Spectator theory for three-nucleon electromagnetic currents

In this talk I present some of the more recent developments within the Covariant Spectator Theory. My focus will be on aspects of the derivation of gauge invariant electromagnetic threenucleon currents which are consistent with the hadronic equations and with the basic assumptions of this framework. Important dynamical ingredients of the three-nucleon currents are also discussed, namely the three-nucleon bound state vertex function and the two-nucleon interaction model they are derived from. THE COVARIANT SPECTATOR THEORY The Covariant Spectator Theory (CST) was introduced already several decades ago by Franz Gross [1]. Its purpose is to include relativity in a manifestly covariant way in fewbody problems, while keeping their complexity at a level that is still manageable for numerical calculations. It has been already applied successfully to the description of a variety of systems, including the deuteron and nucleon-nucleon (NN) scattering [2, 3], elastic and inelastic electron scattering off the deuteron [4, 5, 6], and the 3N bound state [7, 8]. The CST is based on Relativistic Quantum Field Theory, where an exact and complete scattering amplitude can be expressed in terms of the Bethe-Salpeter equation (BSE) [9]. The Spectator Equation (SE) is a particular re-organization of the complete BSE for a system of heavy particles (nucleons) that interact via the exchange of lighter particles (mesons). Ignoring vertex and self-energy corrections as well as genuine many-body forces, the scattering amplitude is given as an infinite sum of ladder and crossed ladder diagrams of all orders in the coupling constants. It can be generated by an integral equation if the propagators and the irreducible kernel are chosen in a suitable way. While the BSE includes the full off-shell propagators for all heavy particles, the SE restricts all but one of them to their mass shells. Consequently, contributions to the scattering amplitude which are generated by one equation through iterations may appear as part of the irreducible kernel of the other. When their respective kernels are truncated— which in practical calculations is unavoidable since the complete kernels themselves contain already an infinite number of diagrams—the BSE and the SE are no longer equivalent. It has been shown that the truncated SE, in certain circumstances, converges faster to the full result than the truncated BSE [10]. The simplest and most often used cases are truncations at lowest order, leading to the so-called ladder approximation since crossed-ladder graphs are thereby excluded. Spectator theory for three-nucleon electromagnetic currents November 15, 2004 1