Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory

We present the two-loop helicity amplitudes for the scattering of two gluons into two gluons in QCD, which are relevant for next-to-next-to-leading order corrections to jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity variants of dimensional regularization. Summing our expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Glover, Oleari and Tejeda-Yeomans. We also present the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric Yang-Mills theory.Comment: 55 pages, 3 figures, corrected remark below eq. (4.33), other minor changes, version appearing in JHE

Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations

We outline a new algorithm to solve coupled systems of differential equations in one continuous variable $x$ (resp. coupled difference equations in one discrete variable $N$) depending on a small parameter $\epsilon$: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in $\epsilon$ if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the $\epsilon$-expansion of a ladder graph with 6 massive fermion lines

The Complete O(αs2)O(\alpha_s^2) Non-Singlet Heavy Flavor Corrections to the Structure Functions g1,2ep(x,Q2)g_{1,2}^{ep}(x,Q^2), F1,2,Lep(x,Q2)F_{1,2,L}^{ep}(x,Q^2), F1,2,3ν(νˉ)(x,Q2)F_{1,2,3}^{\nu(\bar{\nu})}(x,Q^2) and the Associated Sum Rules

We calculate analytically the flavor non-singlet $O(\alpha_s^2)$ massive Wilson coefficients for the inclusive neutral current non-singlet structure functions $F_{1,2,L}^{ep}(x,Q^2)$ and $g_{1,2}^{ep}(x,Q^2)$ and charged current non-singlet structure functions $F_{1,2,3}^{\nu(\bar{\nu})p}(x,Q^2)$, at general virtualities $Q^2$ in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross-Llewellyn Smith sum rule. There are no logarithmic corrections at large scales $Q^2$ and the effects of the power corrections due to the heavy quark mass are of the size of the known $O(\alpha_s^4)$ corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region $Q^2 \gg m_{c,b}^2$. We also study the target mass corrections to the above sum rules.Comment: 50 pages LATEX, 35 figure

A toolbox to solve coupled systems of differential and difference equations

We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter \ep (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t.\ \ep and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package \texttt{SolveCoupledSystem} which is based on the packages \texttt{Sigma}, \texttt{HarmonicSums} and \texttt{OreSys}. In all applications the representation in $x$-space is obtained as an iterated integral representation over general alphabets, generalizing Poincar\'{e} iterated integrals

Urbano o rural: ¿Dónde es más feliz la gente y por qué?

Using data from a worldwide sample, we investigate how happy people look like and if these “happiness characteristics” are more present in big urban towns or in small rural villages. We found evidence that (i) people seem to be slightly happier in rural settlements, (ii) happier people have some particular characteristics (e.g., higher levels of trust in others and being more interested in politics) and (iii) these positive attitudes are slightly more present in rural contexts. Then, we discuss some conceivable explanations to what we have seen.Utilizando datos de una muestra mundial, investigamos cómo es la gente feliz y si estas “características de felicidad” están más presentes en las grandes ciudades urbanas o en los pequeños pueblos rurales. Encontramos pruebas de que (i) la gente parece ser ligeramente más feliz en los asentamientos rurales, (ii) las personas más felices tienen algunas características particulares (por ejemplo, mayores niveles de confianza en los demás y estar más interesados en la política) y (iii) estas actitudes positivas están ligeramente más presentes en los contextos rurales. A continuación, se discuten algunas explicaciones concebibles a lo que hemos visto.Instituto Complutense de Estudios InternacionalesTRUEpu

An Analysis on the Experimental Design of “My Money or Yours: House Money Payment Effects"

Considering the expanding usage of experiments in Economics, the present article chooses one published paper in the area, dealing with the house money effect and analyzes it in a didactic way as concepts relating to the experimental design of lab experiments are evoked and discussed. In order to do so, three sections are outlined. First of all, the house money effect is explained and the article under scrutiny is placed in the context of what had already been done before; secondly, some of the experimental design concepts are summarised and then applied to soundly describe the experimental design of their experiment. Finally, after briefly presenting their results, there is an analytical overview of what has been done after their work and a personal take on possible lines for further research

Comportamento, economia e felicidade

Considerando que um dos objetivos práticos da Economia seja elevar o bem-estar das pessoas, é crucial entender como a felicidade é afetada por variáveis econômicas, tais quais desemprego ou inflação, por variáveis contextuais, tais qual estar casado, e por variáveis institucionais, tais qual participação política. Explora-se essas relações através de busca na literatura teórica e empírica, acompanhada de análise de estatísticas descritivas de dados recentes. Trata-se do papel do fellowfeeling. Considera-se como os vieses e as heurísticas comportamentais afetam as decisões e o consequente bem-estar derivado delas pelos indivíduos. Explora-se o papel das políticas de nudges como ferramentas úteis para auxiliar os indivíduos a fazer aquilo que gostariam de fazer e propõe-se algumas ideias, decorrentes das relações antes vistas. Alguns dos principais resultados encontrados são a importância do entorno para o indivíduo, seja o contexto em que está o país, seja as pessoas que estão ao seu redor e suas condições, e o efeito gerado por vieses comportamentais que distanciam a atitude do desejo ou distanciam o indivíduo duma correta percepção acerca da realidade, mas que podem ser corrigidos e usados para o benefício geral pelos formuladores de políticas públicas. A partir do presente trabalho, abrem-se múltiplas linhas de pesquisa.Considering that a practical goal of Economics is to raise people's well-being, it is crucial to understand how happiness is affected by economic variables such as unemployment or inflation, by contextual variables such as being married and by institutional variables such as political participation. These relationships are explored through searching in the theoretical and empirical literature, followed by analysis of descriptive statistics of recent data. The role of fellow-feeling is addressed. It is considered how biases and behavioral heuristics affect decisions and the consequent well-being derived from them by individuals. The role of nudge policies is explored as useful tools to assist individuals in doing what they would like to do and some ideas arising from the correlations previously seen are proposed. Some of the main results found are the importance of the environment to the individual, either the context in which the country is or the people around oneself and their conditions. Also, the effect generated by behavioral biases that distance attitude from desire or that distance the individual from a correct perception about reality, although they can be corrected and used for the general benefit by the policymakers. From the present work, multiple lines of research are opened

Urban or Rural: Where are people happier and why?

Using data from a worldwide sample, we investigate how happy people look like and if these “happiness characteristics” are more present in big urban towns or in small rural villages. We found evidence that (i) people seem to be slightly happier in rural settlements, (ii) happier people have some particular characteristics (e.g., higher levels of trust in others and being more interested in politics) and (iii) these positive attitudes are slightly more present in rural contexts. Then, we discuss some conceivable explanations to what we have seen

Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in

hep-ph/030416