Compton scattering in scalar electrodynamics

Abstract

The goal of this project is to compute the Compton scattering cross-section for scalar electrodynamics. A comparison with the experimental result is also made. 1 The project In our group we were concerned about the possibility of predicting the spin nature of electrons by just measuring scattered photons against free electrons. So, we decided to compute the total cross-section for Compton scattering with scalar electrodynamics and compare it with experimental proof. The starting point is the gauge invariant Lagrangian which describes the interaction of a scalar particle with a massless vector boson. L = − 4 (∂μAν − ∂νAμ) + [(∂μ + ieAμ)φ]† [(∂ + ieA)φ] , = Lfree + ieAμ (φ∗∂μφ− φ∂μφ∗) + e2AμAμφ∗φ . (1) We can extract the vertices using the rules given by Ref. [1]: – For each interaction in the Lagrangian, we introduce a momentum conservation delta, (2π)4δ( ∑ p). – Introduce a factor coming from the degeneracy of identical particles in the interaction and the couplings coming from iLint. – For each field derivative ∂μφ, a −ipμ factor is associated with the momentum of the incoming particle. Then, for the photon-scalar interaction, we have −ie(pμ + pμ)(2π)δ(p− p′ − k) , (2) and for the 2-photon-scalar interaction 2iegμν(2π)δ(p− p′ − k − k′) . (3) The next step consists of applying the recipe. – Draw all topologically distinct diagrams. – For each internal scalar field of momentum k, we attach the propagator D(k) = i/(k2−m2 + ie). – For each external photon line, we attach a polarization vector μ. From Fig. 1, we obtain the following amplitude *Work performed as a student project under the supervision of C. Rojas.