1. Meeting

Held on 30th of April 2014 in Weimar, Germany, on the occasion of Loops & Legs in Quantum Field Theory
Participants: S. Borowka, C. Duhr, T. Hahn, G. Heinrich, J. Henn, W. Kilgore, A. von Manteuffel, E. Panzer

Please feel free to add/extend/elaborate on anyone/anything I missed.

What is a graph?

Each entry in the database should define precisely one integral, i.e. subgraphs with contracted/deleted edges are different graphs/entries in the database. The problem of finding a unique identifier/name for a graph is not essential; this may be added later but can probably be supplied by Reduze. Internally, a graph should be described by

  • A list of (internal) edges $[e_1,e_2,\ldots]$
  • Each internal edge $e=[v_1,v_2,n,m]$ connects two vertices $v_1$ and $v_2$ and represents a scalar propagator $(p^2 + m^2)^{-n}$ of mass m raised to the power $n \neq 0$
  • A list $[[v_1,p_1],[v_2,p_2],\ldots]$ assigning external momenta $p_i$ to the vertices $v_i$
  • It was agreed that we should not include tensor integrals (irreducible scalar products…) at first. This restriction to scalar integrals can be relaxed in the future.

How to search?

A convenient and powerful search engine is important. Ideally one could search/filter by graph invariants (number of massive edges, number of loops, number of vertices, …) and also search for a specific graph (by entering an edge list; note that this feature requires a tool for testing graph isomorphism since edges and vertices might be reordered). This should not be a problem and is an (important) technical point.

It is agreed that a picture for a graph is very important to aid search and to make sure that one has found the graph one was looking for. Public tools for automated generation of graph layouts exist (e.g. graphviz).

What to provide?

Subject to availability:

  • Picture of the graph.
  • Links to literature where results on the graph are given. It is agreed that a collection of such links, combined with a powerful search engine, is already in itself of great value.
  • Links to (or directly in the database) analytic results for the corresponding integral. This will save a lot of time and errors when typing in results printed in papers by hand. Any explicit result must clearly specify the conventions and the domain of validity (Euclidean region or explicit statement of the constraints on the kinematic variables where it holds in the physical region).
  • Links to (or in a perfect world supplied/generated automatically by the database from analytic formulae) a program that performs numeric evaluation of the integral.
  • Options to export/download the graph in a format that can directly be input to SecDec/Reduze/…

What about conventions?

Analytic results might be given in many different conventions ($D=4-\varepsilon$ or $D=4-2\varepsilon$, overall pre factors, pre factors per loop, $\Gamma$-functions included or not) and in terms of special functions in varying notation (e.g. HPL have two different conventions). Hence any result should include a uniform section at the beginning defining all the conventions used.

Since changing conventions seems to be rather simple, one could also agree on storing all analytic results inside the database in one fixed common set of conventions. The advantage would be that the user could request the result in any convention he likes (e.g. the database server could run a script to transform from the fixed convention to the desired one).

To ensure correct use of an analytic result, a test case should be supplied in the form: If everything (i.e. implementation of HPL or MPL) is done correctly, then the integral at point (s=…, m =…, …) must evaluate to 1.234…


  • Nobody should be able to completely delete content
  • A history for each entry is desirable (e.g. to see that the entry was corrected on … such that author X can see if he should again check his computation based on the results he downloaded before …), e.g. bug list
  • Each change to the database knows which moderator did it / is responsible
  • Use of the database should be acknowledged by a citation, but furthermore of course the original source of the result must be cited.
  • Box "Checked it" for feedback from (registered!?) users who verified the data in some way (with explanation); would provide some way of estimating the likeliness of errors in the result
  • Check out [http://www.symbolicdata.org] for a possibility of storage
  • A wishlist for (uncalculated) graphs was discussed.

Data record for a graph in the database

  • Internal edges $[[v_1,v_2,m,n],\ldots]$
  • External momenta $[[v_1,p_1],\ldots]$
  • loop number, number of internal edges, number of vertices, number of external vertices, number of massive internal edges, number of massive external momenta, degree sequence of vertices
  • dimension
  • pictures
  • links (with comments of content, known misprints etc.) to literature on the graph (i.e. analytic results)
  • links to (or directly) analytic results (including domain of validity)
  • links to programs for numeric evaluation
  • remarks on checks performed on the result
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