### Regular Series

#### Vol. 48 (2017), No. 1, pp. 1 – 107

Ultraviolet Cutoffs and the Photon Mass

Acta Phys. Pol. B 48, 5 (2017)

page 5 •

abstract

The momentum UV cutoff in Quantum Field Theory is usually treated as an auxiliary device allowing to obtain finite amplitudes satisfying all physical requirements. It is even absent (not explicit) in the most popular approach — the dimensional regularization. We point out that if the momentum cutoff is to be treated as a bona fide physical scale, presumably equal or related to the Planck scale, the field theory must have a very special features in order not to lead to unacceptable predictions. One of such predictions would be a non-zero mass of the photon. In the naive approach, even with the cutoff equal to the Planck scale, this mass would grossly exceed the existing experimental bounds. We present this danger doing an explicit calculation using a concrete realization of the physical cutoff and speculate about the way to restore gauge symmetry order-by-order in the inverse powers of the cutoff scale.

On the D-branes Standard-like Models

Acta Phys. Pol. B 48, 13 (2017)

page 13 •

abstract

Based on the low-energy effective field theory of D-branes, the mass spectrum of an extended Standard Model with two-Higgs doublets used to generate all the mass terms is investigated. Besides the gauge bosons, the fermion mass spectrum is weighted by the Higgs VEVs with a partial hierarchy and the smallness of neutrino masses is exhibited. With reference to the known data, the involved scales of the model are approached.

Acta Phys. Pol. B 48, 23 (2017)

page 23 •

abstract

Quark–hadron phase transition at the end of evolution of the dense matter created in heavy-ion collisions is studied with particular attention given to the fluctuation of spatial patterns that is expected in a second-order phase transition, as found in the Ising model. Since QCD thermodynamics cannot easily be applied at low temperature and density, an event generator is constructed to simulate the dynamical properties of contraction due to confinement forces, and randomization due to the thermal behavior of a large quark system on the edge of hadronization. Fluctuations of the positions of emitted pions in the $(\eta ,\phi )$ space are analyzed using normalized factorial moments in a wide range of bin sizes. The scaling index $\nu$ is found to be very close to the predicted value in the Ginzburg–Landau formalism. The erraticity indices $\mu _q$ are determined in a number of ways that lead to the same consistent values. They are compared to the values from the Ising model, showing significant difference in a transparent plot. Experimental determination of $\nu$ and $\mu _q$ at the LHC are now needed to check the reality of the theoretical study, and to provide guidance for improving the model description of quark–hadron phase transition.

Classification of the Traceless Ricci Tensor in 4-dimensional Pseudo-Riemannian Spaces of Neutral Signature

Acta Phys. Pol. B 48, 53 (2017)

page 53 •

abstract

The traceless Ricci tensor $C_{ab}$ in 4-dimensional pseudo-Riemannian spaces equipped with the metric of the neutral signature is analyzed. Its algebraic classification is given. This classification uses the properties of $C_{ab}$ treated as a matrix. The Petrov–Penrose types of Plebański spinors associated with the traceless Ricci tensor are given. Finally, the classification is compared with a similar classification in the complex case.

Analysis of the New Technique to Solution of Fractional Wave- and Heat-like Equation

Acta Phys. Pol. B 48, 77 (2017)

page 77 •

abstract

We have applied the new approach of homotopic perturbation method (NHPM) for wave- and heat-like equation featuring time-fractional derivative. A combination of NHPM and multiple fractional power series form has been used the first time to present analytical solution. In order to illustrate the simplicity and ability of the suggested approach, some specific and clear examples have been given. All computations were done using Mathematica.

Asymmetric Bistability in the Rössler System

Acta Phys. Pol. B 48, 97 (2017)

page 97 •

abstract

Symmetric pairs of coexisting attractors are commonly found in symmetric dynamical systems when symmetry breaking occurs. By contrast, asymmetric bistability is rarely reported in either symmetric or asymmetric dynamical systems because such behavior typically occurs in narrow regions of parameter space and thus is often unnoticed. This paper describes an exploration of the regular parameter space of the Rössler system and shows examples of strange attractors coexisting with other strange attractors and with limit cycles, and asymmetric pairs of limit cycles in limited parameter space. A particular 1D path through parameter space is chosen to illustrate the various regions and the bifurcations that accompany the birth and death of the coexisting asymmetric attractors.

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