Logic of Negation-Complete Interactive Proofs (Formal Theory of Epistemic Deciders)

We produce a decidable classical normal modal logic of internalised negation-complete and thus disjunctive non-monotonic interactive proofs (LDiiP) from an existing logical counterpart of non-monotonic or instant interactive proofs (LiiP). LDiiP internalises agent-centric proof theories that are negation-complete (maximal) and consistent (and hence strictly weaker than, for example, Peano Arithmetic) and enjoy the disjunction property (like Intuitionistic Logic). In other words, internalised proof theories are ultrafilters and all internalised proof goals are definite in the sense of being either provable or disprovable to an agent by means of disjunctive internalised proofs (thus also called epistemic deciders). Still, LDiiP itself is classical (monotonic, non-constructive), negation-incomplete, and does not have the disjunction property. The price to pay for the negation completeness of our interactive proofs is their non-monotonicity and non-communality (for singleton agent communities only). As a normal modal logic, LDiiP enjoys a standard Kripke-semantics, which we justify by invoking the Axiom of Choice on LiiP's and then construct in terms of a concrete oracle-computable function. LDiiP's agent-centric internalised notion of proof can also be viewed as a negation-complete disjunctive explicit refinement of standard KD45-belief, and yields a disjunctive but negation-incomplete explicit refinement of S4-provability.Comment: Expanded Introduction. Added Footnote 4. Corrected Corollary 3 and 4. Continuation of arXiv:1208.184

Bottom quark electroproduction in variable flavor number schemes

Two variable flavor number schemes are used to describe bottom quark production in deep inelastic electron-proton scattering. In these schemes the coefficient functions are derived from mass factorization of the heavy quark coefficient functions presented in a fixed flavor number scheme. Also one has to construct a parton density set with five light flavors (u,d,s,c,b) out of a set which only contains four light flavors (u,d,s,c). In order $\alpha_s^2$ the two sets are discontinuous at $\mu=m_b$ which follows from mass factorization of the heavy quark coefficient functions when it is carried out in the ${\bar {\rm MS}}$-scheme. Both variable flavor number schemes give almost identical predictions for the bottom structure functions $F_{2,b}$ and $F_{L,b}$. Also they both agree well with the corresponding results based on fixed order four-flavor perturbation theory over a wide range in $x$ and $Q^2$.Comment: Latex with seventeen PostScript figure

The Ratio R=FL/FTR=F_L/F_T in DIS as a Probe of the Charm Content of the Proton

We analyze the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ in heavy-quark leptoproduction as a probe of the charm content of the proton. To estimate the charm-initiated contributions, we use the ACOT($\chi$) variable-flavor-number scheme. Our analysis shows that charm densities of the recent CTEQ sets of parton distributions have sizeable impact on the Callan-Gross ratio in a wide region of $x$ and $Q^2$. In particular, the ACOT($\chi$) predictions for the quantity $R(x,Q^2)$ are about half as large as the corresponding expectations of the photon-gluon fusion mechanism for $x\sim 10^{-2}-10^{-1}$ and $Q^2\gg m^2$. This is because the structure functions $F_T (x,Q^2)$ and $F_L (x,Q^2)$ have different dependences on the mass logarithms of the type $\alpha_{s}\ln(Q^{2}/m^{2})$. On the other hand, our recent studies indicate that, contrary to the production cross sections, the Callan-Gross ratio is sufficiently stable under radiative corrections to the photon-gluon fusion component for $x\gtrsim 10^{-4}$. We conclude that the quantity $R(x,Q^2)$ in heavy-quark leptoproduction is perturbatively stable but sensitive to resummation of the mass logarithms. For this reason, in contrast to the structure functions, the ratio $R(x,Q^2)=F_L/F_T$ could be good probe of the charm density in the proton.Comment: 10 pages, 4 figures, revtex

The Gluonic Operator Matrix Elements at O(\alpha_s^2) for DIS Heavy Flavor Production

We calculate the $O(\alpha_s^2)$ gluonic operator matrix elements for the twist--2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region $Q^2 \gg m^2$, up to the linear terms in the dimensional parameter $\varepsilon$, ($D= 4 + \varepsilon$). These quantities are required for the description of parton distribution functions in the variable flavor number scheme (VFNS). The $O(\alpha_s^2 \varepsilon)$ terms contribute at the level of the $O(\alpha_s^3)$ corrections through renormalization. We also comment on additional terms, which have to be considered in the fixed (FFNV) and variable flavor number scheme, adopting the $\overline{\rm MS}$ scheme for the running coupling constant.Comment: 12 pages Latex, 1 style fil

Supersymmetric Scaling Violations (I). Solving the Supersymmetric DGLAP Evolution

We analize the renormalization group equations of supersymmetric QCD with N=1 for the evolution of parton distributions. For this purpose we develope a simple recursive algorithm in x-space to include both regular regions and supersymmetric regions in the evolution in the step approximation. Supersymmetric distributions are generated within a radiative model, with vanishing initial conditions for the superpartners. Here we focus on a scenario with broken susy, characterized by a lighter gluino coupled to the standard evolution and a decoupled scalar quark. Predictions for the all the distributions are presented.Comment: 33 pages, 14 figures. revised final version, in press on Nucl. Phys.

Treatment of Heavy Quarks in Deeply Inelastic Scattering

We investigate a simplified version of the ACOT prescription for calculating deeply inelastic scattering from Q^2 values near the squared mass M_H^2 of a heavy quark to Q^2 much larger than M_H^2.Comment: 14 pages, 5 figure

A New 5-Flavour LO Analysis and Parametrization of Parton Distributions in the Real Photon

New, radiatively generated, LO quark (u,d,s,c,b) and gluon densities in a real, unpolarized photon are presented. We perform a global 3-parameter fit, based on LO DGLAP evolution equations, to all available data for the structure function F2^gamma(x,Q^2). We adopt a new theoretical approach called ACOT(chi), originally introduced for the proton, to deal with the heavy-quark thresholds. This defines our basic model (CJKL model), which gives a very good description of the experimental data on F2^gamma(x,Q^2), for both Q^2 and x dependences. For comparison we perform a standard fit using the Fixed Flavour-Number Scheme (FFNS_CJKL model), updated with respect to the previous fits of this type. We show the superiority of the CJKL fit over the FFNS_CJKL one and other LO fits to the F2^gamma(x,Q^2) data. The CJKL model gives also the best description of the LEP data on the Q^2 dependence of the F2^gamma, averaged over various x-regions, and the F_2,c^gamma, which were not used directly in the fit. Finally, a simple analytic parametrization of the resulting parton densities obtained with the CJKL model is given.Comment: 43 pages, RevTeX4 using axodraw style, 3 tex and 12 postscript figures, version submitted to Phys. Rev. D, small text changes, one reference added, FORTRAN program available at http://www.fuw.edu.pl/~pjank/param.html and at http://www-zeuthen.desy.de/~alorca/id4.htm