Finite-Energy Sum Rules in γN →ηN · •Finite-Energy Sum Rules analysis of →(𝜂, )...
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Finite-Energy Sum Rules in →0 − Jannes Nys JPAC Collaboration
Transcript of Finite-Energy Sum Rules in γN →ηN · •Finite-Energy Sum Rules analysis of →(𝜂, )...
Finite-Energy Sum Rules in 𝛾𝑁 → 0−𝑁
Jannes Nys
JPAC Collaboration
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)]
• Finite-Energy Sum Rules• 𝜂′/𝜂 beam asymmetry predictions• 𝜋Δ beam asymmetry• Lots of other reactions
Overview
Connect low- and high-energy dynamics.
Baryon resonances
Meson exchanges
Formalism
• No kinematic singularities• No kinematic zeros• Discontinuities:
• Unitarity cut• Nucleon pole
Dispersion relations
Dispersion relations - FESR
Analyticity results in Finite-Energy Sum Rules.
Nucleon pole Low-energy model Regge pole
Crossing variable: 𝜈 =𝑠−𝑢
4 𝑀
s-channel: + 𝜈u-channel: - 𝜈
Λ
∞Fixed 𝒕
Low energies
Low energy models• BnGa, Julich-Bonn, ANL-Osaka, SAID, MAID
• Isospin decomposed amplitudes:
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:
High energies
Regge pole model
Analytic continuation in J
Partial waves have pole at 𝛼
Work at leading order in energy
∞
High energies
Regge pole model
Dominant: vector exchanges
𝐴2′ = 𝐴1 + 𝑡𝐴2
𝛽𝛾𝜂𝑒(t)
𝛽𝑝𝑝𝑒(t)
𝐽(𝑚2)
High energies
Regge pole model
𝐴2′ = 𝐴1 + 𝑡𝐴2
𝐽(𝑚2)
FESR - procedure
Dispersion relations
Nucleon pole Low-energy model Regge pole
LHS of FESR RHS of FESR
Procedure
Nucleon pole Low-energy model Regge pole
1. Calculate LHS of FESR• Pole term• Dispersive integral (using Eta-MAID 2001)
2. Parametrize RHS, i.e. Regge residues 𝛽𝑖𝜎(𝑡), inspired by (1)
3. Fit parameters of 𝛽𝑖𝜎(𝑡) to high energy data
4. Evaluate RHS of FESR5. Compare LHS and RHS
LHS of FESR RHS of FESR
Matching: natural exchanges
Nucleon pole Low-energy model Regge pole
± ∓ ± ±
−𝑡
−𝑡
Factorization
±
∓
Non-sense wrong signature zero (NWSZ)
𝜶 = 𝟎
𝐹3 = 2 𝑀𝑁𝐴1 − 𝑡𝐴4
n n
Matching: natural exchanges
Nucleon pole Low-energy model Regge pole
Matching: unnatural exchanges
Nucleon pole Low-energy model Regge pole
Look for unnatural contributions in the beam asymmetry
Matching: unnatural exchanges
Nucleon pole Low-energy model Regge pole
Look for unnatural contributions in the beam asymmetry
Parametrization
Single particle Regge pole𝛽
𝑡 − 𝑚2
𝛽(𝑡)
𝐽 − 𝛼(𝑡)
Parametrization
Single particle Regge pole𝛽
𝑡 − 𝑚2
𝛽(𝑡)
𝐽 − 𝛼(𝑡)
• 𝛽 𝑡 ~(𝛼 + 1)(𝛼 + 2) (𝛼 + 3)…~1
Γ(𝛼+1)negative integer spin poles
• 𝛽 𝑡 ~𝜶 (𝛼 + 1)(𝛼 + 2) 𝛼 + 3 …~1
Γ(𝛼)non-positive integer spin poles
Data
𝜔
[V. Mathieu]
[Data: Dewire 1971, Braunschweig 1970]
𝜸𝒑 → 𝝅𝟎𝒑 𝜸𝒑 → 𝜼𝒑
Results
Fill up the dip with non-factorizable 𝜌 (natural)
I = 1 (𝜌) I = 0 (𝜔)
Natural dominant: Σ = +1Unnatural dominant: Σ = −1
Prediction for GlueX
[Al Ghoul et al. (GlueX) arXiv:1701.08123 ]
Fits to FESR and pion production data
Pure prediction: proof of Regge pole dominance at high s, small t
Fits to FESR and pion production data
Fit
Comparison for 𝛾𝑝 → 𝜂𝑝𝜌 + 𝜔 𝜌 + 𝜔𝑏 + ℎ 𝜌2 + 𝜔2
Other photoproductionreactions
𝜂′/𝜂 beam asymmetry
Dominant exchanges: 𝜌, 𝜔Variations: 𝑏, ℎ radiative decays
Sizable deviation from 1:• Non-negligible contributions from hidden strangeness• Signicant deviation from the quark model description
V.Mathieu, J.Nys et al. (JPAC) [arXiv:1704.07684]
Quark model predictions:
𝜋∆ photoproduction
Issues in the beam asymmetry at Elab = 16 GeVGlueX will publish @ 9 GeV
𝜋
𝑎2
?
Various explanations:• Conspiracy (other particles)• Absorption (rescattering)• S-channel electric born term (gauge invariance)
Σ = +1: naturalΣ = −1: unnatural
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
Conclusions
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
Backup
