Effects of Spin 3/2 Nucleon Resonances in Kaon Photoproduction A. J. - PowerPoint PPT Presentation

Effects of Spin 3/2 Nucleon Resonances in Kaon Photoproduction A. J. Arifi 1 & T. Mart 2 RCNP, Osaka University 1 Physics Department, University of Indonesia 2 J-Park Hadron Workshop March 2nd, 2016 A. J. Arifi (RCNP) Kaon photoproduction 1 / 28

Publication T. Mart, S. Clymton, and A.J. Arifi, Phys. Rev. D 92, 094019 (2015) Nucleon resonances with spin 3/2 and 5/2 in the isobar model for kaon photoproduction A. J. Arifi (RCNP) Kaon photoproduction 2 / 28

Overview Introduction 1 Motivation Objective Formalism 2 Isobar Model Fitting Procedure Result and Discussion 3 Fitting Result Plots of Observables Summary 4 A. J. Arifi (RCNP) Kaon photoproduction 3 / 28

Motivation Kaon photoproduction provides an essential tool for the studies of strange hadron. Figure: Kaon photoproduction on proton (a) and nucleus (b) A. J. Arifi (RCNP) Kaon photoproduction 4 / 28

Motivation Experimental side — abundant data are available on kaon photoproduction and we have included 7433 data points in this research. The experimental data are from CLAS Collaboration, GRAAL Collaboration, LEPS Collaboration, MAMI Collaboration. Theoretical side — we have used Isobar model to describe kaon photoproduction. Some formulations have been well-established but the formulation of nucleon resonances spin 3/2 or higher is still plagued with the problem of consistency. A. J. Arifi (RCNP) Kaon photoproduction 5 / 28

Objective we aim to study the effect of inclusion of spin 3/2 nucleon resonances with two different formulations using isobar model. Model A R.A. Adelseck, C. Bennhold, and L.E. Wright, Phys. Rev. C32, 1681(1985) J. C. David, C. Fayard, G. H. Lamot, and B. Saghai, Phys. Rev. C53, 2613 (1996) Model B V. Pascalutsa, Phys. Lett. B503, 85 (2001) A. J. Arifi (RCNP) Kaon photoproduction 6 / 28

Channels of Kaon Photoproduction Figure: (a) Baryon Octet (b) Pseudoscalar meson nonet based on conservation of strangeness and isospin , there are six possible channels of kaon photoproduction 1 . γ + p → K + + Λ 4 . γ + n → K 0 + Σ 0 2 . γ + p → K + + Σ 0 5 . γ + n → K 0 + Λ 3 . γ + p → K 0 + Σ + 6 . γ + n → K + + Σ − A. J. Arifi (RCNP) Kaon photoproduction 7 / 28

Kaon Photo- & Electroproduction Figure: (a) Kaon Photoproduction (b) Kaon Electroproduction Elementary process of kaon electroproduction e ( k i ) + p ( p ) → e ′ ( k f ) + K + ( q ) + Λ( p Λ ) , (1) it’s equivalent to virtual photoproduction γ ν ( k ) + p ( p ) → K + ( q ) + Λ( p Λ ) , (2) with k = k f − k i . but, we use real photon which has properties k 2 = 0 and k · ǫ = 0 for the case of kaon photoproduction . A. J. Arifi (RCNP) Kaon photoproduction 8 / 28

Feynman Diagram of Kaon Photoproduction Figure: (a) s -channel (b) u -channel (c) t -channel of kaon photoproduction Contribution of mediator particles are categorized into background and resonances . So, the amplitude reads M = M background + M resonances (3) A. J. Arifi (RCNP) Kaon photoproduction 9 / 28

Hadronic Form Factor We include the hadronic form factors in the hadronic vertices by adopting the method developed by Haberzettl. F (Λ , s ) sin 2 θ had cos 2 φ had + F (Λ , u ) sin 2 θ had sin 2 φ had ˜ F = + F (Λ , t ) cos 2 θ had , (4) where, Λ 4 F (Λ , x ) = (5) Λ 4 + ( x − m 2 ) 2 and x = s , t , u (mandelstam variables) A. J. Arifi (RCNP) Kaon photoproduction 10 / 28

Nukleon Resonances Table: Status, mass and width of nucleon resonances used in our model Resonances Status Mass (MeV) Width (MeV) N(1440) P 11 **** 1430 ± 20 350 ± 100 115 +10 N(1520) D 13 **** 1515 ± 5 − 15 1535 +20 N(1535) S 11 **** 150 ± 25 − 10 1655 +15 N(1650) S 11 **** 140 ± 30 − 10 150 +100 N(1700) D 13 *** 1700 ± 50 − 50 100 +150 N(1710) P 11 *** 1710 ± 30 − 50 1720 +30 250 +150 N(1720) P 13 **** − 20 − 100 1875 +45 N(1875) D 13 *** 200 ± 25 − 55 N(1880) P 11 ** 1870 ± 35 235 ± 65 90 +30 N(1895) S 11 ** 1895 ± 15 − 15 N(1900) P 13 *** 1900 250 N(2120) D 13 ** 2140 330 ± 45 A. J. Arifi (RCNP) Kaon photoproduction 11 / 28

Model A Propagator k + √ s p + / / g µν + γ ν γ µ − 2 � P 3 / 2 = s ( p + k ) µ ( p + k ) ν µν 3( s − m 2 N ∗ + im N ∗ Γ N ∗ ) − 1 � √ s { γ µ ( p + k ) ν − γ ν ( p + k ) µ } , (6) Electromagnetic vertex factor � g a 1 � ( k 2 ǫ ν − k · ǫ k ν ) − k ) k ν � Γ ν ( ± ) N ∗ p γ ( k 2 / √ s ± m p ǫ − k · ǫ/ = N ∗ p γ k 2 p · ǫ k ν − p · k ǫ ν k · ǫ k ν − k 2 ǫ ν � + g b + g c ( √ s ± m p ) 2 ( √ s ± m p ) 2 Γ ± , (7) N ∗ p γ N ∗ p γ Hadronic vertex factor K Λ N ∗ = g K Λ N ∗ Γ µ ( ± ) m N ∗ p µ Λ Γ ∓ , (8) A. J. Arifi (RCNP) Kaon photoproduction 12 / 28

Model B Propagator p + / k + m N ∗ / − g µν + 1 3 γ µ γ ν + 2 � P 3 / 2 = 3 s ( p + k ) µ ( p + k ) ν µν ( s − m 2 N ∗ + im N ∗ Γ N ∗ ) + 1 � 3 √ s { γ µ ( p + k ) ν − γ ν ( p + k ) µ } , (9) Electromagnetic vertex factor i � Γ ν ( ± ) g (1) ( ǫ ν / k − k ν / p + g (2) ( k ν p · ǫ − ǫ ν p · k ) = − ǫ ) / N ∗ p γ m 2 N ∗ + g (3) p ν ( / ǫ ) + g (4) γ ν ( / ǫ/ k − / ǫ/ k / k / ǫ − / k ) / p � + g (5) γ ν ( p · k / ǫ − p · ǫ/ k ) Γ ± , (10) Hadronic vertex factor g KYN ∗ � q ) γ µ + / p Λ q µ − / � Γ µ ( ± ) qp µ = Γ ∓ ( p Λ · q − / p Λ / , (11) K Λ N ∗ Λ m 2 N ∗ A. J. Arifi (RCNP) Kaon photoproduction 13 / 28

where we define g (1) − 2 ig a N ∗ p γ + 3 ig c N ∗ p γ + g d = N ∗ p γ , g (2) − 2 ig a N ∗ p γ − g b N ∗ p γ + 2 ig c N ∗ p γ − 2 g d = N ∗ p γ , g (3) − ig a N ∗ p γ + ig c = N ∗ p γ , (12) g (4) − ig a N ∗ p γ + ig c = N ∗ p γ , g (5) − 2 ig a N ∗ p γ + ig c N ∗ p γ − g d = N ∗ p γ , and parities are also defined by Γ + = i γ 5 and Γ − = 1. A. J. Arifi (RCNP) Kaon photoproduction 14 / 28

Scattering Amplitude The corresponding scattering amplitude is written as M ( ± ) u Λ Γ µ ( ± ) µν Γ ν ( ± ) K Λ N ∗ P 3 / 2 = ¯ N ∗ p γ u p , (13) res 6 � A i ( s , t , u , k 2 ) M i u p , = u Λ ¯ (14) i =1 Then, we decompose them into invariant matrices as below 1 M 1 = 2 γ 5 ( / ǫ/ k − / k / ǫ ) , M 2 = γ 5 [(2 q − k ) · ǫ P · k − (2 q − k ) · kP · ǫ ] , ǫ − q · ǫ/ M 3 = γ 5 ( q · k / k ) , (15) i ǫ µνρσ γ µ q ν ǫ ρ k σ , M 4 = γ 5 ( q · ǫ k 2 − q · kk · ǫ ) , M 5 = k − k 2 / M 6 = γ 5 ( k · ǫ/ ǫ ) A. J. Arifi (RCNP) Kaon photoproduction 15 / 28

Amplitude of Model B �� � 1 A 1 = m p 2 ( m p + m Λ ) ( c Λ − m Λ m p − 3 sc s ) + m Λ (2 sc s − c k ) � 1 2 ( m p + m Λ )( m Λ − 3 m p c s − 1 ± m N ∗ s c Λ m p ) �� +2 c Λ − 2 m 2 G 1 Λ − 3 c 1 − 1 s c Λ c k �� � � m p c Λ + m Λ ( k 2 − s ) 1 � � + 2 ( m p + m Λ ) + b p c Λ ± m N ∗ m Λ b p ��� s c Λ ( k 2 − s ) + m Λ m p + 1 3( c 1 − b p c s ) + 1 G 2 � 2 ( m p + m Λ ) �� c k c s − 3 c 1 − k 2 �� � � b p c Λ − c k m 2 G 3 , +2 Λ − 3 sc 1 ± m N ∗ m Λ (16) A. J. Arifi (RCNP) Kaon photoproduction 16 / 28

m p � s c Λ k 2 �� m Λ k 2 ± m N ∗ � 3( k 2 − 2 b q ) − 2 G 1 A 2 = t − m 2 k �� 3 s ( c 1 − b p c s ) − m Λ m p k 2 � 1 + ± m N ∗ m p t − m 2 k s c Λ k 2 �� � 3( b p c s − c 1 ) − 1 G 2 × 4 k 2 � � G 3 , + c Λ ± m N ∗ m Λ (17) t − m 2 k �� �� � � 1 3( m p − m Λ ) + 2 G 1 A 3 = 2 m p 3 s − m Λ m p ± m N ∗ s c Λ m p �� m p c Λ + m Λ ( k 2 − s ) � � s c Λ ( k 2 − s ) + 1 m Λ m p + 1 ± m N ∗ 2 ��� c 1 + b p (1 + 1 G 2 � +3 s c Λ ) � �� � 3 c 1 + 1 G 3 , − 2 m Λ c k ± m N ∗ s c Λ c k (18) A. J. Arifi (RCNP) Kaon photoproduction 17 / 28

�� �� � � − 1 3( m p + m Λ ) − 2 G 1 A 4 = 2 m p 3( c Λ + sc s ) + m Λ m p ± m N ∗ s m p c Λ �� m p c Λ + m Λ ( k 2 − s ) � � s c Λ ( k 2 − s ) + 1 m Λ m p + 1 ± m N ∗ 2 �� � �� G 2 − 2 � 3 c 1 + 1 G 3 , +3 ( c 1 − b p c s ) m Λ c k ± m N ∗ s c Λ c k (19) � �� � 3( k 2 − 2 b q ) + 2 1 m p G 1 A 5 = − m Λ c 5 ± m N ∗ s c Λ c 5 t − m 2 2 k �� � + 1 1 m Λ m p c 5 − 3 s ( c 1 + 3 b p c s − 2 b p ) ± m N ∗ m p t − m 2 2 k �� � � G 2 − � 3( b p + b Λ ) − 2 2 c 5 G 3 , × s c Λ c 5 c Λ ± m N ∗ m Λ (20) t − m 2 k A. J. Arifi (RCNP) Kaon photoproduction 18 / 28

�� �� � � 1 3 m p c s + 1 G 1 A 6 = 2 m p m Λ m p + 3 sc s − c Λ ± m N ∗ s m p c Λ − m Λ � �� � � � + 1 3( c 1 + b p c s ) − 1 s c Λ m 2 G 2 m p c Λ − m p m Λ ± m N ∗ p + m p m Λ 2 �� �� � � G 3 , +2 m p c Λ − m Λ s ± m N ∗ m p m Λ − c Λ (21) where g ( i ) g K Λ N ∗ G ( i ) = N ∗ + im N ∗ Γ N ∗ ) , (22) 3 m 4 N ∗ ( s − m 2 which g ( i ) are as in equation (12) for i = 1 , ..., 5. A. J. Arifi (RCNP) Kaon photoproduction 19 / 28