arXiv subjects

H. B. Nielsen

Publications and source records attributed to H. B. Nielsen.

At least 145 records · Page 8Linked to original sources

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

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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arXiv1998

Thermodynamic Properties of the Piecewise Uniform String

The thermodynamic free energy F is calculated for a gas whose particles are the quantum excitations of a piecewise uniform bosonic string. The string consists of two parts of length L_I and L_II, endowed with different tensions and mass densities, adjusted in such a way that the velocity of sound always equals the velocity of light. The explicit calculation is done under the restrictive condition that the tension ratio x = T_I/T_II approaches zero. Also, the length ratio s = L_II/L_I is assumed to be an integer. The expression for F is given on an integral form, in which s is present as a parameter. For large values of s, the Hagedorn temperature becomes proportional to the square root of s.

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arXiv1997

Masses of Quarks and Leptons and Mixing Angles in Anti-GUT Theory

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.

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arXiv1997

Anti-Grand Unification and Critical Coupling Universality

The present work considers the phase transition between the confinement and "Coulomb" phases in U(1), SU(2) and SU(3)-sectors of Anti-grand unified theory described by regularized Wilson loop action. It was shown the independence of the critical coupling constants of the regularization method ("universality").

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arXiv1997

Standard Model Parameters from the Multiple Point Principle and Anti-GUT

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.

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arXiv1997

Fermion and Higgs Masses and the AGUT Model

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.

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arXiv1997

The Initial Value Problem For Maximally Non-Local Actions

We study the initial value problem for actions which contain non-trivial functions of integrals of local functions of the dynamical variable. In contrast to many other non-local actions, the classical solution set of these systems is at most discretely enlarged, and may even be restricted, with respect to that of a local theory. We show that the solutions are those of a local theory whose (spacetime constant) parameters vary with the initial value data according to algebraic equations. The various roots of these algebraic equations can be plausibly interpreted in quantum mechanics as different components of a multi-component wave function. It is also possible that the consistency of these algebraic equations imposes constraints upon the initial value data which appear miraculous from the context of a local theory.

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arXiv1997

Standard Model Couplings with $α^{-1}=137 \pm 9$ from Multiple Point Criticality and 3 Generations of Gauge Bosons: No GUT, No SUSY

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.

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arXiv1997

Dynamical Determination of the Top Quark and Higgs Masses and Fermion Masses in the Anti-Grand Unification Model

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.

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arXiv1997

A Natural Solution to the Neutrino Mixing Problem

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.

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arXiv1997

Fermion masses, neutrino mixing and CP violation from the anti-grand unification model

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.

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arXiv1996

Influence from the Future

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.

hep-ph↗

arXiv1996

Gauge Couplings calculated from Multiple Point Criticality yield $α^{-1}=136._8\pm 9$: At Last the Elusive Case of $U(1)$

We calculate the $U(1)$ continuum gauge coupling using the values of action parameters at the multiple point in the phase diagram of a lattice gauge theory. The multiple point is where a maximum number of phases convene. We obtain for the running inverse finestructure constant the values $α_1^{-1}=56\pm 5$ and $α_1^{-1}=99\pm 5$ at respectively the Planck scale and the $M_Z$ scale. The gauge group underlying the phase diagram in which we seek multiple point values of action parameters is what we call the Anti Grand Unified Theory (AGUT) gauge group $SMG^3$ which is the Cartesian product of 3 standard model groups (SMGs). There is one SMG factor for each of the $N_{gen}=3$ generations of quarks and leptons. In our model, this gauge group $SMG^3$ is the predecessor to the usual standard model group. The latter arises as the diagonal subgroup surviving the Planck scale breakdown of $SMG^3. This breakdown leads to a weakening of the $U(1)$ coupling by a $N_{gen}$-related factor. The most important correction obtained from using multiple point parameter values (in a multi-parameter phase diagram instead of the single critical parameter value obtained say in the 1-dimensional phase diagram of a Wilson action) comes from including the influence of having phases confined solely w.r.t. discrete subgroups. In particular, what matters is that the degree of first-orderness is taken into account in making the transition from these latter phases at the multiple point to the totally Coulomb-like phase. Combined with the results of earlier work on the non-Abelian gauge couplings, the results presented here lead to our prediction of $α^{-1}=136._8\pm 9$ as the value for the fine-structure constant at low energies.

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arXiv1996

Dynamical determination of the top quark and Higgs masses in the Standard Model

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.

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arXiv1996

Fermion Masses and Anti-grand Unification

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.

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arXiv1996

Extending the Standard Model Using Charge Quantisation Rules

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.

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