Christoph Luhn

A SUSY GUT of flavour with S4 × SU(5) to NLO

We construct a Supersymmetric (SUSY) Grand Unified Theory (GUT) of Flavour based on S4 × SU(5), together with an additional (global or local) Abelian symmetry, and study it to next-to-leading order (NLO) accuracy. The model includes a successful description of quark and lepton masses and mixing angles at leading order (LO) incorporating the Gatto-Sartori-Tonin (GST) relation and the Georgi-Jarlskog (GJ) relations. We study the vacuum alignment arising from F-terms to NLO and such corrections are shown to have a negligible effect on the results for fermion masses and mixings achieved at LO. Tri-bimaximal (TB) mixing in the neutrino sector is predicted very accurately up to NLO corrections of order 0.1%. Including charged lepton mixing corrections implies small deviations from TB mixing described by a precise sum rule, accurately maximal atmospheric mixing and a reactor mixing angle close to three degrees.

Trimaximal mixing with predicted theta_13 from a new type of constrained sequential dominance

Following the recent T2K indication of a sizeable reactor angle, we present a class of models which fix θ13 while preserving trimaximal solar mixing. The models are based on a new type of constrained sequential dominance involving new vacuum alignments, along the (1,2,0) T or (1,0,2) T directions in flavour space. We show that such alignments are easily achieved using orthogonality, and may replace the role of the subdominant flavon alignment (1,1,1) T in

Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models

Recent T2K results indicate a sizeable reactor angle θ13 which would rule out exact tri-bimaximal lepton mixing. We study the vacuum alignment of the Altarelli-Feruglio A4 family symmetry model including additional flavons in the 1′ and 1″ representations and show that it leads to trimaximal mixing in which the second column of the lepton mixing matrix consists of the column vector

A new family symmetry for SO(10) GUTs

{{{{{\left( {1,1,1} \right)}^T}}} \left/ {{\sqrt {3} }} \right.}

Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification

, with a potentially large reactor angle. In order to limit the reactor angle and control the higher order corrections, we propose a renormalisable S4 model in which the 1′ and 1″ flavons of A4 are unified into a doublet of S4 which is spontaneously broken to A4 by a flavon which enters the neutrino sector at higher order. We study the vacuum alignment in the S4 model and show that it predicts accurate trimaximal mixing with approximate tri-bimaximal mixing, leading to a new mixing sum rule testable in future neutrino experiments. Both A4 and S4 models preserve form dominance and hence predict zero leptogenesis, up to renormalisation group corrections.

A Supersymmetric Grand Unified Theory of Flavour with PSL(2,7) x SO(10)

We argue that the projective special linear group PSL2(7)PSL2(7), also known as Σ(168)Σ(168), has unique features which make it the most suitable discrete family symmetry for describing quark and lepton masses and mixing in the framework of SO(10)SO(10) type unified models. In such models flavon fields in the sextet representation of PSL2(7)PSL2(7) play a crucial role both in obtaining tri-bimaximal neutrino mixing as well as in generating the third family charged fermion Yukawa couplings. In preparation for physical applications, we derive the triplet representation of PSL2(7)PSL2(7) in the basis S,T,U,VS,T,U,V where S,T,US,T,U are the familiar triplet generators of S4S4 in the diagonal charged lepton basis where T is diagonal. We also derive an analogous basis for the real sextet representation and identify the vacuum alignments which lead to tri-bimaximal neutrino mixing and large third family charged fermion Yukawa couplings.

SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry

We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo–Kobayashi–Maskawa (CKM) unitarity triangle, α≈90°α≈90°. The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU(5)SU(5), a discrete family symmetry such as A4A4 or S4S4, a shaping symmetry including products of Z2Z2 and Z4Z4 groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of α≈90°α≈90° by a combination of purely real or purely imaginary vacuum expectation values (vevs) of the flavons responsible for family symmetry breaking. This leads to quark mass matrices with 1–3 texture zeros that satisfy the “phase sum rule” and lepton mass matrices that satisfy the “lepton mixing sum rule” together with a new prediction that the leptonic CP violating oscillation phase is close to either 0°, 90°, 180°, or 270° depending on the model, with neutrino masses being purely real (no complex Majorana phases). This leads to the possibility of having right-angled unitarity triangles in both the quark and lepton sectors.

Spontaneous breaking of SU(3) to finite family symmetries — a pedestrian’s approach

We construct a realistic Supersymmetric Grand Unified Theory of Flavour based on PSL(7)×SO(10), where the quarks and leptons in the 16 of SO(10) are assigned to the complex triplet representation of PSL(7), while the flavons are assigned to a combination of sextets and anti-triplets of PSL(7). Using a D-term vacuum alignment mechanism, we require the flavon sextets of PSL(7) to be aligned along the 3-3 direction leading to the third family Yukawa couplings, while the flavon anti-triplets describe the remaining Yukawa couplings. Other sextets are aligned along the neutrino flavour symmetry preserving directions leading to tri-bimaximal neutrino mixing via a type II see-saw mechanism, with predictions for neutrinoless double beta decay and cosmology.

A new family symmetry for SO(10)SO(10) GUTs

Abstract We propose a supersymmetric (SUSY) SU ( 5 ) Grand Unified Theory (GUT) including a single right-handed neutrino singlet and an adjoint matter representation below the GUT scale and extend this model to include an A 4 family symmetry and a gauged anomaly-free Abelian group. In our approach hierarchical neutrino masses result from a combined type I and type III seesaw mechanism, and the A 4 symmetry leads to tri-bimaximal mixing which arises indirectly. The mixing between the single right-handed neutrino and the matter in the adjoint is forbidden by excluding an adjoint Higgs, leading to a diagonal heavy Majorana sector as required by constrained sequential dominance. The model also reproduces a realistic description of quark and charged lepton masses and quark mixings, including the Georgi–Jarlskog relations and the leptonic mixing sum rules s = r cos δ and a = − r 2 / 4 with r = θ C / 3 .

A supersymmetric grand unified theory of flavour with PSL2(7)×SO(10)PSL2(7)×SO(10)

Non-Abelian discrete family symmetries play a pivotal role in the formulation of models with tri-bimaximal lepton mixing. We discuss how to obtain symmetries such as