Z.Phys. A354 (1996) 421-429 We analyze the analytic structure of meson propagators in the
Nambu--Jona-Lasinio model with a proper-time regulator. We show that the
regulator produces unphysical ...complex singularities. As a result the naive use
of the Wick rotation is no longer allowed. Formulas involving integration over
mesonic momenta, such as meson-loop contributions or dispersion relations for
meson Green's functions, cannot be written in usual forms.
Instead of using a simple reggeon-exchange model, we provide a model-independent estimate of high-energy contribution to the Adler-Weisberger sum-rule. Results and conclusions of the paper remain ...unchanged.
We analyze the analytic structure of meson propagators in the Nambu--Jona-Lasinio model with a proper-time regulator. We show that the regulator produces unphysical complex singularities. As a result ...the naive use of the Wick rotation is no longer allowed. Formulas involving integration over mesonic momenta, such as meson-loop contributions or dispersion relations for meson Green's functions, cannot be written in usual forms.
Nucl.Phys. A608 (1996) 411-436 The effects of meson loops in the vacuum sector of the Nambu--Jona-Lasinio
model are calculated. Using the effective action formalism we take consistently
all ...next-to-leading-order $1 \over \Nc$ terms into account. This leads to a
symmetry-conserving approach, in which all features of spontaneously broken
chiral symmetry, such as the Goldstone theorem, the Gold\-ber\-ger--Treiman and
the Gell-Mann--Oakes--Renner relations are preserved. Contributions to $\langle
\overline{q}q \rangle$ and $F_\pi$ are calculated, and are shown to be
substantial, at the level of $\sim 30\%$, consistent with the $1 \over \Nc$
expansion. The leading nonanalytic terms in the chiral expansion of $\langle
\overline{q}q \rangle$, $F_\pi$ and $m_\pi$ agree have the same form as the
one-loop results of chiral perturbation theory.
The effects of meson loops in the vacuum sector of the Nambu--Jona-Lasinio model are calculated. Using the effective action formalism we take consistently all next-to-leading-order \(1 \over \Nc\) ...terms into account. This leads to a symmetry-conserving approach, in which all features of spontaneously broken chiral symmetry, such as the Goldstone theorem, the Gold\-ber\-ger--Treiman and the Gell-Mann--Oakes--Renner relations are preserved. Contributions to \(\langle \overline{q}q \rangle\) and \(F_\pi\) are calculated, and are shown to be substantial, at the level of \(\sim 30\%\), consistent with the \(1 \over \Nc\) expansion. The leading nonanalytic terms in the chiral expansion of \(\langle \overline{q}q \rangle\), \(F_\pi\) and \(m_\pi\) agree have the same form as the one-loop results of chiral perturbation theory.
PDF