The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme

We report on our latest results in the calculation of the two--mass contributions to 3--loop operator matrix elements (OMEs). These OMEs are needed to compute the corresponding contributions to the deep-inealstic scattering structure functions and to generalize the variable flavor number scheme by including both charm and bottom quarks. We present the results for the non-singlet and $A_{gq,Q}$ OMEs, and compare the size of their contribution relative to the single mass case. Results for the gluonic OME $A_{gg,Q}$ are given in the physical case, going beyond those presented in a previous publication where scalar diagrams were computed. We also discuss our recently published two--mass contribution to the pure singlet OME, and present an alternative method of calculating the corresponding diagrams.Comment: 20 pages Latex, 5 Figures, different style file

The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element Agg,Q(3)A_{gg,Q}^{(3)}

We calculate the two-mass QCD contributions to the massive operator matrix element $A_{gg,Q}$ at $\mathcal{O} (\alpha_s^3)$ in analytic form in Mellin $N$- and $z$-space, maintaining the complete dependence on the heavy quark mass ratio. These terms are important ingredients for the matching relations of the variable flavor number scheme in the presence of two heavy quark flavors, such as charm and bottom. In Mellin $N$-space the result is given in the form of nested harmonic, generalized harmonic, cyclotomic and binomial sums, with arguments depending on the mass ratio. The Mellin inversion of these quantities to $z$-space gives rise to generalized iterated integrals with square root valued letters in the alphabet, depending on the mass ratio as well. Numerical results are presented.Comment: 99 pages LATEX, 2 Figure

One-step microwave synthesis of palladium-carbon nanotubes hybrids with improved catalytic performance

7 páginas, 7 figuras, 3 tablas.-- El pdf del artículo es la versión pre-print.A fast and easy one-step linker-free approach for the synthesis of palladium nanoparticle/multiwall carbon nanotube (Pd-NP/MWCNT)hybrid materials is described using microwave irradiation for the effective decomposition of Pd2dba3 complex in the presence of MWCNTs. High loadings of Pd nanoparticles (up to 40 wt.%) having sizes between 3 and 5 nm are deposited on the surface of MWCNTs within a time of only 2 minutess. The Pd-NP/MWCNT materials serve as efficient catalysts in C-C coupling as well as in hydrogenation reactions, all characterized by high conversion rates using a small amount of catalysts, high turnover frequency values and good recyclbility.Financial support from the Spanish Ministerio de Ciencia e Innovación (MICINN) and the European Regional Development Fund (ERDF) under projects CTQ2008-01784 and MAT2007-66927-C02-01, and the Gobierno de Aragón (DGAPI086- 08) is gratefully acknowledged. M.C. thanks MICINN for her Grant No. BES-2008-003503.Peer reviewe

A Categorical Model for Classical and Quantum Block Designs

Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show that models of this structure in the category of matrices and natural numbers recover the traditional classical combinatorial objects, while models in the category of completely positive maps yield a new definition of quantum designs. We show that this generalizes both a previous notion of quantum designs given by Zauner and the traditional description of block designs. Furthermore, we demonstrate that there exists a functor which relates every categorical block design to a quantum one.Comment: In Proceedings ACT 2023, arXiv:2312.08138. 19 page

O ( α2s^s_2 ) polarized heavy flavor corrections to deep-inelastic scattering at Q2^2 ≫ m2^2

We calculate the quarkonic O(α$^2_s$) massive operator matrix elements $\Delta$A$_{Qg}$ (N),$\Delta$A$^{PS}_{Qq}$(N) and $\Delta$A$^{NS}_{qq}$,$_Q$(N) for the twist–2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region Q$^2$ ≫ m$^2$ to O(ε) in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin space, without applying the integration-by-parts method. The result is given in terms of harmonic sums. This leads to a significant compactification of the operator matrix elements and massive Wilson coefficients in the region Q$^2$ ≫ m$^2$ derived previously in [1], which we partly confirm, and also partly correct. The results allow to determine the heavy flavor Wilson coefficients for g$_1$(x, Q$^2$) to O(α$^2_s$ ) for all but the power suppressed terms ∝ (m$^2$/Q$^2$)$^k$ , k ≥ 1. The results in momentum fraction z-space are also presented. We also discuss the small x effects in the polarized case. Numerical results are presented. We also compute the gluonic matching coefficients in the two–mass variable flavor number scheme to O(ε)

O(αs2O(\alpha_s^2) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at Q2≫m2Q^2 \gg m^2

We calculate the quarkonic $O(\alpha_s^2)$ massive operator matrix elements $\Delta A_{Qg}(N), \Delta A_{Qq}^{\rm PS}(N)$ and $\Delta A_{qq,Q}^{\rm NS}(N)$ for the twist--2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region $Q^2 \gg m^2$ to $O(\varepsilon)$ in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin space, without applying the integration-by-parts method. The result is given in terms of harmonic sums. This leads to a significant compactification of the operator matrix elements and massive Wilson coefficients in the region $Q^2 \gg m^2$ derived previously in \cite{BUZA2}, which we partly confirm, and also partly correct. The results allow to determine the heavy flavor Wilson coefficients for $g_1(x,Q^2)$ to $O(\alpha_s^2)$ for all but the power suppressed terms $\propto (m^2/Q^2)^k, k \geq 1$. The results in momentum fraction $z$-space are also presented. We also discuss the small $x$ effects in the polarized case. Numerical results are presented. We also compute the gluonic matching coefficients in the two--mass variable flavor number scheme to $O(\varepsilon)$.Comment: 58 pages Latex, 12 Figure

O(αs2\alpha_s^2) polarized heavy flavor corrections to deep-inelastic scattering at Q2^2 ≫ m2^2

We calculate the quarkonic O($\alpha_s^2$) massive operator matrix elements and for the twist–2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region $Q^2>>M^2$ to O($\epsilon$) in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin space, without applying the integration-by-parts method. The result is given in terms of harmonic sums. This leads to a significant compactification of the operator matrix elements and massive Wilson coefficients in the region derived previously in [1], which we partly confirm, and also partly correct. The results allow to determine the heavy flavor Wilson coefficients for $g1(x,Q^2)$ to $O(\alpha_s^2)$ for all but the power suppressed terms proportional to ($m^2/Q^2)^k, k>=1$. The results in momentum fraction z-space are also presented. We also discuss the small x effects in the polarized case. Numerical results are presented. We also compute the gluonic matching coefficients in the two–mass variable flavor number scheme to $O(\epsilon)$

ViewPoint Oriented Software Development

In this paper we propose a new approach to software development which explicitly avoids the use of a single representation scheme or common schema. Instead, multiple ViewPoints are utilised to partition the domain information, the development method and the formal representations used to express software specifications. System specifications and methods are then described as configurations of related ViewPoints. This partitioning of knowledge facilitates distributed development, the use of multiple representation schemes and scalability. Furthermore, the approach is general, covering all phases of the software process from requirements to evolution. This paper motivates and systematically characterises the concept of a "ViewPoint", illustrating the concepts using a simplified example

Recent 3-Loop Heavy Flavor Corrections to Deep-Inelastic Scattering

We report on recent progress in calculating the three loop QCD corrections of the heavy flavor contributions in deep--inelastic scattering and the massive operator matrix elements of the variable flavor number scheme. Notably we deal with the operator matrix elements $A_{gg,Q}^{(3)}$ and $A_{Qg}^{(3)}$ and technical steps to their calculation. In particular, a new method to obtain the inverse Mellin transform without computing the corresponding $N$--space expressions is discussed.Comment: Proc RADCOR 2023, 7 pages, 1 figur