Mindmap

# Desireable features

1. Easy search for Feynman graphs

# Thoughts, ideas, problems, dreams, issues, hopes

Feel free to add and comment, but please do not delete anything.

### Ways of contribution / management / infrastructure

The project should always be accessible, therefore hosting it on a university / working group web page might not be optimal since groups move, websites get closed (Example: HPL). Great idea from Christian: Get a computer science student involved, working out the technical infrastructure, web-interface etc. could be a great master's thesis project!

Probably new entries (contributions by researchers) should need approval by some editor (to check that all necessary information is given and correctly entered into the database).

In any case, each contribution must be associated to some person or group that is responsible for it!

### Checking for / assuring correctness

One way of checking analytic results is by simply using Sector decomposition to evaluate at a few phase-space points. This could be automated!

### Database access / search

###### What kinds of graphs should be stored?
• Only scalar graphs!? Tensor reductions is a different topic. But: some master integrals involve irreducible numerators. So probably one should include these. But then graphs need also a specification of numerator scalar products of loop momenta! Comment: for phenomenological applications (QCD) it is crucial to have full sets of master integrals. Often it is desirable to give them in Henn's normal form (pure functions) which might be involved to define.
• Should one allow to include non-standard propagators (like HQET etc.)? This would make the graph data structure even more complicated. Comment: Probably this should be included at some point.
###### How to search for a graph? Any classifications?
• Ideally a graph is just a topological graph. It is specified by: List of vertices with incoming momenta (none, light-like, or some non-zero square) and list of edges (internal propagators) with specification of masses
• In particular, one and the same topology of edges and vertices will be needed in many different kinematic setups (distributions of masses on internal and external edges). These can not be unified since different setups can have different divergences and totally different epsilon-expansions
• So should one only search for the topology first and then expand each toplogoy in the different kinematic setups? This might be useful because:
1. Only for special kinematics there will be results available
2. Different kinematics can give very different results (e.g. polylog vs. Bessel-functions vs. elliptic functions)
• But note also that some kinematic limits are non-singular, i.e. can be determined as a well-defined limit of a (more complicated) kinematic setup. Should one store such limits separately? If not, such limits would have to be computed automatically.
• I heared that some people are used to specify a graph / master integral by its momentum space representation. Of course this is very ambiguous (different parametrizations of loop momenta yield different-looking momentum-space representations), but maybe a tool would be useful to transform such a representation into a graphical one. This seems to be discussed here. Comment: Reduze implements several algorithms to identify momentum based sectors and graphs.
• Possible search criteria / filtering options: loop number, vertex number, edge number, vertex degree sequence, number of external momenta, number of massive internal propagators

### References / literature

Known errors / misprints should be pointed out (and corrected)!

Hire Bas Tausk!

### Explicit results

One set of conventions must be agreed upon for storing the data. For access, it would be nice to have automatic conversion into popular other conventions.

Even when results for arbitrary dimensions and propagator powers are available in e.g. hypergeometric expressions, it might be useful to also provide epsilon-expansions near $D=4-2\varepsilon$ since the expansion is usually what is needed (a hypergeometric result is nice, but still often needs to be expanded).

Ideally, a script on the server allows to download epsilon-expansions in any format (FORM, Mathematica, Maple, GiNaC, … also LaTeX and pdf). This should not be very complicated to achieve.

Simplest are representations in the Euclidean region. Should continuations to physical region be stored explicitly or computed automatically? Comment: It is easy to make an error here, continuations should be stored explicitely. Also for non-planar graphs there might not be any "real" result in the first place.

• qcdloop.fnal.gov/ One loop integrals up to finite parts. Great: Clear documentation (conventions fixed, graphs clear using momentum space representations and pictures), references to literature. Note: Here we have the same graph (the box) with many different kinematic dressings, each treated individually. Whatever we do should at least contain this amount of information. Maybe a first step could be to extend this to arbitrary order in $\varepsilon$
• nauty and Traces Efficient graph isomorphy testing, automorphism group, determines a unique label / representative in each isomorphism class!
• GraphState description of a canonical graph label ("Nickel index") and a Python library
• www.cs.sunysb.edu/~algorith/ Might contain something useful
• Looptools One loop results, seems to be software only (no references) and requires installation. I think we should aim to give everything directly online.
• Feynman diagrams and Szymanzik Polynomials in Mathematica Just curious
• FeynArts, FormCalc
• Qgraf flexible and powerful tool for multiloop Feynman graph generation
• xloops Last news entry is from 2004!?
• Maple support for Feynman diagrams Anybody ever used this?
• Feynman Diagram Library This is a list of graphs only (pictures); no results, no references included. Most graphs are tree level and focus is on different particles and tensor integrals.
• github.com/photino/jquery-feyn Modern, SVG, MathJax-in-Browser Feynman Graph drawing tool
• Some (partly outdated) collections of links to computer programs for Feynman integral computations: CPC, CEDAR HepForge, KIT, DESY Zeuthen

# Off topic

Why has no one done this before?