arXiv subjects
Publications and source records attributed to Fyodor V. Tkachov.
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.
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].
Using the techniques of [arXiv:0911.4271], upper bounds for a given confidence level are modified in an optimal fashion to incorporate the a priori information that the parameter being estimated is non-negative. A paradox with different confidence intervals for the same confidence level is clarified. The "lossy compression" nature of the device of confidence intervals is discussed and a "lossless" option to present results is pointed out.
The method of quasi-optimal weights provides a comprehensive, asymptotically optimal, transparent and flexible alternative to the least squares method. The optimality holds for a general non-linear, non-gaussian case.
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.
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].
A systematic framework for jet definition is developed from first principles of physical measurement, quantum field theory, and QCD. A jet definition is found which: is theoretically optimal in regard of both minimization of detector errors and inversion of hadronization; is similar to a cone algorithm with dynamically negotiated jet shapes and positions found via shape observables that generalize the thrust to any number of axes; involves no ad hoc conventions; allows a fast computer implementation [hep-ph/9912415]. The framework offers an array of options for systematic construction of quasi-optimal observables for specific applications.
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.
A quantitative description of the qualitative feature of multi-hadron final states known as the "number of jets" is given by a sequence of infrared finite shape observables (jet discriminators) that: take continuous values between 0 and 1; are stable-unlike clustering algorithms-against small variations of the input (data errors, Sudakov effects etc.); have a form of multiparticle correlators that is natural in the context of quantum field theory and hence are better suited for a systematic study of theoretical uncertainties (logarithmic and power corrections).
This treatment of power corrections (in a special case of Euclidean asymptotic regimes and vacuum condensates) remains exemplary. Unlike A.Mueller's 1985 "renormalon" paper, this trail-blazing Letter: 1) was based on the correct mechanism of factorization for power corrections (--> comments appended to the main text); 2) used a method (which subsequently became Asymptotic Operation; hep-ph/9703424 and refs. therein) that automatically yields exact diagrammatic formulas for the coefficients of power corrections, which directly allow non-perturbative operator interpretation (without any 'matchings'); 3) did not conjure irrelevant mathematical concepts (Borel summation) nor introduce arbitrary hypotheses ("renormalons") to explain what is clear already from careful analysis of diagrams (coefficients of power corrections are not perturbatively calculable). Incidentally, January 4 is the birthday of Sir Isaac Newton whose example as regards non-invention of arbitrary hypotheses proves so hard for theorists to follow.
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.
This summary of several talks given in 1990-1993 discusses the problem of asymptotic expansions of multiloop Feynman diagrams in masses and external momenta - a central problem in perturbative quantum field theory. Basic principles of the theory of asymptotic operation -- the most powerful tool for that purpose -- are discussed. Its connection with the conventional methods is explained (the BPHZ theory, the method of leading logarithmic approximation etc.). The problem of non-euclidean asymptotic regimes is discussed as well as ways of its solution.
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].
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.
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the corresponding Feynman-parametrized integrands into a form that is optimal for numerical integration, with all the poles in D-4 explicitly extracted.
For any near-threshold asymptotic regime and for any Feynman diagram (involving loop and/or phase space integrals), a systematic prescription for explicitly constructing all-logs, all-powers (all-twists) expansions in perfectly factorized form with explicit integrals for coefficients, is presented. The distribution-theoretic nature of the method of asymptotic operation employed allows treatment of totally exclusive phase space in the same manner as loop integrals.
The pinched/non-pinched classification of intersections of causal singularities of propagators in Minkowski space is reconsidered in the context of the theory of asymptotic operation as a first step towards extension of the latter to non-Euclidean asymptotic regimes. A highly visual distribution-theoretic technique of singular wave fronts is tailored to the needs of the theory of Feynman diagrams. Besides a simple derivation of the usual Landau equations in the case of the conventional singularities, the technique naturally extends to other types of singularities e.g. due to linear denominators in non-covariant gauges etc. As another application, the results of Euclidean asymptotic operation are extended to a class of quasi-Euclidean asymptotic regimes in Minkowski space.
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.