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Karol Kampf, Jiri Novotny, Jaroslav Trnka
Renormalization and additional degrees of freedom within
the chiral effective theory for spin-1 resonances
Abstract
We study in detail various aspects of the renormalization of the spin-1
resonance propagator in the effective field theory framework. First, we
briefly review the formalisms for the description of spin-1 resonances in
the path integral formulation with the stress on the issue of propagating
degrees of freedom. Then we calculate the one-loop 1-- meson self-energy
within the Resonance chiral theory in the chiral limit using different
methods for the description of spin-one particles, namely the Proca field,
antisymmetric tensor field and the first order formalisms. We discuss in
detail technical aspects of the renormalization procedure which are
inherent to the power-counting non-renormalizable theory and give a formal
prescription for the organization of both the counterterms and
one-particle irreducible graphs. We also construct the corresponding
propagators and investigate their properties. We show that the additional
poles corresponding to the additional one-particle states are generated by
loop corrections, some of which are negative norm ghosts or tachyons. We
count the number of such additional poles and briefly discuss their
physical meaning.
LU TP 09-33
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