# Ivo de Varzielas - The University of Oxford

## Contact Details

NameIvo de Varzielas |
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AffiliationThe University of Oxford |
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CityOxford |
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CountryUnited Kingdom |
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## Pubs By Year |
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## Pub CategoriesHigh Energy Physics - Phenomenology (37) High Energy Physics - Experiment (1) Cosmology and Nongalactic Astrophysics (1) |

## Publications Authored By Ivo de Varzielas

We analyse the minima of scalar potentials for multi-Higgs models where the scalars are arranged as either one triplet or two triplets of the discrete symmetries $A_4$, $S_4$, $\Delta(27)$, $\Delta(54)$, as well as $\Delta(3n^2)$ and $\Delta(6n^2)$ with $n>3$. The results should be useful for both multi-Higgs models involving electroweak doublets and multi-flavon models involving electroweak singlets, where in both cases the fields transform as triplets under some non-Abelian discrete symmetry. Read More

CP-odd invariants are useful for studying the CP properties of Lagrangians in any basis. We explain how to build basis invariants for the scalar sector, and how to distinguish CP-odd invariants from CP-even invariants. Up to a certain order, we use these methods to systematically build all the CP-odd invariants. Read More

Although $SO(10)$ Supersymmetric (SUSY) Grand Unification Theories (GUTs) are very attractive for neutrino mass and mixing, it is often quite difficult to achieve successful leptogenesis from the lightest right-handed neutrino $N_1$ due to the strong relations between neutrino and up-type quark Yukawa couplings. We show that in a realistic model these constraints are relaxed, making $N_1$ leptogenesis viable. To illustrate this, we calculate the baryon asymmetry of the Universe $ Y_B $ from flavoured $ N_1 $ leptogenesis in a recently proposed $ \Delta(27) \times SO(10) $ SUSY GUT. Read More

We perform a bottom-up search for discrete non-Abelian symmetries capable of quantizing the Cabibbo angle that parameterizes CKM mixing. Given a particular Abelian symmetry structure in the up and down sectors, we construct representations of the associated residual generators which explicitly depend on the degrees of freedom present in our effective mixing matrix. We then discretize those degrees of freedom and utilize the Groups, Algorithms, Programming (GAP) package to close the associated finite groups. Read More

CP-odd invariants provide a basis independent way of studying the CP properties of Lagrangians. We propose powerful methods for constructing basis invariants and determining whether they are CP-odd or CP-even, then systematically construct all of the simplest CP-odd invariants up to a given order, finding many new ones. The CP-odd invariants are valid for general potentials when expressed in a standard form. Read More

We propose a renormalisable model based on $\Delta(27)$ family symmetry with an $SO(10)$ grand unified theory (GUT) leading to a novel form of spontaneous geometrical CP violation. The symmetries, including $\Delta(27)$ and $\mathbb{Z}_{9} \times \mathbb{Z}_{12} \times \mathbb{Z}_{4}^{R}$, are broken close to the GUT breaking scale to yield the minimal supersymmetric standard model (MSSM) with the standard R-parity. $SO(10)$ is broken via $SU(5)$ with doublet-triplet splitting achieved by a version of the Dimopoulos-Wilczek (missing VEV) mechanism. Read More

Non-Abelian family symmetries offer a very promising explanation for the flavour structure in the Standard Model and its extensions. We explore the possibility that dark matter consists in fermions that transform under a family symmetry, such that the visible and dark sector are linked by the familons - Standard Model gauge singlet scalars, responsible for spontaneously breaking the family symmetry. We study three representative models with non-Abelian family symmetries that have been shown capable to explain the masses and mixing of the Standard Model fermions. Read More

The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal. This structure may be related to the existence of a discrete non-Abelian family symmetry. In this paper the family symmetry is the non-Abelian discrete group $\Delta(27)$, a subgroup of $SU(3)$ with triplet and anti-triplet representations. Read More

The invariant approach is a powerful method for studying CP violation for specific Lagrangians. The method is particularly useful for dealing with discrete family symmetries. We focus on the CP properties of unbroken $\Delta(27)$ invariant Lagrangians with Yukawa-like terms, which proves to be a rich framework, with distinct aspects of CP, making it an ideal group to investigate with the invariant approach. Read More

We estimate the Baryon Asymmetry of the Universe (BAU) arising from leptogenesis within a class of minimal predictive seesaw models involving two right-handed neutrinos and simple Yukawa structures with one texture zero. The two right-handed neutrinos are dominantly responsible for the "atmospheric" and "solar" neutrino masses with Yukawa couplings to $(\nu_e, \nu_{\mu}, \nu_{\tau})$ proportional to $(0,1,1)$ and $(1,n,n-2)$, respectively, where $n$ is a positive integer. The neutrino Yukawa matrix is therefore characterised by two proportionality constants with their relative phase providing a leptogenesis-PMNS link, enabling the lightest right-handed neutrino mass to be determined from neutrino data and the observed BAU. Read More

Two puzzling facts of our time are the observed patterns in the fermion masses and mixings and the existence of non-baryonic dark matter, which are both often associated with extensions of the Standard Model at higher energy scales. In this paper, we consider a solution to these two problems with the flavour symmetry ${\mathbb A}_4\times {\mathbb Z}_2\times {\mathbb Z}_2^\prime$, in a model which has been shown before to explain large leptonic mixings with a specific texture. The model contains 3 generations of $SU(2)_L$-doublet scalar fields, arranged as an ${\mathbb A}_4$-triplet, that spontaneously break the electroweak symmetry, and a "dark sector" of ${\mathbb Z}_2$-odd fields, containing one Majorana neutrino and an ${\mathbb A}_4$-triplet $SU(2)_L$-doublet scalar field, the lightest of which provides a candidate for dark matter. Read More

We propose a renormalisable model based on $A_4$ family symmetry with an $SU(5)$ grand unified theory (GUT) which leads to the minimal supersymmetric standard model (MSSM) with a two right-handed neutrino seesaw mechanism. Discrete $\mathbb{Z}_9\times \mathbb{Z}_6$ symmetry provides the fermion mass hierarchy in both the quark and lepton sectors, while $\mathbb{Z}_4^R$ symmetry is broken to $\mathbb{Z}_2^R$, identified as usual R-parity. Proton decay is highly suppressed by these symmetries. Read More

Flavor symmetries successfully explain lepton and quark masses and mixings yet it is usually hard to distinguish different models that predict the same mixing angles. Further experimental input could be available, if the agents of flavor breaking are sufficiently low in mass and detectable or if new physics with non-trivial flavor charges is sufficiently low in mass and detectable. The recent hint for lepton-nonuniversality in the ratio of branching fractions $B \to K \mu \mu$ over $B \to K e e$, $R_K$, suggests the latter, at least for indirect detection via rare decays. Read More

We propose the use of basis invariants, valid for any choice of CP transformation, as a powerful approach to studying specific models of CP violation in the presence of discrete family symmetries. We illustrate the virtues of this approach for examples based on $A_4$ and $\Delta(27)$ family symmetries. For $A_4$, we show how to elegantly obtain several known results in the literature. Read More

We discuss how the double missing partner mechanism solution to the doublet-triplet splitting problem in four-dimensional supersymmetric SU(5) Grand Unified Theories (GUTs) can be combined with predictive models for the quark-lepton Yukawa coupling ratios at the GUT scale. It is argued that towards this goal a second SU(5) breaking Higgs field in the adjoint representation is very useful and we discuss all possible renormalizable superpotentials with two adjoint Higgs fields and calculate the constraints on the GUT scale and effective triplet mass from a two-loop gauge coupling unification analysis. Two explicit flavour models with different predictions for the GUT scale Yukawa sector are presented, including shaping symmetries and a renormalizable messenger sector. Read More

We propose a renormalizable multi-Higgs model with $A_{4}\otimes Z_{2}\otimes Z^{\prime}_{2}$ symmetry, accounting for the experimental deviation from the tribimaximal mixing pattern of the neutrino mixing matrix. In this framework we study the charged lepton and neutrino masses and mixings. The light neutrino masses are generated via a radiative seesaw mechanism, which involves a single heavy Majorana neutrino and neutral scalars running in the loops. Read More

We consider Delta(27) models featuring geometrical CP violation, and analyse several structures that can obtain the observed lepton masses and mixing. The leptonic structures considered are entirely consistent with structures that reproduce the experimental data in the quark sector. This constitutes an existence proof of geometrical CP violation models accounting for the masses and mixing of all fermions. Read More

We present a model for quark masses and mixing, featuring geometrical CP violation through a \Delta(27) triplet. By employing a single U(1)_F or Z_N symmetry in addition to \Delta(27), we forbid all terms in the scalar potential that would spoil the calculable phases the triple acquires. The quark sector is realised by mimicking an existing scheme that reproduces the masses and CKM mixing, with the extra symmetry enabling the hierarchies in the Yukawa couplings through a Froggatt-Nielsen mechanism. Read More

We review and clarify some cases of geometrical CP violation, the framework of spontaneous CP violation through complex phases with values that are independent of parameters of the potential. We present a flavour model based on Delta(27) featuring spontaneous CP violation, that can reproduce all quark masses and mixing data. The scalar sector of the model has exotic properties that can be tested at the LHC. Read More

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. Read More

The ultraviolet completion of flavour models can strongly improve the predictivity of the respective effective models. We consider $A_4$ models, existing minimal UV completions and construct several next-to-minimal UV complete models. We compare the results of these possibilities to the experimental data including $\theta_{13}$. Read More

We construct for the first time a flavor model, based on the smallest discrete symmetry Delta(27) that implements spontaneous CP violation with a complex phase of geometric origin, which can actually reproduce all quark masses and mixing data. We show that its scalar sector has exotic properties that can be tested at the LHC. Read More

We introduce several methods to obtain calculable phases with geometrical values that are independent of arbitrary parameters in the scalar potential. These phases depend on the number of scalars and on the order of the discrete non-Abelian group considered. Using these methods we present new geometrical CP violation candidates with vacuum expectation values that must violate CP (the transformation that would make them CP conserving is not a symmetry of the potential). Read More

We consider in detail the non-renormalisable scalar potential of three Higgs doublets transforming as an irreducible triplet of Delta(27) or Delta(54). We start from a renormalisable potential that spontaneously leads to a vacuum with CP-violating phases independent of arbitrary parameters - geometrical CP violation. Then we analyse to arbitrarily high order non-renormalisable terms that are consistent with the symmetry and we demonstrate that inclusion of non-renormalisable terms in the potential can preserve the geometrical CP-violating vacuum. Read More

We present a new (supersymmetric) framework for obtaining an excellent description of quark, charged lepton and neutrino masses and mixings from a Delta(6n^2) family symmetry with multiplet assignments consistent with an underlying SO(10) Grand Unification. It employs a Higgs mediator sector in place of the usual Froggatt-Nielsen messengers, with quark and lepton messengers, and provides significant improvements over existing models of this type having unsuppressed Yukawa couplings to the third generation and a simplified vacuum alignment mechanism. The neutrino mass differences are naturally less hierarchical than those of the quarks and charged leptons. Read More

We present a framework of underlying SU(3) x SU(3) family symmetries consistent with Pati-Salam unification and discuss advantages that can justify introducing multiple non-Abelian factors. Advantages include improved vacuum alignment and increased predictivity. We explore in this framework deviations from tri-bi-maximal neutrinos, such as relatively large theta13. Read More

Spontaneous CP-violating phases that do not depend on the parameters of the Higgs sector - the so-called calculable phases - are investigated. The simplest realization is in models with 3 Higgs doublets, in which the scalar potential is invariant under non-Abelian symmetries. The non-Abelian discrete group Delta(54) is shown to lead to the known structure of calculable phases obtained with Delta(27). Read More

The exact alignment of the Yukawa structures on multi-Higgs doublet models provides cancellation of tree-level flavour changing couplings of neutral scalar fields. We show that family symmetries can provide a suitable justification for the Yukawa alignment. Read More

Flavour models may display a relation between the CP-violating asymmetry for leptogenesis and low-energy parameters. If the flavour symmetry produces an exact mass independent lepton mixing scheme at leading order (with type I see-saw) the CP-violating asymmetry would vanish in the absence of corrections. We present a model displaying the link between deviations from the mixing scheme and leptogenesis. Read More

Effective Flavour Models do not address questions related to the nature of the fundamental renormalisable theory at high energies. We study the ultraviolet completion of Flavour Models, which in general has the advantage of improving the predictivity of the effective models. In order to illustrate the important features we provide minimal completions for two known A4 models. Read More

In models with flavour symmetries added to the gauge group of the Standard Model the CP-violating asymmetry necessary for leptogenesis may be related with low-energy parameters. A particular case of interest is when the flavour symmetry produces an exact mass independent lepton mixing scheme, leading to a vanishing CP-violating asymmetry. We present a model-independent discussion that confirms this always occurs for unflavoured leptogenesis in type I see-saw scenarios. Read More

The seesaw mechanism can play a key role in the generation of the leptonic mixing in unified models. We consider an unified model with a family symmetry and extended seesaw, and obtain viable fermion masses and mixing (leptonic mixing is close to tri-bi-maximal). Read More

We present a Grand Unified model based on SO(10) with a Delta(27) family symmetry. Fermion masses and mixings are fitted and agree well with experimental values. An extended seesaw mechanism plays a key role in the generation of the leptonic mixing, which is approximately tri-bi-maximal. Read More

Assuming high-energy tri-bi-maximal mixing we study the radiative running of leptonic mixing angles and obtain limits on the high-energy scale from requiring consistency with the observed mixing. We construct a model in which a non-Abelian discrete family symmetry leads both to a quasi-degenerate neutrino mass spectrum and to near tri-bi-maximal mixing. Read More

We consider how, for quasi-degenerate neutrinos with tri-bi-maximal mixing at a high-energy scale, the mixing angles are affected by radiative running from high to low-energy scales in a supersymmetric theory. The limits on the high-energy scale that follow from consistency with the observed mixing are determined. We construct a model in which a non-Abelian discrete family symmetry leads both to a quasi-degenerate neutrino mass spectrum and to near tri-bi-maximal mixing. Read More

Family symmetries are possibly the most conservative extension of the Standard Model that attempt explanations of the pattern of fermion masses and mixings. The observed large mixing angles in the lepton sector may be the first signal for the presence of a non-Abelian family symmetry. We investigate the possibilities of simultaneously explaining the observed pattern of masses of the quarks (hierarchical masses and small mixing angles) and of the leptons (near tri-bi-maximal mixing, thus large mixing angles). Read More

**Affiliations:**

^{1}The University of Oxford,

^{2}The University of Oxford

**Category:**High Energy Physics - Phenomenology

The observed large mixing angles in the lepton sector may be the first signal for the presence of a non-Abelian family symmetry. However, to obtain the significant differences between the mixing of the neutrino and charged fermion sectors, the vacuum expectation values involved in the breaking of such a symmetry in the two sectors must be misaligned. We investigate how this can be achieved in models with an SU(3) family symmetry consistent with an underlying GUT. Read More