A
bstract
Grand unification of gauge couplings and fermionic representations remains an appealing proposal to explain the seemingly coincidental structure of the Standard Model. However, to realise ...the Standard Model at low energies, the unified symmetry group has to be partially broken by a suitable scalar potential in just the right way. The scalar potential contains several couplings, whose values dictate the residual symmetry at a global minimum. Some (and possibly many) of the corresponding symmetry-breaking patterns are incompatible with the Standard Model and therefore non-admissible.
Here, we initiate a systematic study of radiative symmetry breaking to thereby constrain viable initial conditions for the scalar couplings, for instance, at the Planck scale. We combine these new constraints on an admissible scalar potential with well-known constraints in the gauge-Yukawa sector into a general blueprint that carves out the viable effective-field-theory parameter space of any underlying theory of quantum gravity.
We exemplify the constraining power of our blueprint within a non-supersymmetric SO(10) GUT containing a
16
H
- and a
45
H
-dimensional scalar representation. We explicitly demonstrate that the requirement of successful radiative symmetry breaking to the correct subgroups significantly constraints the underlying microscopic dynamics. The presence of non-admissible radiative minima can even entirely exclude specific breaking chains: in the SO(10) example, Pati-Salam breaking chains cannot be realised since the respective minima are never the deepest ones.
A
bstract
Based on the Multiple Point Principle, the Higgs boson mass has been predicted to be 135 ± 9 GeV — more than two decades ago. We study the Multiple Point Principle and its prospects with ...respect to the Two-Higgs-Doublet model (THDM). Applying the bilinear formalism we show that concise conditions can be given with a classification of different kinds of realizations of this principle. We recover cases discussed in the literature but identify also different realizations of the Multiple Point Principle.
We present a new version of PyR@TE, a Python tool for the computation of renormalization group equations for general, non-supersymmetric gauge theories. Its new core relies on a recent paper by Poole ...& Thomsen (2019) to compute the β-functions. In this framework, gauge kinetic mixing is naturally implemented, and the Weyl consistency relations between gauge, quartic and Yukawa couplings are automatically satisfied. One of the main new features is the possibility for the user to compute the gauge coupling β-functions up to the three-loop order. Large parts of the PyR@TE code have been rewritten and improved, including the group theory module PyLie. As a result, the overall performance in terms of computation speed was drastically improved and the model file is more flexible and user-friendly.
Program Title: PyR@TE 3
CPC Library link to program files:https://doi.org/10.17632/8h454kdd5n.2
Licensing provisions: Apache 2.0
Programming language: Python 3
Journal reference of previous version: PyR@TE 1, PyR@TE 2 2
Does the new version supersede the previous version?: Yes.
Reasons for new version: The software was essentially rewritten and new functionalities were added. The performance in terms of computation speed was improved by a factor of 100 to 10000 compared to the previous version. The code now relies on Python 3 instead of the deprecated Python 2.
Summary of revisions: The core of the software was rewritten, based on a new formalism. One of the major new features is the possibility of computing the 3-loop RGEs for gauge couplings. The structure and the syntax of the model file were enhanced. The output of the software was improved.
Nature of problem : Computing the renormalization group equations for any renormalizable, 4-dimensional, non-supersymmetric quantum field theory.
Solution method: Group theory, tensor algebra.
References:
1 F. Lyonnet, I. Schienbein, F. Staub, A. Wingerter, PyR@TE: Renormalization group equations for general gauge theories 185 (3) 1130–1152. http://dx.doi.org/10.1016/j.cpc.2013.12.002.
2 F. Lyonnet, I. Schienbein, PyR@TE 2: A Python tool for computing RGEs at two-loop 213 181–196. http://dx.doi.org/10.1016/j.cpc.2016.12.003.
Recently, Poole and Thomsen presented the renormalization group equations (RGEs) in the MS scheme for dimensionless parameters of a general renormalizable gauge theory in a new formalism based on the ...local renormalization group. In this paper, we apply the dummy field method to the expressions in this formalism in order to derive the RGEs for the dimensionful couplings, which so far have been missing in this approach. The complete set of RGEs has been implemented in a new version of the public code PyR@TE dedicated to the automatic computation of the RGEs for any general renormalizable (nonsupersymmetric) gauge theory.
Recently, Poole and Thomsen presented the renormalization group equations (RGEs) in the MS¯ scheme for dimensionless parameters of a general renormalizable gauge theory in a new formalism based on ...the local renormalization group. In this paper, we apply the dummy field method to the expressions in this formalism in order to derive the RGEs for the dimensionful couplings, which so far have been missing in this approach. The complete set of RGEs has been implemented in a new version of the public code pyr@te dedicated to the automatic computation of the RGEs for any general renormalizable (nonsupersymmetric) gauge theory.
We present a new version of PyR@TE, a Python tool for the computation of renormalization group equations for general, non-supersymmetric gauge theories. Its new core relies on a recent paper by Poole ...& Thomsen (arXiv:1906.04625) to compute the \(\beta\)-functions. In this framework, gauge kinetic mixing is naturally implemented, and the Weyl consistency relations between gauge, quartic and Yukawa couplings are automatically satisfied. One of the main new features is the possibility for the user to compute the gauge coupling \(\beta\)-functions up to the three-loop order. Large parts of the PyR@TE code have been rewritten and improved, including the group theory module PyLie. As a result, the overall performance in terms of computation speed was drastically improved and the model file is more flexible and user-friendly.
In the general Two-Higgs Doublet Model it has been shown that the Higgs potential can be expressed in terms of gauge-independent quantities. In particular, stability, electroweak symmetry breaking, ...and CP symmetry can be understood in a concise way, avoiding unphysical gauge degrees of freedom. We complete this program and show how all the masses, the trilinear and quartic scalar interactions, the gauge-boson-Higgs interactions, as well as the Yukawa couplings in the general THDM can be expressed in a gauge-invariant way.
A
bstract
In the general Two-Higgs Doublet Model it has been shown that the Higgs potential can be expressed in terms of gauge-independent quantities that transform covariantly under unitary mixing ...of the doublets. In particular, stability, electroweak symmetry breaking, and CP symmetry can be understood in a concise way, avoiding unphysical gauge degrees of freedom. We complete this program and show how all the masses, the trilinear and quartic scalar interactions, the gauge-boson-Higgs interactions, as well as the Yukawa couplings in the general THDM can be expressed in a gauge-invariant way.
Based on the Multiple Point Principle, the Higgs boson mass has been predicted to be 135 +- 9 GeV - more than two decades ago. We study the Multiple Point Principle and its prospects with respect to ...the Two-Higgs-Doublet model (THDM). Applying the bilinear formalism we show that concise conditions can be given with a classification of different kinds of realizations of this principle. We recover cases discussed in the literature but identify also different realizations of the Multiple Point Principle.
Phys. Rev. D 102, 076002 (2020) Recently, Poole & Thomsen have presented the Renormalization Group Equations
(RGEs) in the $\overline{\mathrm{MS}}$ scheme for dimensionless parameters of a
general ...renormalizable gauge theory in a new formalism based on the Local
Renormalization Group. In this Letter, we apply the dummy field method to the
expressions in this formalism in order to derive the RGEs for the dimensionful
couplings which so far have been missing in this approach. The complete set of
RGEs has been implemented in a new version of the public code PyR@TE
(arXiv:2007.12700) dedicated to the automatic computation of the RGEs for any
general renormalizable (non-supersymmetric) gauge theory.
PDF
