The Three Loop Two-Mass Contribution to the Gluon Vacuum Polarization

We calculate the two-mass contribution to the 3-loop vacuum polarization of the gluon in Quantum Chromodynamics at virtuality $p^2 = 0$ for general masses and also present the analogous result for the photon in Quantum Electrodynamics.Comment: 5 pages Late

The two-mass contribution to the three-loop pure singlet operator matrix element

We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function $F_2(x,Q^2)$ at $O(\alpha_s^3)$ as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.Comment: 28 papges Latex, 3 figure

The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the polarized structure function $g_1(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable $N$ and the momentum fraction $x$, and derive heavy flavor corrections to the Bjorken sum-rule. Numerical results are presented for the charm quark contribution. Results on the structure function $g_2(x,Q^2)$ in the twist-2 approximation are also given.Comment: 29 pages, 8 Figure

Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results

We present recent analytic results for the 3-loop corrections to the massive operator matrix element $A_{Qg}^{(3)}$for further color factors. These results have been obtained using the method of arbitrarily large moments. We also give an overview on the results which were obtained solving all difference and differential equations for the corresponding master integrals that factorize at first order.Comment: 11 pages Latex, To appear in the Proceedings of: QCDEV2017, JLAB, Newport News, VA, USA, May 22-26, 2017; Po

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

Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra

Three loop ladder and $V$-topology diagrams contributing to the massive operator matrix element $A_{Qg}$ are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable $N$ and the dimensional parameter $\varepsilon$. Given these representations, the desired Laurent series expansions in $\varepsilon$ can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of $N$ are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of $V$-topologies.Comment: 110 pages Latex, 4 Figure

The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function F2(x,Q2)F_2(x,Q^2) and the Anomalous Dimension

The pure singlet asymptotic heavy flavor corrections to 3-loop order for the deep-inelastic scattering structure function $F_2(x,Q^2)$ and the corresponding transition matrix element $A_{Qq}^{(3), \sf PS}$ in the variable flavor number scheme are computed. In Mellin-$N$ space these inclusive quantities depend on generalized harmonic sums. We also recalculate the complete 3-loop pure singlet anomalous dimension for the first time. Numerical results for the Wilson coefficients, the operator matrix element and the contribution to the structure function $F_2(x,Q^2)$ are presented.Comment: 85 pages Latex, 14 Figures, 2 style file

The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering

We calculate the massive two--loop pure singlet Wilson coefficients for heavy quark production in the unpolarized case analytically in the whole kinematic region and derive the threshold and asymptotic expansions. We also recalculate the corresponding massless two--loop Wilson coefficients. The complete expressions contain iterated integrals with elliptic letters. The contributing alphabets enlarge the Kummer-Poincar\'e letters by a series of square-root valued letters. A new class of iterated integrals, the Kummer-elliptic integrals, are introduced. For the structure functions $F_2$ and $F_L$ we also derive improved asymptotic representations adding power corrections. Numerical results are presented.Comment: 42, pages Latex, 8 Figure

Preditores de fibrilação atrial de novo em unidade de cuidados intensivos não cardíaca

OBJECTIVE: To assess the predictors of de novo atrial fibrillation in patients in a non-cardiac intensive care unit. METHODS: A total of 418 hospitalized patients were analyzed between January and September 2016 in a non-cardiac intensive care unit. Clinical characteristics, interventions, and biochemical markers were recorded during hospitalization. In-hospital mortality and length of hospital stay in the intensive care unit were also evaluated. RESULTS: A total of 310 patients were included. The mean age of the patients was 61.0 ± 18.3 years, 49.4% were male, and 23.5% presented de novo atrial fibrillation. The multivariate model identified previous stroke (OR = 10.09; p = 0.016) and elevated levels of pro-B type natriuretic peptide (proBNP, OR = 1.28 for each 1,000pg/mL increment; p = 0.004) as independent predictors of de novo atrial fibrillation. Analysis of the proBNP receiver operating characteristic curve for prediction of de novo atrial fibrillation revealed an area under the curve of 0.816 (p 5,666pg/mL. There were no differences in mortality (p = 0.370), but the lengths of hospital stay (p = 0.002) and stay in the intensive care unit (p = 0.031) were higher in patients with de novo atrial fibrillation. CONCLUSIONS: A history of previous stroke and elevated proBNP during hospitalization were independent predictors of de novo atrial fibrillation in the polyvalent intensive care unit. The proBNP is a useful and easy- and quick-access tool in the stratification of atrial fibrillation risk.Objetivo: Avaliar quais os preditores de fibrilação atrial de novo em doentes de uma unidade de cuidados intensivos não cardíaca. Métodos: Foram analisados 418 doentes internados entre janeiro e setembro de 2016 em uma unidade de cuidados intensivos não cardíaca. Registaram-se as características clínicas, as intervenções efetuadas e os marcadores bioquímicos durante a internação. Avaliaram-se ainda a mortalidade hospitalar e o tempo de internação hospitalar e na unidade de cuidados intensivos. Resultados: Foram incluídos 310 doentes, com média de idades de 61,0 ± 18,3 anos, 49,4% do sexo masculino, 23,5% com fibrilação atrial de novo. O modelo multivariável identificou acidente vascular cerebral prévio (OR de 10,09; p = 0,016) e valores aumentados de proBNP (OR de 1,28 por cada aumento em 1.000pg/mL; p = 0,004) como preditores independentes de fibrilação atrial de novo. A análise por curva Característica de Operação do Receptor do proBNP para predição de fibrilação atrial de novo revelou área sob a curva de 0,816 (p 5.666pg/mL. Não se verificaram diferenças na mortalidade (p = 0,370), porém a duração da internação hospitalar (p = 0,002) e na unidade de cuidados intensivos (p = 0,031) foi superior nos doentes com fibrilação atrial de novo. Conclusões: História de acidente vascular cerebral prévio e proBNP elevado em internação constituíram preditores independentes de fibrilação atrial de novo na unidade de cuidados intensivos polivalente. O proBNP pode constituir ferramenta útil, de fácil e rápido acesso na estratificação do risco de fibrilação atrial.info:eu-repo/semantics/publishedVersio