Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic

In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parametrisations with respect to the central decision problems. The model checking problem (MC) of PDL is NP-complete. The subject of this research is to identify a list of parametrisations (formula-size, treewidth, treedepth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) showing a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is in FPT. Finally, we introduce a variant of the satisfiability problem, asking for teams of a given size, and show for this problem an almost complete picture.Comment: Update includes refined result

Octet Magnetic Moments with Null Instantons and Semibosonized Nambu-Jona-Lasinio Model

It is shown that the difference between the magnetic moment results in the quark model with null instantons and semibosonized Nambu-Jona-Lasinio model lies in the description of the magnetic moment of the $\Lambda$-hyperon.Comment: RevTex, 6 pages, submitted to Progr.Theor.Phy

Analysis of dynamical corrections to baryon magnetic moments

We present and analyze QCD corrections to the baryon magnetic moments in terms of the one-, two-, and three-body operators which appear in the effective field theory developed in our recent papers. The main corrections are extended Thomas-type corrections associated with the confining interactions in the baryon. We investigate the contributions of low-lying angular excitations to the moments quantitatively and show that they are completely negligible. When the QCD corrections are combined with the non-quark model contributions of the meson loops, we obtain a model which describes the moments within a mean deviation of 0.04 $\mu_N$. The nontrivial interplay of the two types of corrections to the quark-model moments is analyzed in detail, and explains why the quark model is so successful. In the course of these calculations, we parametrize the general spin structure of the $j={1/2}^+$ baryon wave functions in a form which clearly displays the symmetry properties and the internal angular momentum content of the wave functions, and allows us to use spin-trace methods to calculate the many spin matrix elements which appear in the expressions for the moments. This representation may be useful elsewhere.Comment: 32 pages, 3 figures, submitted to Phys. Rev.

Decuplet baryon magnetic moments in a QCD-based quark model beyond quenched approximation

We study the decuplet baryon magnetic moments in a QCD-based quark model beyond quenched approximation. Our approach for unquenching the theory is based on the heavy baryon perturbation theory in which the axial couplings for baryon - meson and the meson-meson-photon couplings from the chiral perturbation theory are used together with the QM moment couplings. It also involves the introduction of a form factor characterizing the structure of baryons considered as composite particles. Using the parameters obtained from fitting the octet baryon magnetic moments, we predict the decuplet baryon magnetic moments. The $\Omega^-$ magnetic moment is found to be in good agreement with experiment: $\mu_{\Omega^-}$ is predicted to be $-1.97 \mu_N$ compared to the experimental result of ($-$2.02 $\pm$ 0.05) $\mu_N$.Comment: 19 pages, 2 figure

Diffractive Dissociation and Eikonalization in High Energy pp and p pˉ {\bar p} Collisions

We show that eikonal corrections imposed on diffraction dissociation processes calculated in the triple Regge limit, produce a radical change in the energy dependence of the predicted cross section. The induced correction is shown to be in general agreement with the new experimental data measured at the Tevatron.Comment: 11 pages LATEX, ( two figures not included obtainable from authors) (TAUP 2066-93 and FERMILAB PUB 93/ T

Asymptotic behaviour of the total cross section of p-p scattering and the Akeno cosmic ray data

I present a new determination of the total cross section for proton-proton collisions from the recent Akeno results on absorption of the cosmic ray protons in the p-Air collisions. Extrapolation to the SSC energy suggests $\sigma_{tot}(p-p) \approx (160-170) mb$. I also comment on a possible sensitivity of the p-Air cross section determinations to assumptions on the inelasticity of nuclear collisions at high energy.Comment: . 6 pages, 0 figure

Deformation of grain boundaries in polar ice

The ice microstructure (grain boundaries) is a key feature used to study ice evolution and to investigate past climatic changes. We studied a deep ice core, in Dome Concordia, Antarctica, which records past mechanical deformations. We measured a "texture tensor" which characterizes the pattern geometry and reveals local heterogeneities of deformation along the core. These results question key assumptions of the current models used for dating

Calculable Upper Limit on the Mass of the Lightest Higgs Boson in Any Perturbatively Valid Supersymmetric Theory

We show that there is a calculable upper limit on the mass of the lightest Higgs boson in any supersymmetric theory that remains perturbative up to a high scale . There are no restrictions on the Higgs sector, or the gauge group or particle content. We estimate the value of the upper limit to be m_{\hcirc} < 146 GeV for 100 GeV < $M_t$ < 145 GeV, from all effects except possibly additional heavy fermions beyond top (which could increase the limit by 0-20 GeV if any existed); for $M_t$ > 145 GeV the limit decreases monotonically. We expect to be able to decrease the value of the upper limit by at least a few percent by very careful analysis of the conditions. It is not normal in models for the actual mass to saturate the upper limit.Comment: 8 pages, UM-TH-92-24, Plain TeX. (One table available by fax on request to [email protected]

Studying minijets via the pTp_T dependence of two-particle correlation in azimuthal angle ϕ\phi

Following my previous proposal that two-particle correlation functions can be used to resolve the minijet contribution to particle production in minimum biased events of high energy hadronic interactions, I study the $p_T$ and energy dependence of the correlation. Using HIJING Monte Carlo model, it is found that the correlation $c(\phi_1,\phi_2)$ in azimuthal angle $\phi$ between two particles with $p_T>p_T^{cut}$ resembles much like two back-to-back jets as $p_T^{cut}$ increases at high colliding energies due to minijet production. It is shown that $c(0,0)-c(0,\pi)$, which is related to the relative fraction of particles from minijets, increases with energy. The background of the correlation for fixed $p_T^{cut}$ also grows with energy due to the increase of multiple minijet production. Application of this analysis to the study of jet quenching in ultrarelativistic heavy ion collisions is also discussed.Comment: 11 pages Latex text and 8 ps figures, LBL-3349

Effective field theory and the quark model

We analyze the connections between the quark model (QM) and the description of hadrons in the low-momentum limit of heavy-baryon effective field theory in QCD. By using a three-flavor-index representation for the effective baryon fields, we show that the ``nonrelativistic'' constituent QM for baryon masses and moments is completely equivalent through O(m_s) to a parametrization of the relativistic field theory in a general spin--flavor basis. The flavor and spin variables can be identified with those of effective valence quarks. Conversely, the spin-flavor description clarifies the structure and dynamical interpretation of the chiral expansion in effective field theory, and provides a direct connection between the field theory and the semirelativistic models for hadrons used in successful dynamical calculations. This allows dynamical information to be incorporated directly into the chiral expansion. We find, for example, that the striking success of the additive QM for baryon magnetic moments is a consequence of the relative smallness of the non-additive spin-dependent corrections.Comment: 25 pages, revtex, no figure