arXiv subjects

Luís Lavoura

Publications and source records attributed to Luís Lavoura.

At least 19 recordsLinked to original sources

arXiv2026

Assessing boundedness from below in the $\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetric three-Higgs-doublet model: algorithm and machine learning

The scalar potential of any particle-physics model must be bounded from below (BFB). We consider the extension of the Standard electroweak Model with three $SU(2)$ doublets of scalars and a symmetry under which each of those doublets changes sign. In the absence of necessary and sufficient conditions for boundedness from below (BnessFB) for this specific model, we argue that one may use increasingly stringent sets of necessary conditions. We introduce a Mathematica code, StableWein, that implements this idea. The user is allowed to choose the level of accuracy that they want in the determination of BnessFB; more precision means the use of more necessary conditions, and usually entails a longer running time for the code. Our investigation suggests that our procedure and code can be extremely precise in the determination of the potentials that are BFB. In addition, we introduce a machine-learning code that identifies, with more than 99% accuracy, which potentials are BFB.

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arXiv2026

Conditions for boundedness from below of a $Δ(54)$-symmetric three-Higgs-doublet model

We investigate the orbit space of the scalar potential of a $Δ(54)$-symmetric three-Higgs-doublet model. We find that, if the potential enjoys $CP$ invariance, then its three-dimensional orbit space is a polytope; if the potential has no $CP$ symmetry, then its four-dimensional orbit space has a boundary that is sometimes slightly concave, but seems never to be convex. Consequently, we conjecture necessary and sufficient conditions for the potential to be bounded from below; brute-force minimization of a large number of potentials affirms the accuracy of our conjecture. We list all possible charge-conserving and charge-breaking minima of the potential.

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arXiv2026

On the addition of an $SU(2)$ quadruplet of scalars to the Standard Model

We consider the extension of the Standard electroweak Model through an $SU(2)$ quadruplet of scalars with hypercharge either $3/2$ or $1/2$ (with an additional reflection symmetry in the latter case). We establish, through $\textit{exact analytical equations}$, the boundaries of the phase spaces of the gauge-invariant terms that appear in the (renormalizable) scalar potentials. We devise procedures for the determination of necessary and sufficient bounded-from-below conditions on those potentials; we emphasize that one mostly needs to scan the scalar potential over a few $\textit{lines}$, instead of $\textit{surfaces}$, in order to establish the boundedness-from-below; this fact allows one $\textit{to reduce by three orders of magnitude the computational time}$ devoted to that establishment.

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arXiv2025

Vacuum Stability Conditions for New $SU(2)$ Multiplets

We consider the addition to the Standard Model of a scalar $SU(2)$ multiplet $Δ_n$ with dimension $n$ going from $1$ to $6$. The multiplet $Δ_n$ is assumed to have null vacuum expectation value and an arbitrary (free) hypercharge. We determine the shape of the phase space for the new terms that appear in the scalar potential (SP); we observe in particular that, in the case of a 6-plet, the phase space is slightly concave along one of its boundaries. We determine the bounded-from-below and vacuum stability conditions on the SP for each value of $n$.

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arXiv2025

Theorem on vacuum stability

We consider an extension of the Standard Model with one or more scalar multiplets beyond the Higgs doublet $Φ$. The additional scalar multiplets are supposed to carry arbitrary hypercharges. We prove that, in such a model, if the field configuration where only $Φ$ has a nonzero vacuum expectation value (VEV) is a local minimum of the potential, then it has a lower value of the potential than any field configuration where both $Φ$ and other scalar multiplets have nonzero VEVs.

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arXiv2025

On the extension of the SM through a scalar quadruplet

We consider the extension of the Standard Model (SM) through a scalar quadruplet with hypercharge either $1/2$ or $3/2$; in the first case, we assume $CP$ invariance of the scalar potential (SP). We write down the unitarity conditions on the SP. We use a partly numerical method to find the bounded-from-below conditions on the SP. We determine the masses of the new scalars of the model. We compute the three- and four-Higgs couplings and compare them to the ones of the SM.

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arXiv2024

Constraints on large scalar multiplets added to the Standard Model

We study the extension of the Standard Model (SM) by introducing a scalar multiplet with arbitrary isospin $J$ and hypercharge $Y$. We explicitly consider various possible values of the weak isospin $J$, up to and including $J=7/2$. The mass differences among the components of the multiplet originate from its coupling to the Higgs doublet of the SM, as present in the scalar potential (SP). We derive exact bounded-from-below (BFB) and unitarity (UNI) conditions for this model, even when the SP includes the most general quartic terms involving the multiplet components. We find that the upper bound on the mass differences depends not only on the UNI conditions but also on the BFB ones, thus imposing constraints on the mass differences. We compare these constraints to those derived from the oblique parameters (OPs) and from solutions of the renormalization-group equations (RGEs).

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arXiv2024

On the addition of a large scalar multiplet to the Standard Model

We consider the addition of a single $SU(2)$ multiplet of complex scalar fields to the Standard Model (SM). We explicitly consider the various possible values of the weak isospin $J$ of that multiplet, up to and including $J = 7/2$. We allow the multiplet to have arbitrary weak hypercharge. The scalar fields of the multiplet are assumed to have no vacuum expectation value; the mass differences among the components of the multiplet originate in its coupling, present in the scalar potential (SP), to the Higgs doublet of the SM. We derive exact bounded-from-below and unitarity conditions on the SP, thereby constraining those mass differences. We compare those constraints to the ones that may be derived from the oblique parameters.

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arXiv2024

The oblique parameters from arbitrary new fermions

We compute the six oblique parameters $S, T, U, V, W, X$ in a New Physics Model with an arbitrary number of new fermions, in arbitrary representations of $SU(2) \times U(1)$, and mixing arbitrarily among themselves. We show that $S$ and $U$ are automatically finite, but $T$ is finite only if there is a specific relation between the masses of the new fermions and the representations of $SU(2) \times U(1)$ that they sit in. We apply our general computation to two illustrative cases.

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arXiv2024

Unitarity constraints on large multiplets of arbitrary gauge groups

We impose partial-wave unitarity on $2 \to 2$ tree-level scattering processes to derive constraints on the dimensions of large scalar and fermionic multiplets of arbitrary gauge groups. We apply our results to scalar and fermionic extensions of the Standard Model, and also to the Grand Unified Theories (GUTs) based on the groups $SU(5)$, $SO(10)$, and $E_6$. We find scenarios within the latter two GUTs that violate the unitarity condition; this may require a reevaluation of the validity of perturbation theory in those scenarios.

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arXiv2023

Oblique corrections when $m_W \neq m_Z \cos{θ_W}$ at tree level

The parametrization of the oblique corrections through $S$, $T$, and $U$ -- later extended by $V$, $W$, and $X$ -- is a convenient way of comparing the predictions for various electroweak observables at the one-loop level between the Standard Model and its extensions. That parametrization assumes that the extensions under consideration have ${SU(2)\times U(1)}$ gauge symmetry \emph{and} the tree-level relation $m_W = m_Z \cos{θ_W}$ between the Weinberg angle and the gauge-boson masses. In models where that relation does not hold at the Lagrangian level, the parameter $T$ is not ultraviolet-finite, making the parametrization inadequate. We present expressions that parametrize the difference of the various predictions of two models with $m_W \neq m_Z \cos{θ_W}$ in terms of oblique parameters. The parameter $T$ does not play a role in those expressions. Conveniently, they may be reached from the ones that were derived for models with tree-level $m_W = m_Z \cos{θ_W}$, by performing a simple substitution for $T$. We also discuss the difficulties in using oblique parameters when comparing a model with $m_W \neq m_Z \cos{θ_W}$ to the Standard Model. Finally, we compute the relevant five oblique parameters $S$, $U$, $V$, $W$, and $X$ in the SM extended by both, hypercharge $Y=0$ and $Y=1$, triplet scalars.

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arXiv2023

The $Z b \bar b$ vertex in a left-right model

We consider the one-loop corrections to the $Z b \bar b$ vertex in a $CP$-conserving left--right model (LRM), $viz$. a model with gauge group $SU(2)_L \times SU(2)_R \times U(1)$. We allow the gauge coupling constants of $SU(2)_L$ and $SU(2)_R$ to be different. The spontaneous symmetry breaking is accomplished only by doublets and/or singlets of $SU(2)_L$ and $SU(2)_R$. The lightest massive neutral gauge boson of our LRM is assumed to have the same Yukawa couplings to bottom-quark pairs as the $Z$ of the Standard Model (SM); this assumption has the advantage that, then, the infrared divergences automatically cancel down in the subtraction of the $Z b \bar b$ vertex in the SM from the same vertex in the LRM. We effect a proper renormalization of the $Z b \bar b$ vertex and check explicitly both its gauge invariance and the cancellation of all the ultraviolet divergences. We find out that a LRM with the above assumptions cannot achieve a better fit to the $Z b \bar b$ vertex than a multi-Higgs extension of the SM, $viz$. both models can only achieve a decent fit when one admits scalar particles with very low masses $\lesssim 50$ GeV. This is true even when we allow for markedly different gauge coupling constants of $SU(2)_L$ and $SU(2)_R$.

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arXiv2023

Oblique corrections from leptoquarks

We present general formulas for the oblique-correction parameters $S$, $T$, $U$, $V$, $W$, and $X$ in a model of New Physics having arbitrary numbers of scalar leptoquarks of the five permissible types. We allow for a general mixing among the scalars of the various electric charges, $\textit{viz.}$ $-4/3$, $-1/3$, $2/3$, and $5/3$. We then extend the formulas to the case of a New Physics model with additional scalars in any representations of the gauge group $SU(2) \times U(1)$, mixing arbitrarily among themselves.

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arXiv2023

Oblique corrections from triplet quarks

We present general formulas for the oblique-correction parameters $S$, $T$, $U$, $V$, $W$, and $X$ in an extension of the Standard Model having arbitrary numbers of singlet, doublet, and triplet quarks with electric charges $-4/3$, $-1/3$, $2/3$, and $5/3$ that mix with the standard quarks of the same charge.

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arXiv2023

The centers of discrete groups as stabilizers of Dark Matter

The most usual option to stabilize Dark Matter (DM) is a $Z_2$ symmetry. In general, though, DM may be stabilized by any $Z_N$ with $N \ge 2$. We consider the way $Z_N$ is a subgroup of the internal-symmetry group $G$ of a model; we entertain the possibility that $Z_N$ is the center of $G$, yet $G$ is not of the form $Z_N \times G^\prime$, where $G^\prime$ is a group smaller (i.e. of lower order) than $G$. We examine all the discrete groups of order smaller than 2001 and we find that many of them cannot be written as the direct product of a cyclic group and some other group, yet they have a non-trivial center that might be used in Model Building to stabilize DM.

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arXiv2021

Prescription for finite oblique parameters $S$ and $U$ in extensions of the SM with $m_W \neq m_Z \cos{θ_W}$

We consider extensions of the Standard Model with neutral scalars in multiplets of $SU(2)$ larger than doublets. When those scalars acquire vacuum expectation values, the resulting masses of the gauge bosons $W^\pm$ and $Z^0$ are not related by $m_W = m_Z \cos{θ_W}$. In those extensions of the Standard Model the oblique parameters $S$ and $U$, when computed at the one-loop level, turn out to be either gauge-dependent or divergent. We show that one may eliminate this problem by modifying the Feynman rules of the Standard Model for some vertices containing the Higgs boson; the modifying factors are equal to $1$ in the limit $m_W = m_Z \cos{θ_W}$. We give the result for $S$ in a model with arbitrary numbers of scalar $SU(2)$ triplets with weak hypercharges either $0$ or $1$.

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arXiv2013

Reproducing lepton mixing in a texture zero model

We note that the emerging features of lepton mixing can be reproduced if, with inverted neutrino mass ordering, both the smallest neutrino mass and the $ττ$ element of the neutrino mass matrix vanish. Then, the atmospheric neutrino mixing angle is less than maximal and the Dirac phase $δ$ is close to $π$. We derive the correlations among the mixing parameters and show that there is a large cancellation in the effective mass responsible for neutrinoless $ββ$ decay. Three simple seesaw models leading to our scenario are provided.

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arXiv2013

Flavour models for TM1 lepton mixing

We present a framework for lepton flavour models such that the first column of the lepton mixing matrix is (2,-1,-1)/sqrt(6). We show that the flavour symmetry group adequate for this purpose is S4. Our models are based on a vacuum alignment that can be obtained in a supersymmetric framework.

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