On the Definition of Gauge Field Operators in Lattice Gauge-Fixed Theories

We address the problem of defining the gauge four-potential on the lattice, in terms of the natural link variables. Different regularized definitions are shown, through non perturbative numerical computation, to converge towards the same continuum renormalized limit.Comment: 8 pages, LaTeX2e/LaTeX209, 3 eps figure

Optical Potentials Derived from Nucleon-Nucleon Chiral Potentials at N4LO

Background: Elastic scattering is probably the main event in the interactions of nucleons with nuclei. Even if this process has been extensively studied in the last years, a consistent description, i.e., starting from microscopic two- and many-body forces connected by the same symmetries and principles, is still under development. Purpose: In a previous paper we derived a theoretical optical potential from NN chiral potentials at fourth order (N3LO). In the present work we use NN chiral potentials at fifth order (N4LO), with the purpose to check the convergence and to assess the theoretical errors associated with the truncation of the chiral expansion in the construction of an optical potential. Methods: The optical potential is derived as the first-order term within the spectator expansion of the nonrelativistic multiple scattering theory and adopting the impulse approximation and the optimum factorization approximation. Results: The pp and np Wolfenstein amplitudes and the cross section, analyzing power, and spin rotation of elastic proton scattering from 16O, 12C, and 40Ca nuclei are presented at an incident proton energy of 200 MeV. The results obtained with different versions of chiral potentials at N4LO are compared. Conclusions: Our results indicate that convergence has been reached at N4LO. The agreement with the experimental data is comparable with the agreement obtained in our previous work. We confirm that building an optical potential within chiral perturbation theory is a promising approach for describing elastic proton-nucleus scattering.Comment: Physical Review C, in prin

Electromagnetic proton-neutron knockout off 16O: new achievements in theory

Results for the cross sections of the exclusive 16O(e,e'pn)14N and 16O(gamma,pn)14N knockout reactions are presented and discussed in different kinematics. In comparison with earlier work, a complete treatment of the center-of-mass (CM) effects in the nuclear one-body current is considered in connection with the problem of the lack of orthogonality between initial bound and final scattering states. The effects due to CM and orthogonalization are investigated in combination with different treatments of correlations in the two-nucleon overlap function and for different parametrizations of the two-body currents. The CM effects lead in super-parallel kinematics to a dramatic increase of the 16O(e,e'pn) cross section to the 1_2^+ excited state (3.95 MeV) of 14N. In all the situations considered the results are very sensitive to the treatment of correlations. A crucial role is played by tensor correlations, but also the contribution of long-range correlations is important.Comment: 13 pages, 10 figure

Polar Varieties and Efficient Real Elimination

Let $S_0$ be a smooth and compact real variety given by a reduced regular sequence of polynomials $f_1, ..., f_p$. This paper is devoted to the algorithmic problem of finding {\em efficiently} a representative point for each connected component of $S_0$ . For this purpose we exhibit explicit polynomial equations that describe the generic polar varieties of $S_0$. This leads to a procedure which solves our algorithmic problem in time that is polynomial in the (extrinsic) description length of the input equations $f_1, >..., f_p$ and in a suitably introduced, intrinsic geometric parameter, called the {\em degree} of the real interpretation of the given equation system $f_1, >..., f_p$.Comment: 32 page

Polar Varieties, Real Equation Solving and Data-Structures: The hypersurface case

In this paper we apply for the first time a new method for multivariate equation solving which was developed in \cite{gh1}, \cite{gh2}, \cite{gh3} for complex root determination to the {\em real} case. Our main result concerns the problem of finding at least one representative point for each connected component of a real compact and smooth hypersurface. The basic algorithm of \cite{gh1}, \cite{gh2}, \cite{gh3} yields a new method for symbolically solving zero-dimensional polynomial equation systems over the complex numbers. One feature of central importance of this algorithm is the use of a problem--adapted data type represented by the data structures arithmetic network and straight-line program (arithmetic circuit). The algorithm finds the complex solutions of any affine zero-dimensional equation system in non-uniform sequential time that is {\em polynomial} in the length of the input (given in straight--line program representation) and an adequately defined {\em geometric degree of the equation system}. Replacing the notion of geometric degree of the given polynomial equation system by a suitably defined {\em real (or complex) degree} of certain polar varieties associated to the input equation of the real hypersurface under consideration, we are able to find for each connected component of the hypersurface a representative point (this point will be given in a suitable encoding). The input equation is supposed to be given by a straight-line program and the (sequential time) complexity of the algorithm is polynomial in the input length and the degree of the polar varieties mentioned above.Comment: Late

Correlation functions at small quark masses with overlap fermions

We report on recent work on the determination of low-energy constants describing Delta{S}=1 weak transitions, in order to investigate the origins of the Delta{I}=1/2 rule. We focus on numerical techniques designed to enhance the statistical signal in three-point correlation functions computed with overlap fermions near the chiral limit.Comment: Talk presented at Lattice2004(weak), Fermilab, 21-26 June 2004, 3 pages, 2 figure

Polar Varieties and Efficient Real Equation Solving: The Hypersurface Case

The objective of this paper is to show how the recently proposed method by Giusti, Heintz, Morais, Morgenstern, Pardo \cite{gihemorpar} can be applied to a case of real polynomial equation solving. Our main result concerns the problem of finding one representative point for each connected component of a real bounded smooth hypersurface. The algorithm in \cite{gihemorpar} yields a method for symbolically solving a zero-dimensional polynomial equation system in the affine (and toric) case. Its main feature is the use of adapted data structure: Arithmetical networks and straight-line programs. The algorithm solves any affine zero-dimensional equation system in non-uniform sequential time that is polynomial in the length of the input description and an adequately defined {\em affine degree} of the equation system. Replacing the affine degree of the equation system by a suitably defined {\em real degree} of certain polar varieties associated to the input equation, which describes the hypersurface under consideration, and using straight-line program codification of the input and intermediate results, we obtain a method for the problem introduced above that is polynomial in the input length and the real degree.Comment: Late

Numerical techniques for lattice QCD in the ϵ\epsilon--regime

In lattice QCD it is possible, in principle, to determine the parameters in the effective chiral lagrangian (including weak interaction couplings) by performing numerical simulations in the $\epsilon$--regime, i.e. at quark masses where the physical extent of the lattice is much smaller than the Compton wave length of the pion. The use of a formulation of the lattice theory that preserves chiral symmetry is attractive in this context, but the numerical implementation of any such approach requires special care in this kinematical situation due to the presence of some very low eigenvalues of the Dirac operator. We discuss a set of techniques (low-mode preconditioning and adapted-precision algorithms in particular) that make such computations numerically safe and more efficient by a large factor.Comment: Plain TeX source, 32 pages, figures include

A co-ultramicronized palmitoylethanolamide/luteolin composite mitigates clinical score and disease-relevant molecular markers in a mouse model of experimental autoimmune encephalomyelitis

Background: Persistent and/or recurrent inflammatory processes are the main factor leading to multiple sclerosis (MS) lesions. The composite ultramicronized palmitoylethanolamide, an endogenous N-acylethanolamine, combined with the flavonoid luteolin, PEALut, have been found to exert neuroprotective activities in experimental models of spinal and brain injury and Alzheimer disease, as well as a clinical improvement in human stroke patients. Furthermore, PEALut enhances the expression of different myelin proteins in oligodendrocyte progenitor cells suggesting that this composite might have protective effects in MS experimental models. Methods: The mouse model of experimental autoimmune encephalomyelitis (EAE) based on active immunization with a fragment of myelin oligodendrocyte glycoprotein (MOG35-55) was used. The daily assessment of clinical score and the expression of serum amyloid A (SAA1), proinflammatory cytokines TNF-\u3b1, IL-1\u3b2, IFN-\u3b3, and NLRP3 inflammasome, as well as TLR2, Fpr2, CD137, CD3-\u3b3, and TCR-\u3b6 chain, heterodimers that form T cell surface glycoprotein (TCR), and cannabinoid receptors CB1, CB2, and MBP, were evaluated in the brainstem and cerebellum at different postimmunization days (PIDs). Results: Vehicle-MOG35-55-immunized (MOG35-55) mice developed ascending paralysis which peaked several days later and persisted until the end of the experiment. PEALut, given intraperitoneally daily starting on day 11 post-immunization, dose-dependently improved clinical score over the range 0.1-5 mg/kg. The mRNA expression of SAA1, TNF-\u3b1, IL-1\u3b2, IFN-\u3b3, and NLRP3 were significantly increased in MOG35-55 mice at 14 PID. In MOG35-55 mice treated with 5 mg /kg PEALut, the increase of SAA1, TNF- \u3b1, IL-1\u3b2, and IFN-\u3b3transcripts at 14 PID was statistically downregulated as compared to vehicle-MOG35-55 mice (p < 0.05). The expression of TLR2, Fpr2, CD137, CD3-\u3b3, TCR-\u3b6 chain, and CB2 receptors showed a significant upregulation in vehicle-MOG35-55 mice at 14 PID. Instead, CB1 and MBP transcripts have not changed in expression at any time. In MOG/PEALut-treated mice, TLR2, Fpr2, CD137, CD3-\u3b3, TCR-\u3b6 chain, and CB2 mRNAs were significantly downregulated as compared to vehicle MOG35-55 mice. Conclusions: The present results demonstrate that the intraperitoneal administration of the composite PEALut significantly reduces the development of clinical signs in the MOG35-55 model of EAE. The dose-dependent improvement of clinical score induced by PEALut was associated with a reduction in transcript expression of the acute-phase protein SAA1, TNF-\u3b1, IL-1\u3b2, IFN-\u3b3, and NLRP3 proinflammatory proteins and TLR2, Fpr2, CD137, CD3-\u3b3, TCR-\u3b6 chain, and CB2 receptors