Bled Workshops in Physics Vol. 16, No. 1 p. 81 A Proceedings of the Mini-Workshop Exploring Hadron Resonances Bled, Slovenia, July 5 - 11, 2015 Eta and kaon production in a chiral quark model B. Golli Faculty of Education, University of Ljubljana, 1000 Ljubljana, Slovenia and Jozef Stefan Institute, 1000 Ljubljana, Slovenia Abstract. We apply a coupled channel formalism incorporating quasi-bound quark-model states to calculate the pion- and photo-production amplitudes of r| mesons and kaons. The meson-baryon and photon-baryon vertices are determined in the Cloudy Bag Model. Our model predicts sizable amplitudes in the P13, P33 and S11 partial waves in agreement with the recent partial-wave analyses of the MAID and the Bonn-Gatchina groups. 1 The model This work is a continuation of a joint project on the description of baryon resonances by the Coimbra group (Manuel Fiolhais and Pedro Alberto) and the Ljubljana group (Simon Sirca and B. G.) [1-8]. In the present work we extend our method which incorporates excited baryons represented as quasi-bound quarkmodel states into a coupled channel formalism using the K-matrix approach to calculate the scattering and photo-production amplitudes of strange mesons. In our approach the T matrix for inelastic meson scattering is obtained by solving the Heitler's equation Tmbm 'b ' = Kmbm 'b ' + i Tmbm "b " Km "b " m 'b ', (1) M ''B '' and similarly for the process yN —» MB: Tmbyn = Kmbyn + i Tmbm'b'Km'b'yn . (2) M'B ' The K-matrix is split in the resonant and the background contribution K — V" VBR VB 'R + Kbkg . (3) Km'b ' MB — Zr(W)(W -Wr) + KM'B ' MB . (3) in the case of photoproduction, the meson-baryon vertex is replaced by the corresponding electro-magnetic vertex V^R. The vertices are calculated in a version of the Cloudy Bag Model extended to the pseudo-scalar SU(3) meson octet [9] and the p meson: Hint — dr qAa(Y5^a + Y • Aa)q 5s + -f qAay^q(^ x a — 1,2,...,8. (4) 82 B. Golli The model provides a consistent parameterization of the baryon-meson and baryonphoton coupling constants and form factors in terms of f (equivalent to fn) and the bag radius Rbag. We use the following values Rbag = 0.83 fm and f = 76 MeV (consistent with the ground state calculations), while f for n and K can be increased in accordance with the phenomenological relations fK = 1.2 fn, fn = 1.2 fn. In addition, the bare masses of the resonances are also free parameters. 2 Pion scattering into the nN, KA and KL channels The nN, KA and KI channels contribute significantly in the P11, P13 and S11 partial waves and less in the D13 partial wave; we have not included the latter partial wave in the present contribution. The KI channel is dominated by the S11, P13 and P33 partial waves; its contribution in the P31, S31 and D33 waves turns out to be less important. 0.6 - 0.5 - nN 0.4 _ nN 0.3 0.2 _ KA KZ 0.1 - 0 0.1 - 1100 0.2 - 0.1 - 0 0.1 - W [MeV] 1100 1200 1300 1400 1500 1600 1700 1800 W [MeV] 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 nN nN KA KZ 5FI: imï P11 1100 1200 1300 1400 1500 1600 1700 1800 W [MeV] 0.2 0.1 0 -0.1 1100 1200 1300 1400 1500 1600 1700 1800 W [MeV] Fig. 1. The real and the imaginary part of the scattering T matrix for the elastic and the r|N, KA and KZ channels. The data points are from the SAID partial-wave analysis [14]. Fig. 1 shows the results for positive parity I = 2 partial waves. The P13 partial wave has not been considered in our previous calculations. In the present calculation we have included both resonances, the N(1720) and the N(1900), assuming one quark is excited to the d-state. The spin 1/2 (3/2) configuration turns out to dominate the lower (upper) resonance; the mixing angle of 10° provides the best agreement with experiment. Furthermore, in order to reproduce the experimental behaviour of ReT it has been necessary to include the second (volume) term in (4). Here a value of f closer to 93 MeV yields a better agreement with experiment. This term turns out to be important also in the P31 partial wave but is less significant in other partial waves discussed here. Eta and kaon production ... 83 In the P33 partial wave (see Fig. 2) q production in the qA channel turns out to be almost negligible, but the KI channel yields rather important contribution which is also reflected in the photoproduction amplitudes, discussed in the following. W [MeV] W [MeV] Fig. 2. The T matrix for the elastic and the r|A and KZ P33 channels. Notation as in Fig. 1. The important contribution of the qN and KA channels in the S11 partial wave has already been discussed in our previous paper [7]. In the present approach we have not assumed a fixed mixing angle ($ « 30°) between the spin 1 and 2 three-quark configuration but have rather generated the configuration mixing through pion and kaon loops. This improves the behaviour of the T matrix at lower W but somewhat weakens the photoproduction amplitudes. W [MeV] W [MeV] Fig. 3. The T matrix in the S11 partial wave. Notation as in Fig. 1. 3 Photoproduction of n mesons on the proton Our model predicts that the N(1535) S11 resonance dominates q production, in accordance with the most recent MAID analysis [11] and the two analyses of the Bonn-Gatchina group [13] (disregarding the overall sign) (see Fig. 4). In the P11 partial wave the q photoproduction amplitude is small; in addition, the contribution from the Roper resonance is almost negligible. On the other hand, the resonant contribution from the two resonances in the P13 partial wave dominates the M1+ and E1+ photoproduction amplitudes (see Fig. 5). While the 84 B. Golli 1600 1650 W [MeV] 20 15 10 5 0 -5 -10 -15 -20 =----^miinnur 1500 1550 1600 1650 W [MeV] nN MAID BoGa Fig. 4. The Eo+ photoproduction amplitude (in units mfm 1 ) compared to the recent MAID analysis [11] and the BG2014-01 and BG2014-02 solutions of the Bonn-Gatchina group [13]. Re E0+ S11 1500 1550 1700 1750 1700 1750 Mi + amplitude remains close to the values obtained in the recent MAID and the Bonn-Gatchina analyses, the value of the Ei + multipole seems to give a too strong value in the region of the lower N(1720) resonance - but is in agreement with our result for the nN —» nN channel. Re M + P13__„------------- n N -\ MAID ......... BoGa i-1 au^î - Re E1+ P13 / / n N - . MAID ....... BoGa i-1 0 -0.5 " Im M1+ P13 - n N - MAID --------- BoGa i-1 1500 1550 1600 1650 1700 1750 W [MeV] 05 - Im E1+ P13 n N ^ . MAID BoGa 1500 1550 1600 1650 1700 1750 W [MeV] 1500 1550 1600 1650 1700 1750 W [MeV] 1500 1550 1600 1650 W [MeV] 1500 1550 1600 1650 1700 1750 W [MeV] 1500 1550 1600 1650 W [MeV] Fig. 5. As Fig. 4 for the M1 + and E1 + multipoles. 0 1700 1750 0 0 0 1700 1750 4 K+A photoproduction The situation is similar to n production; the dominant contribution is the E0+ and arises through the excitation of the S11 resonances (see Fig. 6). The contribution of the P11 resonances is negligible. The strengths of the E1+ and M1+ multipoles in the P13 partial wave are almost equal, in agreement with the multipole analyses (see Fig. 7). Eta and kaon production ... 85 1600 1620 1640 1660 1680 1700 1720 1740 W [MeV] 1600 1620 1640 1660 1680 1700 1720 1740 W [MeV] 1600 1620 1640 1660 1680 1700 1720 1740 W [MeV] Fig. 6. The Eo+ amplitude for the K+ A channel. Notation as in Fig. 4; KAON-MAID taken from [12]. Fig. 7. As in Fig. 6 for the M-| + and Ei + multipoles. 5 KL photoproduction We present only the results for the K0I+ channel since the background contribution here is considerably smaller than in the K+ I- channel in which the behaviour close to the threshold is governed by the kaon pole term absent in the former channel. The K0I+ amplitudes consist of the isospin singlet and isospin triplet part, i.e. A(y + p -> K0I+) = V2Aj,V2) - 1 A(3/2). The E0+ multipole is dominated by the S11 resonances (see Fig. 8) while the contribution from the S31 resonance is negligible. The experimental situation here is rather unclear since even the two recent analyses of the Bonn-Gatchina group considerably differ from each other. Nontheless, the strength predicted by our model is in agreement with the multipole analysis. The M1+ amplitude (see Fig. 9) is well described by the A(1600) resonance and the tail of the dominating A(1232) resonance. Let us notice that the same resonant mechanism governs the K+I0 channel (the P33 resonant contribution is a factor of —2 larger than the one shown in Fig. 9). The contribution from the P13 resonances is small. The situation is reversed in the case of the Ei+ multipole; 86 B. Golli there is no quark contribution in the P33 partial wave (similarly as in the nN channel), the main contribution arises from the quark s to d transition in the two P13 resonances. TTTW Re E0+ S11 44JJ_LLJ T TIT TT T kV- MAID -------- BoGa i-1 1675 1700 1725 1750 W [MeV] Im E0+ S11 k°e+-MAID ■ BoGa i 1675 1700 1725 1750 W [MeV] Fig. 8. The Eo+ photoproduction amplitude for the K°Z+ channel. Notation as in Fig. 6 2 2 0 0 1775 1775 1.6 - kV MAID 1.2 - BoGa 0.8 - 0.4 - 0 |M i+1 1725 1750 W [MeV] KV MAID BoGa - iEJ 1725 1750 1775 W [MeV] Fig. 9. The absolute values of the photoproduction amplitude for yN —> K°Z+. The thin solid line is the P33 contribution. Notation as in Fig. 6. 2 0 1675 1700 1775 1675 1700 Acknowledgment. We would like to thank Lotar Tiator for sending us the preliminary results of the etaMAID analysis; see also the contribution of Jugoslav Stahov to these Proceedings. References 1. M. Fiolhais, B. Golli, S. Sirca, Phys. Lett. B 373, 229 (1996). 2. P. Alberto, M. Fiolhais, B. Golli, and J. Marques, Phys. Lett. B 523, 273 (2001). 3. B. Golli, S. Sirca, L. Amoreira, M. Fiolhais Phys.Lett. B553, 51-60 (2003). 4. P. Alberto, L. Amoreira, M. Fiolhais, B. Golli, and S. Sirca, Eur. Phys. J. A 26, 99 (2005). 5. B. Golli and S. Sirca, Eur. Phys. J. A 38, 271 (2008). 6. B. Golli, S. Sirca, and M. Fiolhais, Eur. Phys. J. A 42,185 (2009). 7. B. Golli, S. Sirca, Eur. Phys. J. A 47, 61 (2011). 8. B. Golli, S. Sirca, Eur. Phys. J. A 49,111 (2013). 9. E. A. Veit, B. K. Jennings, A. W. Thomas, R. C. Barret, Phys. Rev. D 31,1033 (1985). 10. D. Drechsel, S.S. Kamalov, L. Tiator, Eur. Phys. J. A 34, 69 (2007). 11. J. Stahov et al., contribution to these Proceedings. 12. (Kaon MAID Partial Wave Analysis) http://www.kph.uni-mainz.de/MAID/kaon/ 13. (Bonn Gatchina Partial Wave Analysis) http://pwa.hiskp.uni-bonn.de/ 14. (SAID Partial Wave Analysis) http://gwdac.phys.gwu.edu/ Povzetki v slovenščini 105 Popolni eksperimenti pri fotoprodukciji psevdoskalarnih mezonov Yannick Wunderlich Helmholtz-Institut fuer Strahlen- und Kernphysik, Universitaet Bonn, Nussallee 14-16, 53115 Bonn, Germany Predstavim problem, kako enolično izvrednotiti amplitude za fotoprodukcijo iz tako imenovanih popolnih eksperimentov. Pri tem smo lahko pozorni na določanje amplitude za celotno tvorbo ali pa na določanje multipolov. Na kratko obravnavam oba primera. Podrobneje opisem preliminarne rezultate prilagajanja multipolov kakor tudi dolocanja njihovih napak pri nedavnih meritvah polarizacije v podrocju resonance A. Novi spektroskopski rezultati iz laboratorija Belle Marko Bracko Univerza v Mariboru, Smetanova ulica 17, SI-2000 Maribor, in Institut J. Stefan, Jamova cesta 39, SI-1000 Ljubljana V prispevku predstavimo izbrane rezultate spektroskopskih meritev, opravljenih na izmerjenih podatkih, pridobljenih z detektorjem Belle, ki je stal ob trkalniku KEKB v laboratoriju KEK v Cukubi, na Japonskem. Trkalnik je obratoval med letoma 1999 in 2010, v tem casu pa je s stabilnim delovanjem pri trkih elektronov in pozitronov razlicnih energijpostal prava "tovarna" parov mezonov B, mezonov D in se leptonov tau. Ogromne kolicine kakovostnih podatkov so omogocile tudi stevilne spektroskopske meritve. Izbor tukajpredstavljenih rezultatov ustreza zanimanju in razpravam na delavnici. Produkcija mezonov eta in kaonov v kiralnem kvarkovem modelu Bojan Golli Pedagoska fakulteta, Univerza v Ljubljani in Institut J. Stefan, Ljubljana, Slovenija Formalizem sklopljenih kanalov, ki vkljucuje kvazi vezana veckvarkovska stanja, uporabimo za izracun sipalnih in fotoprodukcijskih amplitud mezonov eta in kaonov. Sklopitvene konstante in oblikovne faktorje dolocimo v modelu oblacne vrece. Model napove znatne amplitude v parcialnih valovih P13, P33 in S11, v skladu z najnovejšimi analizami parcialnih valov skupine iz Mainza in skupine iz Bonna in Peterburga.