### Regular Series

#### Vol. 43 (2012), No. 8, pp. 1663 – 1789

On a Time-changed Geometric Brownian Motion and Its Application in Financial Market

Acta Phys. Pol. B 43, 1667 (2012)

page 1667 •

abstract

In this paper, we introduce a time-changed geometric Brownian motion and investigate the corresponding martingale properties and fractional Fokker–Planck type equation. As an application, we prove that the market model considered is arbitrage-free and gives pricing formulae for the prices of European call options when the underlying asset price follows the time-changed geometric Brownian motion.

Algebraic Properties of Translational Shape Invariant Potentials in Arbitrary Steps

Acta Phys. Pol. B 43, 1683 (2012)

page 1683 •

abstract

Within the framework of supersymmetric quantum mechanics, we investigate the general algebraic properties of translational shape invariant potentials in arbitrary $k$ steps, in which the $k$ remainders $R_s (a_m)$ are analytic functions of the parameter $a_m$ that is related to others by translation: $a_m=a_{m-1}+\delta$. The present study is based on the fact that the simplified potential algebra of shape invariance condition in $k$ steps is equivalent to that of generalized deformed oscillators with a built-in $Z_k$-grading structure. We shall show that, despite the complexity in the study, the general algebraic properties still can be systematically determined.

Coulomb-gas Approach for Percolation Theory

Acta Phys. Pol. B 43, 1707 (2012)

page 1707 •

abstract

The aim of this work is to present a non-trivial confirmation of the powerful Coulomb gas-techniques for Boundary Conformal Field Theory (BCFT). We show that we can re-derive the known Cardy’s result of percolation problem via the techniques developed by S. Kawai in the Coulomb gas formalism.

Particle Spectra in Statistical Models with Energy and Momentum Conservation

Acta Phys. Pol. B 43, 1713 (2012)

page 1713 •

abstract

Single particle momentum spectra are calculated within three micro-canonical statistical ensembles, namely, with conserved system energy, system momentum, as well as system energy and momentum. Deviations from the exponential spectrum of the grand canonical ensemble are quantified and discussed. For mean particle multiplicity and temperature, typical for $p+p$ interactions at the LHC energies, the effect of the conservation laws extends to transverse momenta as low as about 3 GeV/$c$. The presented results should be considered as the next step in development of statistical models for particle production in high energy collisions. They can be useful to interpret spectra measured in nuclear collisions at high energies, in particular, their system size dependence.

On the Anomalous CP Violation and Noncontractibility of the Physical Space

Acta Phys. Pol. B 43, 1723 (2012)

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abstract

There is a growing evidence for the anomalously large semileptonic CP asymmetry in the $B$ meson system measured at the Tevatron. The noncontractible space, as an alternative symmetry-breaking mechanism to the Higgs mechanism, can change standard field theoretic calculations of the physical processes mediated through quantum loops for large external momenta or large internal masses. The presence of the $W$ bosons and $t$ quarks in loops of the $B$ meson mixing can enhance the corresponding semileptonic CP asymmetry when the loop integration is up to the universal Lorentz and gauge invariant UV-cutoff. We show that the enhancement is roughly 13%, thus the possible deviation is measurable at the Tevatron, LHCb, SuperKEKB and SuperB facilities.

Metamorphosis Versus Decoupling in Non-Abelian Gauge Theories at Very High Energies

Acta Phys. Pol. B 43, 1735 (2012)

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abstract

In the present paper, we study the limit of zero mass in non-Abelian gauge theories both with Higgs mechanism and in the nonlinear realization of the gauge group (Stückelberg mass). We argue that in the first case the longitudinal modes undergo a metamorphosis process to the Goldstone scalar modes, while in the second, we guess, a decoupling process associated to a phase transformation. The two scenarios yield strikingly different behaviors at high energy, mainly ascribed to the presence of a massless Higgs doublet among the physical modes in the case of Higgs mechanism (i.e. not only the Higgs boson). The aim of this work is to show that the problem of unitarity at high energy in non-Abelian gauge theory with no Higgs boson can open new perspectives in quantum field theory.

full authors' list

L.-C. Wang, D.-H. Zhang, S. Yan, Y.-J. Li, J.-X. Cheng, J.-S. Li, S. Kodaira, N. Yasuda

Fragmentation Cross Sections of $^{56}$Fe at 471 $A$ MeV on Al, C and CH$_{2}$ Targets

Acta Phys. Pol. B 43, 1769 (2012)

page 1769 •

abstract

We have measured the fragmentation cross sections of $^{56}$Fe on Al, C and CH$_{2}$ targets at 471 $A$ MeV using CR-39 plastic nuclear track detector. Cross sections for H target are calculated based on the results of C and CH$_{2}$ targets. Here, we present the results of total charge changing cross sections and the partial cross sections for fragments with charge $Z_{\rm F}\geq 5$. The total charge changing cross sections agree well with other previous experimental results at different energies and the theoretical prediction of Bradt–Peters semi-empirical formula, which are approximately independent of the beam energy but increase with the increase of the target mass. The partial cross sections show a significant enhancement for the fragments with even-$Z$ nuclei, especially for the fragments with charge $10\leq {Z_{\rm F}}\leq 20$. For the collisions of $^{56}$Fe on all targets reported in this paper, we firstly present the partial cross section results of the fragments with charge $5\leq {Z_{\rm F}}\leq 9$ using CR-39 detector. Finally, the partial cross sections is compared with the prediction of the improved quantum molecular dynamical model (ImQMD) and the GEMINI model, the production of charged projectile fragments can be well described by the models.

The Mass Calculations for the Neutron Star PSR J1614-2230

Acta Phys. Pol. B 43, 1783 (2012)

page 1783 •

abstract

The mass of the neutron star PSR J1614-2230 is calculated in the framework of relativistic mean field theory. In our calculations, we choose nine nucleon coupling constants (i.e. CZ11, DD-MEI, GL85, GL97, NL1, NL2, NLSH, TM1 and TM2), assuming that the neutron star only consists of neutrons, protons and electrons. It is found that the NLSH set give the hardest equation of state and the largest mass of neutron star. It is also found that, corresponding to the CZ11 set, the neutron star mass is 1.9702 $M_{\odot }$ which is approximate the mass of the neutron star PSR J1614-2230. Thus, we may obtain a possible model for it.

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