Qiang Zhao Centre for Nuclear and Radiation Physics Department of Physics, University of Surrey, Guildford, U.K. Locality of quark-hadron duality and its manifestation in exclusive meson photoproduction reaction above the resonance region Locality of quark-hadron duality and its manifestation in exclusive meson photoproduction reaction above the resonance region CNRP Qiang Zhao MeNu2004, IHEP, Beijing, Sept. 2, 2004 In collaboration with F.E. Close (Oxford Univ.)

Outline What is quark-hadron duality? Physics in the interplay of pQCD and non-pQCD -- above the resonance region Quark-hadron duality in the quark model Quark-hadron duality in exclusive photoproduction reaction Summary

Bloom-Gilman Duality The electroproduction of N* at low energies and momentum transfers empirically averages smoothly around the scaling curve for nucleon structure function F 2 (W 2,Q 2 ) measured at large momentum transfers for both proton and neutron targets. Quark-hadron duality Degrees-of-freedom duality Hadronic degrees of freedom  Quark and gluon degrees of freedom Low-energy resonance phenomena  High-energy scaling behaviour Bloom and Gilman, PRD4, 2901 (1971); Close, Gilman and Karliner, PRD6, 2533 (1972); I. Niculescu et al, Phys. Rev. Lett. 85, 1182 (2000); 85, 1186 (2000). Nachtmann scaling variable:  =2x/[1+(1+4M 2 x 2 /Q 2 ) 1/2 ], where x=Q 2 /2M 2

 M N N EM Strong N*,  *  + p  D 13 F 15 Low-energy QCD phenomena: resonance production Theory QCD phenomenology: quark model, hadronic model … Lattice QCD ? Experiment –Jefferson Lab –MAMI –ELSA –ESRF –SPring-8 –BES

A,  C, M B, N D, N For exclusive scattering processes at high energy and large transverse momentum, the differential cross section for a two-body reaction A + B  C + D has a behaviour: Brodsky and Farrar, PRL31, 1153 (1973); PRD11, 1309 (1975). Matveev, Muradian and Tavkhelidze, Nuovo Cim. Lett. 7, 719 (1973). Lepage and Brodsky, PRD22, 2157 (1980). Quark counting rules (QCR)  p  n s =(p A +p B ) 2 =(p C +p D ) 2 t =(p A –p C ) 2 =(p B –p D ) 2

Anderson et al., PRD14, 679 (1976) Other channels are also measured Exclusive photoproduction reactions at fixed scattering angles

Oscillatory deviations from the scaling behavior of dimensional quark- counting rules above the nucleon resonance region. Figure from JLab proposal PR94-104, Gao and Holt (co-spokesperson) Scaled? Oscillating?

Soft contribution dominant Isgur and Llewellyn Smiths, PRL52, 1080 (1984) Dashed curves: Soft contributions Solid curves: Leading asymptotic contributions Dot-dashed: Bound on the leading asymptotic contributions

Theoretical explanations for the deviations i) The channel-opening of new flavours Brodsky, De Teramond, PRL 60, 1924 (1988). ii) Interference between pQCD and sizeable long-range component. Brodsky, Carlson, and Lipkin, PRD 20, 2278 (1979); Miller, PRC 66, (R) (2002); Belitsky, Ji and Yuan, PRL 91, (2003). iii) PQCD color transparency effects Ralston and Pire, PRL 49, 1605 (1982); 61, 1823 (1988). iv) Restricted locality of quark-hadron duality Close and Zhao, PRD 66, (2002); PLB 553, 211(2003); Zhao and Close, PRL 91, (2003); work in preparation.

Close, Gilman, and Karliner, PRD6, 2533 (1972); Close and Isgur, PLB 509, 81 (2001)  p,n hadrons F 1 p,n ~  1/2 +  3/2 g 1 p,n ~  1/2   3/2 F 1 n / F 1 p =2/3 g 1 p / F 1 p =5/9 g 1 n / F 1 n =0 For F 1 p,n and g 1 p, duality is recognized with the sum over both 56 and 70 states and negative parity ones. For g 1 n, the duality could be localized to 56 states alone. How does the square of sum become the sum of squares? --- Close and Isgur Bloom-Gilman duality realized in the quark model

, k PiPi q PfPf q1q1 q2q2 r R r1r1 r2r2  z x y  PiPi PfPf q Sum over intermediate states: Manifestation of duality in exclusive reaction

Forward scattering (Close and Isgur’s duality) :   0  Large angle scattering:  = 90  where the coherent term (~e 1 e 2 ) is suppressed due to destructive interferences. i) At high energies, i.e. in the state degeneracy limit, all terms of N > 0 (L=0, …, N) vanish due to destructive cancellation: (–C 22 +C 20 )  0; (3C 44 –10C 42 +7C 40 )  0; … R(t) : QCR-predicted scaling factor. ii)At intermediate high energies, i.e. state degeneracy is broken, terms of N > 0 (L=0, …, N) will not vanish: (–C 22 +C 20 )  0; (3C 44 –10C 42 +7C 40 )  0; … Deviation from QCR is expected !

Effective theory for pion photoproduction Effective chiral Lagrangian for quark-pseudoscalar meson coupling: where the vector and axial vector current are: with the chiral transformation The quark and meson field in the SU(3) symmetry: and The quark-meson pseudovector coupling: Manohar and Georgi, NPB 234, 189 (1984); Li, PRD50, 5639 (1994); Zhao, Al-Khlili, Li and Workman, PRC65, (2002)

 M N N    N*,  * Tree level diagrams  N*,  *   contact-channel  … s-channel u-channel t-channel Internal quark correlations are separated out

Sum of resonance excitations In the SU(6)  O(3) symmetry limit, resonances of n  2 are explicitly included via partial wave decomposition. At high energies, states of n > 2 (L=0, …, n) will be degenerate in n. The direct (incoherent) processes in the s- and u-channel are dominant over the coherent ones. c.m.-c.m. correlation c.m.-int. correlation int.-int. correlation

Pion (   ) photoproduction in the resonance region Zhao, Al-Khalili, Li and Workman, PRC65, (2002) [56, 4 10; 0,0, 3/2 + ]P33(1232) [70, 2 8; 1,1, J – ]S11(1535), D13(1520) [70, 2 10; 1,1, J – ]S31(1620), D33(1700) [56, 2 8; 2,0, 1/2 + ]P11(1440) [56, 4 10; 2,0, 3/2 + ]P33(1600) [70, 2 8; 2,0, 1/2 + ]P11(1710) [70, 2 10; 2,0,1/2 + ]P31(1750) [56, 2 8; 2,2, J + ]P13(1720), F15(1680) [56, 4 10; 2,2, J + ] P31(1910), P33(1920), F35(1905), F37(1950) [70, 2 8; 2,2, J + ] P11(2100), P13(1900), F15(2000), F17(1990) [70, 2 10; 2,2, J + ]P33(1985), F35(2000) Resonances of n  2 included in the SU(6)  O(3) quark model

Pion photoproduction above the resonance region High energy degenerate limit: Mass-degeneracy breaking (L-depen.) is introduced into n=3, 4. For n=3, the L-dependent multiplets do not contribute at  =90  since they are proportional to cos . For n=4, non-vanishing P, F, and H partial waves will contribute and produce deviations. At  =90 , destructive interferences occur within states of a given n, i.e., with the same parity. The new data are from: Zhu et al., [Jlab Hall A Colla.], PRL91, (2003).

Further manifestations of Bloom-Gilman duality Onset of scaling with the local sum and average Jeschonnek and Van Orden, PRD 69, (2004). Onset of scaling with the local sum and average Dong and He, NPA720, 174 (2003).

Summary and discussion Nonperturbative resonance excitations due to quark correlations, are an important source for deviations from QCR at 2  s 1/2  3.5 GeV. Features distinguishable from other models: i)The deviations can be dominantly produced by “restrictedly localized” resonance excitations, i.e. the destructive cancellation occurs within states of the same parity. ii)The deviation pattern need have no simple periodicity. iii)The Q 2 dependence of the deviations would exhibit significant shifts in both magnitude and position. Open questions...