Vector meson production in pp scattering at CSR -- (I) Formalism. Qiang Zhao

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1 Hadron Physics at COSY and CSR, IMP, Lanzhou, Jan. 5, 006 Vector meson production in pp scattering at CSR -- (I) Formalism Qiang Zhao Theory Division, Institute of High Energy Physics, CAS, P.R. China Baryons studied in EM and/or strong interaction processes A quark model framework for studying baryon resonances in pp ppv Brief comments

2 Baryons studied in EM and/or strong interaction processes γ, N, ½ + N*, Δ* π, 0 N, ½ + N*, Δ*, LI,J P() Δ P(440) S(55) D(50)

3 PDG004: nucleon resonances (**) not wellestablished

4 8 Lambda resonances

5 The missing resonance problem The non-relativistic constituent quark model (NRCQM) makes great success in the description of hadron spectroscopy: baryon (qqq), meson (qq*) However, it also predicted a much richer baryon spectrum, where some of those have not been seen in πn scatterings. Missing Resonances.

6 Dilemma: a) The NRCQM is WRONG: quark-diquark configuration? b) The NRCQM is CORRECT, but those missing states have only weak couplings to πn, i.e. small g πn*n. (Isgur, 980) Looking for missing resonances in N* ηn, KΣ, KΛ, ρn, ωn, φn, γn (Exotics: Pentaquarks, hybrids) u N* + u u ud u u d ρ0 p

7 Status of baryon resonances studied in meson photo- & electroproduction EM γ N N*,Δ* M (π,η, ω, φ, ρ, K ) Strong N (N, Λ, Σ ) i) Large degrees of freedom involved at hadronic level ii) Broad widths for most resonances iii) Interferences among various production mechanisms Δ γ + p D F 5 Measurements of various spin observables Measurements of different production mechanisms

8 Theory Perturbative QCD cannot be applied Isobaric model ( >0 parameters) Old quark model (N* γn, N M) QCD-inspired quark model phenomenology Experiment Jefferson Lab (USA) MAMI (Germany) ELSA (Germany) ESRF (France) SPring-8 (Japan) BES (Beijing) CSR (Lanzhou)

9 A quark model framework for studying baryon resonances Basic assumptions: The exchanged meson fields are fundamental ones which are coupled to the quarks in the baryons via effective Lagrangians (Ref: Manohar and Georgi, NPB 4, 89 (984) ); The baryons are treated as a three-quark system, which are representations of SU(6) O() symmetry. M M B B B B

10 . Effective Lagrangian for quark-pseudoscalar-meson interactions:

11 Quark-pseudoscalar-meson coupling at tree level: where and From quark to hadron degrees of freedom: for π ± for π 0 For pseudoscalar meson photo- and electroproduction: Li, PRD5, 496 (995); Zhao, PRC6, 0505 (00); Zhao, Al-Khalili, Li, Workman, PRC65, (00); Zhao, Saghai and Li, JPG8, 9 (00)

12 . Effective Lagrangian for quark-vector-meson interactions: Vector meson fields in the SU()-flavour symmetry: For vector meson photo- and electroproduction: Zhao, Li, & Bennhold, PLB46, 4(998); PRC58, 9(998); Zhao, Didelez, Guidal, & Saghai, NPA660, (999); Zhao, PRC6, 050(00); Zhao, Saghai, Al-Khalili, PLB509, (00); Zhao, Al-Khalili, & Bennhold, PRC64, 050(R)(00); PRC65, 00(R) (00); Zhao, Al-Khalili, & Cole, PRC7, (005)

13 Transition amplitude: M=M(s) + M(u) + M(seagull) + M(t) s-channel γ, k V, q γ, k V, q N ( ) Δ ( ) N, P i N, P f + N, P i N ( ) Δ ( ) N, P f u-channel seagull γ, k V, q γ, k V, q γ, k V ±, q N ( ) Δ ( ) N, P i N, P f + N ( ) Δ ( ) N, P i N, P f N, P i N, P f A major advantage: A complete set of SU(6) O() baryons are included with a small number of parameters

14 . Some results for vector meson photo- and electroproduction Diff. X-section at small Q e e Q, γ* W ω N N Ambrozewicz et al., [JLab E9-06 Colla.], PRC70, 050 (004)

15 Theoretical curves versus GRAAL data Total cross sections γ+p ω+p

16 Differential cross section γ+p ω+p Full dot: GRAAL Empty circle: SAPHIR

17 Polarized beam asymmetry Without s- and u-channel, the asymmetry should be zero due to helicity conservation. Effects without contributions from: D(50) [dashed]; P(70) [dotted]; F5(680) [dot-dashed]

18 4. Quark model approach for meson production in pp pp V i) s-channel transition M s = π 0, η, ρ 0 N*, Δ* P' a p v P' b + P' a P' b M s = π 0, η, ρ 0 N*, Δ* P' b p v P' a + P' b P' a

19 ii) u-channel transition P' a + P' a M u = π 0, η, ρ 0 N*, Δ* p v P' b p v P' b P' b + P' b M u = π 0, η, ρ 0 N*, Δ* p v P' a p v P' a

20 iii) t-channel transition P' a P' a M t = π 0 ρ 0 p v + ρ 0 π 0 p v P'b P' b P' b P' b M t = π 0 ρ 0 p v + ρ 0 π 0 p v P'a P' a

21 D) s- and u-channel amplitudes

22 Example of treating the transition amplitude: m m 6λ/ ρ r m r r Jacobi coordinate

23 SU(6) O() symmetry The quark model wavefunctions are also representations of S group. Therefore, the tree-level quark-meson interactions can be expressed as π 0, η, ρ 0 P' a p v N*, Δ* P' b

24 Some thoughts about pp pp K + K at sub-threshold π 0 φ P' a K + φn bound state? J P = / ; / ρ 0 K p P' b X: / ; / φn and KΛ mixing? J P = / ; H. Gao & H. Lee; Z.Y. Zhang et al. M(p) + M(K) < W < M(p) + M(φ).86 GeV < W <.896 GeV.94 GeV < M(X) <.958 GeV.4 GeV < On-shell Λ* <.465 GeV ~ 0 MeV mass window! Λ(405) (/-); Λ(50)(/-) Requires p-wave between KΛ*

25 Brief comments Meson production in pp scattering provides more information about the meson-baryon, baryon-baryon interactions. See: exp. talks by Busche theory talks by Meiβner, Zou Based on the high luminosities, it might be possible to isolate certain kinematical regions where some specific dynamical processes can be examined. The pp scattering at the resonance energy region raises challenges for theories which must cope with many non-perturbative mechanisms.

26 Many Thanks!