2. The dominant contributions to the imaginary and real part of the Eo+ amplitude (in units of mfm) for the proton (upper two panels) and for the neutron (lower two panels). Apart of the separate contributions from the s —> p3/2 and s —> p1/2 transitions the vertex correction is also displayed. The Bonn-Gatchina results are taken from the 2014-2 dataset and multiplied by — 1. 8 0 6 2 4 4 2 6 0 8 0 6 4 2 6 0 8 2 behaviour of the amplitudes is reflected in the cross-section as a peak (bump) present only in the neutron channel (see Fig. 3). Though the strength in our model is lower compared to the Bonn-Gatchina analysis, the qualitative agreement does offer a possible and straightforward explanation of this structure in terms of the quark model: a combination of a peculiar property of the (relativistic) wave functions of the Sn resonances and the presence of the KI threshold. Let us stress that the proposed explanation of the considered peak would not be possible in a framework of the nonrelativistic quark model in which the radial behaviour of the quark wave function depends only on the orbital momentum quantum number. 48 B. Golli and S. Sirca BoGa p BoGa Eo+ BoGa n BoGa Eo+ model p -- Eo+ model n — Eo+ - 1500 1550 1600 1650 W [MeV] Fig. 3. The total cross-sections for yp 3, 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 1650 W [MeV] > np and yu —> nn (multiplied by the conventional factor of 2) (right panel), the ratio of the neutron and the proton cross-section (left panel). Thinner circles and lines: contribution of the Sn partial wave. The BoGa curves have been reconstructed from the Bonn-Gatchina 2014-2 data set [17]. 4 Relation to the Single Quark Transition Model Our model can be envisioned as a version of the Single Quark Transition Model (SQTM) in which the photon interacts with a single quark in the three-quark core and the other two quarks act as spectators. The general form of the SQTM operator is a product of the boost operator and current operators [21]: BjA = M^sLr(l, S, L, A) = R^zT(I, lz, S, Sz = A - lz), (7) ISL H. S where Mîsl = ChlsA-uRisiz, (limiO) = 1 and < 1 ||T(S)||2> = v/ÏS+T. In our approach the quark states are labeled by the total angular momentum j, rather than the orbital angular momentum and spin. In this case it is more convenient to expand (7) as BjA = X MajlIla2],