International Journal of Modern Physics A

This brief review grew out from the HEP concluding talk of the 25th Anniversary of the Rencontres du Vietnam, held in August 2018, at Quy Nhon. The first two-thirds gives a summary and highlights, or snapshot, of High Energy Physics at the end of Large Hadron Collider (LHC) Run 2. It can be viewed as the combined effort of the program organizers, the invited plenary speakers, and finally filtered into the present mosaic. It certainly should not be viewed as comprehensive. In the second one-third, a more personal perspective and outlook is given, including my take on the flavor anomalies, and why the next three years, the period of Long Shutdown 2 plus first year (or more) of LHC Run 3, would be bright and flavorful, with much hope for uncovering New Physics. We advocate extra Yukawa couplings as the most likely, next, New Physics to be tested, the effect of which is already written in our Matter Universe.

We argue that quaternions form a natural language for the description of quantum-mechanical wave functions with spin. We use the quaternionic spinor formalism which is in one-to-one correspondence with the usual spinor language. No unphysical degrees of freedom are admitted, in contrast to the majority of literature on quaternions. In this paper, we first build a Dirac Lagrangian in the quaternionic form, derive the Dirac equation and take the nonrelativistic limit to find the Schrödinger’s equation. We show that the quaternionic formalism is a natural choice to start with, while in the transition to the noninteracting nonrelativistic limit, the quaternionic description effectively reduces to the regular complex wave function language. We provide an easy-to-use grammar for switching between the ordinary spinor language and the description in terms of quaternions. As an illustration of the broader range of the formalism, we also derive the Maxwell’s equation from the quaternionic Lagrangian of Quantum Electrodynamics. In order to derive the equations of motion, we develop the variational calculus appropriate for this formalism.

The low-temperature expansion of the free energy of an atom/plane system is considered for a general symmetric form of the tensor conductivity of the plane. It is shown that the first correction is proportional to the second order of the temperature $\sim T^2$ and comes from the TM mode. The agreement of the expansion and exact expressions for different models of conductivity is numerically demonstrated.

We present a lattice calculation of the nucleon isovector axial and induced pseudoscalar form factors on the CLS ensembles using $N_f=2$ dynamical flavors of nonperturbatively ${𝒪}(a)$-improved Wilson fermions and an ${𝒪}(a)$-improved axial current together with the pseudoscalar density. Excited-state effects in the extraction of the form factors are treated using a variety of methods, with a detailed discussion of their respective merits. The chiral and continuum extrapolation of the results is performed both using formulae inspired by Heavy Baryon Chiral Perturbation Theory (HBChPT) and a global approach to the form factors based on a chiral effective field theory (EFT) including axial vector mesons. Our results indicate that careful treatment of excited-state effects is important in order to obtain reliable results for the axial form factors of the nucleon, and that the main remaining error stems from the systematic uncertainties of the chiral extrapolation. As final results, we quote $g_A=1.278\pm 0.068_{-0.087}^{+0.000}$, $〈r_A^2〉=0.360\pm 0.036_{-0.088}^{+0.080}{\mathrm{\text{fm}}}^2$, and $g_P=7.7\pm 1.8_{-2.0}^{+0.8}$ for the axial charge, axial charge radius and induced pseudoscalar charge, respectively, where the first error is statistical and the second is systematic.

Within the standard $V-A$ theory of weak interactions, Quantum Electrodynamics (QED) and the linear $\sigma$-model $(\mathrm{\text{L}}\sigma \mathrm{\text{M}})$ of strong low-energy hadronic interactions we analyze gauge and infrared properties of hadronic structure of the neutron and proton in the neutron ${\beta }^{-}$-decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order $O(\alpha /\pi )$, induced by hadronic structure of the nucleon, to the rate of the neutron ${\beta }^{-}$-decay is gauge noninvariant and unrenormalizable. We show that a gauge noninvariant contribution does not depend on the electron energy in agreement with Sirlin’s analysis of contributions of strong low-energy interactions (Phys. Rev. 164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative ${\beta }^{-}$-decay and neutron ${\beta }^{-}$-decay, caused by hadronic structure of the nucleon, are canceled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalizable even formally. Such an unrenormalizability can be explained by the fact that the effective $V-A$ vertex of hadron–lepton current–current interactions is not a vertex of the combined quantum field theory including QED and $\mathrm{\text{L}}\sigma \mathrm{\text{M}}$, which are renormalizable theories. We assert that for a consistent gauge invariant and renormalizable analysis of contributions of hadronic structure of the nucleon to the radiative corrections of any order to the neutron decays one has to use a gauge invariant and fully renormalizable quantum field theory including the Standard Electroweak Model (SEM) and the $\mathrm{\text{L}}\sigma \mathrm{\text{M}}$, where the effective $V-A$ vertex of hadron–lepton current–current interactions is caused by the $W^{-}$-electroweak-boson exchange.

We study the effect of the running gravitational constant on a system of particles (galaxies) interact via gravitational potential. The gravitational potential is derived based on the entropic modified Newtonian force by logarithmic and power correction terms. We derive the partition function for many-body system and the exact equations of state including the thermodynamic properties. A modified parameter B emerged from the thermodynamics derivation. Moreover, an extension of the study is done to determine the distribution function for point mass and extended mass structure galaxies. In particular, the rotation velocity of some galaxies is studied, and the results confronted the observed data which fit well only for short distance with considering the logarithmic correction effect. This leads us to conclude that the logarithmic correction effect explains the rotation velocity data for short and long distances at least qualitatively.

We make progress towards a derivation of a low energy effective theory for SU(2) Yang–Mills theory. This low energy action is computed to 1-loop using the renormalization group technique, taking proper care of the Slavnov–Taylor identities in the Maximal Abelian Gauge. After that, we perform the Spin-Charge decomposition in a way proposed by Faddeev and Niemi. The resulting action describes a pair of nonlinear O(3) and $\sigma$-models interacting with a scalar field. The potential of the scalar field is a Mexican hat and the location of the minima sets the energy scale of solitonic configurations of the $\sigma$-model fields whose excitations correspond to glueball states.

We have treated the Euclidean three-dimensional O(1) ghost model with a modified version of the effective average action (EAA) renormalization group (RG) method, developed by us. We call it Fourier–Wetterich RG approach and it is used to investigate the occurrence of a periodic condensate in terms of the functional RG. The modification involves additional terms in the ansatz of the EAA, corresponding to the Fourier-modes of the periodic condensate. The RG flow equations are derived keeping the terms up to the fourth order of the gradient expansion (GE), however the numerical calculations are conducted in the second order (or next-to-leading order, NLO) of the GE. The expansion of the flow equations around the nontrivial minimum of the local potential takes into account properly the vertices induced by the periodic condensate even if the wave function renormalization is set to be field-independent. The numerical analysis reveals several different phases with three multicritical points.