arXiv subjects

Francisco J. de Anda

Publications and source records attributed to Francisco J. de Anda.

At least 19 recordsLinked to original sources

arXiv2024

Orbifold Modular GUT of Flavour

We discuss an $SU(5)$ Grand Unified Theory (GUT) based on the 10d orbifold $(\mathbb{T}^2)^3/(\mathbb{Z}_4\times\mathbb{Z}_2)$ plus three modular $S_4$ groups with moduli at respective fixed points $i,i+2,ω=e^{2iπ/3}$. The resulting model has hierarchical quark and charged lepton mass matrices, arising from a double weighton mechanism, and reproduces the highly predictive Littlest Seesaw Mechanism in the neutrino sector. The down quark mass matrix has an upper triangular form, contributing to CKM mixing, while the charged lepton mass matrix has a lower triangular form with suppressed contributions to PMNS mixing. The orbifold yields successful $SU(5)$ breaking with doublet-triplet splitting of the Higgs multiplets.

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arXiv2023

Can $E_8$ unification at low energies be consistent with proton decay?

A model is presented that achieves unification of the full Standard Model (SM) field content into a single superfield. It has $E_8$ as a gauge group and simple SUSY in ten spacetime dimensions. The extra dimensions are orbifolded such that they reduce the gauge symmetry directly to the SM one. At low energies, only the SM field content remains with viable unified Yukawa couplings. Full unification can be achieved at energies as low as $10^6\ \rm{GeV}$ with controlled proton decay.

hep-ph↗

arXiv2023

Modular flavour symmetry and orbifolds

We develop a bottom-up approach to flavour models which combine modular symmetry with orbifold constructions. We first consider a 6d orbifold $\mathbb{T}^2/\mathbb{Z}_N$, with a single torus defined by one complex coordinate $z$ and a single modulus field $τ$, playing the role of a flavon transforming under a finite modular symmetry. We then consider 10d orbifolds with three factorizable tori, each defined by one complex coordinate $z_i$ and involving the three moduli fields $τ_1, τ_2, τ_3$ transforming under three finite modular groups. Assuming supersymmetry, consistent with the holomorphicity requirement, we consider all 10d orbifolds of the form $(\mathbb{T}^2)^3/(\mathbb{Z}_N\times\mathbb{Z}_M)$, and list those which have fixed values of the moduli fields (up to an integer). The key advantage of such 10d orbifold models over 4d models is that the values of the moduli are not completely free but are constrained by geometry and symmetry. To illustrate the approach we discuss a 10d modular seesaw model with $S_4^3$ modular symmetry based on $(\mathbb{T}^2)^3/(\mathbb{Z}_4\times\mathbb{Z}_2)$ where $τ_1=i,\ τ_2=i+2$ are constrained by the orbifold, while $τ_3=ω$ is determined by imposing a further remnant $S_4$ flavour symmetry, leading to a highly predictive example in the class CSD$(n)$ with $n=1-\sqrt{6}$.

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arXiv2023

Scotogenic majorana neutrino masses in a predictive orbifold theory of flavour

The use of extra space-time dimensions provides a promising approach to the flavour problem. The chosen compactification of a 6-dimensional orbifold implies a remnant family symmetry $A_4$. This makes interesting predictions for quark and lepton masses, for neutrino oscillations and neutrinoless double beta decay, providing also a very good global description of all flavour observables. Due to an auxiliary $\mathbb{Z}_4$ symmetry, we implement a scotogenic Majorana neutrino mass generation mechanism with a viable WIMP dark matter candidate.

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arXiv2022

Revamping Kaluza-Klein dark matter in an orbifold theory of flavor

We suggest a common origin for dark matter, neutrino mass and family symmetry within the orbifold theory proposed in [arXiv:1910.05605v2,arXiv:2004.06735v2]. Flavor physics is described by an $A_4$ family symmetry that results naturally from compactification. WIMP Dark matter emerges from the first Kaluza-Klein excitation of the same scalar that drives family symmetry breaking and neutrino masses through the inverse seesaw mechanism. In addition to the "golden" quark-lepton mass relation and neutrino predictions for $0νββ$ decay, the model provides a good global description of all flavor observables.

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arXiv2022

Sculpting the Standard Model from low-scale Gauge-Higgs-Matter $E_8$ Grand Unification in ten dimensions

The construction and general implications of a model with complete supersymmetric unification of the Standard Model matter content, interactions and families' replication into a single $E_{8}$ gauge superfield in ten dimensions is presented. The gauge and extended Poincaré symmetries are broken through compactification of the $\mathbb{T}^6/(\mathbb{Z}_3\times \mathbb{Z}_3)$ orbifold with Wilson lines, which reduces the original symmetry and matter content into those of the Standard Model plus additional heavier states. Proton decay can be suppressed automatically while the compactification scale may be as low as $10^9~\rm{GeV}$, so that the corresponding GUT-scale physics may be potentially accessible and testable by future collider measurements.

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arXiv2021

Complete $E_8$ Unification in 10 Dimensions

A grand unification model with a single $E_8$ gauge superfield in 10 dimensions is presented. It is shown that, through the orbifold $T^6/(\mathbb{Z}_6\times \mathbb{Z}_2)$ and its corresponding Wilson lines, the symmetry is broken to the Standard Model one. Furthermore it is shown that the model is anomaly free at all levels without the need to add any extra field content. Thus a complete unification of the Standard Model into a single gauge superfield is achieved consistently.

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arXiv2021

Quark and Lepton Mass and Mixing with non-universal $Z'$ from a 5d Standard Model with gauged $SO(3)$

We propose a theory of quark and lepton mass and mixing with non-universal $Z'$ couplings based on a 5d Standard Model with quarks and leptons transforming as triplets under a new gauged $SO(3)$ isospin. In the 4d effective theory, the $SO(3)$ isospin is broken to $U(1)'$, through a $S^1/(\mathbb{Z}_2\times \mathbb{Z}'_2)$ orbifold, then subsequently dynamically broken, resulting in a massive $Z'$. Quarks and leptons in the 5d bulk appear as massless modes, with zero Yukawa couplings to the Higgs on the brane, and zero couplings to $Z'$, at leading order, due to the $U(1)'$ symmetry. However, after the $U(1)'$ breaking, both Yukawa couplings and non-universal $Z'$ couplings are generated by heavy Kaluza-Klein exchanges. Hierarchical quark and lepton masses result from a hierarchy of 5d Dirac fermion masses. Neutrino mass and mixing arises from a novel type Ib seesaw mechanism, mediated by Kaluza-Klein Dirac neutrinos. The non-universal $Z'$ couplings may contribute to semi-leptonic $B$ decay ratios which violate $μ- e$ universality. In this model such couplings are related to the corresponding quark and lepton effective Yukawa couplings.

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arXiv2020

Gauge couplings evolution from the Standard Model, through Pati-Salam theory, into $E_8$ unification of families and forces

We explore the potential of ultimate unification of the Standard Model matter and gauge sectors into a single $E_8$ superfield in ten dimensions via an intermediate Pati-Salam gauge theory. Through a consistent realisation of a $\mathbb{T}^6/(\mathbb{Z}_6\times \mathbb{Z}_2)$ orbifolding procedure accompanied by the Wilson line breaking mechanism and Renormalisation Group evolution of gauge couplings, we have established several benchmark scenarios for New Physics that are worth further phenomenological exploration.

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arXiv2020

Scotogenic dark matter in an orbifold theory of flavor

We propose a flavour theory in which the family symmetry results naturally from a six-dimensional orbifold compactification. "Diracness" of neutrinos is a consequence of the spacetime dimensionality, and the fact that right-handed neutrinos live in the bulk. Dark matter is incorporated in a scotogenic way, as a result of an auxiliary $\mathbb{Z}_3$ symmetry, and its stability is associated to the conservation of a "dark parity" symmetry. The model leads naturally to a "golden" quark-lepton mass relation.

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arXiv2020

Exceptional Unification of Families and Forces

This work considers the remarkable suggestion that the three families of quarks and leptons may be unified, together with the Higgs and gauge fields of the Standard Model (SM), into a single "particle", namely the $\textbf{248}$ vector superfield of a ten-dimensional $E_8$ super Yang Mills (SYM) theory. Towards a realistic model along these lines, a class of orbifoldings based on $T^6/(\mathbb{Z}_N\times \mathbb{Z}_M)$ are proposed and explored, that can in principle break $E_8$ SYM down to the minimal supersymmetric standard model (MSSM), embedded in a larger group such as $E_6$, $SO(10)$ or $SU(5)$, together with other gauge group factors which can be broken by Wilson lines. A realistic model based on $T^6/(\mathbb{Z}_6\times \mathbb{Z}_2)$ is presented. The orbifold breaks $E_8$ SYM down to a Pati-Salam gauge group in 4d, together with other gauge groups, which are further broken to the SM by Wilson lines in the right-handed sneutrino directions, yielding proto-realistic fermion mass matrices, and experimental signals associated with a low Pati-Salam gauge group breaking scale.

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arXiv2020

Emergent gravity from off-shell energy fixing

Off-shell processes do not preserve the Energy Momentum Tensor (EMT) in QFT. Fixing the EMT throughout off-shell processes, implies a graviton-like quantum field to emerge without dynamics. Its dynamics are generated through quantum corrections. This Fixed Off-Shell Energy Condition (FOSEC) implies the existence of a linear gravity-like theory, and in special cases the full Poincarè gauge theory. In this work it is shown that imposing the FOSEC in QFT implies the emergence of a viable quantum theory of gravity.

hep-th↗

arXiv2020

Probing the predictions of an orbifold theory of flavor

We examine the implications of a recently proposed theory of fermion masses and mixings in which an $A_4$ family symmetry emerges from orbifold compactification. We analyse two variant schemes concerning their predictions for neutrino oscillations, neutrinoless double-beta decay and the golden quark-lepton unification mass relation. We find that upcoming experiments DUNE as well as LEGEND and nEXO offer good chances of exploring a substantial region of neutrino parameters.

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arXiv2020

Gauge-flavon unification

In this paper we propose the idea that flavons can emerge from extra dimensional gauge fields, referred to as gauge-flavon unification (GFU) analogous to gauge-Higgs unification (GHU). We assume that there is a gauged family symmetry in extra dimensions and that the flavons are the extra dimensional components of the gauge field. This provides a simple mechanism to align the VEVs of the flavons through a combination of Wilson lines and orbifold symmetry breaking. We present some simple 5d examples of GFU based on $SO(3)$ and $SU(4)$ gauged family symmetry, the latter case yielding $SU(3)\times U(1)$ gauged family symmetry in 4d, broken by triplet and antitriplet flavons, with effective couplings to fermions. We also present a general formalism for Wilson lines and orbifolds, in any number of dimensions, including non-commutative aspects Wilson lines, which may be useful for aligning additional flavons as required for realistic models.

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arXiv2020

$SU(5)$ Grand Unified Theory with $A_4$ Modular Symmetry

We present the first example of a grand unified theory (GUT) with a modular symmetry interpreted as a family symmetry. The theory is based on supersymmetric $SU(5)$ in 6d, where the two extra dimensions are compactified on a $T_2/\mathbb{Z}_2$ orbifold. We have shown that, if there is a finite modular symmetry, then it can only be $A_4$ with an (infinite) discrete choice of moduli, where we focus on $τ= ω=e^{i2π/3}$, the unique solution with $|τ|=1$. The fields on the branes respect a generalised CP and flavour symmetry $A_4\ltimes \mathbb{Z}_2$ which is isomorphic to $S_4$ which leads to an effective $μ-τ$ reflection symmetry at low energies, implying maximal atmospheric mixing and maximal leptonic CP violation. We construct an explicit model along these lines with two triplet flavons in the bulk, whose vacuum alignments are determined by orbifold boundary conditions, analogous to those used for $SU(5)$ breaking with doublet-triplet splitting. There are two right-handed neutrinos on the branes whose Yukawa couplings are determined by modular weights. The charged lepton and down-type quarks have diagonal and hierarchical Yukawa matrices, with quark mixing due to a hierarchical up-quark Yukawa matrix.

hep-ph↗

arXiv2020

Flavour and CP predictions from orbifold compactification

We propose a theory for fermion masses and mixings in which an $A_4$ family symmetry arises naturally from a six-dimensional spacetime after orbifold compactification. The flavour symmetry leads to the successful "golden" quark-lepton unification formula. The model reproduces oscillation parameters with good precision, giving sharp predictions for the CP violating phases of quarks and leptons, in particular $δ^\ell \simeq +268 ^\circ$. The effective neutrinoless double-beta decay mass parameter is also sharply predicted as $\langle m_{ββ}\rangle \simeq 2.65\ meV$.

hep-ph↗

arXiv2019

Flavon alignments from orbifolding: $SU(5)\times SU(3)$ model with $\mathbb{T}^6/Δ(54)$

We systematically develop the formalism necessary for ensuring that boundary conditions of flavon fields in extra dimensions are consistent with heterotic string theory. Having developed a set of consistency conditions on the boundary conditions, we explore a series of examples of orbifolds in various dimensions to see which ones can satisfy them. In addition we impose the further phenomenological requirements of having non-trivial flavon vacuum alignments and also of having quarks and leptons located appropriately in extra dimensions. The minimal successful case seems to be a 10d theory with a $SU(3)_{fl}$ gauged flavour symmetry, where the six-dimensional torus is compactified on a $\mathbb{T}^6/Δ(54)$ orbifold. We construct a realistic $SU(5)$ grand unified theory along these lines, leading to tribimaximal-reactor lepton mixing, which we show to be consistent with current neutrino data.

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arXiv2018

$SU(3) \times SO(10)$ in 6d

We discuss a simple and elegant $SU(3)\times SO(10)$ family unified gauge theory in 6d compactified on a torus with the orbifold $T_2/Z_2^3$ and supplemented by a $Z_6\times Z_3$ discrete symmetry. The orbifold boundary conditions generate all the desired $SU(3)$ breaking vacuum alignments, including the $(0,1,-1)$ and $(1,3,-1)$ alignments of the Littlest Seesaw model for atmospheric and solar neutrino mixing, as well as the usual $SO(10)$ breaking with doublet-triplet splitting. The absence of driving and messenger fields considerably simplifies the field content of the model. It naturally explains why there are three families of quarks and leptons, and accounts for all their masses, mixing angles and CP phases via rather elegant looking Yukawa and Majorana matrices in the theory basis. The resulting model controls proton decay and allows successful Leptogenesis.

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