arXiv subjects

C. D. Froggatt

Publications and source records attributed to C. D. Froggatt.

At least 73 records · Page 4Linked to original sources

arXiv2001

Quantum Numbers of AGUT Higgs Fields from the Quark-Lepton Spectrum

A series of Higgs field quantum numbers in the anti-grand unification model, based on the gauge group $SMG^3 \times U(1)_f$, is tested against the spectrum of quark and lepton masses and mixing angles. A more precise formulation of the statement that the couplings are assumed of order unity is given. It is found that the corrections coming from this more precise assumption do not contain factors of order of the number of colours, $N_c= 3$, as one could have feared. We also include a combinatorial correction factor, taking account of the distinct internal orderings within the chain Feynman diagrams in our statistical estimates. Strictly speaking our model predicts that the uncertainty in its predictions and thus the accuracy of our fits should be $\pm 60\%$. Many of the best fitting quantum numbers give a higher accuracy fit to the masses and mixing angles, although within the expected fluctuations in a $χ^2$. This means that our fit is as good as it can possibly be.

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arXiv2001

Spontaneously Generated Gauge Invariance

We argue that the non-observability of the spontaneous breakdown of Lorentz symmetry (SBLS) caused by the vacuum expectation values of vector fields could provide the origin of all internal symmetries observed. Remarkably, the application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads by itself to the appearance of a symmetry and, what is more, to the massless vector field(s) gauging this symmetry. A simple model for the SBLS based on massive vector and real scalar field interactions is considered; it is found that spontaneously broken gauge symmetries could also appear, when SBLS happens and is required to be physically unobservable.

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arXiv2001

Lorentz Invariance and Origin of Symmetries

In this letter we reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can only be imposed in the sense that all Lorentz non-invariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. Remarkably, the application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads by itself to the appearance of a symmetry and, what is more, to the massless vector fields gauging this symmetry in both Abelian and non-Abelian cases. In contrast, purely global symmetries are only generated as accidental consequences of the gauge symmetry.

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arXiv2001

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.

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arXiv2001

Standard Model Higgs Boson Mass from Borderline Metastability of the Vacuum

We have studied imposing the condition that the Standard Model effective Higgs potential should have two approximately degenerate vacua, such that the vacuum we live in is just barely metastable: the one in which we live has a vacuum expectation value of 246 GeV and the other one should have a vacuum expectation value of order the Planck scale. Alone borderline metastability gives, using the experimental top quark mass 173.1 \pm 4.6 GeV, the Higgs mass prediction 121.8 \pm 11 GeV. The requirement that the second minimum be at the Planck scale already gave the prediction 173\pm 4 GeV for the top quark mass according to our 1995 paper.

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arXiv2000

Neutrino Oscillations in Extended Anti-GUT Model

What we call the Anti-GUT model is extended a bit to include also right-handed neutrinos and thus make use of the see-saw mechanism for neutrino masses. This model consists in assigning gauge quantum numbers to the known Weyl fermions and the three see-saw right-handed neutrinos. Each family (generation) is given its own Standard Model gauge fields and a gauge field coupled to the $B-L$ quantum number for that family alone. Further we assign a rather limited number of Higgs fields, so as to break these gauge groups down to the Standard Model gauge group and to fit, w.r.t. order of magnitude, the spectra and mixing angles of the quarks and leptons. We find a rather good fit, which for neutrino oscillations favours the small mixing angle MSW solution, although the mixing angle predicted is closest to the upper side of the uncertainty range for the measured solar neutrino mixing angle. An idea for making a ``finetuning''-principle to ``explain'' the large ratios found empirically in physics, and answer such questions as ``why is the weak scale low compared to the Planck scale?'', is proposed. A further very speculative extension is supposed to ``explain'' why we have three families.

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arXiv2000

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.

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arXiv2000

From Prototype SU(5) to Realistic SU(7) SUSY GUT

We construct a realistic SU(7) model which provides answers to many questions presently facing the prototype SU(5) SUSY GUT. Among them are a solution to the doublet-triplet splitting problem, string scale unification, proton decay, the hierarchy of baryon vs lepton number violation and neutrino masses.

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arXiv2000

The Majorana particles and the Majorana sea

Can one make a Majorana field theory for fermions starting from the zero mass Weyl theory, then adding a mass term as an interaction? The answer to this question is: yes we can. We can proceed similarly to the case of the Dirac massive field theory. In both cases one can start from the zero mass Weyl theory and then add a mass term as an interacting term of massless particles with a constant (external) field. In both cases the interaction gives rise to a field theory for a free massive fermion field. We present the procedure for the creation of a mass term in the case of the Dirac and the Majorana field and we look for a massive field as a superposition of massless fields.

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arXiv1999

The Quark Lepton Mass Problem and the Anti-Grand Unification Model

The fermion mass problem and the ideas of mass protection are briefly reviewed. The Fritzsch ansatz for the quark mass matrices and a recent variant, based on a lightest flavour mixing mechanism in which all the CKM mixing angles disappear in the chiral symmetry limit of vanishing up and down quark masses, are discussed. The Anti-Grand Unification Model (AGUT) and the Multiple Point Principle (MPP) used to calculate the values of the Standard Model gauge coupling constants in the theory are described. The application of the MPP to the pure Standard Model predicts the top quark mass to be $173 \pm 5$ GeV and the Higgs particle mass to be $135 \pm 9$ GeV. Mass protection by the chiral quantum numbers of the maximal AGUT gauge group $SMG \times U(1)_f$ provides a successful fit to the charged fermion mass spectrum, with an appropriate choice of Higgs fields to break the AGUT gauge group down to the Standard Model gauge group (SMG) close to the Planck scale. The puzzle of the neutrino masses and mixing angles presents a challenge to the AGUT model and approaches to this problem are briefly discussed.

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arXiv1999

Why do we have parity violation?

We discuss here two of the questions posed at the beginning of the Bled 1998 workshop: Why is the weak charge dependent on handedness? Why do we have parity violation in the Standard Model? It is argued that the quarks and leptons must be protected from gaining a fundamental mass, very large compared to the electroweak scale, by gauge invariance and hence that their gauge charges must depend on handedness. Furthermore we argue that it is the conservation of parity in the electromagnetic and strong interactions rather than parity violation in the weak interactions that needs an explanation. We derive this parity conservation and indeed the whole system of Weyl fermion representations in the Standard Model from a few simple assumptions: Mass protection, small representations, anomaly cancellation and the Standard Model gauge group $S(U(2)\times U(3))$.

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arXiv1999

Masses and mixing angles and going beyond the Standard Model

The idea, following Michel and O'Raifeartaigh, of assigning meaning to the (gauge) \underline{group} and not only the Lie algebra for a Yang Mills theory is reviewed. Hints from the group and the fermion spectrum of the Standard Model are used to suggest the putting forward of our AGUT-model, which gives a very good fit to the orders of magnitudes of the quark and lepton masses and the mixing angles including the CP-breaking phase. But for neutrino oscillations modifications of the model are needed. Baryogenesis is not in conflict with the model.

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arXiv1999

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.

hep-ph↗

arXiv1999

CP Violation in the Next to Minimal Supersymmetric Standard Model

We consider spontaneous CP violation in the Next to Minimal Supersymmetric Standard Model (NMSSM), 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 an unacceptably light neutral Higgs.

hep-ph↗

arXiv1998

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 $ν_μ$ and $ν_τ$, with $Δm^2_{atm} \sim 10^{-3} \eV^2$, 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.

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arXiv1998

The Problem of the Quark-Lepton Mass Spectrum

We review some approaches to the quark-lepton mass problem. The ideas of mass-protection and approximate chiral flavour symmetries as a framework for resolving the mass hierarchy problem are presented. Dynamical calculations of the top quark and Higgs particle masses, based on infra-red fixed points and the so-called multiple point principle respectively, are discussed. We also consider mass matrix texture and the neutrino mass puzzle.

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arXiv1998

Agut Masses

From considerations of the number of matrix elements of different orders of magnitude in the quark and charged lepton mass matrices, we suggest that the underlying gauge group responsible for the spectrum should have several---actually of the order of 7 to 10---cross product factors. This is taken to support our AGUT gauge group $SMG^3 \times U(1)_f$ which, under certain simple conditions, is the maximal group transforming the known 45 Weyl quark-lepton fields into each other. We describe the AGUT fit to the charged fermion mass spectrum, and briefly discuss baryogenesis and the neutrino mass problem.

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arXiv1998

The Fermion Mass Problem and the Anti-Grand Unification Model

We describe the Anti-Grand Unification Model (AGUT) and the Multiple Point Principle (MPP) used to calculate the values of the Standard Model gauge coupling constants in the theory, from the requirement of the existence of degenerate vacua. The application of the MPP to the pure Standard Model predicts the existence of a second minimum of the Higgs potential close to the cut-off, which we take to be the Planck scale, giving our Standard Model predictions for the top quark and Higgs masses: $M_t = 173 \pm 5$ GeV and $M_H = 135 \pm 9$ GeV. We also discuss mass protection by chiral charges and present a fit to the charged fermion mass spectrum using the chiral quantum numbers of the maximal AGUT gauge group $SMG^3 \times U(1)_f$, where $SMG \equiv SU(3) \times SU(2) \times U(1)$. The neutrino mass and mixing problem is then briefly discussed for models with chiral flavour charges responsible for the charged fermion mass hierarchy.

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