arXiv subjects
Publications and source records attributed to Ernest Ma.
The A_4 model of leptons was proposed originally for nearly degenerate neutrino masses. With minimal modification, it is shown to accommodate as well the cases of normal hierarchy and inverted hierarchy. In all cases, this new model predicts sin^2 2 theta_{atm} = 1 and tan^2 theta_{sol} = 0.5 for U_{e3} = 0. It also predicts their deviations from 1 and 0.5 respectively for U_{e3} not equal to zero.
We discuss the possibility of flavor symmetries to explain the pattern of charged lepton and neutrino masses and mixing angles. We emphasize what are the obstacles for the generation of an almost maximal atmospheric mixing and what are the minimal ingredients to obtain it. A model based on the discrete symmetry $S_3$ is constructed, which leads to the dominant $μτ$-block in the neutrino mass matrix, thus predicting normal hierarchy. This symmetry makes it possible to reproduce current data and predicts $0.01\lesssimθ_{13}\lesssim 0.03$ and strongly suppressed neutrinoless $2β$-decay. Moreover, it implies a relation between lepton and quark mixing angles: $θ_{23}^q \approx 2(π/4-θ_{23})$. The Cabibbo mixing can also be reproduced and $θ_{13}^q\sim θ_{12}^qθ_{23}^q$. $S_3$ is thus a candidate to describe all the basic features of Standard Model fermion masses and mixing.
We consider N=1 supersymmetric gauge theories based on the group SU(N)_1 x SU(N)_2 x ... x SU(N)_k with matter content (N,N*,1,...,1) + (1,N,N*,...,1) + >... + (N*,1,1,...,N) as candidates for the unification symmetry of all particles. In particular we examine to which extent such theories can become finite and we find that a necessary condition is that there should be exactly three families. We discuss further some phenomenological issues related to the cases (N,k) = (3,3), (3,4), and (4,3), in an attempt to choose those theories that can become also realistic. Thus we are naturally led to consider the SU(3)^3 model which we first promote to an all-loop finite theory and then we study its additional predictions concerning the top quark mass, Higgs mass and supersymmetric spectrum.
Exotic fermions of half-integral charges at the TeV energy scale are predicted by the quartification model of Babu, Ma, and Willenbrock. We add to these one copy of their scalar analogs and discuss the ensuing phenomenological implications, i.e. radiative contributions to lepton masses and flavor-changing leptonic decays.
The seemingly disparate notions of chiral color and quark-lepton nonuniversality are combined, and shown to be essential to each other as part of an underlying (and unifying) larger symmetry, i.e. supersymmetric SU(3)^6. Both phenomena are accessible experimentally at the TeV energy scale.
The standard model of leptons is extended to accommodate a discrete Z_3 X Z_2 family symmetry. After rotating the charged-lepton mass matrix to its diagonal form, the neutrino mass matrix reveals itself as very suitable for explaining atmospheric and solar neutrino oscillation data. A generic requirement of this approach is the appearance of three Higgs doublets at the electroweak scale, with observable flavor violating decays.
An approximate Z_3 family symmetry is proposed for leptons which results in a neutrino mass matrix with sin^2 2 theta_atm = 1 and tan^2 theta_sol = 0.5, but the latter value could easily be smaller. A generic requirement of this approach is the appearance of three Higgs doublets at the electroweak scale, resulting in possibly observable flavor violating leptonic decays, such as mu -> eee and mu -> e gamma.
With the recent experimental advance in our precise knowledge of the neutrino oscillation parameters, the correct form of the 3 X 3 neutrino mass matrix is now approximately known. I discuss how this may be obtained from symmetry principles, using as examples the finite groups A_4 and Z_3, in two complete theories of leptons (and quarks).
The 3 X 3 Majorana neutrino mass matrix is written as a sum of 3 terms, i.e. M_nu = M_A + M_B + M_C, where M_A is proportional to the identity matrix and M_B and M_C are invariant under different Z_3 transformations. This M_nu is very suitable for understanding atmospheric and solar neutrino oscillations, with sin^2 (2 theta_atm) and tan^2 (theta_sol) fixed at 1 and 0.5 respectively, in excellent agreement with present data. It has in fact been proposed before, but only as an ansatz. This paper uncovers its underlying symmetry, thus allowing a complete theory of leptons and quarks to be constructed.
It has recently been proposed that all fundamental fermion masses (whether Dirac or Majorana) come from effective dimension-five operators in the context of a truly minimal left-right model. We show how a particularly economical scheme emerges in a supersymmetric framework, where chiral symmetry breaking originates in the gaugino sector.
The neutrino sector in a left-right extension of the Standard Model depends on how SU(2)_R is broken. I list all possible scenarios, including the ones where the Majorana nu_R mass is naturally much smaller than the SU(2)_R breaking scale, which is desirable for generating the proper baryon asymmetry of the Universe. The best such choice is identified and discussed.
We propose that quarks and leptons are interchangeable entities in the high-energy limit. This naturally results in the extension of [SU(3)]^3 trinification to [SU(3)]^4 quartification. In addition to the unbroken color SU(3)_q of quarks, there is now also a color SU(3)_l of leptons which reduces to an unbroken SU(2)_l. We discuss the natural occurrence of SU(2)_l doublets at the TeV energy scale, which leads remarkably to the unification of all gauge couplings without supersymmetry. Proton decay occurs through the exchange of scalar bosons, with a lifetime in the range 10^{34} - 10^{36} years.
With the recent experimental advance in our precise knowledge of the neutrino oscillation parameters, the correct form of the 3 X 3 neutrino mass matrix is now approximately known. I discuss how this may be obtained from symmetry principles, using as examples the finite groups A_4 and Z_4, predicting as a result three nearly degenerate Majorana neutrino masses in the 0.2 eV range.
Following the newly formulated notion of form invariance of the neutrino mass matrix, a complete model of leptons is constructed. It is based on a specific unitary 3 X 3 matrix U in family space, such that U^2 is the simple discrete symmetry nu_e to -nu_e, nu_mu to nu_tau. Thus U also generates the cyclic group Z_4. The charged-lepton mass matrix is nearly diagonal while the neutrino mass matrix is of the form suitable for explaining maximal (large) mixing in atmospheric (solar) neutrino oscillations in the context of three nearly degenerate neutrino masses. Observable lepton flavor violation is predicted. Quarks may be treated in the same way as the charged leptons.
A natural theoretical framework is presented which allows for small departures from quark-lepton universality such that different G_F and sin^2(theta_W) values are applicable for different processes. In particular, the inequality (G_F)^{NC}_{lq} < (G_F)^{CC}_{lq} < (G_F)^{CC}_{ll} < (G_F)^{NC}_{ll} holds. New physics is predicted at the TeV scale.
We propose a left-right model of quarks and leptons based on the gauge group $SU(3)_C \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$, where the scalar sector consists of only two doublets: (1,2,1,1) and (1,1,2,1). As a result, any fermion mass, whether it be Majorana or Dirac, must come from dimension-five operators. This allows us to have a common view of quark and lepton masses, including the smallness of Majorana neutrino masses as the consequence of a double seesaw mechanism.
Consider the most general $3 \times 3$ Majorana neutrino mass matrix $\cal M$. Motivated by present neutrino-oscillation data, much theoretical effort is directed at reducing it to a specific texture in terms of a small number of parameters. This procedure is often {\it ad hoc}. I propose instead that for any $\cal M$ one may choose, it should satisfy the condition $U {\cal M} U^T = {\cal M}$, where $U \neq 1$ is a specific unitary matrix such that $U^N$ represents a well-defined discrete symmetry in the $ν_{e,μ,τ}$ basis, $N$ being a particular integer not necessarily equal to one. I illustrate this idea with a number of examples, including the realistic case of an inverted hierarchy of neutrino masses.
There is new experimental evidence which may be interpreted as a small departure from quark-lepton universality. We propose to understand this as the result of a hierarchy of mass scales in analogy to $m_u, m_d << Λ_{QCD}$ for strong isospin. We show $(G_F)^{NC}_{lq} < (G_F)^{CC}_{lq} < (G_F)^{CC}_{ll} < (G_F)^{NC}_{ll}$ in principle, but all are still approximately equal. New physics is predicted at the TeV scale.