abstract

This paper presents the operator form of the effective potential \(V\) governing the time evolution in \(2\) and \(3\) and \(n\) dimensional subspace of states. The general formula for the \(n\) dimensional case is considered the starting point for the calculation of the explicit formulae for \(2\) and \(3\) dimensional degenerate and non-degenerate cases. We relate the \(2\) and \(3\) dimensional cases to some physical systems which are currently investigated.

abstract

We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence principle. We find a suitable Hilbert space formulation of our construction for: (1) real shifts, (2) purely imaginary shifts. The representations involving imaginary shifts are free of spectrum doubling. We determine the corresponding coordinate and momentum operators satisfying the canonical commutation relations. The eigenvalues of the coordinate operator are in both cases discrete.

abstract

We study an ideally oriented system of Gay–Berne particles with embedded longitudinal dipole moments. While keeping the translational degrees of freedom of the molecules unrestricted we assume that their dipoles can be oriented either parallel or antiparallel to the positive \(z\) axis of the laboratory frame. At high temperatures, this frustrated Gay–Berne mesogen exhibits an ideally oriented nematic phase, which is the reference state of the system. In the limit of vanishing dipole moment nematic, smectic-A and smectic \(B\) phases are stable. Interestingly, by changing the magnitude and location of the molecular dipole in the nematic reference state we found dipole-induced smectic \(A\), smectic \(B\) and tetragonal crystal phases, in addition to crystalline structures with smectic \(A_{d}\) and \(A_{2}\)-like dipolar organization. Various singlet, pair and triplet distribution functions were evaluated to elucidate short and long range organization in these phases. In particular, the importance of triplet correlations for a proper understanding of the structures and their local, dipolar organization is demonstrated.

abstract

Chiral restoration at finite temperatures is studied in chiral quark models with non-local regulators. At the leading-\(N_{\rm c}\) level we find transition temperature of the order 100 MeV. Meson-loop contributions are also analyzed and found to have a very small effect.

abstract

A procedure for reducing the functional integral of QED to an integral over bosonic gauge invariant fields is presented. Next, a certain averaging method for this integral, giving a tractable effective quantum field theory, is proposed. Finally, the current–current propagator and the chiral anomaly are calculated within this new formulation. These results are part of our programme of analyzing gauge theories with fermions in terms of local gauge invariants.

abstract

The possibility of detecting the charged Higgs through its hadronic decay modes, using the ATLAS detector at the LHC is presented in this paper. Calculations are carried out in the context of the Minimal Supersymmetric Standard Model with the assumption that the mass scale of supersymmetric partners of ordinary matter is above the charged Higgs mass. For the charged Higgs mass below the top quark mass, the decay \(H^\pm \rightarrow c\bar {s}\) can be used to determine the mass of the charged Higgs assuming it is discovered through other channels, for instance \(H^\pm \rightarrow \tau \nu \), by observing the excess of \(\tau \) production over the Standard Model prediction. Above the top quark mass, the charged Higgs can be detected through \(H^\pm \rightarrow t\,b\) up to 400 GeV\(/c^2\) for low or high \(\tan \beta \) (\(\lt 2\), or \(\gt 20\)).

abstract

The possibility of detecting the charged Higgs through the process \(H^\pm \rightarrow Wh^0\) is studied with the ATLAS detector. Good reconstruction of the charged Higgs mass is achieved for masses below and above the top-quark mass and the \(t\bar {t}\) background can be suppressed substantially. However, because the signal rates are low, the discovery potential of this channel is limited to a rather narrow area of MSSM parameter space. The results can be applied to other models, for instance, NMSSM where the discovery potential could extend to a significant area of the parameter space.

abstract

We continue the analysis of \(S\)-wave production amplitudes for the reaction \(\pi ^- p \rightarrow \pi ^+ \pi ^- n\) involving the data obtained by the CERN–Cracow–Munich collaboration on a transversely polarized target at 17.2 GeV/\(c\) \(\pi ^-\) momentum. This study deals with the region below the \(K\overline {K}\) threshold. In particular, we study the “up-steep” solution containing a narrow \(S\)-wave resonance under the \(\rho (770)\). This solution exhibits a considerable inelasticity \(\eta \) which does not have any physical interpretation. Assuming that this inelasticity behaviour represents an unlikely fluctuation we impose \(\eta \equiv 1\) for all data points. This leads to non-physical results in one third of the \(\pi ^+ \pi ^- \) effective mass bins and in the remaining mass bins some parameters behave in a queer way. The situation is even worse for the “down-steep” solution. We conclude that the 17.2 GeV data cannot be described by a relatively narrow \(f_{0}(750)\). The “down-flat” and “up-flat” solutions which easily pass the \(\eta \equiv 1\) constraint exhibit a slow increase of phase shifts in the \(\rho (770)\) mass range.

abstract

We describe key elements of the perturbative similarity renormalization group procedure for Hamiltonians using two, third-order examples: \(\phi ^3\) interaction term in the Hamiltonian of scalar field theory in 6 dimensions and triple-gluon vertex counterterm in the Hamiltonian of QCD in 4 dimensions. These examples provide insight into asymptotic freedom in Hamiltonian approach to quantum field theory. The renormalization group procedure also suggests how one may obtain ultraviolet-finite effective Schrödinger equations that correspond to the asymptotically free theories, including transition from quark and gluon to hadronic degrees of freedom in case of strong interactions. The dynamics is invariant under boosts and allows simultaneous analysis of bound state structure in the rest and infinite momentum frames.

abstract

The contribution of the six quark cluster formation of the overlapping nucleons to the \({\mit \Lambda }\)-binding energy difference between the mirror hypernuclei pair \(^6_{\mit \Lambda }\)He–\(^6_{\mit \Lambda }\)Li has been estimated in the hybrid quark nucleon model. The contribution is small and model dependent. It makes the neutron rich nucleus \(^6_{\mit \Lambda }\)He more bound compared to its proton rich partner \(^6_{\mit \Lambda }\)Li.

abstract

The semiclassical model of nuclear reactions with loosely bound projectiles (V.P. Aleshin, B.I. Sidorenko, Acta Phys. Pol. B29, 325 (1998)) is refined and compared with experimental data of Rama Rao et al. on the excitation function for the production of \(^{232,\,233}\)Pa in \(^6\)Li+\(^{232}\)Th collisions at \(E=30\)–50 MeV. The main contribution to the production of \(^{232}\)Pa is the 2 neutron emission from excited states of \(^{234}\)Pa formed in the \((^6\)Li,\(\alpha )\) reaction. The main source of \(^{233}\)Pa is the \((^6\)Li,\(\alpha p)\) reaction followed by \(\gamma \) transitions from excited states of \(^{233}\)Th to \(^{233}\)Th (g.s.) which transforms to \(^{233}\)Pa through \(\beta ^- \) decay. The ground state of \(^6\)Li regarded as a combination of \(n+p+\alpha \) is modeled with the \(K=2\), \({l}_x={l}_y=0\) hyperspherical function. The calculation underpredicts the excitation function of \(^{232}\)Pa by a factor of 0.6 and overpredicts the excitation function of \(^{233}\)Pa by a factor of 2.3, on the average. With the more realistic wave function of \(^6\)Li both factors are expected to be closer to 1.

abstract

Microscopic analysis of recent data on beta-decay of even neutron-deficient nuclides between \(^{100}\)Sn and \(^{108}\)Sn is performed within the self-consistent finite Fermi-system theory and BCS plus Quasiparticle Random Phase Approximation with \(G\)-matrix interaction and proton–neutron pairing. Strength functions of Gamow–Teller \(\beta \)-decay are calculated. The mechanisms of reduction of the GT strength are discussed.

abstract

We argue that the measurement of open charm gives a unique opportunity to test the validity of \(p\)QCD-based and statistical models of nucleus–nucleus collisions at high energies. We show that various approaches used to estimate \(D\)-meson multiplicity in central Pb+Pb collisions at 158 \(A\,\)GeV give predictions which differ by more than a factor of 100. Finally we demonstrate that decisive experimental results concerning the open charm yield in \(A+A\) collisions can be obtained using data of the NA49 experiment at the CERN SPS.