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LSZ-reduction, resonances and non-diagonal propagators: fermions and scalars

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Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1710.07165.pdf
(Preprint), 356KB

NPB937_394.pdf
(Publisher version), 362KB

1710.07165v2.pdf
(Preprint), 279KB

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Citation

Lewandowski, A. (2018). LSZ-reduction, resonances and non-diagonal propagators: fermions and scalars. Nuclear Physics B, 937, 394-421. doi:10.1016/j.nuclphysb.2018.10.020.

Cite as: https://hdl.handle.net/21.11116/0000-0000-3DF9-4
Abstract
It is well-known that the determination of indirect CP-violation in models
with highly mixed and unstable gauge-singlet neutrinos requires a careful
analysis of the matrix of propagators in the vicinity of its poles. In this
paper, in a system with an arbitrary number of unstable mixed Majorana or Dirac
particles, a simple prescription is given for obtaining, roughly speaking,
"square-rooted residues" of propagators, i.e. for obtaining the matrices
$\zeta^{a}_{\ b}$ that (in a special case of stable particles) together with
the ordinary $u$ and $v$ spinors convert the amputated Green's functions in the
$\overline{{\rm MS}}$ scheme (or any other scheme for that matter) into the
$S$-matrix elements. Corresponding prescription for the scalar case is provided
as well.