Strangeness Photoproduction from the Deuteron and Hyperon–nucleon Interaction

Pronounced effects due to final state hyperon–nucleon interaction are predicted in strangeness photoproduction reaction on the deuteron. Use is made of the covariant reaction formalism and the P– matrix approach to the hyperon–nucleon interaction. PACS numbers: 25.20.Lj, 25.30.Rw, 13.60.Le, 13.60.Rj Typeset using REVTEX 1 The first measurement of kaon photoproduction on the deuteron are anticipated this year [1]. These data may open a new window on the ΛN and ΣN forces since the final state Y N interaction (FSI) plays an important role in the γd → KY N reaction. This problem has been addressed by several authors starting from the pioneering paper by Renard and Renard [2-3]. Two points make the present work different from the previous studies: (i) the use of the covariant formalism both for the reaction mechanism and the deuteron wave function, and (ii) the P–matrix approach to the FSI which takes into account the subnuclear degrees of freedom and disentangle the dynamical singularities from kinematical threshold effects [4]. Our main result is a prediction of the spectacular effects in the reaction cross section due to the Y N FSI. The reaction γd → KY n, Y = Λ,Σ is a 2 → 3 process. The corresponding double differential cross–section reads dσ ≡ d σ d|pK |dΩK = 1 211π5 pK kMdEK λ(s2, m 2 Y , m 2 n) s2 ∫ dΩ∗Y n|T | . (1) Here k, pK , EK and ΩK correspond to the deuteron rest system with z-axis defined by the incident photon beam direction k. The solid angle Ω∗Y n is defined in the Y n center-ofmomentum system. The quantity λ(x, y, z) is the standard kinematical function λ(x, y, z) = x − 2(y + z)x+ (y − z). We shall use the covariant relativistic approach to calculate the amplitude T of the process γd → KY N . The amplitude will be approximated by the two leading diagrams, namely the tree (pole, or plane waves) graph and the triangle graph with FSI. It will be demonstrated that within the covariant approach one easily retrieves the usual nonrelativistic impulse approximation and the Migdal-Watson approach to FSI. We start with the tree diagram. To calculate it two blocks have to be specified: (i) the elementary photoproduction amplitude M on the proton, and (ii) the deuteron vertex Γd. The elementary amplitude used in the present calculation was derived from the tree level effective Lagrangian [5]. Taken into account were resonances with the spin ≤ 5/2 in the s–channel the spin–1/2 resonances in the u–channel, and K(892) and K1(1270) resonances in the t– channel. This amplitude 2 has the following decomposition over invariant terms [6] M = uY 6