arXiv subjects
Publications and source records attributed to S. M. Barr.
A mechanism for lifting the cosmological upper bound on the axion decay constant, $f_a$, is proposed. It entails the near masslessness of the radial mode whose vacuum expectation value is $f_a$. Energy in the coherent oscillations of the axion field in the early universe gets fed into the motion of the radial mode, from which it is then redshifted away.
A model is presented that fits the quark and lepton masses and mixings wherein five dimensionless parameters and a phase account for fifteen dimensionless observables. Among these are the Wolfenstein parameters $ρ$ and $η$, the $ν_e-ν_μ$ and $ν_e-ν_τ$ mixing angles which are predicted to be small and comparable while the $ν_μ-ν_τ$ mixing angle is predicted to be large. The model is based on supersymmetric SO(10) with the form of the mass matrices motivated by simplicity at the level of grand unification.
It is shown that in SO(10) there is a general connection between the suppression of higgsino mediated proton decay and the value of $α_s$. However, agreement with the experimental value of $α_s$ can be obtained if there are relatively large negative threshold corrections to $α_s$ coming from superheavy split multiplets. It is shown that such split multiplets can arise in SO(10) without fine-tuning of parameters.
A minimal SO(10) Higgs structure involving a single adjoint field along with spinors, vectors and singlets has been shown to break the SO(10) gauge symmetry to the standard model while stabilizing the F-flat directions and solving the doublet-triplet splitting problem naturally. With this minimal set of Higgs fields, we show how to construct quark and lepton mass matrices which explain well the many features of the observed spectrum, including the Georgi-Jarlskog mass relations. A large mixing of the muon- and tau-neutrinos results naturally as observed in the atmospheric neutrino data. A particular model relying on a family symmetry has been constructed which realizes the desired mass matrices.
A structure is proposed for the mass matrices of the quarks and leptons that arises in a natural way from the assumption that the breaking of SO(10) gauge symmetry is achieved by the smallest possible set of vacuum expectation values. This structure explains well many features of the observed spectrum of quarks and leptons. It reproduces the Georgi-Jarlskog mass relations and postdicts the charm quark mass in reasonable agreement with data. It also predicts a large mixing angle between ν_μ and ν_τ, as suggested by atmospheric neutrino data. The mixing angles of the electron neutrino are predicted to be small.
It has recently been shown how to break SO(10) down to the Standard Model in a realistic way with only one adjoint Higgs. The expectation value of this adjoint must point in the B-L direction. This has consequences for the possible form of the quark and lepton mass matrices. These consequences are explored in this paper, and it is found that one is naturally led to consider a particular form for the masses of the heavier generations. This form implies typically that there should be large (nearly maximal) mixing of the mu- and tau-neutrinos. An explanation that does not involve large tan beta also emerges for the fact that b and tau are light compared to the top quark.
One of the puzzles of the Standard Model is why the mass parameter which determines the scale of the Weak interactions is closer to the scale of QCD than to the Grand Unification or Planck scales. We discuss a novel approach to this problem which is possible in theories in which different regions of the universe can have different values of the physical parameters. In such a situation, we would naturally find ourselves in a region which has parameters favorable for life. We explore the whole range of values of the mass parameter in the Higgs potential, $μ^2$, from $+M_P^2$ to $-M_P^2$ and find that there is only a narrow window, overlapping with the observed value, in which life is likely to be possible. The observed value of $μ^2$ is fairly typical of the values in this range. Thus multiple domain theories in which $μ^2$ varies among domains may give a promising approach to solving the fine tunign problem and explaining the closeness of the QCD scale and the Weak scale.
In theories in which different regions of the universe can have different values of the the physical parameters, we would naturally find ourselves in a region which has parameters favorable for life. We explore the range of anthropically allowed values of the mass parameter in the Higgs potential, $μ^2$. For $μ^2<0$, the requirement that complex elements be formed suggests that the Higgs vacuum expectation value $v$ must have a magnitude less than 5 times its observed value. For $μ^2>0$, baryon stability requires that $|μ|<<M_P$, the Planck Mass. Smaller values of $|μ^2|$ may or may not be allowed depending on issues of element synthesis and stellar evolution. We conclude that the observed value of $μ^2$ is reasonably typical of the anthropically allowed range, and that anthropic arguments provide a plausible explanation for the closeness of the QCD scale and the weak scale.
It is shown that the doublet-triplet splitting problem can be solved in SO(10) using the Dimopoulos-Wilczek mechanism with a very economical Higgs content and simple structure. Only one adjoint Higgs field is required, together with spinor and vector fields. The successful SUSY GUT prediction of gauge coupling unification is preserved. Higgsino-mediated proton decay can be suppressed below (but not far below) present limits without fine-tuning.
It is shown, using a modification of an idea of Sen, that completely realistic supersymmetric grand-unified theories based on SU(6) or larger unitary groups can be constructed using the sliding-singlet mechanism. These models have a simple structure, preserve the successful prediction of $\sin^2 θ_W$, and can suppress Higgsino-mediated proton decay to an acceptable level in a simple way.
An approach to solving the Strong CP Problem in supersymmetric theories is discussed which uses abelian family symmetries to align the mass matrices of the quarks and squarks. In this way both the Strong CP Problem and the characteristic flavor and CP problems of supersymmetry can be solved in a single way.
It is argued that in the context of supersymmetry, the Strong CP Problem is most naturally seen as an aspect (particularly severe) of the whole complex of flavor-violating and CP-violating problems of supersymmetry. It is shown that certain approaches to solving these flavor problems also allow simple solutions to the Strong CP Problem. The idea of ``flavor alignment" suggested by Nir and Seiberg allows not only flavor violation to be controlled but supersymmetric contributions to the theta parameter to be made acceptably small. Another approach to the flavor-violation problem, namely low-energy supersymmetry breaking, allows another class of solutions to the Strong CP Problem to be viable.
Several experimental results could be interpreted as evidence that certain neutrino mixing angles are large, of order unity. However, in the context of grand unified models the neutrino angles come out characteristically to be small, like the KM angles. It is shown how to construct simple grand-unified models in which neutrino angles are not only large but completely predicted with some precision. Six models are presented for illustration.
It has been shown that the Dimopoulos-Wilczek (or missing-VEV) mechanism for doublet-triplet splitting can be implemented in $SU(5) \times SU(5)$ models, which requires no adjoint Higgs fields. This is an advantage from the point of view of string theory construction. Here the stability of the gauge hierarchy is examined in detail, and it is shown that it can be guaranteed much more simply than in $SO(10)$. In fact a $Z_2$ symmetry ensures the stability of the DW form of the expectation values to all orders in GUT-scale VEVs. It is also shown that models based on $SO(10) \times SU(5)$ have the advantages of $SU(5) \times SU(5)$ while permitting complete quark-lepton unification as in $SO(10)$.
It is shown that a gauged SO(3) family symmetry can suppress flavor-changing processes from squark-mass non-degeneracy to an acceptable level. The potentially dangerous SO(3) D-terms can be rendered harmless if the CP-violating phases appearing in the SO(3)-breaking sector are small, which can naturally be the case if CP is a spontaneously broken symmetry. This approach has certain advantages over models based on global or non-abelian discrete symmetries, and dovetails with some recent proposals for explaining the pattern of quark and lepton masses. Moreover this approach relates the near-degeneracy of the squark masses to an approximate CP invariance which can also explain the smallness of the electron and neutron electric dipole moments.
In a recent paper a model of quark and lepton masses was proposed. Without any family symmetries almost all the qualitative and quantitative features of the quark and lepton masses and Kobayashi-Maskawa mixing angles are explained, primarily as consequences of various aspects of $SO(10)$ symmetry. Here the model is discussed in much greater detail. The threefold mass hierarchy as well as the relations $m_τ^0 \simeq m_b^0, ~m_μ^0 \simeq 3m_s^0,~ m_e^0 \simeq {1 \over 3} m_d^0, ~m_u^0/m_t^0 \ll m_d^0/m_b^0, ~{\rm tan}θ_C \simeq \sqrt{m_d^0/m_s^0},~ V_{cb} \ll \sqrt{m_s^0/m_b^0}$ and $V_{ub} \sim V_{us}V_{cb}$ follow from a simple Yukawa structure at the unification scale. The model also gives definite predictions for $\tan β$, the neutrino mixing angles, and proton decay branching ratios. The $(ν_μ-ν_τ)$ mixing angle is typically large, tan$β$ is close to either $m_t^0/m_b^0$ or $m_c^0/m_s^0$, and proton decay is in the observable range, but there is a group theoretical suppression factor in the rate.
Typically in unified theories the neutrino mixing angles, like the Cabibbo-Kobayashi-Maskawa (CKM) angles of the quarks, are related to the small mass ratios between fermions of different generations and are therefore quite small. A new approach for explaining the intergenerational mass hierarchies is proposed here which, while giving small CKM angles, naturally leads to neutrino angles of order unity. Such large mixing angles may be required for a resolution of the atmospheric neutrino anomaly and may also be relevant for the solar neutrino puzzle. The mechanism presented here provides a framework in which novel approaches to the fermion mass question can arise. In particular, within this framework a variant of the texture idea allows highly predictive models to be constructed, an illustrative example of which is given. It is shown how the neutrino mixing angles may be completely determined in such schemes.
It is shown that in realistic SUSY GUT models of quark and lepton masses both the proton decay rate and branching ratios differ in general from those predicted in the minimal $SU(5)$ supersymmetric model. The observation of proton decay, and in particular the branching ratio $B[(p \rightarrow π^+ \overlineν)/(p \rightarrow K^+ \overlineν)]$, would thus allow decisive tests of these fermion mass schemes. It is shown that the charged lepton decay modes $p \rightarrow K^0 μ^+, p \rightarrow K^0 e^+$ arising through gluino dressing diagrams are significant and comparable to the neutrino modes in large tan$β$ models. Moreover, it is found that in certain classes of models the Higgsino-mediated proton decay amplitudes are proportional to a model-dependent group-theoretical factor which in some cases can be quite small. The most interesting such class consists of $SO(10)$ models in which the dominant flavor-symmetric contribution to the up-quark mass matrix comes from an effective operator of the form ${\bf 16}_i{\bf 16}_j {\bf 10}_H {\bf 45}_H$, where $\langle {\bf 45}_H \rangle$ points approximately in the $I_{3R}$ direction. This class includes a recent model of quark and lepton masses proposed by the authors.