International Journal of Modern Physics A

This note summarises and celebrates the important contributions of Yoichiro Nambu to the tricky question of the origin of particle masses.

In this paper we examine, from the purely theoretical point of view and in a model-independent way, the case, when matter, gauge and Higgs fields are allowed to propagate in the bulk of five-dimensional brane world models with compact extra dimension, and the Standard Model fields and their interactions are supposed to be reproduced by the corresponding zero Kaluza–Klein modes. An unexpected result is that in order to avoid possible pathological behavior in the fermion sector, it is necessary to impose constraints on the fermion field Lagrangian. In the case when the fermion zero modes are supposed to be localized at one of the branes, these constraints imply an additional relation between the vacuum profile of the Higgs field and the form of the background metric. Moreover, this relation between the vacuum profile of the Higgs field and the form of the background metric results in the exact reproduction of the gauge boson and fermion sectors of the Standard Model by the corresponding zero mode four-dimensional effective theory in all the physically relevant cases, allowed by the absence of pathologies. Meanwhile, deviations from these conditions can lead either back to pathological behavior in the fermion sector or to a variance between the resulting zero mode four-dimensional effective theory and the Standard Model, which, depending on the model at hand, may, in principle, result in constraints putting the theory out of the reach of the present day experiments.

We revisit the possibility of relating lepton mixing angles with lepton mass hierarchies in a model-independent way. Guided by the existence of such relations in the quark sector, we first consider all the mixing angles, both in charged lepton and neutrino sectors to be related to the respective mass ratios. This allows us to calculate the leptonic mixing angles observed in neutrino oscillations as functions of the lightest neutrino mass. We show that for both normal and inverted hierarchical neutrino masses, this scenario does not give rise to correct leptonic mixing angles. We then show that correct leptonic mixing angles can be generated with normal hierarchical neutrino masses if the relation between mixing angle and mass ratio is restricted to 1–2 and 1–3 mixing in both charged lepton and neutrino sectors leaving the 2–3 mixing angles as free parameters. We then restrict the lightest neutrino mass as well as the difference between 2–3 mixing angles in charged lepton and neutrino sectors from the requirement of producing correct leptonic mixing angles. We constrain the lightest neutrino mass to be around 0.002 eV and leptonic Dirac CP phase ${\delta }_{\mathrm{\text{CP}}}$ such that ${sin}^2{\delta }_{\mathrm{\text{CP}}}\sim (0.35\text{–}0.50)$. We also construct the leptonic mass matrices in terms of 2–3 mixing angles and lightest neutrino mass and briefly comment on the possibility of realizing texture zeros in the neutrino mass matrix.

Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we compute the renormalized vacuum expectation value of several observables (in particular, of the stress–energy tensor) for a massless scalar field confined within a rectangular box of arbitrary dimension.

A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta referring to other space–time directions. The corresponding commutation relations are formulated by using quaternions. At the beginning, this extended quantization concept is applied to the variables of quantum mechanics. The resulting Dirac equation and the corresponding generalized expression for plane waves are formulated and some consequences for quantum field theory are considered. Later, the quaternionic quantization principle is transferred to canonical quantum gravity. Within quantum geometrodynamics as well as the Ashtekar formalism, the generalized algebraic properties of the operators describing the gravitational observables and the corresponding quantum constraints implied by the generalized representations of these operators are determined. The generalized algebra also induces commutation relations of the several components of the quantized variables with each other. Finally, the quaternionic quantization procedure is also transferred to ${𝒩}=1$ supergravity. Accordingly, the quantization principle has to be generalized to be compatible with Dirac brackets, which appear in canonical quantum supergravity.

Two most popular GUT scenarios, namely, the left–right symmetric model (LRM) and models coming from $E_6$ grand unification (effective rank 5 models (ER5M’s)) are considered. Both models forecast existence of the extra neutral gauge boson. Its contributions to the decay of the Higgs boson being an analog of the Standard Model (SM) Higgs boson

Dyon solutions with axial symmetry in Yang–Mills–Higgs theory, including monopole–antimonopole pairs (MAP), monopole–antimonopole chains (MAC) and vortex-rings are introduced previously. The previously studied cases include at most a bifurcation for MAP systems and two for MAC dyon solutions. Here, for the case of $\varphi$-winding number $n=4$, a rich set of solutions including nine branches and four bifurcations, has been obtained for electrically charged four-pole MAC solutions. Also, the transition between two different charge configurations at a lower energy bifurcating branch is detected for the first time. This study also improves and completes some aspects of a previous study on the electrically neutral case. In the case of $n=3$, in addition to previously found bifurcation, another bifurcation at small values of Higgs self-coupling constant $\lambda$, has been obtained here.

We have investigated the Regge trajectories of exotic hadrons by considering different possible pentaquark configurations with finite quark mass in the flux tube model. Significant deviation is observed in the linear behavior of the Regge trajectories for pentaquark systems in view of the universal value of the Regge slope parameter for hadrons. The modified Regge trajectories are also compared with the available experimental and lattice data. It is observed that the nonlinear Regge trajectories of such pentaquark systems can be well described by the relativistic corrections in view of the current quark masses and the high rotational speed of the quarks at the end of flux tube structure.

We suggest that classicalization can cure nonlocal quantum field theories from acausal divergences in scattering amplitudes, restoring unitarity and causality. In particular, in “trans-nonlocal” limit, the formation of nonperturbative classical configurations, called classicalons, in scatterings like $\varphi \varphi \to \varphi \varphi$, can avoid typical acausal divergences.

By considering the 12-dimensional superalgebra, inferences are drawn about the finiteness of the 12-dimensional theory unifying the superstring models. The dimensional reduction of the nonsupersymmetric theory in four dimensions to a supersymmetric action in three dimensions is established for the bosonic sector. It is found to be the quotient by ${\mathbb{Z}}_2$ of the integration over the fiber coordinate of a theory with $N=1$ supersymmetry. Consequently, a flow on the moduli space of Spin(7) manifolds from a $G_2$ structure with $N=1$ supersymmetry yielding a phenomelogically realistic particle spectrum to a $G_2$ holonomy manifold compatible with supersymmetry in three dimensions and a nonsupersymmetric action in four dimensions, solving the quantum cosmological constant problem, is proven to exist. The projection of the representations of the $(10,2)$ superalgebra of the 12-dimensional theory to four dimensions include nonperturbative string solitons that are more stable because the dynamics is described by supersymmetric theory with a higher degree of finiteness.

I revisit here the decoupling theorem in top-quark productions/decays, which states that the angular distribution of any final-particle produced in those processes does not depend on any possible nonstandard top-quark decay interactions at their leading order when certain conditions are satisfied. Toward a simple, intuitive and visual understanding of this theorem, I will study to what extent we could explain why such a theorem holds without relying on any specific/detailed calculations.

The decay of the Higgs particle into two photons through a $W$ loop was calculated in a straightforward way four years ago on the basis of the standard model. This calculation was carried out in the unitary gauge. Nevertheless, all attempts to reproduce this correct answer using the Feynman rules in the $R_1$ gauge, or the more general $R_{\xi }$ gauge, have failed. In this paper, a detailed analysis is carried out to compare the unitary gauge with the $R_{\xi }$ gauge; through this comparison, the underlying reason is determined why the answer cannot be obtained using the Feynman rules in the $R_{\xi }$ gauge.

This is the first example where the use of the Feynman rules in the $R_{\xi }$ gauge leads to an incorrect answer, and this incorrect answer cannot be ruled out by any simple argument such as gauge invariance. It means that great care must be exercised in using Feynman rules.