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Sector decomposition in its practical aspect is a constructive method used to evaluate Feynman integrals numerically. We present a new program performing the sector decomposition and integrating the expression afterwards. The program can be also used in order to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin--Barnes representations. The program is parallelizable on modern multicore computers and even on multiple computers. Also we demonstrate some new numerical results for four-loop massless propagator master integrals.
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The program FIESTA has been completely rewritten. Now it can be used not only as a tool to evaluate Feynman integrals numerically, but also to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin-Barnes representations. Other important improvements to the code are complete parallelization (even to multiple computers), high-precision arithmetics (allowing to calculate integrals which were undoable before), new integrators and Speer sectors as a strategy, the possibility to evaluate more general parametric integrals.
Up to the moment there are two known algorithms of sector decomposition: an original private algorithm of Binoth and Heinrich and an algorithm made public lastyear by Bogner and Weinzierl. We present a new program performing the sector decomposition and integrating the expression afterwards. The program takes a set of propagators and a set of indices as input and returns the epsilon-expansion of the corresponding integral.
We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator $M(z,p)$ of the parton fields is a function ${cal M} ( u, -z^2)$ of Lorentz invariants $ u =-(zp)$, the Ioffe time, and the invariant interval $z^2$. This observation allows to extract the Ioffe-time distribution ${cal M} ( u, -z^2)$ from Euclidean separations $z$ accessible on the lattice. Another basic feature is the use of the ratio ${mathfrak M} ( u,-z^2) equiv {cal M} ( u, -z^2)/{cal M} (0, -z^2)$, that allows to eliminate artificial ultraviolet divergence generated by the gauge link for space-like intervals. The remaining $z^2$-dependence of the reduced Ioffe-time distribution ${mathfrak M} ( u,-z^2) $ corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions $f(x,mu^2)$ using matching relations. The $ u$-dependence of ${mathfrak M} ( u,-z^2) $ governs the $x$-dependence of parton densities $f(x,mu^2)$. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.
Euclidean Signed Distance Field (ESDF) is useful for online motion planning of aerial robots since it can easily query the distance and gradient information against obstacles. Fast incrementally built ESDF map is the bottleneck for conducting real-time motion planning. In this paper, we investigate this problem and propose a mapping system called FIESTA to build global ESDF map incrementally. By introducing two independent updating queues for inserting and deleting obstacles separately, and using Indexing Data Structures and Doubly Linked Lists for map maintenance, our algorithm updates as few as possible nodes using a BFS framework. Our ESDF map has high computational performance and produces near-optimal results. We show our method outperforms other up-to-date methods in term of performance and accuracy by both theory and experiments. We integrate FIESTA into a completed quadrotor system and validate it by both simulation and onboard experiments. We release our method as open-source software for the community.
We explore the complete cross-section for the production of unpolarized hadrons in semi-inclusive deep-inelastic scattering up to power-suppressed $mathcal{O}(1/Q^2)$ terms in the Wandzura-Wilczek-type (WW-type) approximation, which consists in systematically assuming that $bar{q}gq$-correlators are much smaller than $bar{q}q$-correlators. Under the applicability of WW-type approximations, certain relations among transverse momentum dependent parton distribution functions (TMDs) and fragmentation functions (FFs) occur which are used to approximate SIDIS cross-section in terms of a smaller subset of TMDs and FFs. We discuss the applicability of the WW-type approximations on the basis of available data.
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