87 research outputs found
Numerical Multi-Loop Calculations via Finite Integrals and One-Mass EW-QCD Drell-Yan Master Integrals
We study a recently-proposed approach to the numerical evaluation of
multi-loop Feynman integrals using available sector decomposition programs. As
our main example, we consider the two-loop integrals for the
corrections to Drell-Yan lepton production with up to one massive vector boson
in physical kinematics. As a reference, we evaluate these planar and non-planar
integrals by the method of differential equations through to weight five.
Choosing a basis of finite integrals for the numerical evaluation with SecDec3
leads to tremendous performance improvements and renders the otherwise
problematic seven-line topologies numerically accessible. As another example,
basis integrals for massless QCD three loop form factors are evaluated with
FIESTA4. Here, employing a basis of finite integrals results in an overall
speedup of more than an order of magnitude.Comment: 24 pages, 1 figure, 4 tables, 2 ancillary files with analytical
results; in v2: minor improvements in the text with additional references
added. v2 is the version published in JHE
A novel approach to integration by parts reduction
Integration by parts reduction is a standard component of most modern
multi-loop calculations in quantum field theory. We present a novel strategy
constructed to overcome the limitations of currently available reduction
programs based on Laporta's algorithm. The key idea is to construct algebraic
identities from numerical samples obtained from reductions over finite fields.
We expect the method to be highly amenable to parallelization, show a low
memory footprint during the reduction step, and allow for significantly better
run-times.Comment: 4 pages. Version 2 is the final, published version of this articl
On the Limitations of the Color Dipole Picture
We discuss two aspects of the color dipole picture of high energy
photon-proton scattering. First we present bounds on various ratios of deep
inelastic structure functions resulting from the dipole picture that, together
with the measured data, can be used to restrict the kinematical range of its
applicability. The second issue that we address is the choice of energy
variable in the dipole-proton cross section.Comment: 6 pages; talk presented by C.E. at 12th International Conference on
Elastic and Diffractive Scattering (EDS07), DESY Hamburg, May 200
The Complete Two-Loop Integrated Jet Thrust Distribution In Soft-Collinear Effective Theory
In this work, we complete the calculation of the soft part of the two-loop
integrated jet thrust distribution in e+e- annihilation. This jet mass
observable is based on the thrust cone jet algorithm, which involves a veto
scale for out-of-jet radiation. The previously uncomputed part of our result
depends in a complicated way on the jet cone size, r, and at intermediate
stages of the calculation we actually encounter a new class of multiple
polylogarithms. We employ an extension of the coproduct calculus to
systematically exploit functional relations and represent our results
concisely. In contrast to the individual contributions, the sum of all global
terms can be expressed in terms of classical polylogarithms. Our explicit
two-loop calculation enables us to clarify the small r picture discussed in
earlier work. In particular, we show that the resummation of the logarithms of
r that appear in the previously uncomputed part of the two-loop integrated jet
thrust distribution is inextricably linked to the resummation of the non-global
logarithms. Furthermore, we find that the logarithms of r which cannot be
absorbed into the non-global logarithms in the way advocated in earlier work
have coefficients fixed by the two-loop cusp anomalous dimension. We also show
that, given appropriate L-loop contributions to the integrated hemisphere soft
function, one can straightforwardly predict a number of potentially large
logarithmic contributions at L loops not controlled by the factorization
theorem for jet thrust.Comment: 52 pages, 5 figures; in v2: incorporated referee suggestions in text,
including additional figures and footnotes for the purpose of clarification.
v2 is the version published in PR
The Two-Loop Master Integrals for
We compute the full set of two-loop Feynman integrals appearing in massless
two-loop four-point functions with two off-shell legs with the same invariant
mass. These integrals allow to determine the two-loop corrections to the
amplitudes for vector boson pair production at hadron colliders, , and thus to compute this process to next-to-next-to-leading order
accuracy in QCD. The master integrals are derived using the method of
differential equations, employing a canonical basis for the integrals. We
obtain analytical results for all integrals, expressed in terms of multiple
polylogarithms. We optimize our results for numerical evaluation by employing
functions which are real valued for physical scattering kinematics and allow
for an immediate power series expansion.Comment: 26 pages, results included as ancillary files. v2: minor typos
corrected, references added, published on JHE
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