2,035 research outputs found
Replica Fourier Transforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices
The analysis of objects living on ultrametric trees, in particular the
block-diagonalization of 4-replica matrices ,
is shown to be dramatically simplified through the introduction of properly
chosen operations on those objects. These are the Replica Fourier Transforms on
ultrametric trees. Those transformations are defined and used in the present
work.Comment: Latex file, 14 page
Perturbative QCD factorization of and
We prove factorization theorem for the processes and
to leading twist in the covariant gauge by means of the
Ward identity. Soft divergences cancel and collinear divergences are grouped
into a pion wave function defined by a nonlocal matrix element. The gauge
invariance and universality of the pion wave function are confirmed. The proof
is then extended to the exclusive meson decays and
in the heavy quark limit. It is shown that a light-cone
meson wave function, though absorbing soft dynamics, can be defined in an
appropriate frame. Factorization of the decay in
space, being parton transverse momenta, is briefly discussed. We comment
on the extraction of the leading-twist pion wave function from experimental
data.Comment: 21 pages in Latex file, version to appear in Phys. Rev.
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