Understanding the basic features of Cascade Photoproduction

Understanding the basic features of Cascade Photoproduction Collaboration: Helmut Haberzettl (GWU) Yongseok Oh (KNU) K. N. (UGA) Baryon2016, May 16-20, 2016, Tallahassee, FL

Our Ξ collaboration:! Theoretical investigation of the reactions: - ΚΝ KΞ γn KKΞ [JLab] [J-PARC] (initiatives for K L beam at JLab)

Our Ξ collaboration:! Theoretical investigation of the reactions: - ΚΝ KΞ γn KKΞ [JLab] πn KKΞ [J-PARC] pp ΞΞ - - [FAIR] [J-PARC] (initiatives for K L beam at JLab)

Our Ξ collaboration:! Theoretical investigation of the reactions: - ΚΝ KΞ γn KKΞ [JLab] πn KKΞ [J-PARC] pp ΞΞ - - [FAIR] [J-PARC] (initiatives for K L beam at JLab)! Build a reliable model to analyze the cascade spectroscopy data: Start learning the production mechanisms of the established Ξs. [g.s. Ξ 1/2+ (1318)]! To date (in γp K + K + Ξ - ) : σ, dσ/dω Ξ -, dσ/dω K +, dσ/dm Κ + Ξ -, dσ/dm Κ + K + < 3.8 GeV [L. Guo et al., PRC76, 025208, 07] preliminary σ < 5.5 GeV [J. T. Goetz and K. Hicks, PoS Hadron2013, 097, 13] preliminary P, C x, C z < 5 GeV [J. Bono, L. Guo and B. Raue, PoS XLASNPA, 039, 14] No calculation is available so far, except for: Liu and Ko (PRC69, 04), in connection with the Ξ 5 production. Our group (PRC74, 06; PRC83, 12), analyzing the published CLAS data.

Formalism: 2π photoproduction Haberzettl, Nakayama and Oh (in preparation) Basic Idea Hadronic interaction : N π 1 π 2 N [From the three-body Faddeev equation] π 1 π 2 F = F N N

Formalism: 2π photoproduction Haberzettl, Nakayama and Oh (in preparation) Basic Idea Hadronic interaction : N π 1 π 2 N [From the three-body Faddeev equation] π 1 π 2 F = F N N Photoproduction amplitude: γn π 1 π 2 N γ [Attach photon to everywhere possible (and topologically distinct) in the hadronic interaction F ] gauge invariant F µ = F + F + F + F + F F µ ext F µ int

Formalism: 2π photoproduction Haberzettl, Nakayama and Oh (in preparation) Three-body Faddeev equation : Alt-Grassberger-Sandhas (AGS) approach [NPB, 167(1967)] X γ = non-pole two-body interaction Full N π 1 π 2 N interaction F : basic production processes with dressed quantities f 1 = F = F f 2 = = X, T X f + X, X + T X N f f 3 = + X 6= 3-body FSI N βα = +...

Formalism: 2π photoproduction Haberzettl, Nakayama and Oh (in preparation) Full photoproduction amplitude: γn π 1 π 2 N F µ = G 1 0 {F S} µ S 1 =(NL) µ +(1L) µ +(2L) µ +... [Lehman-Szymanzik-Zimmermenn (LSZ) reduction] [Nuovo Cim. 1, 205(1955)] M µ = 1-meson photoproduction amplitude X = non-pole two-body interaction

Formalism: an approximation to 2π photoproduction Simplest approximation to N π 1 π 2 N interaction F : F = F # & = % δ αβ + T βγ X γ ( f α + δ βγ +T βγ X γ αβ $ γ α ' βγ = f α + T βγ X γ f α +... α αβ γ α ( ) α N γα f α

Formalism: an approximation to 2π photoproduction Simplest approximation to N π 1 π 2 N interaction F : F = F # & = % δ αβ + T βγ X γ ( f α + δ βγ +T βγ X γ αβ $ γ α ' βγ = f α + T βγ X γ f α +... α ( ) αβ γ α (approximate by a contact term F c ) α N γα f α q 1 q 2 F + + + p F c p Most general Dirac structure of F c : F c = a 1ˆ1+a 2 p/ m + a 3 p/ 0 m 0 + a 4 p/p/ 0 m 0 m + b 1 q/ m + b 2 q/p/ m m + b 3 p/q/ 0 p 0 m 0 + b 4 m /q/p/ m 0 m m F c (on-shell) = aˆ1+b q//m q = q 1 + q 2 (a i, b i ) = parameters to be fixed (i=1,4)

Formalism: an approximation to 2π photoproduction F + + + F c f Corresponding photoproduction amplitude: γn π 1 π 2 N q 1 q 2 k F µ f µ + F c µ F c F µ p F p c = c F c F c F c + + + F c + F c F c µ int µ ext Gauge invariant ansatz: Q i = charge of particle i

Formalism: f µ for γn KKΞ Nakayama, Oh and Haberzettl (PRC74, 06) Man, Oh and Nakayama (PRC83, 12) f = 1 2 + 2 1 + K K f µ ext = N K-exchange Ξ + (1 2) f µ int = Y Y GKR contact current No contribution from (exchange of S=2 exotic meson) sensitive to S=-1 hyperons Y

Formalism: f µ for γn KKΞ Nakayama, Oh and Haberzettl (PRC74, 06) Man, Oh and Nakayama (PRC83, 12) Additional (gauge invariant) contributions to f µ : f µ trn = Y Y N N Ξ Ξ f µ K* = K*-exchange

γn KKΞ(1320) : our model Λ(1116)1/2+ Σ(1193)1/2+ Λ(1405)1/2- Σ(1385)3/2+ Λ(1520)3/2- the model parameters may be fixed from the relevant decay rates(pdg) and/or quark models and SU(3) symmetry considerations. no enough information to fix the parameters of the model. W thr (KΞ) 1814 MeV Σ 5/2- (2250) M = 2270 ± 50 MeV Σ 9/2- (2250) M = 2210 ± 30 MeV [A. de Bellefon et al., N. Cim. A7( 72)] Strategy: consider all the 3- & 4-star hyperon resonances which affects the fit quality significantly (LASSO). Least Absolute Shrinkage and Selection Operator

LASSO : Minimize: Z = χ 2 + λ Σ g i i LASSO method applied to select the resonances g i

γn KKΞ(1320) : preliminary results

γn KKΞ(1320) : preliminary results Kaon-exchange: responsible for forward (backward) angle peaking of the K + (Ξ - ) distribution

γn KKΞ(1320) : preliminary results K-exchange diagramas (involving resonances Y) off

γn KKΞ(1320) : preliminary results Kaon-exchange: responsible for forward (backward) angle peaking of the K + (Ξ - ) distribution S=-1 resonances needed

γn KKΞ(1320) : preliminary results Λ 3/2+ (1890) Σ 7/2+ (2030)

γn KKΞ(1320) : preliminary results Λ 3/2+ (1890) fitted with only the contact current F c µ Σ 7/2+ (2030)

γn KKΞ(1320) : preliminary results [Jackson, Oh, Haberzettl, K.N., PRC91(2015)065208] Λ 3/2+ (1890) Σ 7/2+ (2030)

γn KKΞ : beam and target asymmetries Kaon exchange alone : Σ = -1 NYK vertex

Summary : γp KKΞ(1320) a) basic features of γp K + K + Ξ - (1318) understood: K-exchange currents (with S=-1 resonances) : essential for describing the dσ/dω data. b) suited for learning about S=-1 hyperon resonances in the 2 GeV mass region: " Λ 3/2+ (1890), Σ 7/2+ (2030) : required to describe the m KΞ data. they are also needed in KN KΞ. c) more data needed, especially, the spin observables: beam-asymmetry : sensitive to the K-exchange currents (Σ =-1). target-asymmetry : sensitive to the ps-pv mixing in the KNY couplings. preliminary P, C x, C z [J. Bono, L. Guo and B. Raue, PoS XLASNPA, 039, 14] preliminary σ [J. T. Goetz and K. Hicks, PoS Hadron2013, 097, 13] d) investigate other charge channels : helps disentagle Λ and Σ hyperons.

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