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arXiv · 1207.4338

Scalar-particle self-energy amplitudes and confinement in Minkowski space

Elmar P. Biernat·Franz Gross·Teresa Peña·Alfred Stadler
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Abstract

We analyze the analytic structure of the Covariant Spectator Theory (CST) contribution to the self-energy amplitude for a scalar particle in a \phi^2 \chi-theory. To this end we derive dispersion relations in 1+1 and in 3+1 dimensional Minkowski space. The divergent loop integrals in 3+1 dimensions are regularized using dimensional regularization. We find that the CST dispersion relations exhibit, in addition to the usual right-hand branch cut, also a left-hand cut. The origin of this "spectator" left-hand cut can be understood in the context of scattering for a scalar \phi^2 \chi^2-type theory. If the interaction kernel contains a linear confining component, its contribution to the self-energy vanishes exactly.

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Elmar P. Biernat, Franz Gross, Teresa Peña, Alfred Stadler. 2012-07-18. Scalar-particle self-energy amplitudes and confinement in Minkowski space. https://doi.org/10.1007/s00601-012-0491-2

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