The diagonal spin basis and calculation of processes involving polarized particles

TL;DR

This paper introduces the Diagonal Spin Basis formalism for covariant calculations involving polarized particles, simplifying spin operator treatment and applicable to various high-energy processes with polarized particles.

Contribution

The authors develop a new covariant formalism, the Diagonal Spin Basis, expressing spin vectors solely in terms of particle 4-momenta, unifying initial and final state spin operators for massive and massless fermions.

Findings

Formalism simplifies calculations of polarized processes.

Applied to multiple high-energy scattering and decay processes.

No issues with spin flip amplitudes in the formalism.

Abstract

The review of developed by the authors new techniques for covariant calculation of matrix elements in QED, the so-called formalism of "Diagonal Spin Basis" (DSB), is presented. In DSB spin 4-vectors of in- and out- fermions are expressed just in terms of their 4-momenta. In this approach the little Lorentz group, common for the initial and final states,is realized. This brings the spin operators of in- and out-particles to coincidence. The developed approach is valid both for massive fermions and for massless ones. There occur no problems with accounting for spin flip amplitudes in it. Just 4-momenta of particles participating in reactions are required in it to construct the mathematical apparatus for calculations of matrix elements. We apply this formalism to the next processes: 1) M\"oller and Bhabha bremsstrahlung ($e^{\pm}e^- \to e^{\pm}e^- \gamma$) in the ultrarelativistic limit when initial particles and photon are helicity polarized; 2) Compton back-scattering of photons of intensive circularly polarized laser wave on a beam of longitudinally polarized ultrarelativistic electrons ($e+n\gamma_0 \to e+\gamma $); 3) $e^+e^-$-pair production by a hard photon in simultaneous collision with several laser beam photons ($\gamma+n \gamma_0 \to e^+ + e^-$); 4) Bethe-Heitler process in the case of a linearly polarized photon emission by an electron with account for proton recoil and form factors; 5) the reaction $ep \to ep \gamma$ with proton polarizability being taken into account in the kinematics when proton bremsstrahlung dominates; 6) orthopositronium 3-photon annihilation ($e^+e^{-} \to 3 \gamma$).