International Journal of Modern Physics A

This paper provides a review of the literature on rigorous definitions and constructions in quantum field theory (QFT), spanning the period of seven decades. Compared with the ideas and constructions found in the modern physics literature, we conclude that none of the existing systems of QFT axioms can cover all the physical situations. Therefore, it is still an outstanding open problem to formulate a complete definition of QFT. We argue that the question is of relevance for both physicists and mathematicians.

Calculation results for the HQET field anomalous dimension and the QCD cusp anomalous dimension, as well as their properties, are reviewed. The HQET field anomalous dimension ${\gamma }_h$ is known up to four loops. The cusp anomalous dimension $\mathrm{\Gamma }(\phi )$ is known up to three loops, and its small-angle and large-angle asymptotics up to four loops. Some (but not all) color structures at four loops are known with the full $\phi$-dependence. Some simple contributions are known at higher loops. For the $\phi \to \infty$ asymptotics of $\mathrm{\Gamma }(\phi )$ (the light-like cusp anomalous dimension) and the ${\phi }^2$-term of the small-$\phi$ expansion (the Bremsstrahlung function), the ${𝒩}=4$ SYM results are equal to the highest-weight parts of the QCD results. There is an interesting conjecture about the structure of $\mathrm{\Gamma }(\phi )$ which holds up to three loops; at four loops it holds for some color structures and breaks down for other ones. In the cases when it holds, it related highly nontrivial functions of $\phi$, and it cannot be accidental; however, the reasons of this conjecture and its failures are not understood. The cusp anomalous dimension at the Euclidean angle $\varphi \to \pi$ is related to the static quark–antiquark potential due to conformal symmetry; in QCD, this relation is broken by an anomalous term proportional to the $\beta$-function.

Some new results are also presented. Using the recent four-loop result for ${\gamma }_h$, here we obtain analytical expressions for some terms in the four-loop on-shell renormalization constant of the massive quark field $Z_Q^{\mathrm{\text{os}}}$ which were previously known only numerically. We also present two new contributions to ${\gamma }_h$, $\mathrm{\Gamma }(\phi )$ at five loops and to the quark–antiquark potential at four loops.

This paper continues our work on black holes in the framework of the Regge calculus, where the discrete version (with a certain edge length scale $b$ proportional to the Planck scale) of the classical solution emerges as an optimal starting point for the perturbative expansion after functional integration over the connection, with the singularity resolved. An interest in the present discrete Kerr–Newman-type solution (with the parameter $a\gg b$) may be to check the classical prediction that the electromagnetic contribution to the metric and curvature on the singularity ring is (infinitely) greater than the contribution of the $\delta$-function-like mass distribution, no matter how small the electric charge is. Here, we encounter a kind of a discrete diagram technique, but with three-dimensional (static) diagrams and with only a few diagrams, although with modified (extended to complex coordinates) propagators. The metric (curvature) in the vicinity of the former singularity ring is considered. The electromagnetic contribution does indeed have a relative factor that is infinite at $b\to 0$, but, taking into account some existing estimates of the upper bound on the electric charge of known substances, it is not so large for habitual bodies and can only be significant for practically nonrotating black holes.

Investigation of the optical properties of a black hole described by the so-called “eye of the storm” space–time has been the main aim of the work. Such a space–time is regular and recovers the Minkowski space–time at asymptotical infinity due to the effect of the so-called “suppression parameter” involved in the metric. It has been shown that an increase in the suppression parameter reduces the inclination angle of photons in the close regions around a black hole due to gravitational lensing. Investigation of the photon motion has also shown that bigger values of this parameter reduce the photon sphere radius as well. It has been also detected that the shape of a black hole shadow is affected in the presence of the suppression parameter and the bigger values of this parameter twist the shape of a shadow stronger. Lastly, it has been demonstrated that the average shadow radius is bigger for smaller suppression parameters and the distortion of the shape of shadow from a circle is bigger for bigger suppression parameters and bigger spin of a black hole.

In this work, we consider a special kind of space–time called AdS accelerating black holes. This is a kind of black holes which have a stringlike singularity along polar axis attached to the black hole and it accelerates the black hole. In these kind of space–times, the growth of Einstein–Hilbert action is independent of the acceleration as found in S. Chen and Y. Pei, Int. J. Theor. Phys. 60, 917 (2021). By using a string as a probe, we found the effect of the acceleration is captured by the string probe [K. Nagasaki, arXiv:2108.05429 [hep-th]]. Here in this work, we consider the case of rotating black holes. By the probe string, we clearly describe the effect of the acceleration and its relation to the rotation of the black holes.

A simple semiclassical Hénon–Heiles model is constructed based on Dirac’s time-dependent variational principle. We obtain an effective semiclassical Hamiltonian using a Hartree-type two-body trial wave function in the Jackiw–Kerman form. Numerical results show that quantum effects can in fact induce chaos in the nonchaotic regions of the classical Hénon–Heiles model.

In the model-independent context, the neutrino mass matrix is assumed to be diagonalized by means of a unitary matrix that possesses the Tri-Bi-Maximal (TBM) flavor mixing pattern. We present an analysis where the TBM deviation is explored by considering different forms with texture zeros, for the charged lepton mass matrix. These last mass matrices are classified into equivalent classes. We are interested in the charged lepton mass matrices with the minimum free parameter number, i.e. the maximum number of texture zeros, that allows us to correctly reproduce the reactor mixing angle value. We show a deviation from the TBM pattern in terms of the charged lepton masses as well as the theoretical expressions and their parameter space for the mixing angles. Finally, we present the phenomenological implications of numerical values of the “Majorana-like” phase factors on the neutrinoless double-beta decay.

In this paper, analytical investigation of the properties of $s$-wave holographic superconductors in the background of a massive gravity theory in the probe limit has been carried out by employing the Sturm–Liouville eigenvalue method. We obtain the analytical expression for the relation between the critical temperature and the charge density. We also obtain the expression for the condensation operator and value of the critical exponent. We observe that as we increase the massive gravity couplings, the critical temperature increases and the condensate decreases. Then we compute the frequency dependence of conductivity by solving analytically the wave equation for electromagnetic perturbations. From the real part of the conductivity, we finally estimate the energy band gap. Our results show that as one keeps on increasing the coupling parameters of the massive gravity background, the band gap energy increases compared to the holographic superconductors constructed in the Einstein gravity background. The results indicate that massive background is more favorable than Einstein gravity background for constructing a gravity dual of the strongly coupled high $T_c$ superconductor as it enhances the value of the critical temperature.

We propose methods to produce gamma light source, muon and energetic meson beams such as charged and neutral Kaons, which are boosted to be collimated and with relatively long lifetime. The first type of method is based on asymmetric electron positron collisions with a center-of-mass energy of, e.g. 1020MeV, and Kaons can be produced at a rate of $10^{4-5}∕\mathrm{\text{s}}$. The electron and positron beams are either asymmetric in energy, e.g. 10GeV electron beam with 26MeV positron beam, or asymmetric in space, e.g. 10GeV electron and positron beams collisions with an angle around 0.05 radius. Such proposals should be able to be achieved with a reasonable budget. The other type of method relies on TeV positron on target experiment, where Kaon beams can be achieved at around $10^7$ per bunch crossing. Such Kaon beams are clean with small contamination, and can have great physics potential on, e.g. hyperon searches through Kaon nuclei collision, Kaon rare decay measurement, and Kaon proton or Kaon lepton collisions. The same technique can also be extended to other final states such as pions and tau leptons.

In this work, we tried to predict the parameters of $B_c^{\ast }$ meson. Simple assumptions gave us the following parameters $m_{B_c^{\ast }}=6329\pm 10$MeV and $f_{B_c^{\ast }}=535.5\pm 57.8$MeV (for ${\mathrm{\Lambda }}_{B_c^{\ast }}=2.26\pm 0.14$GeV in covariant confined quark model). We calculated widths of radiative decays of $B_q^{\ast }$ mesons, where $q=u∕d,s,c$ and compared them with other theoretical works. It was shown that the width of the $B_c^{\ast }$ meson is very sensitive to the mass $m_{B_c^{\ast }}$ as expected and less to the size parameter ${\mathrm{\Lambda }}_{B_c^{\ast }}$.