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Computing decay rates for new physics theories with FeynRules and MadGraph5/aMC@NLO
Johan Alwall, Claude Duhr, Benjamin Fuks, Olivier Mattelaer, Deniz Gizem Ozturk, Chia-Hsien Shen
TL;DR
Calculating all partial widths for new-physics models is complex because allowed channels vary with model parameters and higher-multiplicity decays can matter. The paper adds analytic two-body calculations and automated numerical higher-multiplicity calculations, with comparisons validating the implementations and SPS1a MSSM three-body contributions found negligible to total widths.
Problem
Calculating all partial widths is complex because allowed decay channels depend on the mass spectrum and must be reevaluated for each parameter choice.
Source: §1 · p. 3Method
The paper extends FeynRules to compute analytic two-body rates and adds MadWidth to generate relevant higher-multiplicity diagrams, remove cascades, and target total-width precision.
Source: §1 · pp. 3–4, §4.1 · p. 11Results
Below the percent level, SPS1a MSSM decay-width comparisons agree across FeynRules two-body output, MadWidth, and Bridge; tested two-body comparisons also agree across the Standard Model, SILH, and MSSM.
Source: §5.1 · p. 22, §5.2 · p. 24Takeaways & Limitations
For the SPS1a MSSM scenario, three-body decay contributions to total widths are negligible in a very good approximation.
Source: §5.2 · p. 24Loop-induced decay diagrams are outside the paper’s scope, although they contribute importantly to the Higgs width.
Source: §3 · p. 10
Abstract
from arXiv · showhide
We present new features of the FeynRules and MadGraph5/aMC@NLO programs for the automatic computation of decay widths that consistently include channels of arbitrary final-state multiplicity. The implementations are generic enough so that they can be used in the framework of any quantum field theory, possibly including higher-dimensional operators. We extend at the same time the conventions of the Universal FeynRules Output (or UFO) format to include decay tables and information on the total widths. We finally provide a set of representative examples of the usage of the new functions of the different codes in the framework of the Standard Model, the Higgs Effective Field Theory, the Strongly Interacting Light Higgs model and the Minimal Supersymmetric Standard Model and compare the results to available literature and programs for validation purposes.
PROGRAM SUMMARY
The program combines analytic FeynRules calculations of two-body decay rates with numerical MadGraph5/aMC@NLO calculations of many-body rates. Its computations depend on model complexity and the underlying packages’ requirements.
PROGRAM SUMMARY
- The module pairs analytic two-body decay rates from FeynRules with numerical many-body decay rates from MadGraph5/aMC@NLO.FeynRules squares three-point vertices; MadGraph generates decay diagrams, with cascade decays removed.Source: PROGRAM SUMMARY · p. 2
- It computes tree-level decay widths for arbitrary new-physics models.The package relies on FeynRules and MadGraph5/aMC@NLO; their restrictions apply, and Mathematica 7 or higher is required.Source: PROGRAM SUMMARY · p. 2
- Computations range from a few seconds to several minutes, depending on model complexity.Both deriving Feynman rules from a Lagrangian and calculating decay rates contribute to runtime.Source: PROGRAM SUMMARY · p. 2
1. Introduction
Computing widths for new-physics models is laborious because allowed channels vary with model parameters and higher-multiplicity decays can matter. The paper adds analytic two-body calculations to FeynRules and a MadGraph module that selects higher-multiplicity channels to meet a target precision while avoiding double counting.
1. Introduction
- Width calculations are complex because allowed channels depend on the mass spectrum and must be reevaluated for each parameter choice.Higher-multiplicity decays can be dominant for some particles, and calculating all partial widths can be daunting.Source: §1 · p. 3
- FeynRules is extended to compute analytic two-body decay rates for inclusion in translation-interface output.The workflow this replaces required recomputing numerical widths for each parameter choice and inserting them back into the model implementation.Source: §1 · p. 3
- The UFO format is extended to carry analytic two-body decay formulas for dynamic use when generating scattering processes.UFO is the standard interface from FeynRules to MadGraph5/aMC@NLO, GoSam, and Herwig++.Source: §1 · p. 4
- MadWidth selects final-state multiplicity to reach a target precision on total widths, estimates channel contributions, and avoids double counting.Higher-multiplicity contributions may still be insufficient when loop-induced modes matter or large threshold effects require resummation.Source: §1 · p. 4
- The paper validates its implementations by comparing partial widths across the Standard Model, HEFT, SILH, and MSSM.The planned comparisons cover four selected models; the introduction identifies the Standard Model, Higgs Effective Field Theory, Strongly Interacting Light Higgs model, and Minimal Supersymmetric Standard Model.Source: §1 · p. 4
2. Automatic computation of two-body decay rates with FeynRules
FeynRules derives Feynman rules from a model Lagrangian and supports broad model and operator structures. Its new functions use those vertices to compute analytic tree-level two-body decay rates and make the results available for numerical evaluation and export.
2.1. The Mathematica package FeynRules
- FeynRules automatically derives a quantum field theory model’s Feynman rules from its Lagrangian and supports operators above dimension four, subject to Lorentz and gauge invariance.It also provides interfaces for exporting model information to matrix-element generators.Source: §2.1 · pp. 4–5
- Widths must be recalculated when benchmark inputs change because matrix-element generators often require numerical widths, making repeated manual updates inefficient.Some tools can compute widths on the fly, in which case numerical width values at the FeynRules level are not mandatory.Source: §2.1 · p. 6, §2.2 · p. 6
2.2. Functions dedicated to the computation of decay widths
- Analytic two-body decay rates are computed from FeynRules vertices, with formulas available for all possible external-particle rotations with a massive initial state.The output includes channels whether or not they are kinematically allowed for the current parameter values; numerical evaluation and kinematic checks are available through the supplied functions.Source: §2.2 · pp. 7–8
- FeynRules does not handle N-body decays with N > 2 because matrix elements no longer decouple from phase space, infrared divergences may arise, and multiplicities can double-count channels.Two-body widths are generally a good estimate, but some cases require at least three-body contributions, handled in the MadGraph5 aMC@NLO framework.Source: §2.2 · p. 7
- ComputeWidths[] selects eligible three-point vertices, evaluates squared matrix elements in unitary gauge, and stores analytic results for decay-rate functions to access.The stored results support partial widths, total widths, and branching ratios; total-width values can be used to update particle declarations before export.Source: §2.2 · pp. 8–9
3. Extension of the UFO format to include decay information
The UFO extension carries analytic two-body decay information from FeynRules into model exports, reducing the need to recompute widths for every benchmark point. Matrix-element generators filter kinematically allowed channels at runtime, but the Higgs example also requires contributions beyond tree-level two-body decays.
3. Extension of the UFO format to include decay information
- Starting with FeynRules 2.0, UFO exports include analytic two-body decay information by default, addressing repeated width recalculation for different benchmark points.The feature can be disabled with AddDecays -> False in WriteUFO[].Source: §3 · p. 9
- UFO decay tables include analytic formulas for all possible two-body decays, even kinematically forbidden ones, leaving generators to filter channels and combine widths at runtime.The formulas are stored in decays.py as instances of the Decay class.Source: §3 · pp. 9–10
- For the Higgs, tree-level two-body decays alone do not accurately estimate the width because loop-induced and off-shell three-body contributions matter.Including loop-induced diagrams is outside the paper’s scope; three-body decays are handled in the next section with MadGraph5 aMC@NLO.Source: §3 · p. 10
4. MadWidth – a MadGraph5 aMC@NLO module to compute decay widths
MadWidth extends MadGraph5 aMC@NLO with tree-level decay-width calculations for arbitrary final-state multiplicities, iteratively constructing diagrams while removing cascade and radiative contributions and focusing numerical integration on potentially important channels. It can run automatically when MadEvent or aMC@NLO encounters widths marked Auto, returning total and partial widths in a param card for particle-shower decays.
4. MadWidth – a MadGraph5 aMC@NLO module to compute decay widths
- MadWidth computes tree-level N-body partial widths for arbitrary N in any theory with a UFO implementation, addressing the inefficiency of generating all higher-multiplicity channels directly.It is embedded in MadGraph5 aMC@NLO and, under the narrow-width approximation, builds diagrams from lower multiplicities while removing cascade and radiative contributions.Source: §4 · pp. 10–11
4.1. The MadWidth algorithm
- MadWidth iteratively adds final-state particles up to a user-specified or precision-driven Nmax, retaining contact diagrams and higher-multiplicity modes not accounted for by lower-multiplicity decays.It discards on-shell cascade configurations and radiative diagrams, including contact vertices that arise only to ensure gauge invariance of lower-order interactions.Source: §4.1 · pp. 11–13
4.2. Fast estimation of N-body partial widths
- To prioritize numerical integration, MadWidth estimates each channel using an approximate phase-space volume and squared matrix element, then passes only numerically relevant modes to MadEvent.Its matrix-element approximation simplifies Lorentz structures and is reported to work for non-trivial structures, form factors, and derivative couplings.Source: §4.2 · pp. 13, 14, 16
4.3. Estimation of the numerically relevant Feynman diagrams
- Before diagram generation, a second estimate combines an N-body decay with a two-body decay of one of its final-state particles to screen possible higher-multiplicity modes.In the SPS1a validation, estimates of three-body contributions were correct in order of magnitude or overestimates; when a decays.py file is available, MadWidth uses its analytic two-body results, otherwise it computes partial widths numerically.Source: §4.3 · pp. 16, 18, 19, Table 3 · p. 20
4.2. Fast estimation of N-body partial widths
- For the heaviest sbottom in the SPS1a MSSM, MadWidth’s partial-width estimates reproduce the correct order of magnitude for every channel shown.The estimates are compared with exact results from a Bridge-MadEvent-CalcHep comparison; interference is neglected only during estimation, not in the numerical partial-width calculation.Source: §4.2 · p. 13, Table 2 · p. 17
4.3. Estimation of the numerically relevant Feynman diagrams
- In the SPS1a MSSM, MadWidth’s three-body-channel relevance estimates were either correct in order of magnitude or overestimated, conservatively ensuring potentially important diagrams are generated.The comparison covers three-body contributions to the total widths of all massive particles, with four-body and higher decays neglected; the module can be run from a MadGraph shell or during event generation, using a valid UFO model.Source: §4.3 · p. 19, Table 3 · p. 20
- In MadEvent or aMC@NLO, widths marked Auto trigger MadWidth with default options, and the param card is overwritten before further computation.MadEvent computes the top-quark and Z-boson widths and decay tables while leaving the W-boson and Higgs-boson widths unchanged in the example.Source: §4.3 · p. 21
- MadWidth returns total widths and partial widths in the param card, making its output suitable for particle-shower programs to decay unstable particles.Partial widths are included as comments at the end of each decay-table line.Source: §4.3 · p. 22
5. Illustrative examples
The examples compare FeynRules and MadWidth with each other and with published results or other programs across two- and three-body decays. They report agreement across the tested models, a negligible three-body contribution to SPS1a MSSM total widths, and faster MadWidth timings than Bridge.
5.1. Two-body decays
- FeynRules and MadWidth agree for the tested two-body widths in the Standard Model, SILH, and SPS1a MSSM, validating cases with higher-dimensional operators and Majorana fermions.Tables 4–6 show selected partial widths for these models.Source: §5.1 · p. 22, Table 4 · p. 23, Table 5 · p. 23
5.2. Three-body decays
- MadWidth and SMCalc show good agreement for HEFT Higgs widths, including both two-body and three-body channels.The HEFT example includes only selected dimension-six operators, not the full set.Source: §5.2 · p. 24, Table 7 · p. 25
- Agreement below the percent level is found among the SPS1a MSSM width calculations, and three-body contributions to its total widths are negligible in a very good approximation.The comparison includes FeynRules-generated two-body widths, MadWidth, and Bridge.Source: §5.2 · p. 24, Table 8 · p. 25
- MadWidth is faster than Bridge for computing total widths in HEFT and SPS1a MSSM, with a formidable time gain when three-body decays are included.The reported gain uses MadWidth’s fast estimator to compute only numerically relevant diagrams; generating the FeynRules decay.py file is a one-time step excluded from the timing.Source: §5.2 · p. 26, Table 9 · p. 26
6. Conclusion
The conclusion presents analytic FeynRules routines for two-body partial widths and extends UFO to carry decay and total-width information. MadWidth computes N-body widths at tree level, and validation supports its use in LO generators when the narrow width approximation holds.
6. Conclusion
- FeynRules now computes analytic two-body partial widths automatically from the Lagrangian, while UFO carries the relevant decay and total-width information for MadGraph5 aMC@NLO to use at run-time.MadGraph5 aMC@NLO uses the UFO extension to calculate particle widths at run-time.Source: §6 · pp. 26–27
- MadWidth computes N-body widths efficiently by removing numerically negligible subprocesses, tuning final-state multiplicity to a target precision, and avoiding channel double-counting.The module is intended to work in full generality, including possibly at run-time with the matrix-element generator.Source: §6 · p. 27
- The codes are validated against programs and literature for the SM, HEFT, SILH, and MSSM, but MadWidth’s tree-level predictions are unreliable when higher-order effects matter and are suitable for LO generators when the narrow width approximation holds.The conclusion limits the stated accuracy to tree level/leading order.Source: §6 · p. 27