Regge phenomenology forπ 0,η, andη photoproduction

Transcription

1 Regge phenomenology forπ,η, andη photoproduction V. L. Kashevarov Institut für Kernphysik, Johannes Gutenberg-Universität Mainz Collaboration Meeting PWA with Complete Experiments, Mainz, 5-9 February 26

2 Overview ηmaid23 Regge Regge cuts. results forγp π p 2. adaptation toγp ηp 3. adaptation toγp η p Regge background + nucleon resonances Conclusions Collaboration Meeting PWA with Complete Experiments, Mainz, 5-9 February 26 2

3 ηmaid23 Regge Reggeized model forη andη photoproductin W.-T. Chiang, S.N. Yang, L.Tiator, M.Vanderhaeghen, D. Drechsel. PRC 68 (23) Main difference: vector meson exchanges are described in terms of Regge trajectories. It should be important for high energies. Tabelle : Parameters for the vector mesons in this model. V m V [MeV] gvnn v κ VNN λ Vηγ λ Vη γ α V (t) ρ t/GeV 2 ω t/GeV 2 κ VNN = g t VNN /gv VNN, wheregv VNN andgt VNN are vector and tensor hadronic couplings respectively. The hadronic couplings were derived by a fit to high energy data. Parameters for Regge trajectoriesα(t) = α +α t were taken from M. Guidal, J.M. Laget, M. Vanderhaeghen, NP A627 (997) 645. λ Vηγ andλ Vη γ are electromagnetic coupling constants. PWA Collaboration Meeting, Mainz, 5-9 February, 26 3

4 ηmaid23 Regge The electromagnetic coupling constantsλ Vηγ andλ Vη γ can be determined from the radiative decay widths, Γ V ηγ = α(m2 V m2 η) 3 24m 3 V m2 η λ 2 Vηγ, () where α is the fine-structure constant. Γ η Vγ = α(m2 η m 2 V )3 24m 2 V m3 η λ 2 Vη γ, (2) The values ofλ Vηγ andλ Vη γ were obtained from the widthsγ ρ ηγ = 36keV, Γ ω ηγ = 5.5keV,Γ η ργ = 89keV, andγ η ωγ = 9.keV (PDG-2). PWA Collaboration Meeting, Mainz, 5-9 February, 26 4

5 ηmaid23 Regge The pole-like Feynman propagator was replaced by a Regge propagator for each vector meson: ρ( ) exchange: t m 2 ρ = P ρ Regge = ( s s ) αρ (t) πα ρ sin(πα ρ (t)) S ρ +e iπα ρ(t) 2 Γ(α ρ (t)), (3) ω ( ) exchange: t m 2 ω = P ω Regge = ( s s ) αω (t) πα ω sin(πα ω (t)) S ω +e iπα ω(t) 2 Γ(α ω (t)). (4) The parameters is a mass scale taken ass = GeV 2. S = ± is the signature of the trajectory. The gamma function Γ(α(t)) suppresses poles of the propagator in the unphysical region. PWA Collaboration Meeting, Mainz, 5-9 February, 26 5

6 ηmaid23 Regge Differential cross section dσ/dt for γp ηp. E γ = 2 GeV E γ = 4 GeV E γ = 6 GeV dσ/dt [µb/gev 2 ]. CLAS DESY The solid lines are the predictions from t-channel exchange using Regge trajectories, the dashed (dotted) lines indicate the ρ (ω) contributions only. The data ate lab γ = 4 GeV and 6 GeV are from DESY-97, ate lab γ = 2 GeV are from CLAS-22. PWA Collaboration Meeting, Mainz, 5-9 February, 26 6

7 ηmaid23 Regge For bosonss = ( ) J, so for the vector mesonss =. E γ =4 GeV E γ =6 GeV E γ =8 GeV dσ/dt [µb/gev 2 ] Black lines are ηmaid23 Regge without nucleon resonances. Blue lines are the same, but withs =. Black circles: DESY-97 Red circles: WLS-97 PWA Collaboration Meeting, Mainz, 5-9 February, 26 7

8 Regge cuts:π photoprduction G.R. Goldstein, J.F. Owens III, PRD 7 (973) 865. I.S. Barker, J.K. Storrow, NP B37 (978) 43. A. Donnachie, Yu.S. Kalashnikova, arxiv:57.748v, 27 Jul 25. Regge cuts arise from rescattering two ReggeonsR andr 2 (or more). The exchange of two Reggeons with linear trajectories: yields a cut with a linear trajectoryα c (t): were α i (t) = α i ()+α it,i =,2 (5) α c (t) = α c ()+α ct (6) α c () = α ()+α 2 () (7) α c = α α 2 α +α 2 PWA Collaboration Meeting, Mainz, 5-9 February, 26 8

9 Regge cuts:π photoprduction Donnachie and Kalashnikova (DoKa) assumed: linear non-degenerate ρ and ω trajectories: α ρ = 5+.8t α ω =.44+.9t secondary linear non-degenerate Pomeron (P) andf 2 trajectories: α P.8+t α f2 = t trajectory of the associatedρ P andω P cuts: α c ρ P =.64+.6t α c ω P = 2+.96t trajectories of the associatedρ f 2 andω f 2 cuts: α c ρ f 2 = t α c ω f 2 = t PWA Collaboration Meeting, Mainz, 5-9 February, 26 9

10 Regge cuts:π photoprduction Tabelle 2: Parameters of the vector mesons used by Donachie and Kalashnikova. V g v VNN κ VNN λ Vπ γ ρ 3.4(2.4) 6.(3.7).9 ω 5(9) ().322 κ VNN = g t VNN /gv VNN, wheregv VNN andgt VNN are vector and tensor hadronic couplings respectively. Values in parentheses are parameters used in ηmaid23 Regge. λ ρπ γ andλ ωπ γ are electromagnetic coupling constants. PWA Collaboration Meeting, Mainz, 5-9 February, 26

11 Donnachie and Kalashnikova: Regge cuts:π photoprduction As a physical mass cannot be be associated with a cut, the simplest form of amplitude for a cut term is wherec c is a constant and A c (s,t) = C c D c (s,t) (8) D c (s,t) = e d ct e i 2 πα c(t) s α c(t). (9) where we have retained only the Regge phase and absorbed the rest of thet-dependence in the exponential,α c (t) is the cut trajectory and the constantsc c andd c for each cut term are obtained by fitting data. We need a mechanism to allow us to transfer theπ cut model to scalar photoproduction. The simplest way is to take the cut terms proportional to the dominantω andρexchanges, retaining the kinematical structure and replacingλ Vπ γg VNN D V (s,t),v = ρ,ω by λ Vπ γg VNN (D V (s,t)+c V P n D V P c (s,t)+c V f 2 n D V f 2 c (s,t)), () wherec V P n andc V f 2 n V -f 2 cuts. are respectively the natural-parity constants for the V -P and PWA Collaboration Meeting, Mainz, 5-9 February, 26

12 Regge cuts:π photoprduction E γ =6 GeV E γ =9 GeV E γ =2 GeV E γ =5 GeV dσ/dt [µb/gev 2 ] Σ E γ =4 GeV E γ =6 GeV E γ = GeV Red lines: fit results with the cuts (Fit ). Black lines: without the cuts. Black circles: SLAC-97 data PWA Collaboration Meeting, Mainz, 5-9 February, 26 2

13 Regge cuts:π photoprduction Donnachie and Kalashnikova: These cuts also feed into the unnatural-parity exchange term and are much larger than any cuts generated byb (235) exchange due to its small contribution. So b pole term λ b π γg b NND b (s,t) is replaced by λ b π γg b NND b (s,t)+ V λ Vπ γg VNN (C V P u D V P c (s,t)+c V f 2 u D V f 2 c (s,t)), where thecu V P andc V f 2are the unnatural-parity constants. It turns out that the cuts u dominate unnatural parity exchange so in practice theb pole term could be omitted. () The parameters forρandω were taken to be the same: Cn ρ P Cu ρ P = Cn ω P,C ρ f 2 n = C ω f 2 n, = Cu ω P,C ρ f 2 u = C ω f 2 u. d c of the exponential also was taken to be the same for all terms. So in practice we have only five free parameters to describeπ photoproduction. PWA Collaboration Meeting, Mainz, 5-9 February, 26 3

14 Regge cuts:π photoprduction E γ =6 GeV E γ =9 GeV E γ =2 GeV E γ =5 GeV dσ/dt [µb/gev 2 ] Σ E γ =4 GeV E γ =6 GeV E γ = GeV Red lines: fit results with vector and axial-vector mesons (Fit 2). PWA Collaboration Meeting, Mainz, 5-9 February, 26 4

15 Regge cuts:π photoprduction dσ/dt [µb/gev 2 ] - -2 E γ =6 GeV - -2 E γ =9 GeV - -2 E γ =2 GeV - -2 E γ =5 GeV E γ =4 GeV E γ =6 GeV E γ = GeV Σ E γ =4 GeV E γ =6 GeV E γ = GeV T E γ =4 GeV E γ =6 GeV E γ = GeV P Black lines: Fit 2. Red lines: fit to SLAC-97 (black), Botth-972 (blue), Beinlein-973 (red), Deutsch-972 (magenta) data (Fit 3). PWA Collaboration Meeting, Mainz, 5-9 February, 26 5

16 Regge cuts:π photoprduction dσ/dt [µb/gev 2 ] - -2 E γ =6 GeV - -2 E γ =9 GeV - -2 E γ =2 GeV - -2 E γ =5 GeV E γ =4 GeV E γ =6 GeV E γ = GeV Σ E γ =4 GeV E γ =6 GeV E γ = GeV T E γ =4 GeV E γ =6 GeV E γ = GeV P Black lines: Fit 3 Blue lines: Fit with 6 parameters to all data (Fit 4). Red lines: same as Fit 4, but without P data PWA Collaboration Meeting, Mainz, 5-9 February, 26 6

17 Regge cuts: adaptation to η photoproduction Electromagnetic coupling constants were recalculated according to new experimental data for the radiative decay widts: Parameter [kev] ηmaid-3 Regge PDG-4 Γ ρ ηγ Γ ω ηγ Γ η ργ Γ η ωγ PWA Collaboration Meeting, Mainz, 5-9 February, 26 7

18 Regge cuts: adaptation to η photoproduction Vector and tensor hadronic coupling constants Parameter ηmaid-3 ηmaid-3 Regge Laget-PRC72(25) DoKa g v ρnn k ρnn g v ωnn k ωnn PWA Collaboration Meeting, Mainz, 5-9 February, 26 8

19 Regge cuts: adaptation to η photoproduction ρ: α=5+.8t ω: α=.44+.9t f 2 : α= t P(Pomeron): α=.8+t Regge-cut trajectories: ρ-p(solid) ω-p(dashed) ρ-f 2 (solid) ω-f 2 (dashed) α(t) J P = α(t) J P = ρ: α= t ω: α= t DoKa-25 DoKa-25 DoKa f 2 : α= t P(Pomeron): α=.8+t a 2 : α= t J P = ρ-p(solid) ω-p(dashed) ρ-f 2 (solid) ω-f 2 (dashed) ρ-a 2 (solid) ω-a 2 (dashed) J P = ηmaid26 Regge ηmaid26 Regge ηmaid26 Regge t = M 2 [GeV 2 ] PWA Collaboration Meeting, Mainz, 5-9 February, 26 9

20 Regge cuts: adaptation to η photoproduction dσ/dt [µb/gev 2 ] - -2 E γ =2.2 GeV W=2.238 GeV E γ =2.5 GeV W=2.36 GeV E γ =3 GeV W=2.55 GeV E γ =4 GeV W=2.896 GeV E γ =6 GeV W=3.484 GeV E γ =8 GeV W=3.987 GeV.8 Σ T E Black lines: fit results with 9 parameters PWA Collaboration Meeting, Mainz, 5-9 February, 26 2

21 Regge cuts: adaptation to η photoproduction channel d c C ρ P n Tabelle 3: Fit parameters C ω P n C ρ f 2 n C ω f 2 n C ρ P u C ρ f 2 u η π C ω P u = C ρ P u C ω f 2 u = C ρ f 2 u Two additional fit parameters for η photoproduction: λ b ηγ g v b NN = 5.3, λ b ηγ g t b NN = 9., wheregb v NN andgt b NN are vector and tensor hadronic coulings respectively, andλ b ηγ is electrmagnetic coupling constant of theb meson. PWA Collaboration Meeting, Mainz, 5-9 February, 26 2

22 Regge cuts: adaptation to η photoproduction K + Σ o K o Σ + ω η A2MAMI-5 CBELSA/TAPS-9 CLAS-9 (our Legendre fit result) σ [µb] W [GeV] magenta line: background contribution PWA Collaboration Meeting, Mainz, 5-9 February, 26 22

23 Regge cuts: adaptation to η photoproduction data: A2MAMI (preliminary). Red lines: background contribution dσ/dω [µb/sr] W = 488 MeV cosθ η * PWA Collaboration Meeting, Mainz, 5-9 February, 26 23

24 Regge cuts: adaptation to η photoproduction data: A2MAMI (preliminary). Red lines: background contribution dσ/dω [µb/sr].2 W = 654 MeV cosθ η * PWA Collaboration Meeting, Mainz, 5-9 February, 26 24

25 Regge cuts: adaptation to η photoproduction CBELSA/TAPS data: dσ/dω - 29, T,E,H,P - preliminary dσ/dω [µb/sr].3.2. W=.982 GeV 2.5 GeV 2.29 GeV 2.52 GeV 2.74 GeV 2.97 GeV 2.9 GeV 2.4 GeV 2.63 GeV 2.85 GeV 2.26 GeV GeV GeV cosθ η * GeV GeV 2.3 GeV 2.33 GeV 2.35 GeV 2.37 GeV W=.497 GeV.522 GeV.542 GeV.563 GeV.584 GeV.68 GeV.64 GeV.688 GeV.742 GeV.796 GeV.849 GeV T W=.53 GeV.573 GeV.632 GeV.688 GeV.743 GeV.796 GeV.848 GeV.898 GeV.97 GeV 2.64 GeV 2.53 GeV GeV E H P - - W=.497 GeV W=.497 GeV.522 GeV.542 GeV.563 GeV.584 GeV.68 GeV.522 GeV.542 GeV.563 GeV.584 GeV.68 GeV cosθ η * PWA Collaboration Meeting, Mainz, 5-9 February, 26 25

26 Regge cuts: adaptation to η photoproduction data: A2MAMI-25 (T,F), GRAAL-27 (Σ), CLAS-25 (E) T.2 W=497 MeV T F W=497 MeV F Σ W=496 MeV Σ Ε - W=525 MeV Ε * cosθ η PWA Collaboration Meeting, Mainz, 5-9 February, 26 26

27 Regge cuts: adaptation to η photoproduction Real Regge26 bg Imag Regge26 bg Real MAID-25d2 Imag MAID-25d2 2 E+ [mfm] E+ [mfm] W [MeV] W [MeV].5 M+ [mfm] M- [mfm] W [MeV] W [MeV] PWA Collaboration Meeting, Mainz, 5-9 February, 26 27

28 Regge cuts: adaptation to η photoproduction Real Regge26 bg Imag Regge26 bg Real MAID-25d2 Imag MAID-25d2.5 E2+ [mfm] -.5 E2- [mfm] W [MeV] W [MeV].2 M2+ [mfm] M2- [mfm] W [MeV] W [MeV] PWA Collaboration Meeting, Mainz, 5-9 February, 26 28

29 Regge cuts: adaptation to η photoproduction Real Regge26 bg Imag Regge26 bg Real MAID-25d2 Imag MAID-25d2.4.2 E3+ [mfm].2 E3- [mfm] W [MeV] W [MeV].5. M3+ [mfm] M3- [mfm] W [MeV] W [MeV] PWA Collaboration Meeting, Mainz, 5-9 February, 26 29

30 Regge cuts: adaptation to η photoproduction Real Regge26 bg Imag Regge26 bg Real MAID-25d2 Imag MAID-25d2.2. E4+ [mfm] -.2 E4- [mfm] W [MeV] W [MeV].2 M4+ [mfm] -.2 M4- [mfm] W [MeV] W [MeV] PWA Collaboration Meeting, Mainz, 5-9 February, 26 3

31 Regge cuts: adaptation to η photoproduction Real Regge26 bg Imag Regge26 bg Real MAID-25d2 Imag MAID-25d2.. E5+ [mfm].5 E5- [mfm] W [MeV] W [MeV].2. M5+ [mfm].5 M5- [mfm] W [MeV] W [MeV] PWA Collaboration Meeting, Mainz, 5-9 February, 26 3

32 Regge cuts: adaptation toη photoproductin A2MAMI-5 CBELSA/TAPS-9 CLAS-9 (our Legendre fit result).75 σ [µb] W [GeV] magenta line: Regge background PWA Collaboration Meeting, Mainz, 5-9 February, 26 32

33 Regge cuts: adaptation toη photoproductin black: A2MAMI (preliminary), blue: CLAS-29. Red lines: Regge background dσ/dω [µb/sr] W=.898 GeV W=.9 GeV W=.94 GeV W=.98 GeV W=.92 GeV.2.8 W=.99 GeV.2.8 W=.925 GeV.2.8 W=.93 GeV W=.938 GeV W=.944 GeV W=.95 GeV W=.956 GeV - - cosθ η * PWA Collaboration Meeting, Mainz, 5-9 February, 26 33

34 Regge cuts: adaptation toη photoproductin data: CLAS-29. Red lines: Regge background. W=.925 GeV W=.935 GeV W=.945 GeV W=.965 GeV W=.975 GeV W=.985 GeV W=.995 GeV W=2.5 GeV dσ/dω [µb/sr].5 W=2.5 GeV W=2.25 GeV W=2.35 GeV W=2.45 GeV W=2.55 GeV W=2.65 GeV W=2.75 GeV W=2.85 GeV..5 W=2.95 GeV W=2. GeV W=2.3 GeV W=2.5 GeV W=2.7 GeV W=2.9 GeV W=2.2 GeV W=2.23 GeV..5. W=2.25 GeV W=2.27 GeV W=2.29 GeV W=2.3 GeV W=2.33 GeV W=2.35 GeV W=2.38 GeV W=2.42 GeV.5. W=2.46 GeV W=2.5 GeV W=2.54 GeV W=2.58 GeV W=2.62 GeV W=2.66 GeV W=2.75 GeV - W=2.795 GeV cosθ η * PWA Collaboration Meeting, Mainz, 5-9 February, 26 34

35 Regge cuts: adaptation toη photoproductin data: CBELSA/TAPS-29 W=.9344 GeV W=.9585 GeV W=.9824 GeV W=2.59 GeV W=2.29 GeV dσ/dω [µb/sr] W=2.52 GeV W=2.749 GeV W=2.973 GeV W=2.96 GeV W=2.46 GeV W=2.634 GeV W=2.85 GeV W=2.264 GeV W= GeV W= GeV W= GeV W= GeV W=2.32 GeV W=2.334 GeV W=2.355 GeV cosθ η * PWA Collaboration Meeting, Mainz, 5-9 February, 26 35

36 Regge cuts: adaptation toη photoproductin data: GRAAL-25. Red lines: Regge background Σ.2 W=.932 GeV W=.925 GeV. Σ cos Θ PWA Collaboration Meeting, Mainz, 5-9 February, 26 36

37 Regge+Resonances for η photoproductin 5 S (535) S (65).5 black dashed: Rho black dash-dotted: Omega black solid: Rho+Omega. D 3 (52) D 5 (675) σ [µb] red line: all black line: Regge bg green circles: A2MAMI-5 magenta circles: CB/ELSA-9.5 F 5 (68) D 3 (7) P (7) 5 P 3 (72) blue solid: P (44).6 F 5 (86).6 F 7 (99).8 H 9 (222) D 3 (875) F 5 (2).6 G 9 (225) P (88) D 5 (26) P (23).4 S (895).4 D 3 (25).4 D 5 (257) P 3 (9) G 7 (29) W [GeV] PWA Collaboration Meeting, Mainz, 5-9 February, 26 37

38 Regge+Resonances for η photoproductin data:a2mami (preliminary). Red lines: bg + resonances, black: bg dσ/dω [µb/sr] W = 488 MeV cosθ η * PWA Collaboration Meeting, Mainz, 5-9 February, 26 38

39 Regge+Resonances for η photoproductin data: A2MAMI (preliminary). Red lines: bg + resonances, black: bg dσ/dω [µb/sr] cosθ η * PWA Collaboration Meeting, Mainz, 5-9 February, 26 39

40 Regge+Resonances for η photoproductin data: A2MAMI-25 (T,F), GRAAL-27 (Σ), CLASS-25 (E) T.2 W=497 MeV T F W=497 MeV F Σ W=496 MeV Σ Ε - W=525 MeV Ε * cosθ η PWA Collaboration Meeting, Mainz, 5-9 February, 26 4

41 Regge+Resonances for η photoproductin CBELSA/TAPS data: dσ/dω - 29, T,E,H,P - preliminary dσ/dω [µb/sr].3.2. W=.982 GeV 2.5 GeV 2.29 GeV 2.52 GeV 2.74 GeV 2.97 GeV 2.9 GeV 2.4 GeV 2.63 GeV 2.85 GeV 2.26 GeV GeV GeV cosθ η * GeV GeV 2.3 GeV 2.33 GeV 2.35 GeV 2.37 GeV W=.497 GeV.522 GeV.542 GeV.563 GeV.584 GeV.68 GeV.64 GeV.688 GeV.742 GeV.796 GeV.849 GeV T W=.53 GeV.573 GeV.632 GeV.688 GeV.743 GeV.796 GeV.848 GeV.898 GeV.97 GeV 2.64 GeV 2.53 GeV GeV E H P - - W=.497 GeV W=.497 GeV.522 GeV.542 GeV.563 GeV.584 GeV.68 GeV.522 GeV.542 GeV.563 GeV.584 GeV.68 GeV cosθ η * PWA Collaboration Meeting, Mainz, 5-9 February, 26 4

42 Regge+Resonances forη photoproductin black solid: Rho+Omega black dashed: Rho black dash-dotted: Omega.3 F 7 (99) solid F 5 (2) solid magenta: full solution D 5 (26) solid D 3 (25) solid.75 S (895) G 7 (29) solid P 3 (9).2 σ [µb] W [GeV] PWA Collaboration Meeting, Mainz, 5-9 February, 26 42

43 Regge+Resonances forη photoproductin data: A2MAMI (preliminary). Red lines: bg + resonances, black: bg dσ/dω [µb/sr] W=.898 GeV W=.9 GeV W=.94 GeV W=.98 GeV W=.92 GeV.2.8 W=.99 GeV.2.8 W=.925 GeV.2.8 W=.93 GeV W=.938 GeV W=.944 GeV W=.95 GeV W=.956 GeV - - cosθ η * PWA Collaboration Meeting, Mainz, 5-9 February, 26 43

44 Regge+Resonances forη photoproductin data: CBELSA/TAPS-29. Red lines: bg + resonances, black: bg W=.9344 GeV W=.9585 GeV W=.9824 GeV W=2.59 GeV W=2.29 GeV dσ/dω [µb/sr] W=2.52 GeV W=2.749 GeV W=2.973 GeV W=2.96 GeV W=2.46 GeV W=2.634 GeV W=2.85 GeV W=2.264 GeV W= GeV W= GeV W= GeV W= GeV W=2.32 GeV W=2.334 GeV W=2.355 GeV cosθ η * PWA Collaboration Meeting, Mainz, 5-9 February, 26 44

45 Regge+Resonances forη photoproductin data: GRAAL-25. Red lines: bg + resonances, black: bg W=.932 GeV.2. Σ W=.925 GeV. Σ cos Θ PWA Collaboration Meeting, Mainz, 5-9 February, 26 45