Dirac neutrinos and anomaly-free discrete gauge symmetries

Relying on Dirac neutrinos allows an infinity of anomaly-free discrete gauge symmetries to be imposed on the Supersymmetric Standard Model, some of which are GUT-compatible.Comment: 24 pages, minor changes, existence of flipped discrete gauge symmetries is pointed ou

Simple Finite Non-Abelian Flavor Groups

The recently measured unexpected neutrino mixing patterns have caused a resurgence of interest in the study of finite flavor groups with two- and three-dimensional irreducible representations. This paper details the mathematics of the two finite simple groups with such representations, the Icosahedral group A_5, a subgroup of SO(3), and PSL_2(7), a subgroup of SU(3).Comment: 42 pages, matches published version, references adde

Quintics with Finite Simple Symmetries

We construct all quintic invariants in five variables with simple Non-Abelian finite symmetry groups. These define Calabi-Yau three-folds which are left invariant by the action of A_5, A_6 or PSL_2(11).Comment: 18 pages, typos corrected, matches published versio

What is the Discrete Gauge Symmetry of the MSSM?

We systematically study the extension of the Supersymmetric Standard Model (SSM) by an anomaly-free discrete gauge symmetry Z_N. We extend the work of Ibanez and Ross with N=2,3 to arbitrary values of N. As new fundamental symmetries, we find four Z_6, nine Z_9 and nine Z_18. We then place three phenomenological demands upon the low-energy effective SSM: (i) the presence of the mu-term in the superpotential, (ii) baryon-number conservation upto dimension-five operators, and (iii) the presence of the see-saw neutrino mass term LHLH. We are then left with only two anomaly-free discrete gauge symmetries: baryon-triality, B_3, and a new Z_6, which we call proton-hexality, P_6. Unlike B_3, P_6 prohibits the dimension-four lepton-number violating operators. This we propose as the discrete gauge symmetry of the Minimal SSM, instead of R-parity.Comment: Typo in item 2 below Eq.(6.9) corrected (wrong factor of "3"); 27 pages, 5 table

Common gauge origin of discrete symmetries in observable sector and hidden sector

An extra Abelian gauge symmetry is motivated in many new physics models in both supersymmetric and nonsupersymmetric cases. Such a new gauge symmetry may interact with both the observable sector and the hidden sector. We systematically investigate the most general residual discrete symmetries in both sectors from a common Abelian gauge symmetry. Those discrete symmetries can ensure the stability of the proton and the dark matter candidate. A hidden sector dark matter candidate (lightest U-parity particle or LUP) interacts with the standard model fields through the gauge boson Z', which may selectively couple to quarks or leptons only. We make a comment on the implications of the discrete symmetry and the leptonically coupling dark matter candidate, which has been highlighted recently due to the possibility of the simultaneous explanation of the DAMA and the PAMELA results. We also show how to construct the most general U(1) charges for a given discrete symmetry, and discuss the relation between the U(1) gauge symmetry and R-parity.Comment: Version to appear in JHE

Geometrical CP violation in multi-Higgs models

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). We also extend to non-renormalisable potentials the proof that more than two scalars are needed to obtain these geometrical CP violation candidates.Comment: 8 pages, 2 figures. v2: table added, accepted by JHE

Spontaneous breaking of SU(3) to finite family symmetries: a pedestrian's approach

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 A4, semidirect product of Z7 and Z3, and Delta(27) from an underlying SU(3) gauge symmetry. Higher irreducible representations are required to achieve the spontaneous breaking of the continuous group. We present methods of identifying the required vacuum alignments and discuss in detail the symmetry breaking potentials.Comment: 21 page

Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models

Recent T2K results indicate a sizeable reactor angle theta_13 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 (1,1,1)^T/sqrt{3}, 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.Comment: 24 pages, 2 figures, version to be published in JHE

Non-Abelian Discrete Flavor Symmetries on Orbifolds

We study non-Abelian flavor symmetries on orbifolds, $S^1/Z_2$ and $T^2/Z_3$. Our extra dimensional models realize $D_N$, $\Sigma(2N^2)$, $\Delta(3N^2)$ and $\Delta(6N^2)$ including $A_4$ and $S_4$. In addition, one can also realize their subgroups such as $Q_N$, $T_7$, etc. The $S_3$ flavor symmetry can be realized on both $S^1/Z_2$ and $T^2/Z_3$ orbifolds.Comment: 16 page