GroupMath: A Mathematica package for group theory calculations

Fonseca, Renato M.

doi:10.48550/arxiv.2011.01764

Cited by 5 publications

(5 citation statements)

References 23 publications

(63 reference statements)

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“…3 The list of Lie groups and their invariant tensors in table 1 [22,23], suggests that similar states exist if G is the exceptional group F 4 or E 8 . Concerning F 4 , its G ij matrix of vectors is a sub-group of SO( 26) vectors with rank 24 (ignoring Lorentz indices and derivatives) [24]. Concerning E 8 , its 248 × 248 matrix of vectors G ij has rank 240; we don't know if the bound state built with the i 1 •••i 248 tensor is long-lived or can fragment into smaller bound states built with the A ijk and…”

Section: Plmentioning

confidence: 99%

Gravitational Vector Dark Matter

Groß¹,

Karamitsos²,

Landini³

et al. 2020

Preprint

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A new dark sector consisting of a pure non-abelian gauge theory has no renormalizable interaction with SM particles, and can thereby realise gravitational Dark Matter (DM). Gauge interactions confine at a scale Λ DM giving bound states with typical lifetimes τ ∼ M 4 Pl /Λ 5 DM that can be DM candidates if Λ DM is below 100 TeV. Furthermore, accidental symmetries of group-theoretical nature produce special gravitationally stable bound states. In the presence of generic Plancksuppressed operators such states become long-lived: SU(N ) gauge theories contain bound states with τ ∼ M 8 Pl /Λ 9 DM ; even longer lifetimes τ = (M Pl /Λ DM ) 2N −4 /Λ DM arise from SO(N ) theories with N ≥ 8, and possibly from F 4 or E 8 . We compute their relic abundance generated by gravitational freeze-in and by inflationary fluctuations, finding that they can be viable DM candidates for Λ DM 10 10 GeV.

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Section: Plmentioning

confidence: 99%

Gravitational Vector Dark Matter

Groß¹,

Karamitsos²,

Landini³

et al. 2020

Preprint

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“…For this simple 4F operator c 1 S = c 1 F and n 1 F = n 1 S ±1, while y i S and y i F are related by ±1/2. For other operators the relations may be more complicated, but with the help of, for example, GroupMath [24] any necessary set of rules can be calculated in an automated way. A list of valid models can then be arrived at by inserting a set of seed fields.…”

Section: Class Namementioning

confidence: 99%

Mapping the SMEFT to discoverable models

Cepedello¹,

Esser²,

Hirsch³

et al. 2022

Preprint

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The matching of specific new physics scenarios onto the SMEFT framework is a well-understood procedure. The inverse problem, the matching of the SMEFT to UV scenarios, is more difficult and requires the development of new methods to perform a systematic exploration of models. In this paper we use a diagrammatic technique to construct in an automated way a complete set of possible UV models (given certain, well specified assumptions) that can produce specific groups of SMEFT operators, and illustrate its use by generating models with no tree-level contributions to four-fermion (4F) operators. Those scenarios, which only contribute to 4F at one-loop order, can contain relatively light particles that could be discovered at the LHC in direct searches. For this class of models, we find an interesting interplay between indirect SMEFT and direct searches. We discuss some examples on how this interplay would look like when combining low-energy observables with the SMEFT Higgs-fermion analyses and searches for resonance at the LHC.

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“…where i stands for a gauge group G; e.g., 4C stands for the gauge coupling constant of SUð4Þ C , and the beta function coefficient is given by (For the Dynkin index and the branching rules, see, e.g., Refs. [30,45] or calculated by using appropriate computer programs such as Susyno [46], LieART [47,48], and GroupMath [49]. For the RGEs at the two-loop level, see, e.g., Refs.…”

Section: Gauge Coupling Constantsmentioning

confidence: 99%

Pseudo-Nambu-Goldstone dark matter model inspired by grand unification

et al. 2021

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A pseudo-Nambu-Goldstone boson (pNGB) is an attractive candidate for dark matter (DM) due to the simple evasion of the current severe limits of DM direct detection experiments. One of the pNGB DM models has been proposed based on a gauged Uð1Þ B−L symmetry. The pNGB has long enough lifetime to be a DM and thermal relic abundance of pNGB DM can be fit with the observed value against the constraints on the DM decays from the cosmic-ray observations. The pNGB DM model can be embedded into an SOð10Þ pNGB DM model in the framework of an SOð10Þ grand unified theory, whose SOð10Þ is broken to the Pati-Salam gauge group at the unified scale, and further to the Standard Model gauge group at the intermediate scale. Unlike the previous pNGB DM model, the parameters such as the gauge coupling constants of Uð1Þ B−L , the kinetic mixing parameter of between Uð1Þ Y and Uð1Þ B−L are determined by solving the renormalization group equations for gauge coupling constants with appropriate matching conditions. From the constraints of the DM lifetime and gamma-ray observations, the pNGB DM mass must be less than Oð100Þ GeV. We find that the thermal relic abundance can be consistent with all the constraints when the DM mass is close to half of the CP even Higgs masses.

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GroupMath: A Mathematica package for group theory calculations

Abstract: GroupMath is a Mathematica package which performs several calculations related to semi-simple Lie algebras and the permutation groups, both of which are important in particle physics as well as in other areas of research.

Cited by 5 publications

References 23 publications

Gravitational Vector Dark Matter

Gravitational Vector Dark Matter

Mapping the SMEFT to discoverable models

Pseudo-Nambu-Goldstone dark matter model inspired by grand unification

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