rundex

JAX port of RunDec v3.1 — running and decoupling of the strong coupling αs and quark masses in QCD.

Original Mathematica package by K.G. Chetyrkin, J.H. Kühn, M. Steinhauser, and F. Herren.
References: hep-ph/0004189, arXiv:1703.03751.

Installation

pip install rundex

Requires Python ≥ 3.10, JAX ≥ 0.4, and diffrax.

Quick start

import jax
jax.config.update("jax_enable_x64", True)  # required for physics-level precision

from rundex import AlphasExact, AlphasLam, LamExpl, LamImpl

# Λ_MS^(5) from αs(MZ)
lam = LamExpl(0.118, 91.18, nf=5, loops=5)   # → 0.2086 GeV

# αs(μ) from Λ (analytic expansion)
als = AlphasLam(lam, mu=1000.0, nf=5, loops=5)

# αs(μ) by numerically integrating the RGE
als = AlphasExact(0.118, mu0=91.18, mu=1000.0, nf=5, loops=5)

# Optional: compile once for fixed (nf, loops) to avoid retracing
from rundex import compiled_AlphasExact
alphas_exact_5l_nf5 = compiled_AlphasExact(nf=5, loops=5)
als_fast = alphas_exact_5l_nf5(0.118, 91.18, 1000.0)

Note on 64-bit precision
JAX defaults to 32-bit floats. Always call jax.config.update("jax_enable_x64", True) before importing or calling any rundex function. The package itself does not set this flag so it does not interfere with the rest of your JAX code.

Development

git clone ...
pip install -e ".[dev]"
pytest

Numerical tests are cross-validated against rundec-python (CRunDec C++ wrapper), which is a test-only dependency not required by rundex itself.

Implemented RunDec functions (subset)

The following RunDec functions are currently ported to rundex:

• LamExpl
• LamImpl
• AlphasLam
• AlphasExact
• AlL2AlH
• AlH2AlL
• mMS2mMS
• mMS2mOS
• mMS2m1S
• mOS2mMS
• mOS2mSI
• DecMqUpOS
• DecMqDownOS
• mL2mH
• mH2mL

Not all RunDec functionality is ported yet.

Compiled helpers (available for all ported functions)

Each ported function above has a compiled helper named compiled_<FunctionName>. Use these when you call the same function many times with fixed discrete settings (for example fixed nf, loops, and fixed threshold/light-quark data).

Examples:

• compiled_LamExpl(nf, loops)
• compiled_LamImpl(nf, loops)
• compiled_AlphasLam(nf, loops)
• compiled_AlphasExact(nf, loops)
• compiled_AlL2AlH(decpar, loops)
• compiled_AlH2AlL(decpar, loops)
• compiled_mMS2mMS(nf, loops)
• compiled_mMS2mOS(nf, loops, mq=None, fdelm=1.0)
• compiled_mMS2m1S(nl, loops, mq=None, fdelm=1.0)
• compiled_mOS2mMS(nf, loops, mq=None, fdelm=1.0)
• compiled_mOS2mSI(nf, loops, mq=None, fdelm=1.0)
• compiled_DecMqUpOS(nf, loops)
• compiled_DecMqDownOS(nf, loops)
• compiled_mL2mH(decpar, loops)
• compiled_mH2mL(decpar, loops)

When to use which:

• Use regular functions for one-off calls or frequently changing setup parameters.
• Use compiled helpers for repeated calls with fixed setup parameters.