MatchPy: Pattern Matching in Python

Krebber, Manuel; Barthels, Henrik

doi:10.21105/joss.00670

“…the operator. We automate the operator-closure process by applying the methods discussed below through a pattern-matching algorithm [81,82]. The program is a part of our public example-code repository.…”

Section: Jhep01(2021)074mentioning

confidence: 99%

Exploding operators for Majorana neutrino masses and beyond

Gargalionis

¹

,

Volkas

²

2021

J. High Energ. Phys.

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Building UV completions of lepton-number-violating effective operators has proved to be a useful way of studying and classifying models of Majorana neutrino mass. In this paper we describe and implement an algorithm that systematises this model-building procedure. We use the algorithm to generate computational representations of all of the tree-level completions of the operators up to and including mass-dimension 11. Almost all of these correspond to models of radiative neutrino mass. Our work includes operators involving derivatives, updated estimates for the bounds on the new-physics scale associated with each operator, an analysis of various features of the models, and a look at some examples. We find that a number of operators do not admit any completions not also generating lower-dimensional operators or larger contributions to the neutrino mass, ruling them out as playing a dominant role in the neutrino-mass generation. Additionally, we show that there are at most five models containing three or fewer exotic multiplets that predict new physics that must lie below 100 TeV. Accompanying this work we also make available a searchable database containing all of our results and the code used to find the completions. We emphasise that our methods extend beyond the study of neutrino-mass models, and may be useful for generating completions of high-dimensional operators in other effective field theories. Example code: ref. [37].

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“…The closure provides enough information to know the number of loops in the neutrino self-energy graph (since the ∆L = 2 operator is generated at tree level) and to estimate the scale of the new physics underlying the operator. We automate the operator-closure process by applying the methods discussed below through a pattern-matching algorithm [77,78]. The program is a part of our public example-code repository.…”

Section: Operator Closures and Neutrino-mass Estimatesmentioning

confidence: 99%

Exploding operators for Majorana neutrino masses and beyond

Gargalionis,

Volkas

2020

Preprint

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Building UV completions of lepton-number-violating effective operators has proved to be a useful way of studying and classifying models of Majorana neutrino mass. In this paper we describe and implement an algorithm that systematises this model-building procedure. We use the algorithm to generate computational representations of all of the tree-level completions of the operators up to and including mass-dimension 11. Almost all of these correspond to models of radiative neutrino mass. Our work includes operators involving derivatives, updated estimates for the bounds on the new-physics scale associated with each operator, an analysis of various features of the models, and a look at some examples. We find that a number of operators do not admit any completions not also generating lower-dimensional operators or larger contributions to the neutrino mass, ruling them out as playing a dominant role in the neutrino-mass generation. Additionally, we show that there are at most five models containing three or fewer exotic multiplets that predict new physics that must lie below 100 TeV. Accompanying this work we also make available a searchable database containing all of our results and the code used to find the completions. We emphasise that our methods extend beyond the study of neutrino-mass models, and may be useful for generating completions of high-dimensional operators in other effective field theories.

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“…To ensure correctness, a match is only made if parameters in the input expression satisfy the assumptions for free variables listed in the FunGrim entry. The pattern matching is currently implemented naively and will fail to match expressions that are mathematically equivalent but structurally different (better implementations are possible [6]).…”

Section: Formulas As Rewrite Rulesmentioning

confidence: 99%