arXiv subjects

H. B. Nielsen

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

At least 109 records · Page 6Linked to original sources

arXiv2003

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.

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arXiv2003

How to generate families of spinors

Using a technique \cite{holgernorma2002} to construct a basis for spinors and ``families'' of spinors in terms of Clifford algebra objects, we define other Clifford algebra objects, which transform the state of one ''family'' of spinors into the state of another ''family'' of spinors, changing nothing but the ''family'' number. The proposed transformation works - as does the technique - for all dimensions and any signature and might open a path to understanding families of quarks and leptons\cite{norma92,norma93,normaixtapa2001,pikanorma2002}.

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arXiv2003

Monopoles and Family Replicated Unification

The present theory is based on the assumption that at the very small (Planck scale) distances our space-time is discrete, and this discreteness influences on the Planck scale physics. Considering our (3+1)-dimensional space-time as a regular hypercubic lattice with a parameter $a=λ_\text{P}$, where $λ_\text{P}$ is the Planck length, we have investigated a role of lattice artifact monopoles which is essential near the Planck scale if the Family replicated gauge group model (FRGGM) is an extension of the Standard Model at high energies. It was shown that monopoles have $N$ times smaller magnetic charge in FRGGM than in SM ($N$ is the number of families in FRGGM). These monopoles can give an additional contribution to beta-functions of the renormalisation group equations for the running fine structure constants $α_\text{i}(μ)$ (i=1,2,3 correspond to the U(1), SU(2), and SU(3) gauge groups of the Standard Model). We have used the Dirac relation for renormalised electric and magnetic charges. Also we have estimated the enlargement of a number of fermions in FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. Different role of monopoles in the vicinity of the Planck scale gives rise or to AntiGUT, or to the new possibility of unification of gauge interactions (including gravity) at the scale $μ_\text{GUT}\approx 10^{18.4}$ GeV. We discussed the possibility of the [SU(5)]$^3$ SUSY or [SO(10)]$^3$ SUSY unifications.

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arXiv2002

Monopoles near the Planck Scale and Unification

Considering our (3+1)-dimensional space-time as, in some way, discrete or l attice with a parameter $a=λ_P$, where $λ_P$ is the Planck length, we have investigated the additional contributions of lattice artifact monopoles to beta-functions of the renormalisation group equations for the running fine structure constants $α_i(μ)$ (i=1,2,3 correspond to the U(1), SU(2) and SU(3) gauge groups of the Standard Model) in the Family Replicated Gauge Group Model (FRGGM) which is an extension of the Standard Model at high energies. It was shown that monopoles have $N_{fam}$ times smaller magnetic charge in FRGGM than in SM ($N_{fam}$ is the number of families in FRGGM). We have estimated al so the enlargement of a number of fermions in FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. We have shown that, in contrast to the case of AntiGUT when the FRGGM undergoes the breakdown at $μ=μ_G\sim 10^{18}$ GeV, we have the possibility of unification if the FRGGM-breakdown occurs at $μ_G\sim 10^{14}$ GeV. By numerical calculations we obtained an example of the unification of all gauge interactions (including gravity) at the scale $μ_{GUT}\approx 10^{18.4}$ GeV. We discussed the possibility of $[SU(5)]^3$ or $[SO(10)]^3$ (SUSY or not SUSY) unifications.

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arXiv2002

Derivation of Lorentz Invariance and Three Space Dimensions in Generic Field Theory

A very general quantum field theory, which is not even assumed to be Lorentz invariant, is studied in the limit of very low energy excitations. Fermion and Boson field theories are considered in parallel. Remarkably, in both cases it is argued that, in the free and lowest energy approximation, a relativistic theory with just three space and one time dimension emerges for each particle type separately. In the case of Fermion fields it is in the form of the Weyl equation, while in the case of the Bosons it is essentially in the form of the Maxwell equations.

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arXiv2002

Non-thermal Leptogenesis from the Heavier Majorana Neutrinos

We investigate a scheme for making leptogenesis by means of the CP violating decays of the seesaw Majorana neutrinos proposed by Fukugita and Yanagida. However, in order to avoid the wash-out of the produced lepton number we propose the production of the Majorana neutrinos to occur non-thermally and sufficiently late. After this time, in consequence, the B-L (baryon minus lepton) quantum number becomes a good ``accidental symmetry'' protecting the asymmetry produced. This non-thermal leptogenesis at late time is realized by a boson decaying into the Majorana neutrinos with a long lifetime. Suggestively this boson could correspond to a scalar field which causes the cosmic inflation, the inflaton, and thus its decay means really the reheating of the Universe. We find that this mechanism works well even if the lightest Majorana neutrinos are not produced sufficiently or not present, and the decays of the heavier seesaw Majorana neutrinos can be responsible to the baryon asymmetry in the present Universe, as we illustrate by the example of the family replicated gauge group model.

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arXiv2002

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 $δ=\fracπ{2}$, in the framework of the MSSM extended by a high-scale $SU(3)_{F}$ chiral family symmetry.

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arXiv2002

Five Adjustable Parameter Fit of Quark and Lepton Masses and Mixings

We develop a model of ours fitting the quark and lepton masses and mixing angles by removing from the model a Higgs field previously introduced to organise a large atmospheric mixing angle for neutrino oscillations. Due to the off-diagonal elements dominating in the see-saw neutrino mass matrix the large atmospheric mixing angle comes essentially by itself. It turns out that we have now only five adjustable Higgs field vacuum expectation values needed to fit all the masses and mixings order of magnitudewise taking into account the renormalisation group runnings in all sectors. The CHOOZ angle comes out close to the experimental bound.

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arXiv2002

Baryogenesis via Lepton Number Violation and Family Replicated Gauge Group

We developed a previous model fitting all quark and lepton -- including neutrino quantities in the region of the Large Mixing Angle-MSW solar solution -- order of magnitudewise by only six adjustable parameters (Higgs vacuum expectation values) to also give an agreeing prediction for the amount of baryogenesis produced in the early time of cosmology. We use Fukugita-Yanagida scheme and take into account now also the effect of the remormalisation equation for the Dirac neutrino sector from Planck scale to the see-saw scale. The present version of our model with many approximately conserved (gauge) charges distinguishing various left- and right-Weyl particles has the largest matrix element of the mass matrix for the three flavour see-saw neutrinos being the off-diagonal elements associated with the second- and third-proto-flavour and gives the ratio of baryon number density to the entropy density to 2.59{+17.0\atop-2.25}\times 10^{-11} which agrees perfectly well as do also all the fermion masses and their mixing angles order of magnitudewise.

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arXiv2002

Family replicated calculation of baryogenesis

In our model with a Standard Model gauge group extended with a baryon number minus lepton number charge for each family of quarks and leptons, we calculate the baryon number relative to entropy produced in early Big Bang by the Fukugita-Yanagida mechanism. With the parameters, i.e., the Higgs VEVs already fitted in a very successful way to quark and lepton masses and mixing angles we obtain the order of magnitude pure prediction Y_B=2.59{+17.0\atop-2.25}\times 10^{-11} which according to a theoretical estimate should mean in this case an uncertainty of the order of a factor 7 up or down (to be compared to Y_B=(1.7-8.1)\times 10^{-11}) using a relatively crude approximation for the dilution factor, while using another estimate based on Buchmüller and Plümacher a factor 500 less, but this should rather be considered a lower limit. With a realistic uncertainty due to wash-out of a factor 100 up or down we even with the low estimate only deviate by 1.5σ.

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arXiv2002

Family replicated fit of all quark and lepton masses and mixings

We review our recent development of family replicated gauge group model, which generates the Large Mixing Angle MSW solution. The model is based on each family of quarks and leptons having its own set of gauge fields, each containing a replica of the Standard Model gauge fields plus a (B-L)-coupled gauge field. A fit of all the seventeen quark-lepton mass and mixing angle observables, using just six new Higgs field vacuum expectation values, agrees with the experimental data order of magnitudewise. However, this model can not predict the baryogenesis in right order, therefore, we discuss further modification of our model and present a preliminary result of baryon number to entropy ratio.

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arXiv2002

Why Nature has made a choice of one time and three space coordinates?

We propose a possible answer to one of the most exciting open questions in physics and cosmology, that is the question why we seem to experience four- dimensional space-time with three ordinary and one time dimensions. We have known for more than 70 years that (elementary) particles have spin degrees of freedom, we also know that besides spin they also have charge degrees of freedom, both degrees of freedom in addition to the position and momentum degrees of freedom. We may call these ''internal degrees of freedom '' the ''internal space'' and we can think of all the different particles, like quarks and leptons, as being different internal states of the same particle. The question then naturally arises: Is the choice of the Minkowski metric and the four-dimensional space-time influenced by the ''internal space''? Making assumptions (such as particles being in first approximation massless) about the equations of motion, we argue for restrictions on the number of space and time dimensions. (Actually the Standard model predicts and experiments confirm that elementary particles are massless until interactions switch on masses.) Accepting our explanation of the space-time signature and the number of dimensions would be a point supporting (further) the importance of the ''internal space''.

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arXiv2002

Family replicated gauge groups and large mixing angle solar neutrino solution

We present a modification of our previous family replicated gauge group model, which now generates the Large Mixing Angle MSW solution rather than the experimentally disfavoured Small Mixing Angle MSW solution to the solar neutrino oscillation problem. The model is based on each family of quarks and leptons having its own set of gauge fields, each containing a replica of the Standard Model gauge fields plus a (B-L)-coupled gauge field. By a careful choice of the Higgs field gauge quantum numbers, we avoid our previous prediction that the solar neutrino mixing angle is equal order of magnitudewise to the Cabibbo angle, replacing it and the well-known Fritzsch relation with the relation θ_{c}\sim (θ_{\odot})^{-1/3} (m_d/m_s)^{2/3}. At the same time we retain a phenomenologically successful structure for the charged quark and lepton mass matrices. A fit of all the seventeen quark-lepton mass and mixing angle observables, using just six new Higgs field vacuum expectation values, agrees with the experimental data within the theoretically expected uncertainty of about 64%, i.e. it fits perfectly order of magnitudewise.

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arXiv2001

How to generate spinor representations in any dimension in terms of projection operators

We present a method to find solutions of the Weyl or the Dirac equation without specifying a representation choice for $γ^a$'s. By taking $γ^a$'s formally as independent variables, we construct solutions out of $2^d$ orthonormal polynomials of $γ^a$'s (in $d$-dimensional space) operating on a ``vacuum state''. Polynomials reduce into $2^{d/2}$ or $2^{(d+1)/2}$ repetitions of the Dirac spinors for $d$ even or odd, respectively. We further propose the corresponding graphic presentation of basic states, which offers an easy way to see all the quantum numbers of states with respect to the generators of the Lorentz group, as well as transformation properties of the states under any operator.

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arXiv2001

Phase Transition in Gauge Theories and Multiple Point Model

In the present paper the phase transition in the regularized U(1) gauge theory is investigated using the dual Abelian Higgs model of scalar monopoles. The corresponding renormalization group improved effective potential, analogous to the Coleman-Weinberg's one, was considered in the two-loop approximation for $β$ functions, and the phase transition (critical) dual and non-dual couplings were calculated in the U(1) gauge theory. It was shown that the critical value of the renormalized electric fine structure constant $α_{\text{crit}}\approx 0.208$ obtained in this paper coincides with the lattice result for compact QED: $α_{\text{crit}}^{\text{lat}}\approx 0.20\pm 0.015$. This result and the behavior of $α$ in the vicinity of the phase transition point were compared with the Multiple Point Model prediction for the values of $α$ near the Planck scale. Such a comparison is very encouraging for the Multiple Point Model assuming the existence of the multiple critical point at the Planck scale.

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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

SUSY a consequence of smoothness?

The consequences of certain simple assumptions like smoothness of ground state properties and vanishing of the vacuum energy (at least perturbatively) are explored. It would be interesting from the point of view of building realistic theories to obtain these properties without supersymmetry. Here we show, however, at least in some quantum mechanical models, that these simple assumptions lead to supersymmetric theories.

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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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