94 research outputs found
Dispersive and chiral symmetry constraints on the light meson form factors
The form factors of the light pseudoscalar mesons are investigated in a
dispersive formalism based on hadronic unitarity, analyticity and the OPE
expansion of the QCD Green functions. We propose generalizations of the
original mathematical techniques, suitable for including additional low energy
information provided by experiment or Chiral Perturbation Theory (CHPT). The
simultaneous treatment of the electroweak form factors of the and
mesons allows us to test the consistency with QCD of a low energy CHPT theorem.
By applying the formalism to the pion electromagnetic form factor, we derive
quite strong constraints on the higher Taylor coefficients at zero momentum,
using information about the phase and the modulus of the form factor along a
part of the unitarity cut.Comment: 29 pages, 3 figure
Analytic continuation and perturbative expansions in QCD
Starting from the divergence pattern of perturbative quantum chromodynamics,
we propose a novel, non-power series replacing the standard expansion in powers
of the renormalized coupling constant . The coefficients of the new
expansion are calculable at each finite order from the Feynman diagrams, while
the expansion functions, denoted as , are defined by analytic
continuation in the Borel complex plane. The infrared ambiguity of perturbation
theory is manifest in the prescription dependence of the . We prove
that the functions have branch point and essential singularities at
the origin of the complex -plane and their perturbative expansions in
powers of are divergent, while the expansion of the correlators in terms of
the set is convergent under quite loose conditionsComment: 18 pages, latex, 5 figures in EPS forma
Comment on "Infrared freezing of Euclidean QCD observables"
Recently, P. M. Brooks and C.J. Maxwell [Phys. Rev. D{\bf 74} 065012 (2006)]
claimed that the Landau pole of the one-loop coupling at is
absent from the leading one-chain term in a skeleton expansion of the Euclidean
Adler function. Moreover, in this approximation one has continuity
along the Euclidean axis and a smooth infrared freezing, properties known to be
satisfied by the "true" Adler function. We show that crucial in the derivation
of these results is the use of a modified Borel summation, which leads
simultaneously to the loss of another fundamental property of the true Adler
function: the analyticity implied by the K\"allen-Lehmann representation
- …