A
bstract
In this article we present a neural network based model to emulate matrix elements. This model improves on existing methods by taking advantage of the known factorisation properties of ...matrix elements. In doing so we can control the behaviour of simulated matrix elements when extrapolating into more singular regions than the ones used for training the neural network. We apply our model to the case of leading-order jet production in
e
+
e
−
collisions with up to five jets. Our results show that this model can reproduce the matrix elements with errors below the one-percent level on the phase-space covered during fitting and testing, and a robust extrapolation to the parts of the phase-space where the matrix elements are more singular than seen at the fitting stage.
In this paper, we present an implementation of the harmonic polylogarithm of Remiddi and Vermaseren E. Remiddi, J.A.M. Vermaseren, Int. J. Modern Phys. A 15 (2000) 725,
hep-ph/9905237 for ...Mathematica. It contains an implementation of the product algebra, the derivative properties, series expansion and numerical evaluation. The analytic continuation has been treated carefully, allowing the user to keep the control over the definition of the sign of the imaginary parts. Many options enables the user to adapt the behavior of the package to his specific problem.
Program title: HPL
Catalogue identifier:ADWX
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/ADWX
Program obtained from: CPC Program Library, Queen's University of Belfast, N. Ireland
Licensing provisions:none
Programming language: Mathematica
No. of lines in distributed program, including test data, etc.:13 310
No. of bytes in distributed program, including test data, etc.: 1 990 584
Distribution format: tar.gz
Computer:all computers running Mathematica
Operating systems:operating systems running Mathematica
Nature of problem: Computer algebraic treatment of the harmonic polylogarithms which appear in the evaluation of Feynman diagrams
Solution method: Mathematica implementation
A
bstract
In this article we present an emulation strategy for one-loop matrix elements. This strategy is based on the factorisation properties of matrix elements and is an extension of the work ...presented in 1. We show that a percent-level accuracy can be achieved even for large multiplicity processes. The point accuracy obtained is such that it dwarfs the statistical accuracy of the training sample which allows us to use our model to augment the size of the training set by orders of magnitude without additional evaluations of expensive one-loop matrix elements.
A
bstract
In this article we present a method for automatic integration of parametric integrals over the unit hypercube using a neural network. The method fits a neural network to the primitive of ...the integrand using a loss function designed to minimize the difference between multiple derivatives of the network and the function to be integrated. We apply this method to two example integrals resulting from the sector decomposition of a one-loop and two-loop scalar integrals. Our method can achieve per-mil and percent accuracy for these integrals over a range of invariant values. Once the neural network is fitted, the evaluation of the integral is between 40 and 125 times faster than the usual numerical integration method for our examples, and we expect the speed gain to increase with the complexity of the integrand.
We present the
Mathematica package
HypExp which allows to expand hypergeometric functions
F
J
−
1
J
around integer parameters to arbitrary order. At this, we apply two methods, the first one being ...based on an integral representation, the second one on the nested sums approach. The expansion works for both symbolic argument
z and unit argument. We also implemented new classes of integrals that appear in the first method and that are, in part, yet unknown to
Mathematica.
Title of program:HypExp
Catalogue identifier:ADXF_v1_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/ADXF_v1_0
Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland
Licence:none
Computers:Computers running
Mathematica under
Linux or
Windows
Operating system:
Linux, Windows
Program language:
Mathematica
No. of bytes in distributed program, including test data, etc.:739 410
No. of lines in distributed program, including test data, etc.:89 747
Distribution format:tar.gz
Other package needed:the package
HPL, included in the distribution
External file required:none
Nature of the physical problem:Expansion of hypergeometric functions around integer-valued parameters. These are needed in the context of dimensional regularization for loop and phase space integrals.
Method of solution:Algebraic manipulation of nested sums and integral representation.
Restrictions on complexity of the problem:Limited by the memory available
Typical running time:Strongly depending on the problem and the availability of libraries.
In this paper we present the package S@M (Spinors@Mathematica) which implements the spinor-helicity formalism in Mathematica. The package allows the use of complex-spinor algebra along with the ...multi-purpose features of Mathematica. The package defines the spinor objects with their basic properties along with functions to manipulate them. It also offers the possibility of evaluating the spinorial objects numerically at every computational step. The package is therefore well suited to be used in the context of on-shell technology, in particular for the evaluation of scattering amplitudes at tree- and loop-level.
Program title: S@M
Catalogue identifier: AEBF_v1_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/AEBF_v1_0.html
Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence,
http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 14 404
No. of bytes in distributed program, including test data, etc.: 77 536
Distribution format: tar.gz
Programming language: Mathematica
Computer: All computers running Mathematica
Operating system: Any system running Mathematica
Classification: 4.4, 5, 11.1
Nature of problem: Implementation of the spinor-helicity formalism
Solution method: Mathematica implementation
Running time: The notebooks provided with the package take only a few seconds to run.
In this Letter we continue the calculation of master integrals for massless three-loop form factors by giving analytical results for those integrals which are relevant for the fermionic contributions ...proportional to NF2, NF⋅N, and NF/N. Working in dimensional regularisation, we express one of the integrals in a closed form which is exact to all orders in ϵ, containing Γ-functions and hypergeometric functions of unit argument. In all other cases we derive multiple Mellin–Barnes representations from which the coefficients of the Laurent expansion in ϵ are extracted in an analytical form. To obtain the finite part of the three-loop quark and gluon form factors, all coefficients through transcendentality six in the Riemann ζ-function have to be included.
NLO high multiplicity processes Maître, D
Journal of physics. Conference series,
05/2015, Letnik:
608, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this presentation some aspects of Next-to-Leading Order (NLO) calculations in QCD are presented. The focus is brought to aspects of such calculations for processes involving a high final-state ...particle multiplicity.
We compute the two-loop corrections to the massless quark form factor γ∗→qq¯ and gluon form factor H→gg to all orders in the dimensional regularisation parameter ε=(4−d)/2. The two-loop contributions ...to the form factors are reduced to linear combinations of master integrals, which are computed in a closed form, expressed as Γ-functions and generalised hypergeometric functions of unit argument. Using the newly developed HypExp-package, these can be expanded to any desired order, yielding Laurent expansions in ε. We provide expansions of the form factors to order ε2, as required for ultraviolet renormalisation and infrared factorisation of the three-loop form factors.
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