arXiv subjects
Publications and source records attributed to C. D. Froggatt.
We explore the possibility of spontaneous CP violation within the Next to Minimal Supersymmetric Standard Model. In the most general form of the model, without a discrete $Z_3$ symmetry, we find that even at tree level spontaneous CP violation can occur, while also permitting Higgs masses consistent with experiment.
The fermion mass problem is briefly reviewed. The observed hierarchy of quark and charged lepton masses strongly suggests the existence of an approximately conserved chiral flavour symmetry beyond the Standard Model. It is argued that in models of this type, the requirement of a natural explanation for both the atmospheric and solar neutrino problems leads to an essentially unique picture of neutrino masses and mixing angles. The anti-grand unification model is used as an explicit example to illustrate these ideas.
We describe a fit to the charged fermion mass hierarchy using the chiral quantum numbers of the maximal anti-grand unification group $SMG^3 \times U(1)_f$, where $SMG \equiv SU(3) \times SU(2) \times U(1)$. This fit suggests a set of Higgs fields responsible for the breakdown, near the Planck scale, of $SMG^3 \times U(1)_f$ to the Standard Model group.
We put forward a model, or rather a relatively broad class of models, beyond the Standard Model based on the two main assumptions: MPP) The coupling constants should be fixed such as to ensure that there be many ``vacuum states'', i.e. Lorentz invariant states of the fields, with the same energy density. Anti-GUT) At high energy, above an essential desert of only Standard Model interactions, there is the bigger gauge group $SMG^3\times U(1)_f$ which means that each family of quarks and leptons has its own set of gauge bosons analogous to those in the Standard Model itself, and then there is one extra abelian gauge boson called $U(1)_f$. In addition we make some further more phenomenological assumptions. We succeed in fitting order of magnitudewise most of the (effective) Yukawa couplings observed in the Standard Model as quark and lepton masses and mixing angles. We have more accurate numbers for the three fine-structure constants and the top and Higgs masses, as well as some suggestive understanding of the fine-tuning wonders for the cosmological constant and the $Θ$-angles. CP-violation is predicted a bit low, but order of magnitudewise in agreement with experiment. In summary, we obtain at least an order of magnitudewise understanding of the Standard Model parameters within our scheme, except for the mysteriously low weak scale compared to the Planck scale, with only 4 continuous parameters being fitted, in addition to our somewhat more discrete choices.
We present two rather differently based predictions for the quark and lepton spectrum: One provides a rather successful fit to the mass suppressions---the well known fermion mass hierarchy---interpreted as due to most mass terms needing to violate approximately conserved quantum numbers corresponding to the AGUT group $ SMG^3\times U(1)_f$. This is actually, under certain conditions, the maximal group transforming the known 45 Weyl components of the quark and leptons into each other. From the fit to the fermion spectrum, we get a picture of the series of Higgs fields causing the breakdown (presumably at the Planck scale) of this AGUT to the Standard Model and, thus, providing the small masses of all quarks and leptons except for the top quark. We separately predict the top quark mass to be $173 \pm 5$ GeV and the Higgs mass to be $135 \pm 9$ GeV, from the assumption that there be two degenerate minima in the effective potential for the Weinberg Salam Higgs field with the second one at the Planck field strength.
We consider the application of the Multiple Point Criticality Principle to the Standard Model and its extension to the anti-grand gauge group $SMG^3 \otimes U(1)_f$ at the Planck scale. In particular we discuss the predictions for the fine structure constants: $α^{-1}(0) = 137 \pm 9$, $α^{-1}_{1}(M_Z) =99 \pm 5$, $α^{-1}_{2}(M_Z) =29 \pm 6$, $α^{-1}_{3}(M_Z) =12 \pm 6$. We also present our Standard Model predictions for the top quark and Higgs masses and a $SMG^3 \otimes U(1)_f$ fit of the quark-lepton masses and mixing angles. We characterise $SMG^3 \otimes U(1)_f$ as the largest possible extension of the Standard Model gauge group satisfying some relatively simple assumptions. The resolution of some other fine-tuning problems ($Λ_{cosmological}$, $Θ_{QCD}$, $M_{Higgs}$) by the multiple point requirement of degenerate vacua is briefly discussed.
The multiple point criticality principle is applied to the pure Standard Model (SM), with a desert up to the Planck scale. We are thereby led to impose the constraint that the effective Higgs potential should have two degenerate minima, one of which should have a vacuum expectation value of order unity in Planck units. In this way we predict a top quark mass of $173 \pm 5$ GeV and a Higgs particle mass of $135 \pm 9$ GeV. The quark and lepton mass matrices are considered in the anti-grand unified extension of the SM based on the gauge group $SMG^3 \otimes U(1)_f$; this group contains three copies of the SM gauge group SMG, one for each generation, and an abelian flavour group $U(1)_f$. The 9 quark and lepton masses and 3 mixing angles are fitted using 3 free parameters, with the overall mass scale set by the electroweak interaction. It is pointed out that the same results can be obtained in an anomaly free $SMG \otimes U(1)^3$ model.
The combined requirements, of (i) a natural solution to the fermion mass hierarchy problem and (ii) an explanation of both the atmospheric and solar neutrino problems, lead to an essentially unique picture of neutrino masses and mixing angles. The electron and muon neutrinos are quasi-degenerate in mass with maximal mixing, giving $ν_e - ν_μ$ vacuum oscillations. The overall neutrino mass scale is set by the atmospheric neutrino requirement $Δm^2 \sim 10^{-2}$ eV$^2$, implying a mass for $ν_e$ and $ν_μ$ of order 1 eV in models with a natural mass hierarchy, whilst the tau neutrino is expected to be much lighter than this and only weakly mixed. We present an explicit example based on the anti-grand unification model of fermion masses.
The fermion masses and mixing angles are fitted using only 3 free parameters in a non-supersymmetric extension of the Standard Model, with new approximately conserved chiral gauge quantum numbers broken by a set of Higgs fields. The fundamental mass scale of this anti-grand unification model is given by the Planck mass. We also calculate neutrino mixing angles and masses, as well as CP violation from the CKM matrix. A good fit is obtained to the observed fermion masses but our predictions of the neutrino masses are too small to lead to any observable neutrino oscillation effects claimed today, without introducing another mass scale. We also give some arguments in support of this type of model based on the observed fermion masses.
We argue that some of the parameters in the laws of Nature would be well understood, under the assumption that there is an influence from the future as well as from the past, in the sense that the principle of locality is not valid at the fundamental level. However, locality is supposed to be broken only in the mild way that all the non-local influence comes from integrals over the whole of space-time and acts at all moments and all places with the same effect. Thus the observable effects of the lack of locality can only be seen in the constants of Nature. Our cleanest prediction is the Higgs boson mass being 149 +/- 26 GeV, which in addition assumes that the pure Standard Model is valid until the Planck scale. Adding the assumption that the two vacuum states needed in our model come about naturally requires a strong first order transition between them; together with the assumption of the Planck units being fundamental, this leads us to also predict the top quark mass as 173 +/- 5 GeV, and a more precise value of the Higgs boson mass as 135 +/- 9 GeV. With the assumption of the anti-grand unified group SMG x SMG x SMG (three copies of the Standard Model gauge group, one for each generation), it is also possible to successfully predict the three fine structure constants in the Standard Model. We also discuss the extension of the SMG x SMG x SMG group by an extra abelian factor U(1)_f and the fermion mass matrices in this model. Other vacua than the present one might appear in the future due to human activity. The breaking of locality is really of the same mild character as suggested by baby universe theory, so the present work may be considered as a development of baby universe theory.
We consider the application of the multiple point criticality principle to the pure Standard Model, with a desert up to the Planck scale. According to this principle, Nature should choose coupling constant values such that the vacuum can exist in degenerate phases. Furthermore we require a strongly first order phase transition between the two vacua, in order that the dynamical mechanism be relevant. Thus we impose the constraint that the effective Higgs potential should have two degenerate minima, one of which should have a vacuum expectation value of order unity in Planck units. In this way we predict a top quark mass of 173 +/- 4 GeV and a Higgs particle mass of 135 +/- 9 GeV. A possible model to explain the multiple point criticality principle is the lack of locality in quantum gravity and the effects of baby universes which, on general grounds, are expected to make coupling constants dynamical.
We present an extension of the Standard Model (SM) without supersymmetry, which we use to calculate order of magnitude values for the elements of the mass matrices in the SM. In our model we can fit the 9 quark and lepton masses and 3 mixing angles using only 3 free parameters, with the overall mass scale set by the electroweak interaction. The specific model described here has the anti-grand unified gauge group SMG^3 x U(1)_f at high energies where SMG = SU(3) x SU(2) x U(1) is the SM gauge group. The SM fermions are placed in representations of the full gauge group so that they do not produce any anomalies.It is pointed out that the same results can be obtained in an anomaly free SMG x U(1)^3 model.
We examine extensions of the Standard Model (SM), basing our assumptions on what has already been observed; we don't consider anything fundamentally different, such as grand unification or supersymmetry, which is not directly suggested by the SM itself. We concentrate on the possibility of additional low mass fermions (relative to the Planck mass) and search for combinations of representations which don't produce any gauge anomalies. Generalisations of the SM weak hypercharge quantisation rule are used to specify the weak hypercharge, modulo 2, for any given representation of the non-abelian part of the gauge group. Strong experimental constraints are put on our models, by using the renormalisation group equations to obtain upper limits on fermion masses and to check that there is no U(1) Landau pole below the Planck scale. Our most promising model contains a fourth generation of quarks without leptons and can soon be tested experimentally.
In the electroweak phase transition there arises the problem of baryon number washout by sphaleron transitions, which can be avoided if the phase transition is strongly enough first order. The phase transition in the Standard Model or in the Minimal Supersymmetric Standard Model seems to be too weak to suppress the sphaleron transitions sufficiently. We report here on an investigation of the Next to Minimal Supersymmetric Standard Model, NMSSM, which contains a Higgs singlet N in addition to the two Higgs doublets of the minimal SUSY model. This next to minimal model has the helpful new feature that the Higgs potential contains a tree level trilinear field term. We consider the most general form of the Higgs potential without imposing a discrete symmetry; in particular we allow the presence of a mu-term in the superpotential. We find that electroweak baryon preservation is compatible with the NMSSM.
We investigate the possibility of adding a fourth generation of quarks. We also extend the Standard Model gauge group by adding another SU(N) component. In order to cancel the contributions of the fourth generation of quarks to the gauge anomalies we must add a generation of fermions coupling to the SU(N) group. This model has many features similar to the Standard Model and, for example, includes a natural generalisation of the Standard Model charge quantisation rule. We discuss the phenomenology of this model and, in particular, show that the infrared quasi-fixed point values of the Yukawa coupling constants put upper limits on the new quark masses close to the present experimental lower bounds.
In the electroweak phase transition there arises the problem of baryon number washout by sphaleron transitions, which can be avoided if the phase transition is strongly enough first order. The minimal supersymmetric standard model has just two Higgs doublets H1 and H2, while the next to minimal model, NMSSM, has an additional singlet, N, this latter giving rise to the helpful feature that the Higgs potential contains a tree level trilinear field term. We use the tunneling criterion for the existence of a first order electroweak phase change. A quantitative statistical analysis indicates that with parameters of the NMSSM satisfying the experimental constraints a strong first order phase change occurs in about 50% of cases.
Different approaches to the fermion mass problem are reviewed. We illustrate these approaches by summarizing recent developments in models of quark and lepton mass matrices. Dynamical calculations of the top quark mass are discussed, based on (a) infrared quasi-fixed points of the renormalisation group equations, and (b) the multiple point criticality principle in the pure Standard Model. We also consider Yukawa unification and mass matrix texture. Models with approximately conserved gauged chiral flavour charges beyond the Standard Model are shown to naturally give a fermion mass hierarchy.
Imposing the constraint that the Standard Model effective Higgs potential should have two degenerate minima ( vacua), one of which should be - order of magnitudewise - at the Planck scale, leads to the top mass being 173 +/- 5 GeV and the Higgs mass 135 +/- 9 GeV. This requirement of the degeneracy of different phases is a special case of what we call the multiple point criticality principle. In the present work we use the Standard Model all the way to the Planck scale, and do not introduce supersymmetry or any extension of the Standard Model gauge group. A possible model to explain the multiple point criticality principle is lack of locality fundamentally.