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18 2.2. Kaon production in the Regge limitAnother expression of practical use involves the combination of a polarised beam impinging on anunpolarized target and a measurement which determines the polarisation of the outgoing hyperon.For this situation, the virtual-photon cross section can be parametrised asd 2 σ ∗dΩ ∗ K= σ unpol(1 + hA LT ′ + P x ⃗x · ⃗P Y + P y ⃗y · ⃗P Y + P z ⃗z · ⃗P Y ) , (2.38)where σ unpol is the unpolarized differential cross section. The recoil-polarisation P i , in turn, can beexpressed as the sum of an induced polarisation Pi 0 and a transferred polarisation P i′P i = P 0i + hP ′i , for i = x, y, z . (2.39)By equating the Eqs. (2.28) and (2.38), it is possible to express the induced and transferredpolarisations in terms of the response functions. In practise, the statistics of an experiment can beimproved by integrating over the angle φ between the lepton and reaction plane. This implies thatthe azimuthal-angle dependence of Eq. (2.28) can be integrated out. As such the number of terms isgreatly reduced. After some easy algebra, one finds for the φ-integrated polarisations 2Px 0 = Pz 0 = P y ′ = 0 ,Py 0 = 1 √ɛ(1 + ɛ)K−102P x ′ = 1 √ɛ(1 − ɛ)K−102P ′ z = √ 1 − ɛ 2 K −10( )sR x′ 0LT cos θK ∗ + c R y′ 0LT + s R z′ 0LT sin θK∗ ,( )cR x′ 0LT ′ cos θ∗ K − s R y′ 0LT+ c R ′ z′ 0LT ′ sin θ∗ K ,)T ′ sin θ∗ K + R z′ 0T ′ cos θ∗ K ,(−R x′ 0(2.40)where K 0 = R 00T+ ɛR00 L .2.2 Kaon production in the Regge limitThe study of kaon production, and by extension all meson-production reactions, is primarily motivatedby the exploration of the nucleon-resonance spectrum. Therefore, analyses of experimental datafocus on the so-called resonance region, which roughly corresponds to W KY 2.5 GeV. Nevertheless,one cannot ignore the contribution of non-resonant diagrams that are looked on as a backgroundwith an eye to extracting nucleon-resonance information. The kaon-production cross section lacksclear indications of dominant resonant states which hints that background contributions are by nomeans subordinate to resonance exchange. As such, the description of the background is crucialin order to extract reliable information on the nucleon-resonance spectrum. The RPR formalismtakes an uncommon approach and first focuses on modelling kaon production at energies beyond theresonance region where only non-resonant diagrams subsist.At high energies, hadronic scattering processes can be elegantly described in the framework of Reggetheory. Based on the observation that it is useful to regard angular momentum as a complex variablewhen discussing solutions of the Schrödinger equation for non-relativistic potential scattering [108], asuccessful theory was developed. It describes a large variety of concepts and results in high-energy2 In literature, one commonly adopts the notation Pi 0 and P i ′ for the φ-integrated induced and transferred polarisations.This notation can lead to confusion with the Pi 0 /P i ′ that feature in the cross-section decomposition of Eq. (2.38). Forthe remainder of this work, the symbols Pi0 and P i ′ will refer to φ-integrated observables.