Trying to understand the Standard Model parameters

We stress the importance of the circa 20 parameters in the Standard Model, which are not fixed by the model but only determined experimentally, as a window to the physics beyond the Standard Model. However, it is a tiny window in as far as these numbers contain only the information corresponding to about one line of text. Looking for a method to study these coupling and mass parameters, we put forward the idea of the Multiple Point Principle as a first step. This principle states that Nature adjusts the coupling and mass parameters so as to make many different vacuum states exist and have approximately the same energy densities (cosmological constants). As an illustrative application, we put up the proposal that a small increase (maybe only an infinitesimal one) in the value of the top quark coupling constant could lead to a new vacuum phase; in this new phase the binding of a bound state of 6 top quarks and 6 anti-top quarks becomes so strong as to become a tachyon and condense in the vacuum. Assuming the existence of a third degenerate vacuum at the fundamental energy scale, we present a solution to the hierarchy problem of why the ratio of the fundamental scale to the electroweak scale is so large. We also present a 5 parameter fit to the orders of magnitude of the quark-lepton masses and mixing angles in the Family Replicated Gauge Group Model. In this model, the Standard Model gauge group and a gauged B-L (baryon number minus lepton number) is extended to one set of gauge fields for each family of fermions.Comment: Institute address corrected and one reference adde

Cosmological constant in SUGRA models with Planck scale SUSY breaking and degenerate vacua

The empirical mass of the Higgs boson suggests small to vanishing values of the quartic Higgs self-coupling and the corresponding beta function at the Planck scale, leading to degenerate vacua. This leads us to suggest that the measured value of the cosmological constant can originate from supergravity (SUGRA) models with degenerate vacua. This scenario is realised if there are at least three exactly degenerate vacua. In the first vacuum, associated with the physical one, local supersymmetry (SUSY) is broken near the Planck scale while the breakdown of the SU(2)W×U(1)Y symmetry takes place at the electroweak (EW) scale. In the second vacuum local SUSY breaking is induced by gaugino condensation at a scale which is just slightly lower than ΛQCD in the physical vacuum. Finally, in the third vacuum local SUSY and EW symmetry are broken near the Planck scale

Neutrino masses and mixings from an SMG \times U(1)^2 model

A natural solution to the fermion mass hierarchy problem suggests the existence of a partially conserved chiral symmetry. We show that this can lead to a reasonably natural solution to the solar and atmospheric neutrino problems without fine-tuning or the addition of new low energy fermions. The atmospheric neutrino atmospheric neutrino anomaly is given by large mixing between $\nu_{\mu}$ and $\nu_{\tau}$, with \Delta m^2_{atm} \sim 10^{-3} \eV^2, and the solar neutrino deficit is due to nearly maximal electron neutrino vacuum oscillations. We present an explicit model for the neutrino masses which is an anomaly free Abelian extension of the standard model that also yields a realistic charged fermion spectrum.Comment: 16 pages, 2 figures. Figures use FeynTeX package.Minor modifications made. Version to appear in Phys.Lett.

Where does Flavour Mixing come from?

We argue that flavour mixing, both in the quark and charged lepton sector, is basically determined by the lightest family mass generation mechanism. So, in the chiral symmetry limit when the up and down quark masses vanish, all the quark mixing angles vanish. This mechanism is not dependent on the number of quark-lepton families nor on any ``vertical'' symmetry structure, unifying quarks and leptons inside a family as in Grand Unified Theories. Together with a hypothesis of maximal CP violation, the model leads to a completely predictive ansatz for all the CKM matrix elements in terms of the quark masses. Some implications for neutrino masses and oscillations are briefly discussed.Comment: 13 page LaTeX file, minor changes in fourth paragraph of Conclusion and in Reference

Lepton Number Violation in Supersymmetric Grand Unified Theories

We argue that the nature of the global conservation laws in Supersymmetric Grand Unified Theories is determined by the basic vacuum configuration in the model rather than its Lagrangian. It is shown that the suppression of baryon number violation in a general (R-parity violating) superpotential can naturally appear in some extended SU(N) SUSY GUTs which, among other degenerate symmetry-breaking vacua, have a missing VEV vacuum configuration giving a solution to the doublet-triplet splitting problem. We construct SU(7) and SU(8) GUTs where the effective lepton number violating couplings immediately evolve, while the baryon number non-conserving ones are safely projected out as the GUT symmetry breaks down to that of the MSSM. However at the next stage, when SUSY breaks, the radiative corrections shift the missing VEV components to some nonzero values of order M_{SUSY}, thereby inducing the ordinary Higgs doublet mass, on the one hand, and tiny baryon number violation, on the other. So, a missing VEV solution to the gauge hierarchy problem leads at the same time to a similar hierarchy of baryon vs lepton number violation.Comment: 15 page LaTeX fil

The Origin of Mass

The quark-lepton mass problem and the ideas of mass protection are reviewed. The hierarchy problem and suggestions for its resolution, including Little Higgs models, are discussed. The Multiple Point Principle is introduced and used within the Standard Model to predict the top quark and Higgs particle masses. Mass matrix ans\"{a}tze are considered; in particular we discuss the lightest family mass generation model, in which all the quark mixing angles are successfully expressed in terms of simple expressions involving quark mass ratios. It is argued that an underlying chiral flavour symmetry is responsible for the hierarchical texture of the fermion mass matrices. The phenomenology of neutrino mass matrices is briefly discussed.Comment: 33 pages, 7 figures, to be published in the Proceedings of the XXXI ITEP Winter School, Moscow, Russia, 18 - 26 February 200

Fermion family recurrences in the Dyson-Schwinger formalism

We study the multiple solutions of the truncated propagator Dyson-Schwinger equation for a simple fermion theory with Yukawa coupling to a scalar field. Upon increasing the coupling constant $g$, other parameters being fixed, more than one non-perturbative solution breaking chiral symmetry becomes possible and we find these numerically. These ``recurrences'' appear as a mechanism to generate different fermion generations as quanta of the same fundamental field in an interacting field theory, without assuming any composite structure. The number of recurrences or flavors is reduced to a question about the value of the Yukawa coupling, and has no special profound significance in the Standard Model. The resulting mass function can have one or more nodes and the measurement that potentially detects them can be thought of as a collider-based test of the virtual dispersion relation $E=\sqrt{p^2+M(p^2)^2}$ for the charged lepton member of each family. This requires three independent measurements of the charged lepton's energy, three-momentum and off-shellness. We illustrate how this can be achieved for the (more difficult) case of the tau lepton

Deriving Gauge Symmetry and Spontaneous Lorentz Violation

We consider a class of field theories with a four-vector field $A_{\mu}(x)$ in addition to other fields supplied with a global charge symmetry - theories which have partial gauge symmetry in the sense of only imposing it on those terms in the Lagrangian density which have derivatives as factors in them. We suppose that spontaneous Lorentz invariance breaking occurs in such a theory due to the four-vector field taking a non-zero vacuum expectation value. Under some very mild assumptions, we show that this Lorentz violation is not observable and the whole theory is practically gauge invariant. A very important presupposition for this theorem is that an initial condition is imposed on the no-derivative expressions corresponding to the early Universe being essentially in a vacuum state. This condition then remains true forever and can be interpreted as a gauge constraint. We formulate the conditions under which the spontaneous Lorentz violation becomes observable. Spontaneously broken Lorentz invariance could be seen by some primordially existing or created "fossil" charges with the property of moving through the Universe with a fixed velocity.Comment: Extended versio

Minimal Mixing of Quarks and Leptons in the SU(3) Theory of Flavour

We argue that flavour mixing, both in the quark and lepton sector, follows the minimal mixing pattern, according to which the whole of this mixing is basically determined by the physical mass generation for the first family of fermions. So, in the chiral symmetry limit when the masses of the lightest ($u$ and $d$) quarks vanish, all the quark mixing angles vanish. This minimal pattern is shown to fit extremely well the already established CKM matrix elements and to give fairly distinctive predictions for the as yet poorly known ones. Remarkably, together with generically small quark mixing, it also leads to large neutrino mixing, provided that neutrino masses appear through the ordinary ``see-saw'' mechanism. It is natural to think that this minimal flavour mixing pattern presupposes some underlying family symmetry, treating families of quarks and leptons in a special way. Indeed, we have found a local chiral $SU(3)_{F}$ family symmetry model which leads, through its dominant symmetry breaking vacuum configuration, to a natural realization of the proposed minimal mechanism. It can also naturally generate the quark and lepton mass hierarchies. Furthermore spontaneous CP violation is possible, leading to a maximal CP violating phase $\delta =\frac{\pi}{2}$, in the framework of the MSSM extended by a high-scale $SU(3)_{F}$ chiral family symmetry.Comment: 52 pages, LaTex, no figures; some typos corrected; journal versio

Light Higgs Boson in the Spontaneously CP Violating NMSSM

We consider spontaneous CP violation in the Next to Minimal Supersymmetric Standard Model, without the usual $Z_3$ discrete symmetry. CP violation can occur at tree level, raising a potential conflict with the experimental bounds on the electric dipole moments of the electron and neutron. One escape from this is to demand that the CP violating angles are small, but we find that this entails a light neutral Higgs particle. This is almost pseudoscalar, can have a high singlet content, and will be hard to detect experimentally.Comment: 14 page LaTeX fil