89,752 research outputs found
On the theory of oscillating airfoils of finite span in subsonic compressible flow
The problem of oscillating lifting surface of finite span in subsonic compressible flow is reduced to an integral equation. The kernel of the integral equation is approximated by a simpler expression, on the basis of the assumption of sufficiently large aspect ratio. With this approximation the double integral occurring in the formulation of the problem is reduced to two single integrals, one of which is taken over the chord and the other over the span of the lifting surface. On the basis of this reduction the three-dimensional problem appears separated into two two-dimensional problems, one of them being effectively the problem of two-dimensional flow and the other being the problem of spanwise circulation distribution. Earlier results concerning the oscillating lifting surface of finite span in incompressible flow are contained in the present more general results
Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
We provide a simple analytic formula for the two-loop six-point ratio
function of planar N = 4 super Yang-Mills theory. This result extends the
analytic knowledge of multi-loop six-point amplitudes beyond those with maximal
helicity violation. We make a natural ansatz for the symbols of the relevant
functions appearing in the two-loop amplitude, and impose various consistency
conditions, including symmetry, the absence of spurious poles, the correct
collinear behaviour, and agreement with the operator product expansion for
light-like (super) Wilson loops. This information reduces the ansatz to a small
number of relatively simple functions. In order to fix these parameters
uniquely, we utilize an explicit representation of the amplitude in terms of
loop integrals that can be evaluated analytically in various kinematic limits.
The final compact analytic result is expressed in terms of classical
polylogarithms, whose arguments are rational functions of the dual conformal
cross-ratios, plus precisely two functions that are not of this type. One of
the functions, the loop integral \Omega^{(2)}, also plays a key role in a new
representation of the remainder function R_6^{(2)} in the maximally helicity
violating sector. Another interesting feature at two loops is the appearance of
a new (parity odd) \times (parity odd) sector of the amplitude, which is absent
at one loop, and which is uniquely determined in a natural way in terms of the
more familiar (parity even) \times (parity even) part. The second
non-polylogarithmic function, the loop integral \tilde{\Omega}^{(2)},
characterizes this sector. Both \Omega^{(2)} and tilde{\Omega}^{(2)} can be
expressed as one-dimensional integrals over classical polylogarithms with
rational arguments.Comment: 51 pages, 4 figures, one auxiliary file with symbols; v2 minor typo
correction
Differential equations for multi-loop integrals and two-dimensional kinematics
In this paper we consider multi-loop integrals appearing in MHV scattering
amplitudes of planar N=4 SYM. Through particular differential operators which
reduce the loop order by one, we present explicit equations for the two-loop
eight-point finite diagrams which relate them to massive hexagons. After the
reduction to two-dimensional kinematics, we solve them using symbol technology.
The terms invisible to the symbols are found through boundary conditions coming
from double soft limits. These equations are valid at all-loop order for double
pentaladders and allow to solve iteratively loop integrals given lower-loop
information. Comments are made about multi-leg and multi-loop integrals which
can appear in this special kinematics. The main motivation of this
investigation is to get a deeper understanding of these tools in this
configuration, as well as for their application in general four-dimensional
kinematics and to less supersymmetric theories.Comment: 25 pages, 7 figure
Traintrack Calabi-Yaus from Twistor Geometry
We describe the geometry of the leading singularity locus of the traintrack
integral family directly in momentum twistor space. For the two-loop case,
known as the elliptic double box, the leading singularity locus is a genus one
curve, which we obtain as an intersection of two quadrics in .
At three loops, we obtain a K3 surface which arises as a branched surface over
two genus-one curves in . We present an
analysis of its properties. We also discuss the geometry at higher loops and
the supersymmetrization of the construction.Comment: 23 pages, 5 figure
Electroweak Effects in the Double Dalitz Decay
We investigate the double Dalitz decays on the
basis of the effective Hamiltonian for the transition ,
and universal form factors suggested by QCD. The correlated mass spectrum of
the two lepton pairs in the decay is derived in
an efficient way, using a QED result for meson decays mediated by two virtual
photons: . A comment is made
on the correlation between the planes of the two lepton pairs. The conversion
ratios are estimated to be , and are enhanced relative to pure QED by .Comment: Two typos corrected: (i) factor inserted in
Eq. (14), (ii) co-ordinate labels inserted in Figs. 1-3. To
appear in Physics Letters
Radiative Corrections to Double Dalitz Decays: Effects on Invariant Mass Distributions and Angular Correlations
We review the theory of meson decays to two lepton pairs, including the cases
of identical as well as non-identical leptons, as well as CP-conserving and
CP-violating couplings. A complete lowest-order calculation of QED radiative
corrections to these decays is discussed, and comparisons of predicted rates
and kinematic distributions between tree-level and one-loop-corrected
calculations are presented for both pi-zero and K-zero decays.Comment: 25 pages, 18 figures, added figures and commentar
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