Regular Series


Vol. 35 (2004), No. 10, pp. 2329 – 2523


Quark–Antiquark Bound States and the Breit Equation

abstract

A non-covariant but approximately relativistic two-body wave equation (Breit equation) describing the quantum mechanics of two fermions interacting with one another through a potential containing scalar, pseudoscalar and vector parts is presented. After expressing the sixteen component two-body wavefunction in terms of a radial and an angular function by means of the multipole expansion, the initial equation can be reduced into a set of sixteen radial equations which, in turn, can be classified in accordance to the parity and the state of the wavefunctions involved. The adequacy of the reduced equations in describing real problems is discussed by applying the theory to QCD problems and the calculation of the energies of bound states of quark–antiquark systems is performed to order \(\alpha ^4\). We show that bound states of heavy quarks can be described adequately by the Breit equation for a funnel interaction between the particles.


Nested Multi-Soliton Solutions with Arbitrary Hopf Index

abstract

Generalized Aratyn–Ferreira–Zimerman O\((3)\) nonlinear sigma model with a particular symmetry breaking term, so-called dielectric function, is discussed. Static multi-soliton configurations with finite energy and nontrivial Hopf index are found. We show that such configurations consist of nested toroidal solitons. Moreover, nontrivial sphaleron-like solutions i.e. configurations with zero total topological charge are also presented.


Chiral Doubling of Heavy–Light Hadrons: BaBar 2317 MeV/\(c^2\) and CLEO 2460 MeV/\(c^2\) Discoveries

abstract

We point out that the very recent discoveries of BaBar (2317) and CLEO II (2460) are consistent with the general pattern of spontaneous breaking of chiral symmetry in hadrons built of heavy and light quarks, as originally suggested by us in 1992 (Phys. Rev. D48, 4370 (1993)), and independently by Bardeen and Hill in 1993 (Phys. Rev. D49, 409 (1994)). The splitting between the chiral doublers follows from a mixing between the light constituent quark mass and the velocity of the heavy quark, and vanishes for a zero constituent quark mass. The strictures of spontaneous chiral symmetry breaking constrain the axial charges in the chiral multiplet, and yield a mass splitting between the chiral doublers of about 345 MeV when the pion coupling to the doublers is half its coupling to a free quark. The chiral corrections are small. This phenomenon is generic and extends to all heavy–light hadrons. We predict the mass splitting for the chiral doublers of the excited mesons \((D_1,D_2)\). We suggest that the heavy–light doubling can be used to address issues of chiral symmetry restoration in dense and/or hot hadronic matter. In particular, the relative splitting between \(D\) and \(D^*\) mesons and their chiral partners decreases in matter, with consequences on charmonium evolution at RHIC.


Quantum Mechanics in a Cut Fock Space

abstract

A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between discrete and continuous spectrum is stressed. In particular a new scaling low for nonlocalized states is obtained. Exact solutions for several cases as well as general properties of the method are given.


Very Forward Two–Photon \(e^{+}e^{-}\) Production and Luminosity Measurement for Ion Collisions at the LHC

abstract

A possible way of using two-photon very forward production of positron–electron pairs for a luminosity measurement of ion collisions at the LHC is discussed. The main characteristics of this process are introduced, and followed by results from fast Monte Carlo simulations of the measurement using the proposed Castor detector. The statistical accuracy of this method is discussed for the considered LHC ion beams.


On the Invariance of Scaled Factorial Moments when Original Distribution is Folded with the Binomial

abstract

It is shown, that the Scaled Factorial Moments of any rank do not change if the original distribution is folded with a binomial one.


Dependence of Proton Production on Centrality in Au–Au Collisions at High Energies

abstract

The rapidity distributions of protons produced in Au–Au collisions at the Alternating Gradient Synchrotron (AGS) energies are investigated by a two-cylinder model. The different distribution shapes for different centrality cuts are mainly determined by different contributions of leading protons. The cylinders contribute the same distribution shape for different centrality cuts. The calculated results are compared and found to be in agreement with the experimental data of the E917 Collaboration.


Density Matrix Constraints on Spin Observables in \(\overline {p} p\rightarrow \overline {\mit \Lambda }\mit \Lambda \)

abstract

We write down the spin density matrix of the reaction \(\overline {p} p\rightarrow \overline {{\mit \Lambda }}{\mit \Lambda }\) in the usual matrix form, its elements are simply given as combinations of the spin observables, which have been measured at CERN with a polarized proton target. Then, we show that the standard properties of any density matrix applied to the matrix obtained allow to carry out a number of interesting, model independent and non-trivial inequalities on spin observables.


Proton One-Quasiparticle States of Heaviest Nuclei

abstract

Proton one-quasiparticle states of heaviest nuclei are calculated within a macroscopic-microscopic approach. Basic characteristics of these states (projection of spin on the symmetry axis, parity, excitation energy, Nilsson label) are given. Much attention is paid to systematics of them (especially of the ground state), as functions of neutron number. Other important properties of the analyzed nuclei, as deformation, deformation energy, shell correction to energy and proton pairing-energy gap parameter, are also given. Heavy and super heavy odd-\(Z\), even-\(N\) nuclei with proton number \(Z=93\)–117 and neutron number \(N=136\)–178 are considered. Most of them are expected to be deformed. It is obtained that characteristics of the ground states, which are known experimentally, is rather well reproduced.


Testing the Mirror World Hypothesis for the Close-in Extrasolar Planets

abstract

Because planets are not expected to be able to form close to stars due to the high temperatures, it has been suggested that the observed close orbiting (\(\sim 0.05\) AU) large mass planets (\(\sim M_{\rm J}\)) might be mirror worlds — planets composed predominately of mirror matter. The accretion of ordinary matter onto the mirror planet (from e.g. the solar wind from the host star) will make the mirror planet opaque to ordinary radiation with an effective radius \(R_{\rm p}\). It was argued in a previous paper, Phys. Lett. B505, 1 (2001), that this radius was potentially large enough to explain the measured size of the first transiting close-in extrasolar planet, HD209458b. Furthermore, Phys. Lett. B505, 1 (2001) made the rough prediction: \(R_{\rm p} \propto \sqrt {\frac {T_{\rm s}}{M_{\rm p}}}\), where \(T_{\rm s}\) is the surface temperature of the ordinary matter in the mirror planet and \(M_{\rm p}\) is the mass of the planet (the latter dependence on \(M_p\) being the more robust prediction). We compare this prediction with the recently discovered transiting planets, OGLE-TR-56b and OGLE-TR-113b.


On the Propagation of Non Stationary Pressure Waves in Stellar Interiors

abstract

An analysis of the propagation of non stationary waves in the adiabatic region of stellar interior is presented. An equation of motion with an effective potential is derived, similar to the Zerilli equation known in the propagation of gravitational waves. The Huyghens principle is violated in this case and the energy diffusion outward null cones is expected. Numerical calculations demonstrate that the diffusion is weak for the case of standard Solar model; thus no significant effect corresponding to quasinormal modes can be expected. The likely reason for the absence of stronger features is the restriction of our analysis to adiabatic regions only, where the breakdown of the Huyghens principle is insignificant.


Rotation Curves of Spiral Galaxies: Influence of Magnetic Fields and Energy Flows

abstract

Physical mechanisms that can influence rotation curves of spiral galaxies are discussed. For dark matter studies, possible contributions due to magnetic fields and non-Newtonian gravitational accelerations should be carefully accounted for. We point out that magnetic fields are particularly important in outermost parts of the disk. In the framework of general relativity the physical reason of an enhanced gravity in spiral galaxies depends on the assumed metric. The additional gravity is provided for Schwarzschild metric by nonluminous mass, whereas for Vaidya metric by emission of radiative energy. In the latter case the non-Newtonian acceleration displays \(1/r\) behaviour. Also matter flows contribute to non-Newtonian gravity.


Low-\(x\) Contribution to the Bjorken Sum Rule Within Unified \(\ln ^2x+\)LO DGLAP Approximation

abstract

The small-\(x\) contributions to the Bjorken sum rule within unified picture \(\ln ^2x+\)LO DGLAP for different input parametrisations \(g_1^{\rm NS}(x,Q_0^2)\) are presented. Theoretical predictions for \(\int _{0}^{0.003} g_1^{\rm NS}(x,Q^2=10) dx\) are compared with the SMC small-\(x\) data. Rough estimation of the slope \(\lambda \), controlling the small-\(x\) behaviour of \(g_1^{\rm NS}\sim x^{-\lambda }\) from the obtained results and SMC data is performed. The crucial role of the running coupling \(\alpha _{\rm s}=\alpha _{\rm s}(Q^2/z)\) at low-\(x\) is taken into account.


Comment on Acta Phys. Pol. B 32 (2001) 3303 Paper by A.M. Oleś “Magnetic Order in Transition Metal Oxides with Orbital Degrees of Freedom”

abstract

We argue that the \(^{3}A_{2}\) state considered by Oleś in Acta Phys. Pol. B 32, 3303 (2001) for the \(d^{~2}\) system occurring in the V\(^{3+}\) ion in V\(_{2}\)O\(_{3}\) and LaVO\(_{3}\) as well as in Ti\(^{2+}\) ion in TiO and in many other oxides is wrong. The proper ground state is \(^{3}T_{1g}\) — its 9-fold degeneracy is further split in a crystal by intra-atomic spin-orbit interactions and lattice distortions.


ERRATUM for Acta Phys. Pol. B 32, 3303 (2001)

Magnetic Order in Transition Metal Oxides with Orbital Degrees of Freedom


ERRATUM for Acta Phys. Pol. B 34, 5443 (2003)

Exploring Supersymmetry at Linear Colliders


top

ver. 2024.03.17 • we use cookies and MathJax