Higher covariant derivative regulators and non-multiplicative renormalization

The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with dimensional regularization to obtain a consistent renormalized 4-dimensional Yang-Mills theory at the one-loop level. This shows that hybrid regularization methods can be applied not only to finite theories, like \eg\ Chern-Simons, but also to divergent theories.Comment: 12 pages, phyzzx, no figure

Higher covariant derivative Pauli-Villars regularization does not lead to a consistent QCD

We compute the beta function at one loop for Yang-Mills theory using as regulator the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Faddeev and Slavnov. This regularization prescription has the appealing feature that it is manifestly gauge invariant and essentially four-dimensional. It happens however that the one-loop coefficient in the beta function that it yields is not $-11/3,$ as it should be, but $-23/6.$ The difference is due to unphysical logarithmic radiative corrections generated by the Pauli-Villars determinants on which the regularization method is based. This no-go result discards the prescription as a viable gauge invariant regularization, thus solving a long-standing open question in the literature. We also observe that the prescription can be modified so as to not generate unphysical logarithmic corrections, but at the expense of losing manifest gauge invariance.Comment: 43 pages, Latex file (uses the macro axodraw.sty, instructions of how to get it and use it included), FTUAM 94/9, NIKHEF-H 94/2

Regularization and Renormalization of Chern-Simons Theory

We analyze some features of the perturbative quantization of Chern-Simons theory (CST) in the Landau gauge. In this gauge the theory is known to be perturbatively finite. We consider the renormalization scheme in which the renormalized parameter $k$ equals the bare or classical one and show that it constitutes a natural parametrization for the quantum theory. The reason is that, although in this renormalization scheme the value of the Green functions depends on the regularization used, comparison among different regularization methods shows that the observables (Wilson loops) are the same function of the shifted monodromy parameter $k+c_v$ for all BRS invariant regulators used so far for CST. We also discuss a particular BRS invariant regularization prescription in which CST is perturbatively defined as the large mass limit of dimensionally regularized topologically massive Yang-Mills theory. With this regularization prescription the radiative corrections induced by two-loop contributions do not entail observable consequences since they can be reabsorbed by a finite rescaling of the fields only. This very mechanism is conjectured to take place at higher perturbative orders. Talk presented by G.G. at the NATO AWR on ``Low dimensional Topology and Quantum Field Theory'', 6-13 September 1992, Cambridge (UK).Comment: 10 pages, Phyzzx, LPTHE 92-4

Non-relativistic pair annihilation of nearly mass degenerate neutralinos and charginos II. P-wave and next-to-next-to-leading order S-wave coefficients

This paper is a continuation of an earlier work (arXiv:1210.7928) which computed analytically the tree-level annihilation rates of a collection of non-relativistic neutralino and chargino two-particle states in the general MSSM. Here we extend the results by providing the next-to-next-to-leading order corrections to the rates in the non-relativistic expansion in momenta and mass differences, which include leading P-wave effects, in analytic form. The results are a necessary input for the calculation of the Sommerfeld-enhanced dark matter annihilation rates including short-distance corrections at next-to-next-to-leading order in the non-relativistic expansion in the general MSSM with neutralino LSP.Comment: LaTeX, 16 pages (+ 36 pages Appendix), 4 figures; v2 - new appendix with analytic results for the P-wave and rest of v^2 corrections to annihilation rates in the wino limit added, matches published versio

Heavy neutralino relic abundance with Sommerfeld enhancements - a study of pMSSM scenarios

We present a detailed discussion of Sommerfeld enhancements in neutralino dark matter relic abundance calculations for several popular benchmark scenarios in the general MSSM. Our analysis is focused on models with heavy wino- and higgsino-like neutralino LSP and models interpolating between these two scenarios. This work is the first phenomenological application of effective field theory methods that we have developed in earlier work and that allow for the consistent study of Sommerfeld enhancements in non-relativistic neutralino and chargino co-annihilation reactions within the general MSSM, away from the pure-wino and pure-higgsino limits.Comment: 38 pages, 14 figures, 3 table

Non-relativistic pair annihilation of nearly mass degenerate neutralinos and charginos I. General framework and S-wave annihilation

We compute analytically the tree-level annihilation rates of a collection of non-relativistic neutralino and chargino two-particle states in the general MSSM, including the previously unknown off-diagonal rates. The results are prerequisites to the calculation of the Sommerfeld enhancement in the MSSM, which will be presented in subsequent work. They can also be used to obtain concise analytic expressions for MSSM dark matter pair annihilation in the present Universe for a large number of exclusive two-particle final states.Comment: LATeX, 24 pages (+ 25 pages Appendix), 11 figures; v2 - replaced incorrect version of Fig. 4 and fixed typos listed in the JHEP erratu

Probabilistic Inference from Arbitrary Uncertainty using Mixtures of Factorized Generalized Gaussians

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both the joint probability density of the variables and the likelihood function of the (objective or subjective) observation are approximated by a special mixture model, in such a way that any desired conditional distribution can be directly obtained without numerical integration. We have developed an extended version of the expectation maximization (EM) algorithm to estimate the parameters of mixture models from uncertain training examples (indirect observations). As a consequence, any piece of exact or uncertain information about both input and output values is consistently handled in the inference and learning stages. This ability, extremely useful in certain situations, is not found in most alternative methods. The proposed framework is formally justified from standard probabilistic principles and illustrative examples are provided in the fields of nonparametric pattern classification, nonlinear regression and pattern completion. Finally, experiments on a real application and comparative results over standard databases provide empirical evidence of the utility of the method in a wide range of applications