### Regular Series

#### Vol. 49 (2018), No. 10, pp. 1733 – 1834

Vacuum Polarization of Massive Fields in the Spacetime of the Higher-dimensional Black Holes

Acta Phys. Pol. B 49, 1737 (2018)

page 1737 •

abstract

Using the Schwinger–DeWitt expansion, we construct and study the approximate vacuum polarization, $\langle \phi ^{2}\rangle _{D},$ of the quantized massive scalar field with a general curvature coupling parameter in higher-dimensional static and spherically-symmetric black hole spacetimes, with a special emphasis put on the electrically charged Tangherlini solutions and the extremal and ultraextremal configurations. For $4 \leq D \leq 7$, the explicit analytic expressions for the vacuum polarization are obtained when the Compton length associated with the quantized field is much less than the characteristic radius of the curvature of the background geometry and the nonlocal contribution to the result ignored. For the conformally coupled fields, the relation between the trace of the stress-energy tensor and the vacuum polarization is examined, which requires knowledge of the higher-order terms in the Schwinger–DeWitt expansion.

Resonance Production of Excited $u$ Quark at FCC-based $\gamma p$ Colliders

Acta Phys. Pol. B 49, 1763 (2018)

page 1763 •

abstract

Several Beyond the Standard Model theories proposed that fermions might have composite substructure. The existence of excited quarks is going to be the noticeable proof for the compositeness of Standard Model fermions. For this reason, excited quarks have been investigated by phenomenological and experimental high-energy physicists at various collider options for the last few decades. The Future Circular Collider (FCC) has been recently planned as particle accelerator to be established at CERN. Beside the $\sqrt {s}=100$ TeV proton–proton collisions, the FCC includes electron–positron and electron–proton collision options. Construction of linear $e^- e^+$ colliders (or dedicated e-linac) tangential to the FCC will afford an opportunity to handle multi-TeV $ep$ and $\gamma p$ collisions. In this respect, we executed a simulation of the resonance production of the excited $u$ quark at the FCC-based $\gamma p$ colliders with choosing both the polarized and unpolarized photon beams. The findings revealed that the chirality structure of the $q^*$–$q$–$\gamma$ vertex can be determined by the photon beam polarization. The attainable mass limits of the excited $u$ quark reached the highest values when the polarized photon beam was chosen. In addition, the ultimate compositeness scale values can be handled by appropriate choice of the photon beam polarization.

Analysis of the Axialvector Doubly Heavy Tetraquark States with QCD Sum Rules

Acta Phys. Pol. B 49, 1781 (2018)

page 1781 •

abstract

In this article, we construct the axialvector-diquark–scalar-antidiquark-type currents to interpolate the axialvector doubly heavy tetraquark states, and study them with the QCD sum rules in details by carrying out the operator product expansion up to the vacuum condensates of dimension 10.

full authors' list

Z. Majka, R. Płaneta, Z. Sosin, A. Wieloch, K. Zelga, M. Adamczyk, K. Pelczar, M. Barbui, S. Wuenschel, K. Hagel, X. Cao, E.-J. Kim, J. Natowitz, R. Wada, H. Zheng, G. Giuliani, S. Kowalski

A Novel Experimental Setup for Rare Events Selection and Its Potential Application to Super-heavy Elements Search

Acta Phys. Pol. B 49, 1801 (2018)

page 1801 •

abstract

The paper presents a novel instrumentation for rare events selection which was tested in our research of short-lived super-heavy elements production and detection. The instrumentation includes an active catcher multi-elements system and dedicated electronics. The active catcher located in the forward hemisphere is composed of 63 scintillator detection modules. Reaction products of damped collisions between heavy-ion projectiles and heavy-target nuclei are implanted in the fast plastic scintillators of the active catcher modules. The acquisition system trigger delivered by logical branch of the electronics allows to record the reaction products which decay via the alpha-particle emissions or spontaneous fission which take place between beam bursts. One microsecond wave form signal from FADCs contains information on heavy implanted nucleus as well as its decays.

Spectral Analysis on Swanson’s Hamiltonian

Acta Phys. Pol. B 49, 1813 (2018)

page 1813 •

abstract

In the original work of non-Hermitian Swanson’s Hamiltonian and subsequent Hermitian counterpart of the same, it has been shown that the only condition $\omega - \alpha -\beta \gt 0$ reflects positive energy eigenvalues. However, we find that the Swanson Hamiltonian reflects both positive as well as negative energy under the same condition ($\omega - \alpha -\beta \gt 0$). In order to complete the work, we also discuss the wave function corresponding to negative energy.

Antiferromagnetic Ising Model in the Framework of Riemannian Geometry

Acta Phys. Pol. B 49, 1823 (2018)

page 1823 •

abstract

A metric is introduced on the three-dimensional space of two long-range sublattice order parameters and a short-range order parameter describing the Ising antiferromagnets in the Bethe approximation. The Riemannian geometry associated with this metric is investigated analytically. In terms of the equilibrium order parameters, thermodynamic curvature scalar ($\mathcal {R}$) is derived and its temperature ($T$) dependence near the Néel transition temperature ($T_{\rm N}$) is analysed. A divergence to infinity is observed for the curvature on both sides of the Néel temperature ($\mathcal {R}\rightarrow \infty$) which can be scaled as $\mathcal {R}\sim \epsilon ^{\lambda }$ for $T\lt T_{\rm N}$, and $\mathcal {R}\sim (-\epsilon )^{\lambda ^\prime }$ for $T\gt T_{\rm N}$, with $\lambda =\lambda ^\prime =-2$ and $\epsilon =1-T/T_{\rm N}$. These observations fit well with those in the calculations of thermodynamic curvature in other spin models such as the spherical model and the ferromagnetic Ising model.

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