### Regular Series

#### Vol. 43 (2012), No. 10, pp. 1913 – 2036

Breaking the Light Speed Barrier

Acta Phys. Pol. B 43, 1917 (2012)

page 1917 •

abstract

As it is well known, classical special relativity allows the existence of three different kinds of particles: bradyons, luxons and tachyons. Bradyons have non-zero mass and hence always travel slower than light. Luxons are particles with zero mass, like the photon, and they always travel with invariant velocity. Tachyons are hypothetical superluminal particles that always move faster than light. The existence of bradyons and luxons is firmly established, while the tachyons were never reliably observed. In quantum field theory, the appearance of tachyonic degrees of freedom indicates vacuum instability rather than a real existence of the faster-than-light particles. However, recent controversial claims of the OPERA experiment about superluminal neutrinos triggered a renewed interest in superluminal particles. Driven by a striking analogy of the old Frenkel–Kontorova model of a dislocation dynamics to the theory of relativity, we conjecture in this note a remarkable possibility of existence of the forth type of particles, elvisebrions, which can be superluminal. The characteristic feature of elvisebrions, distinguishing them from tachyons, is that they are outside the realm of special relativity and their energy remains finite (or may even turn to zero) when the elvisebrion velocity approaches the light velocity.

The Mikhauilov–Novikov–Wang Hierarchy and Its Hamiltonian Structures

Acta Phys. Pol. B 43, 1953 (2012)

page 1953 •

abstract

Using the Lie algebra approach, we construct a Mikhauilov–Novikov–Wang hierarchy associated with the $3\times 3$ matrix spectral problem. It is shown that the hierarchy of nonlinear evolution equations is integrable in the Lax sense and possesses Hamiltonian structures.

On the Phase Diagram of Massive Yang–Mills

Acta Phys. Pol. B 43, 1965 (2012)

page 1965 •

abstract

The phases of a lattice gauge model for the massive Yang–Mills are investigated. The phase diagram supports the recent conjecture on the large energy behavior of nonlinearly realized massive gauge theories (i.e. mass à la Stückelberg, no Higgs mechanism), envisaging a Phase Transition (PT) to an asymptotically free massless Yang–Mills theory.

Charge Asymmetries of Lepton Transverse Momenta in Drell–Yan Processes at the LHC

Acta Phys. Pol. B 43, 1981 (2012)

page 1981 •

abstract

Charged lepton transverse momenta in the Drell–Yan processes play an important role at the LHC in precision measurements of the Standard Model parameters, such as the $W$-boson mass and width, their charge asymmetries and $\sin ^2\theta _W$. Therefore, their distributions should be described as accurately as possible by the Monte Carlo event generators. In this paper, we discuss the problem of matching the hard-process kinematics of the Monte Carlo generator WINHAC with the parton-shower kinematics of the PYTHIA 6.4 generator while interfacing these two programs. We show that improper assignment of the quark and antiquark effective momenta in the LO matrix element computations may affect considerably the predicted lepton transverse momenta and even completely reverse their charge asymmetries at the LHC. We propose two matching schemes in which the NLO QCD distributions of the leptonic kinematical variables can be well reproduced by the LO WINHAC generator.

On the Existence of Jumps in Financial Time Series

Acta Phys. Pol. B 43, 2001 (2012)

page 2001 •

abstract

In this research two methods of detecting jumps are presented. One is based on the nonparametric approach, whereas the other — on the JD($M$)J model. Bayesian inference is applied to detect jumps in the JD($M$)J model. Intraday and daily rates of return are under consideration. The empirical results imply the existence of jumps. The information on existing jumps is exploited in a forecasting experiment focused on Value at Risk predictions.

Cross-correlations Between WTI Crude Oil Market and U.S. Stock Market: A Perspective from Econophysics

Acta Phys. Pol. B 43, 2021 (2012)

page 2021 •

abstract

In this study, we take a fresh look at the cross-correlations between WTI crude oil market and U.S. stock market from the perspective of econophysics. We choose the three major U.S. stock indices (i.e. , DJIA, NASDAQ and S&P 500) as the research objects and select the sample data from Jan 2, 2002 to Jun 29, 2012. In the empirical process, first, using a statistical test in analogy to the Ljung-Box test, we find that there are cross-correlations between WTI and DJIA, WTI and NASDAQ, and WTI and S&P 500 at the 5% significance level. Then, employing the multifractal detrended cross-correlation analysis (MF-DCCA) method, we find that the cross-correlated behavior between WTI crude oil market and U.S. stock market is nonlinear and multifractal. An interesting finding is that the cross-correlation exponent is smaller than the average scaling exponent when q$\lt$0, and larger than the average scaling exponent when q$\gt$0. Finally, using the rolling windows method, which can capture the dynamics of cross-correlations, we find that there are three special periods whose time-varying Hurst exponents are different from the others.

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