Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovl{\psi} \psi and m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.Comment: 20 pages, no figure

The Schro¨\ddot{o}dinger-Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics

In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schr$\ddot{o}$dinger-Poisson equations in the large $N$ limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as $\hbar \sim M^{5/3} G^{1/2} (N/)^{1/6}$, where is $G$ the gravitational constant, $N$ and $M$ are the number and the mass of the bodies, and $$ is their average density. The relevance of this result in the context of large scale structure formation is discussed. In particular, this finding gives a further argument in support of the validity of the Schr$\ddot{o}$dinger method as numerical double of the N-body simulations of dark matter dynamics at large cosmological scales.Comment: Accepted for publication in the Euro. Phys. J.

Weinberg like sum rules revisited

The generalized Weinberg sum rules containing the difference of isovector vector and axial-vector spectral functions saturated by both finite and infinite number of narrow resonances are considered. We summarize the status of these sum rules and analyze their overall agreement with phenomenological Lagrangians, low-energy relations, parity doubling, hadron string models, and experimental data.Comment: 31 pages, noticed misprints are corrected, references are added, and other minor corrections are mad

Cannabis use in male and female first episode of non-affective psychosis patients: Long-term clinical, neuropsychological and functional differences

BACKGROUND: Numerous studies show the existence of a high prevalence of cannabis use among patients with psychosis. However, the differences between men and women who debut with a first episode of psychosis (FEP) regarding cannabis use have not been largely explored. The aim of this study was to identify the specific sex factors and differences in clinical evolution associated with cannabis use. METHOD: Sociodemographic characteristics at baseline were considered in our sample of FEP patients to find differences depending on sex and the use of cannabis. Clinical, functional and neurocognitive variables at baseline, 1-year, and 3-years follow-up were also explored. RESULTS: A total of 549 patients, of whom 43% (N = 236) were cannabis users, 79% (N = 186) male and 21% (N = 50) female, were included in the study. There was a clear relationship between being male and being a user of cannabis (OR = 5.6). Cannabis users were younger at illness onset. Longitudinal analysis showed that women significantly improved in all three dimensions of psychotic symptoms, both in the subgroup of cannabis users and in the non-users subgroup. Conversely, subgroups of men did not show improvement in the negative dimension. In cognitive function, only men presented a significant time by group interaction in processing speed, showing a greater improvement in the subgroup of cannabis users. CONCLUSION: Despite knowing that there is a relationship between cannabis use and psychosis, due to the high prevalence of cannabis use among male FEP patients, the results showed that there were very few differences in clinical and neurocognitive outcomes between men and women who used cannabis at the start of treatment compared to those who did not

A guide to the Choquard equation

We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations $$-\Delta u + V(x)u = \bigl(|x|^{-(N-\alpha)} * |u|^p\bigr)|u|^{p - 2} u \qquad \text{in $\mathbb{R}^N$},$$ and some of its variants and extensions.Comment: 39 page