Finite-Energy Sum Rules. Jannes Nys JPAC Collaboration

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1 Finite-Energy Sum Rules in γn 0 N Jannes Nys JPAC Collaboration

2 Finite-Energy Sum Rules η /η beam asymmetry predictions πδ beam asymmetry Lots of other reactions Overview J. Nys, V. Mathieu et al (JPAC) [Phys. Rev. D (2017)] V. Mathieu, J. Nys, et al. (JPAC) [in preparation] + [Phys. Rev. D (2015)]

3 Overview Baryon resonances Meson exchanges Connect low- and high-energy dynamics.

4 Formalism No kinematic singularities No kinematic zeros Discontinuities: Unitarity cut Nucleon pole

5 Dispersion relations

6 Dispersion relations - FESR Λ Fixed t Crossing variable: ν = s u 4 M s-channel: + ν u-channel: - ν Nucleon pole Low-energy model Regge pole Analyticity results in Finite-Energy Sum Rules.

7 Low energies Low energy models BnGa, Julich-Bonn, ANL-Osaka, SAID, MAID Isospin decomposed amplitudes:

8 Low energies Low energy models BnGa, Julich-Bonn, ANL-Osaka, SAID, MAID Eta-MAID 2001 [Chiang et al., Nucl. Phys. A 700, 429 (2002)] Isospin decomposed amplitudes:

9 High energies Regge pole model Analytic continuation in J Partial waves have pole at α Work at leading order in energy

10 A 2 = A 1 + ta 2 High energies Regge pole model J(m 2 ) Dominant: vector exchanges β γηe (t) β ppe (t)

11 A 2 = A 1 + ta 2 High energies Regge pole model J(m 2 )

12 FESR - procedure

13 Dispersion relations Nucleon pole Low-energy model Regge pole LHS of FESR RHS of FESR

14 Procedure Nucleon pole Low-energy model Regge pole LHS of FESR RHS of FESR 1. Calculate LHS of FESR Pole term Dispersive integral (using Eta-MAID 2001) Parametrize RHS, i.e. Regge residues β σ i (t), inspired by (1) Fit parameters of β σ i (t) to high energy data 4. Evaluate RHS of FESR 5. Compare LHS and RHS

15 Matching: natural exchanges Nucleon pole Low-energy model Regge pole t α = 0 t ± ± ± ± Factorization Non-sense n n wrong signature F 3 = 2 M N A 1 ta 4 zero (NWSZ)

16 Matching: natural exchanges Nucleon pole Low-energy model Regge pole

17 Matching: unnatural exchanges Nucleon pole Low-energy model Regge pole Look for unnatural contributions in the beam asymmetry

18 Matching: unnatural exchanges Nucleon pole Low-energy model Regge pole Look for unnatural contributions in the beam asymmetry

19 Parametrization Single particle β t m 2 Regge pole β(t) J α(t)

20 Parametrization Single particle β t m 2 Regge pole β(t) J α(t) β t ~(α + 1)(α + 2) (α + 3) ~ 1 Γ(α+1) β t ~α (α + 1)(α + 2) α + 3 ~ 1 Γ(α) negative integer spin poles non-positive integer spin poles

21 Data γp π 0 p ω γp ηp [V. Mathieu] [Data: Dewire 1971, Braunschweig 1970]

22 Results I = 1 (ρ) I = 0 (ω) Natural dominant: Σ = +1 Unnatural dominant: Σ = 1 Prediction for GlueX Fill up the dip with non-factorizable ρ (natural)

23 [Al Ghoul et al. (GlueX) arxiv: ]

24 Fits to FESR and pion production data Pure prediction: proof of Regge pole dominance at high s, small t

25 Fits to FESR and pion production data Fit

26 Comparison for γp ηp ρ + ω b + h ρ 2 + ω 2 ρ + ω

27 Other photoproduction reactions

28 η /η beam asymmetry V.Mathieu, J.Nys et al. (JPAC) [arxiv: ] Quark model predictions: Dominant exchanges: ρ, ω Variations: b, h radiative decays Sizable deviation from 1: Non-negligible contributions from hidden strangeness Signicant deviation from the quark model description

29 π photoproduction Issues in the beam asymmetry at Elab = 16 GeV GlueX will 9 GeV a 2? Σ = +1: natural Σ = 1: unnatural π Various explanations: Conspiracy (other particles) Absorption (rescattering) S-channel electric born term (gauge invariance)

30 Global analysis of meson resonance production Status: ~10000 data point collected for plab > 5 GeV for various reactions Couplings are fixed step by step, and propagated using factorization Current status: π, K beams with CEX done. Fit results are rotated to t-channel: decay amplitudes

31 Conclusions

32 Summary Finite-Energy Sum Rules analysis of γn (η, π)n Low-energy model predicts high-energy behavior Information at the amplitude level Ultimately: combined fit of low- and high-energy data η / η beam asymmetry Information about the b, h radiative decays Hidden strangeness information Various other reactions under consideration

33 JPAC website

34 Backup

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