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SymBuild: a package for the computation of integrable symbols in scattering amplitudes
High Energy Physics - Theory · Submitted 13 Sep 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim By using Gr\"obner bases, implementing various simplifications and by the potential utilization of the C++ program SpaSM, integrable symbols in a large class of alphabets (including roots) can be computed to high weights.
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The abstract, sentence by sentence
The article presents and documents the Mathematica package SymBuild. This package implements the computation and manipulation of integrable symbols appearing in various calculations in high-energy scattering amplitudes. By using Gr\"obner bases, implementing various simplifications and by the potential utilization of the C++ program SpaSM, integrable symbols in a large class of alphabets (including roots) can be computed to high weights.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The article presents and documents the Mathematica package SymBuild. | contribution 1.00 | 0.87 | 0.16 | asserted 1.00 |
| s1 | This package implements the computation and manipulation of integrable symbols appearing in various calculations in high-energy scattering amplitudes. | contribution 0.98 | 0.84 | 0.24 | asserted 1.00 |
| s2 | By using Gr\"obner bases, implementing various simplifications and by the potential utilization of the C++ program SpaSM, integrable symbols in a large class of alphabets (including roots) can be computed to high weights. | method 1.00 | 0.80 | 0.16 | hedged possibility 0.53 |
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The paper
Original abstract
The article presents and documents the Mathematica package SymBuild. This package implements the computation and manipulation of integrable symbols appearing in various calculations in high-energy scattering amplitudes. By using Gr\"obner bases, implementing various simplifications and by the potential utilization of the C++ program SpaSM, integrable symbols in a large class of alphabets (including roots) can be computed to high weights.
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References
How the literature uses it
9 arXiv papers cite this in 10 sentences
Papers citing it · 2 sentences without a confident label
Uses its method or tool 7 papers
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The construction of integrable polylogarithmic functions modulo transcendental constants, also known as symbols, has been automated in the package [ref] , and applying it to our case yields the function counts shown on the first line of table [ref].
An Exceptional Cluster Algebra for Higgs plus Jet Production · Adjacent $G_2$ polylogarithmic function counts · 1.00
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We take the union of the logarithms of the two alphabets and, as already mentioned in subsection [ref], find linear relations between them e.g. with (a homemade version of) the approach [ref] .
Novel cluster-algebraic letters for 5- and 6-point QCD processes · Comparison with CITEMARK81Z and new 6-point massless letters · 0.98
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The full space of integrable even/odd weight four pentagon functions (with first and second entry conditions applied, and independent on $W_31$) is 3691- and 1080-dimensional, respectively[The integrable symbols were constructed by means of the Mathematica package SymBuild [ref] .].
The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity · Main result for the remainder function at two loops · 0.98
What it cites · 23 sentences without a confident label
Uses the method or tool of 1 paper
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In the iterative notation, introduced by Dixon et al. [ref] , the symbols are written as[We let the index $j_L$ label the basis elements as $_L=span{S_j_L^(L)}_j_L=1^_L$.]
Hexagon functions and the three-loop remainder function · Iterative notation · 0.84
Cites as background 5 papers
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We shall refrain from presenting a fully self-contained introduction to symbols here and refer to the article [ref] instead.
From polygons and symbols to polylogarithmic functions · Setup and notation · 1.00
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However, once it was realized that a large class of Feynman integrals are given by iterated integrals which in many situations can be efficiently described via their[ These symbol techniques have been used in the mathematical community much earlier, see for example [ref] .] symbols [ref] , further progress became possible.
Classical Polylogarithms for Amplitudes and Wilson Loops · Introduction · 0.99
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For instance, the questions of whether it is possible to devise a formula that would compute the number of integrable symbols of arbitrarily large weight $L$ for a given arbitrary alphabet (even one that is purely rational) is, to our knowledge, unanswered outside of the cases studied in [ref] .
Multiple zeta values and periods of moduli spaces $\mathfrak{M}_{0,n}$ · Conclusions and Outlook · 0.81
Discussion
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