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Register a new userDirect Integration for Multi-leg Amplitudes: Tips, Tricks, and When They Fail
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Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly for multi-particle diagrams. We review a variety of results by the authors in which this method, employed with some care, can compute diagrams of up to eight particles and four loops. We also highlight situations in which this method fails due to an algebraic obstruction. In a large number of cases the obstruction can be associated with a Calabi-Yau manifold.
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One approach to the calculation of cross sections for infrared-safe observables in high energy collisions at next-to-leading order is to perform all of the integrations, including the virtual loop integration, by Monte Carlo numerical integration. In a previous paper, two of us have shown how one can perform such a virtual loop integration numerically after first introducing a Feynman parameter representation. In this paper, we perform the integration directly, without introducing Feynman parameters, after suitably deforming the integration contour. Our example is the N-photon scattering amplitude with a massless electron loop. We report results for N = 6 and N = 8.
In the highly non-equilibrium conditions of laser induced spin dynamics magnetic moments can only be obtained from the spectral information, most commonly from the spectroscopy of semi-core states using the so-called x-ray magnetic circular dichroism (XMCD) sum rules. The validity of the these sum rules in tracking femtosecond spin dynamics remains, however, an open question. Employing the time dependent extension of density functional theory (TD-DFT) we compare spectroscopically obtained moments with those directly calculated from the TD-DFT densities. We find that for experimentally typical pump pulses these two very distinct routes to the spin moment are, for Co and Ni, in excellent agreement, validating the experimental approach. However, for short and intense pulses or high fluence pulses of long duration the XMCD sum rules fail, with errors exceeding 50%. This failure persists only during the pulse and occurs when the pump pulse excites charge out of the $d$-band and into $sp$-character bands, invalidating the semi-core to $d$-state transitions assumed by the XMCD sum rules.
WebFG 2020 is an international challenge hosted by Nanjing University of Science and Technology, University of Edinburgh, Nanjing University, The University of Adelaide, Waseda University, etc. This challenge mainly pays attention to the webly-supervised fine-grained recognition problem. In the literature, existing deep learning methods highly rely on large-scale and high-quality labeled training data, which poses a limitation to their practicability and scalability in real world applications. In particular, for fine-grained recognition, a visual task that requires professional knowledge for labeling, the cost of acquiring labeled training data is quite high. It causes extreme difficulties to obtain a large amount of high-quality training data. Therefore, utilizing free web data to train fine-grained recognition models has attracted increasing attentions from researchers in the fine-grained community. This challenge expects participants to develop webly-supervised fine-grained recognition methods, which leverages web images in training fine-grained recognition models to ease the extreme dependence of deep learning methods on large-scale manually labeled datasets and to enhance their practicability and scalability. In this technical report, we have pulled together the top WebFG 2020 solutions of total 54 competing teams, and discuss what methods worked best across the set of winning teams, and what surprisingly did not help.
We reproduce the two-loop seven-point remainder function in planar, maximally supersymmetric Yang-Mills theory by direct integration of conformally-regulated chiral integrands. The remainder function is obtained as part of the two-loop logarithm of the MHV amplitude, the regularized form of which we compute directly in this scheme. We compare the scheme-dependent anomalous dimensions and related quantities in the conformal regulator with those found for the Higgs regulator.
We explore the relation between resummation and explicit multi-loop calculations for QCD hard-scattering amplitudes. We describe how the factorization properties of amplitudes lead to the exponentiation of double and single poles at each order of perturbation theory. For these amplitudes, previously-observed relations between single and double poles in different 2 to 2 processes can now be interpreted in terms of universal functions associated with external partons and process-dependent anomalous dimensions that describe coherent soft radiation. Catanis proposal for multiple poles in dimensionally-continued amplitudes emerges naturally.
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