51,436 research outputs found
The Pentabox Master Integrals with the Simplified Differential Equations approach
We present the calculation of massless two-loop Master Integrals relevant to
five-point amplitudes with one off-shell external leg and derive the complete
set of planar Master Integrals with five on-mass-shell legs, that contribute to
many amplitudes of interest at the LHC, as for instance three jet
production, jets etc., based on the Simplified Differential
Equations approach.Comment: Revised version accepted for publication in JHEP. Ancillary files
with results can be downloaded from
https://www.dropbox.com/s/90iiqfcazrhwtso/results.tgz?dl=
Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions
We describe the calculation of all planar master integrals that are needed
for the computation of NNLO QCD corrections to the production of two off-shell
vector bosons in hadron collisions. The most complicated representatives of
integrals in this class are the two-loop four-point functions where two
external lines are on the light-cone and two other external lines have
different invariant masses. We compute these and other relevant integrals
analytically using differential equations in external kinematic variables and
express our results in terms of Goncharov polylogarithms. The case of two equal
off-shellnesses, recently considered in Ref. [1], appears as a particular case
of our general solution.Comment: 28 pages, many figures; ancillary files included with arXiv
submissio
Geometric factors in the Bohr--Rosenfeld analysis of the measurability of the electromagnetic field
The Geometric factors in the field commutators and spring constants of the
measurement devices in the famous analysis of the measurability of the
electromagnetic field by Bohr and Rosenfeld are calculated using a
Fourier--Bessel method for the evaluation of folding integrals, which enables
one to obtain the general geometric factors as a Fourier--Bessel series. When
the space region over which the factors are defined are spherical, the
Fourier--Bessel series terms are given by elementary functions, and using the
standard Fourier-integral method of calculating folding integrals, the
geometric factors can be evaluated in terms of manageable closed-form
expressions.Comment: 21 pages, REVTe
Flatness of tracer density profile produced by a point source in turbulence
The average concentration of tracers advected from a point source by a multivariate normal velocity field is shown to deviate from a Gaussian profile. The flatness (kurtosis) is calculated using an asymptotic series expansion valid for velocity fields with short correlation times or weak space dependence. An explicit formula for the excess flatness at first order demonstrates maximum deviation from a Gaussian profile at time t of the order of five times the velocity correlation time, with a t–1 decay to the Gaussian value at large times. Monotonically decaying forms of the velocity time correlation function are shown to yield negative values for the first order excess flatness, but positive values can result when the correlation function has an oscillatory tail
Two-loop Master Integrals with the Simplified Differential Equations approach
We calculate the complete set of two-loop Master Integrals with two off
mass-shell legs with massless internal propagators, that contribute to
amplitudes of diboson production at the LHC. This is done with the
Simplified Differential Equations approach to Master Integrals, which was
recently proposed by one of the authors.Comment: 4 figures, 6 ancillary files. Version as published in JHE
Semiclassical Approximations in Phase Space with Coherent States
We present a complete derivation of the semiclassical limit of the coherent
state propagator in one dimension, starting from path integrals in phase space.
We show that the arbitrariness in the path integral representation, which
follows from the overcompleteness of the coherent states, results in many
different semiclassical limits. We explicitly derive two possible semiclassical
formulae for the propagator, we suggest a third one, and we discuss their
relationships. We also derive an initial value representation for the
semiclassical propagator, based on an initial gaussian wavepacket. It turns out
to be related to, but different from, Heller's thawed gaussian approximation.
It is very different from the Herman--Kluk formula, which is not a correct
semiclassical limit. We point out errors in two derivations of the latter.
Finally we show how the semiclassical coherent state propagators lead to
WKB-type quantization rules and to approximations for the Husimi distributions
of stationary states.Comment: 80 pages, 4 figure
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