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Vakint

Single-scale vacuum-integral matching and evaluation

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Overview

Vakint matches single-scale vacuum integrals to a library of known topologies, canonicalizes their momentum routing, reduces tensor numerators, and evaluates them analytically or numerically. Expressions are represented with Symbolica and contain a numerator multiplied by a topo(...) structure built from propagators.

Separate matching from evaluation
Canonical topology matching is useful on its own and is much cheaper than a complete evaluation. Tensor reduction and analytic backends invoke FORM; numerical sector decomposition invokes pySecDec and FORM. Choose the narrowest operation and evaluation order needed for the task.

Choose a task

To install Symbolica and canonicalize an integral without external tools, follow the Python guide and compare with the generated topology table.
To compile the same matching-only workflow in Rust, use the Rust guide, then continue with the matching tutorial.
To tensor-reduce and evaluate with an explicit backend policy, use the evaluation guide with the exact EvaluationOrder reference.
To embed Vakint in Rust or symbolica.community.vakint, use the interface guide, native Rustdoc, and generated Python signatures before selecting external tools.

Workflow

A complete calculation proceeds through explicit stages:

create one Vakint engine and reuse it, because topology setup has a cost;
parse or construct a Symbolica expression in Vakint’s namespace;
canonicalize the topology and momentum routing;
tensor-reduce the numerator when required;
evaluate the integral with the first supported backend in the configured order;
substitute numerical parameters and external momenta when a numerical result is required.

VakintExpression is the structured sum of numerator/topology terms. A recognized topology can be rendered in canonical long or short form. If unknown integrals are allowed, matching may preserve them, but evaluation still needs a backend that supports the resulting topology.

External tools and reproducibility

Construction validates the selected backends
The default evaluation order includes AlphaLoop, MATAD, FMFT, and pySecDec. Settings validation therefore probes FORM and pySecDec even if a later example only canonicalizes an expression. Vakint requires FORM 4.2.1 or newer and pySecDec 1.6.4 or newer. For matching without evaluation, use an empty evaluation order in Rust; in Python, provide an empty evaluation_order when constructing Vakint.

Analytic AlphaLoop, MATAD, and FMFT methods depend on FORM. The pySecDec method depends on both FORM and pySecDec and requires numerical masses and, where applicable, external momenta. Record tool versions, normalization convention, epsilon depth, decimal precision, backend order, and temporary-output reuse policy with any result intended to be reproduced.

Diagnostics and platform notes

Matching with an empty evaluation order needs neither FORM nor pySecDec. For backend evaluation, check the configured executable paths first. Verbose logging and retained temporary files are useful when an external tool fails:

VAKINT_NO_CLEAN_TMP_DIR=T RUST_LOG=DEBUG cargo run

On macOS, if a GNU-compiler link fails with missing __emul... symbols, retry the build with EXTRA_MACOS_LIBS_FOR_GNU_GCC=T set.

Vakint is used by GammaLoop for vacuum-integral work, but it owns its topology and evaluation conventions independently. Use this guide and the generated API/topology references for the selected version. Contributors can follow topology construction, canonicalization, backend selection, and external-process ownership in the Vakint implementation architecture.