587 research outputs found
Expansion around half-integer values, binomial sums and inverse binomial sums
I consider the expansion of transcendental functions in a small parameter
around rational numbers. This includes in particular the expansion around
half-integer values. I present algorithms which are suitable for an
implementation within a symbolic computer algebra system. The method is an
extension of the technique of nested sums. The algorithms allow in addition the
evaluation of binomial sums, inverse binomial sums and generalizations thereof.Comment: 21 page
The infrared structure of e+ e- --> 3 jets at NNLO reloaded
This paper gives detailed information on the structure of the infrared
singularities for the process e+ e- --> 3 jets at next-to-next-to-leading order
in perturbation theory. Particular emphasis is put on singularities associated
to soft gluons. The knowledge of the singularity structure allows the
construction of appropriate subtraction terms, which in turn can be implemented
into a numerical Monte Carlo program.Comment: 59 pages, additional comments added, version to be publishe
One-loop N-point equivalence among negative-dimensional, Mellin-Barnes and Feynman parametrization approaches to Feynman integrals
We show that at one-loop order, negative-dimensional, Mellin-Barnes' (MB) and
Feynman parametrization (FP) approaches to Feynman loop integrals calculations
are equivalent. Starting with a generating functional, for two and then for
-point scalar integrals we show how to reobtain MB results, using
negative-dimensional and FP techniques. The point result is valid for
different masses, arbitrary exponents of propagators and dimension.Comment: 11 pages, LaTeX. To be published in J.Phys.
Periods and Feynman integrals
We consider multi-loop integrals in dimensional regularisation and the
corresponding Laurent series. We study the integral in the Euclidean region and
where all ratios of invariants and masses have rational values. We prove that
in this case all coefficients of the Laurent series are periods.Comment: 22 pages, appendix added, version to be publishe
Timelike Dipole-Antenna Showers with Massive Fermions
We present a complete formalism for final-state (timelike) dipole-antenna
showers including fermion masses, but neglecting polarization and finite-width
effects. We make several comparisons of tree-level expansions of this shower
algorithm to fixed-order matrix elements for hadronic Z decays, up to and
including Z to 6 partons, to which the algorithm can be consistently matched
over all of phase space. We also compare to analytical resummations at the NLL
level. The shower algorithm has been implemented in the publicly available
VINCIA plugin to the PYTHIA 8 event generator, which enables us to compare to
experimental data at the fully hadronized level. We also include comparisons to
selected observables in b-tagged Z decays.Comment: 50 pages; v3: corrected typo in eq.(35
Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
We evaluate the planar two-loop QCD diagrams contributing to the leading
color coefficient of the heavy-quark pair production cross section, in the
quark-antiquark annihilation channel. We obtain the leading color coefficient
in an analytic form, in terms of one- and two-dimensional harmonic
polylogarithms of maximal weight 4. The result is valid for arbitrary values of
the Mandelstam invariants s and t, and of the heavy-quark mass m. Our findings
agree with previous analytic results in the small-mass limit and numerical
results for the exact amplitude.Comment: 30 pages, 5 figures. Version accepted by JHE
Squeezing the limit: Quantum benchmarks for the teleportation and storage of squeezed states
We derive fidelity benchmarks for the quantum storage and teleportation of
squeezed states of continuous variable systems, for input ensembles where the
degree of squeezing is fixed, no information about its orientation in phase
space is given, and the distribution of phase space displacements is a
Gaussian. In the limit where the latter becomes flat, we prove analytically
that the maximal classical achievable fidelity (which is 1/2 without squeezing,
for ) is given by , vanishing when the degree of squeezing
diverges. For mixed states, as well as for general distributions of
displacements, we reduce the determination of the benchmarks to the solution of
a finite-dimensional semidefinite program, which yields accurate, certifiable
bounds thanks to a rigorous analysis of the truncation error. This approach may
be easily adapted to more general ensembles of input states.Comment: 19 pages, 4figure
Efficient GPU Offloading with OpenMP for a Hyperbolic Finite Volume Solver on Dynamically Adaptive Meshes
We identify and show how to overcome an OpenMP bottleneck in the administration of GPU memory. It arises for a wave equation solver on dynamically adaptive block-structured Cartesian meshes, which keeps all CPU threads busy and allows all of them to offload sets of patches to the GPU. Our studies show that multithreaded, concurrent, non-deterministic access to the GPU leads to performance breakdowns, since the GPU memory bookkeeping as offered through OpenMP’s map clause, i.e., the allocation and freeing, becomes another runtime challenge besides expensive data transfer and actual computation. We, therefore, propose to retain the memory management responsibility on the host: A caching mechanism acquires memory on the accelerator for all CPU threads, keeps hold of this memory and hands it out to the offloading threads upon demand. We show that this user-managed, CPU-based memory administration helps us to overcome the GPU memory bookkeeping bottleneck and speeds up the time-to-solution of Finite Volume kernels by more than an order of magnitude
W boson production at hadron colliders: the lepton charge asymmetry in NNLO QCD
We consider the production of W bosons in hadron collisions, and the
subsequent leptonic decay W->lnu_l. We study the asymmetry between the rapidity
distributions of the charged leptons, and we present its computation up to the
next-to-next-to-leading order (NNLO) in QCD perturbation theory. Our
calculation includes the dependence on the lepton kinematical cuts that are
necessarily applied to select W-> lnu_l events in actual experimental analyses
at hadron colliders. We illustrate the main differences between the W and
lepton charge asymmetry, and we discuss their physical origin and the effect of
the QCD radiative corrections. We show detailed numerical results on the charge
asymmetry in ppbar collisions at the Tevatron, and we discuss the comparison
with some of the available data. Some illustrative results on the lepton charge
asymmetry in pp collisions at LHC energies are presented.Comment: 37 pages, 21 figure
Feynman graph polynomials
The integrand of any multi-loop integral is characterised after Feynman
parametrisation by two polynomials. In this review we summarise the properties
of these polynomials. Topics covered in this article include among others:
Spanning trees and spanning forests, the all-minors matrix-tree theorem,
recursion relations due to contraction and deletion of edges, Dodgson's
identity and matroids.Comment: 35 pages, references adde
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