Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models

Abstract

To explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor symmetries (and their concomitant problems) can be avoided if we extend the gauge group. In the framework of SU (12) we give explicit examples of models having varying degrees of predictability obtained by scanning over groups and representations and identifying cases with operators contributing to mass and mixing matrices that need little finetuning of prefactors. Fitting with quark and lepton masses run to the GUT scale and known mixing angles allows us to make predictions for the neutrino masses and hierarchy, the octant of the atmospheric mixing angle, leptonic CP violation, Majorana phases, and the effective mass observed in neutrinoless double beta decay.

LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory

“…Since it can provide Dynkin indices of irreps it is useful in obtaining renormalization group equations [20,21,22]. In model building it has been used for extensions of the Standard Model in the way of BSM models [23,24,25,26,27,28,29], grand unified models [30,31,32,33,34,35,36,37,38,39,40,41,42,43], and other applications including SUSY models [44,45,46], supergravity models [47] and general particle physics models [48,49]. In UV completions of particle physics models, LieART has found uses in string theory [50,51], holography [52,53,54], (super-)conformal field theory [55,56,57,58,59,60,61,62,63], M-theory [64,65] and F-theory [66,…”

“…Additionally, LieART already had some functionality for finding branching rules. Using projection matrices, Out [36]:= (10,1)+(18,1)+ (28,1) In [37] Out [37]:= (6,1)+(12,1)+(16,1)+ (22,1) The command BranchingRulesTable[algebra, subalgebras] in the subpackage LieART'Tables' (load with « LieART'Tables') of the previous LieART version constructs a series of tables of the branching rules from algebra to each element of subalgebras [3]. However, because of the aforementioned multiple branching rules for some algebra-subalgebra pairs, we modified the command to take an index parameter as well, which determines the branching rules to display: BranchingRulesTable[algebra, subalgebras, index ].…”

A Gauged Flavor Model of Quarks and Leptons

“…As shown in [10], one can derive a reasonable prediction for the Cabbibo angle from the Lagrangian in equation (6). We rederive this result here for our basis and then augment the value when an additional scalar has a VEV.…”

“…The usual model building practice is to extend the standard model (SM) with a discrete symmetry which is used to fit the data. But variations abound, from extending a supersymmetric SM, to discrete group extended grand unified models (For reviews see [1][2][3][4][5]), to top-down fully gauged theories where the gauge group is sufficiently large to accommodate both the GUT and flavor symmetries [6]. Here we take a minimalist approach and look for the smallest fully gauged model that can explain all the data.…”

Family unification in special grand unification

“…There are some attempts to unify GUT and family groups into a larger GUT group in 4D and higher-dimensional theories [35][36][37][38][39][40][41][42]. However, such attempts are based on GUT groups and their limited subgroups so-called regular subgroups: e.g., E 8 ⊃ E 7 ⊃ E 6 ⊃ SO(10) ⊃ SU (5) ⊃ G SM (:= SU (3) C ×SU (2) L ×U (1) Y ).…”