7,268 research outputs found
Discrete scale invariance and complex dimensions
We discuss the concept of discrete scale invariance and how it leads to
complex critical exponents (or dimensions), i.e. to the log-periodic
corrections to scaling. After their initial suggestion as formal solutions of
renormalization group equations in the seventies, complex exponents have been
studied in the eighties in relation to various problems of physics embedded in
hierarchical systems. Only recently has it been realized that discrete scale
invariance and its associated complex exponents may appear ``spontaneously'' in
euclidean systems, i.e. without the need for a pre-existing hierarchy. Examples
are diffusion-limited-aggregation clusters, rupture in heterogeneous systems,
earthquakes, animals (a generalization of percolation) among many other
systems. We review the known mechanisms for the spontaneous generation of
discrete scale invariance and provide an extensive list of situations where
complex exponents have been found. This is done in order to provide a basis for
a better fundamental understanding of discrete scale invariance. The main
motivation to study discrete scale invariance and its signatures is that it
provides new insights in the underlying mechanisms of scale invariance. It may
also be very interesting for prediction purposes.Comment: significantly extended version (Oct. 27, 1998) with new examples in
several domains of the review paper with the same title published in Physics
Reports 297, 239-270 (1998
Status of SM calculations of b > s transitions
We report recent progress in SM calculations of transitions. We
discuss the first NNLL prediction of the branching
ratio, including important additional subtleties due to non-perturbative
corrections and logarithmically-enhanced cut effects, and also recent results
on the inclusive mode . Moreover, new results on
the corresponding exclusive modes are reviewed. Finally, we comment on the
present status of the so-called puzzle in hadronic
transitionsComment: 10 pages, 6 figures, minor changes, published versio
Reconciling the nonrelativistic QCD prediction and the data
It has been a long-standing problem that the rare electromagnetic decay
process is plagued with both large and negative radiative
and relativistic corrections. To date it remains futile to make a definite
prediction to confront with the branching fraction of
recently measured by the \textsf{CLEO-c} and \textsf{BESIII} Collaborations. In
this work, we investigate the joint perturbative and relativistic correction
(i.e. the correction, where denotes the
characteristic velocity of the charm quark inside the ) for this decay
process, which turns out to be very significant. After incorporating the
contribution from this new ingredient, with the reasonable choice of the input
parameters, we are able to account for the measured decay rates in a
satisfactory degree.Comment: 7 pages, 1 figure, version accepted for publication in PRD R
- …