462 research outputs found
Systematics of geometric scaling
Using all available data on the deep-inelastic cross-sections at HERA at
x<0.01, we look for geometric scaling of the form \sigma^{\gamma^*p}(\tau)
where the scaling variable \tau behaves alternatively like \log(Q^2)-\lambda Y,
as in the original definition, or \log(Q^2)-\lambda \sqrt{Y}, which is
suggested by the asymptotic properties of the Balitsky-Kovchegov (BK) equation
with running QCD coupling constant. A ``Quality Factor'' (QF) is defined,
quantifying the phenomenological validity of the scaling and the uncertainty on
the intercept \lambda. Both choices have a good QF, showing that the second
choice is as valid as the first one, predicted for fixed coupling constant. A
comparison between the QCD asymptotic predictions and data is made and the QF
analysis shows that the agreement can be reached, provided going beyond leading
logarithmic accuracy for the BK equation.Comment: 4 pages, 4 figure
Universality and tree structure of high energy QCD
Using non-trivial mathematical properties of a class of nonlinear evolution
equations, we obtain the universal terms in the asymptotic expansion in
rapidity of the saturation scale and of the unintegrated gluon density from the
Balitsky-Kovchegov equation. These terms are independent of the initial
conditions and of the details of the equation. The last subasymptotic terms are
new results and complete the list of all possible universal contributions.
Universality is interpreted in a general qualitative picture of high energy
scattering, in which a scattering process corresponds to a tree structure
probed by a given source.Comment: 4 pages, 3 figure
Hamiltonian solutions of the 3-body problem in (2+1)-gravity
We present a full study of the 3-body problem in gravity in flat
(2+1)-dimensional space-time, and in the nonrelativistic limit of small
velocities. We provide an explicit form of the ADM Hamiltonian in a regular
coordinate system and we set up all the ingredients for canonical quantization.
We emphasize the role of a U(2) symmetry under which the Hamiltonian is
invariant and which should generalize to a U(N-1) symmetry for N bodies. This
symmetry seems to stem from a braid group structure in the operations of
looping of particles around each other, and guarantees the single-valuedness of
the Hamiltonian. Its role for the construction of single-valued energy
eigenfunctions is also discussed.Comment: 25 pages, no figure. v2: some calculation details removed to make the
paper more concise (see v1 for the longer version), minor correction in a
formula in the section on quantization, references added; results and
conclusions unchange
Confronting next-leading BFKL kernels with proton structure function data
We propose a phenomenological study of the Balitsky-Fadin-Kuraev-Lipatov
(BFKL) approach applied to the data on the proton structure function F_2
measured at HERA in the small-x_{Bjorken} region. In a first part we use a
simplified ``effective kernel'' approximation leading to few-parameter fits of
F_2. It allows for a comparison between leading-logs (LO) and next-to-leading
logs (NLO) BFKL approaches in the saddle-point approximation, using known
resummed NLO-BFKL kernels. The NLO fits give a qualitatively satisfactory
account of the running coupling constant effect but quantitatively the chi
squared remains sizeably higher than the LO fit at fixed coupling. In a second
part, a comparison of theory and data through a detailed analysis in Mellin
space (x_{Bjorken} -> omega) leads to a more model independent approach to the
resummed NLO-BFKL kernels we consider and points out some necessary
improvements of the extrapolation at higher orders.Comment: 19 pages, 11 figures, minor corrections, one figure improved, LO fit
with reunning coupling constant and references added, conclusions unchange
Geometric scaling as traveling waves
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-
Piscounov (KPP) equation to the problem of high energy evolution of the QCD
amplitudes. We explain how the traveling wave solutions of this equation are
related to geometric scaling, a phenomenon observed in deep-inelastic
scattering experiments. Geometric scaling is for the first time shown to result
from an exact solution of nonlinear QCD evolution equations. Using general
results on the KPP equation, we compute the velocity of the wave front, which
gives the full high energy dependence of the saturation scale.Comment: 4 pages, 1 figure. v2: references adde
On the linearization of the generalized Ermakov systems
A linearization procedure is proposed for Ermakov systems with frequency
depending on dynamic variables. The procedure applies to a wide class of
generalized Ermakov systems which are linearizable in a manner similar to that
applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into
this category but others, more generic, systems are also included
Traveling wave fronts and the transition to saturation
We propose a general method to study the solutions to nonlinear QCD evolution
equations, based on a deep analogy with the physics of traveling waves. In
particular, we show that the transition to the saturation regime of high energy
QCD is identical to the formation of the front of a traveling wave. Within this
physical picture, we provide the expressions for the saturation scale and the
gluon density profile as a function of the total rapidity and the transverse
momentum. The application to the Balitsky-Kovchegov equation for both fixed and
running coupling constants confirms the effectiveness of this method.Comment: 9 pages, 3 figures, references adde
Noisy traveling waves: effect of selection on genealogies
For a family of models of evolving population under selection, which can be
described by noisy traveling wave equations, the coalescence times along the
genealogical tree scale like , where is the size of the
population, in contrast with neutral models for which they scale like . An
argument relating this time scale to the diffusion constant of the noisy
traveling wave leads to a prediction for which agrees with our
simulations. An exactly soluble case gives trees with statistics identical to
those predicted for mean-field spin glasses in Parisi's theory.Comment: 4 pages, 2 figures New version includes more numerical simulations
and some rewriting of the text presenting our result
Lie symmetries for two-dimensional charged particle motion
We find the Lie point symmetries for non-relativistic two-dimensional charged
particle motion. These symmetries comprise a quasi-invariance transformation, a
time-dependent rotation, a time-dependent spatial translation and a dilation.
The associated electromagnetic fields satisfy a system of first-order linear
partial differential equations. This system is solved exactly, yielding four
classes of electromagnetic fields compatible with Lie point symmetries
Prompt neutrino fluxes from atmospheric charm
We calculate the prompt neutrino flux from atmospheric charm production by
cosmic rays, using the dipole picture in a perturbative QCD framework, which
incorporates the parton saturation effects present at high energies. We compare
our results with the next-to-leading order perturbative QCD result and find
that saturation effects are large for neutrino energies above 10^6 GeV, leading
to a substantial suppression of the prompt neutrino flux. We comment on the
range of prompt neutrino fluxes due to theoretical uncertainties.Comment: 13 pages with 11 figures; expanded discussion, added references,
version to be published in Phys. Rev.
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