Weinberg's theorem for -scattering, including the Adler zero at threshold in the chiral limit, is analytically proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0 and 2 scattering lengths are derived in exact agreement with Weinberg's low energy results. Our proof applies to alternative quark formulations including the Hamiltonian and Euclidean space Dyson-Schwinger approaches. Finally, the threshold -scattering amplitudes are calculated using the DysonSchwinger equations in the rainbow-ladder truncation, confirming the formal derivation.
Assuming a Gaussian approximation for the QCD gluodynamics, all the
nonperturbative physics can be encoded into two parameters: the gluon
correlation length $T_g$ and the gluon condensate $G_2$. These parameters are
sufficient in order to describe the heavy-heavy quark nonperturbative
interaction. In this work we adopt the same framework in order to study
heavy-light bound states in the non-recoil limit. Spontaneous chiral symmetry
breaking and a confining chiral non-invariant interaction emerge quite
naturally. The gap equation is solved and discussed. In particular a relation
between the light quark condensate and $T_g$ is derived. The energy spectrum
for the bound state equation is evaluated and commented.Comment: 15 pages, 2 figures, elsart.st
We introduce a covariant approach in Minkowski space for the description of quarks and mesons that exhibits both chiral-symmetry breaking and confinement. In a simple model for the interquark interaction the quark mass function is obtained and used in the calculation of the pion form factor. We study the effects of the mass function and of the different quark pole contributions on the pion form factor.
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