Perturbation theory with unstable fundamental fields

The difficulties of perturbation theory associated with unstable fundamental fields (such as the lack of exact gauge invariance in each order) are cured if one constructs perturbative expansion directly for probabilities interpreted as distributions in kinematic variables. Such an expansion is made possible by the powerful method of non-Euclidean asymptotic operation [hep-ph/9703424].Comment: PS 8 pp. Final must-have version 16 Nov 98: many clarifications (NB: expanded remark 6 at end) thanks to relaxed formfactor. More at http://www.inr.ac.ru/~ftkachov/unstable/index.ht

Quasi-optimal observables vs. event selection cuts

The method of quasi-optimal observables [hep-ph/0001019] offers a fundamental yet simple and flexible algorithmic framework for data processing in high energy physics to improve upon the practice of event selection cuts.Comment: 3p postscript. Contribution to ACAT'02, Moscow, May 2002. Bibliography seriously updated. See notes appende

Optimal confidence intervals for bounded parameters (a correct alternative to the recipe of Feldman and Cousins)

A priori bound for the parameter to be estimated is incorporated into confidence intervals within frequentistic approach in a straightforward and optimal fashion, ensuring the best resolution of non-boundary values as well as robustness for non-physical values of the estimator.Comment: 8 pages; v3: diagonal in fig.1 corrected; note added on sensitivity limit. http://www.inr.ac.ru/~ftkachov/arXiv/0911.4271

On the structure of systematic perturbation theory with unstable fields

Discussed is the structure of non-trivial counterterms that occur in the systematic gauge-invariant perturbation theory with unstable fields introduced in [hep-ph/9802307].Comment: 4pp PS; talk at QFTHEP'99, 27 May - 2 June 1999, Mosco

Euclidean asymptotic expansions of Green functions of quantum fields (I) Expansions of products of singular functions

The problem of asymptotic expansions of Green functions in perturbative QFT is studied for the class of Euclidean asymptotic regimes. Phenomenological applications are analyzed to obtain a meaningful mathematical formulation of the problem. It is shown that the problem reduces to studying asymptotic expansions of products of a class of singular functions in the sense of the distribution theory. Existence, uniqueness and explicit expressions for such expansions ("asymptotic operation for products of singular functions") in dimensionally regularized form are obtained using the so-called extension principle.Comment: one .sty + one .tex (LaTeX 2.09) + one .ps (GSview) = 72 pp. Many fewer misprints than the journal versio

From jet algorithms to C-algebra. Measurement errors and regularization of cuts

Error enhancement properties of data processing algorithms in elementary particle physics measurements are discussed. It is argued that a systematic use of continuous weights instead of hard cuts may reduce errors of the results at the cost of a marginal increase of computer resources needed.Comment: 12 pp PS. Complements hep-ph/9601308. Useful Notes attached. 7.11.98: maintenanc

On dimensional regularization and mathematical rigour

The controversy concerning the phenomenon of breakdown of dimensional regularization in the problems involving asymptotic expansions of Feynman diagrams in non-Euclidean regimes is discussed with some pertinent bibliographic comments.Comment: 3p, PS. 23-nov-98: maintenanc

Re: Re: A contribution to the history of quarks

The emergence of Boris Struminsky's January, 1965 paper with a footnote that introduced a new quark quantum number now known as color caused a response [arXiv:0908.2772] that is seen, perhaps contrary to what it was intended to convey, to corroborate the general picture that comes out of the evidence summarized in [arXiv:0904.0343].Comment: 2 pages + 2 photo

Approaching the parameter estimation quality of maximum likelihood via generalized moments

A simple criterion is presented for a practical construction of generalized moments that allow one to approach the theoretical Rao-Cramer limit for parameter estimation while avoiding the complexity of the maximum likelihood method in the cases of complicated probability distributions and/or very large event samples.Comment: PS 4 page

Perturbation theory for unstable fundamental fields

The difficulties of standard perturbation theory associated with unstable fundamental fields are cured if one constructs PT directly for probabilities interpreted as distributions in kinematic variables