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F. V. Tkachov

Publications and source records attributed to F. V. Tkachov.

At least 19 recordsLinked to original sources
arXiv2020

Error estimation in the method of quasi-optimal weights

We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large samples are examined, both allowing an analytical investigation. First, a criterion is developed for validity of the assumption of asymptotic normality together with a recipe for the corresponding corrections. Second, a method is derived to take into account the systematic shift of the confidence interval due to the non-linearity of the theoretical mean of the weight as a function of the parameter to be estimated. A numerical example illustrates the two corrections.

physics.data-an↗
arXiv2020

Finite Z-less integral expressions for $β$-functions in the MS4 scheme

The generalized minimal subtraction scheme for ultraviolet renormalization (Kuznetsov and Tkachov, 1988) is fine-tuned with applications in mind. The resulting $\text{MS}^4$ scheme obviates extraneous regularizations and renders momentum integrands integrable by subtracting troublesome asymptotic terms in a physically correct fashion due to the use of special minimal subtraction operators defined congruously with the physically natural Polchinski cutoffs. A direct derivation of the Callan-Symanzik equations avoids divergent renormalization factors or counterterms, and automatically yields explicit exact finite integral expressions for renormalization group functions.

hep-th↗
arXiv2020

Partial D-operators for the generalized IBP reduction

Empirical evidence reveals existence of partial D-operators for the generalized IBP (BT) reduction algorithms that are, counterintuitively, much simpler and much easier to find than the complete D-operators from the foundational Bernstein theorem, allowing one to construct first true two-loop examples of generalized IBP identities.

hep-th↗
arXiv2019

Breaking the 2-loop barrier for generalized IBP reduction

We discuss the problem of constructing differential operators for the generalized IBP reduction algorithms at the 2-loop level. A deeply optimized software allows one to efficiently construct such operators for the first non-degenerate 2-loop cases. The most efficient approach is found to be via the so-called partial operators that are much simpler than the complete ones, and that affect the power of only one of the polynomials in the product.

hep-th↗
arXiv2019

MS4: a BPHZ killer

The UV renormalization scheme $\text{MS}^4$ emerged in the formalization of the reasoning which yielded an array of important algorithms in the 80's. $\text{MS}^4$ guarantees finiteness of renormalized integrals by construction, satisfies the Stueckelberg-Bogolyubov causality axiom for the R-operation, and turns out to be a 4-dimensional analog of t'Hooft's MS-scheme. The well-known IBP reduction algorithm can be ported to $\text{MS}^4$ with modifications, but without problems. $\text{MS}^4$ exhibits transparency of the structure, simplicity of the arithmetic at $D=4$, and new calculational options. A straightforward derivation of RG equations runs in terms of explicitly finite quantities and expresses RG functions in terms of explicitly finite integrals.

hep-ph↗
arXiv2015

The current status of "Troitsk nu-mass" experiment in search for sterile neutrino

We propose a new experiment to search for a sterile neutrino in a few keV mass range at the "Troitsk nu-mass" facility. The expected signature corresponds to a kink in the electron energy spectrum in tritium beta-decay. The new goal compared to our previous experiment will be precision spectrum measurements well below end point. The experimental installation consists of a windowless gaseous tritium source and a high resolution electromagnetic spectrometer. We estimate that the current bounds on the sterile neutrino mixing parameter can be improved by an order of magnitude in the mass range under 5 keV without major upgrade of the existing equipment. Upgrades of calibration, data acquisition and high voltage systems will allow to improve the bounds by another order of magnitude.

physics.ins-det↗
arXiv2015

Confidence intervals with a priori parameter bounds

We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution of the problem. Derived are the solutions for the cases of a continuous distribution with non-negative estimated parameter and a discrete distribution, specifically a Poisson process with background. For both cases, the best upper limit is constructed that accounts for the a priori information. A table is provided with the confidence intervals for the parameter of Poisson distribution that correctly accounts for the information on the known value of the background along with the software for calculating the confidence intervals for any confidence levels and magnitudes of the background (the software is freely available for download via Internet).

physics.data-an↗
arXiv2013

A comment on the LLA method, the kT jet algorithm and the BFKL theory

The leading logarithmic approximation method fails to yield the correct asymptotic behavior in some realistic situations: inclusion of the beta-terms to which the LLA method is insensitive may change a power growth to merely logarithmic. The results of [hep-ph/0101058] indicate that the problem of large-s behavior of total cross sections belongs to this class. Similarly, a reference to the LLA method cannot be sufficient to justify constructions such as the kT jet algorithm.

hep-ph↗
arXiv2011

An upper limit on electron antineutrino mass from Troitsk experiment

An electron antineutrino mass has been measured in tritium beta-decay in the "Troitsk nu-mass" experiment. The setup consists of a windowless gaseous tritium source and an electrostatic electron spectrometer. The whole data set acquired from 1994 to 2004 was reanalysed. A thorough selection of data with the reliable experimental conditions has been performed. We checked every known systematic effect and got the following experimental estimate for neutrino mass squared m_{nu}^{2}=-0.67+/- 2.53 {eV}^{2}. This gives an experimental upper sensitivity limit of m_{nu}<2.2 eV and upper limit estimates m_{nu}<2.12 eV, 95% C.L. for Bayesian statistics and m_{nu}<2.05 eV, 95% C.L. for the Feldman and Cousins approach.

hep-ex↗
arXiv2011

Application of quasi-optimal weights to searches of anomalies. Statistical criteria for step-like anomalies in cumulative spectra

The statistical method of quasi-optimal weights can be used to derive criteria for searches of anomalies. As an example we derive a convenient statistical criterion for step-like anomalies in cumulative spectra such as measured in the Troitsk-nu-mass, Mainz and KATRIN experiments. It is almost as powerful as the locally most powerful one near the null hypothesis and appreciably excels the conventional chi^2 and Kolmogorov-Smirnov tests. It is also compared with an ad hoc criterion of «pairwise correlations of neighbours»; the latter is seen to be less powerful if more sensitive to more general anomalies. As a realistic example, the criteria are applied to the Troitsk-nu-mass data.

physics.data-an↗
arXiv2009

Quantum scale-invariant models as effective field theories

We address the question of whether the quantum scale-invariant theories introduced in [1] are renormalizable or play the role of effective field theories that are valid below the Planck scale $M_P$. We show that starting from two-loop level the renormalization procedure requires introduction of counter-terms with structures different from those in the initial Lagrangian, making these theories non-renormalizable and therefore non-predictive above $M_P$. Despite non-renormalizability, the attractive features of these theories, associated with the stability of the Higgs mass agains radiative corrections and the smallness of the cosmological constant, remain intact.

hep-th↗
arXiv2005

Enhancement of the hadronic b quark decays

A class of previously unknown strong-interaction corrections is found to enhance the rate of non-leptonic decays of the b quark by 5-8 percent. This effect decreases the predicted fraction of semi-leptonic decays and brings it into fair agreement with experimental results. As well as solving a long-standing puzzle of measurements disagreeing with the Standard Model prediction, our work suggests a way for future precise studies of non-leptonic $b$ quark decays and their application to searching for "new physics."

hep-ph↗
arXiv2004

Pouzyry: a novel class of algorithms for restoring a function from a random sample

A novel class of algorithms for restoring a function from a random sample is based on the concept of weak convergence, borrows algorithmic solutions from the Optimal Jet Finder (hep-ph/0301185), offers a considerable algorithmic flexibility, is applicable to non-positive functions, is insensitive to the choice of coordinate axes. A first implementation demonstrates feasibility of the approach.

physics.data-an↗
arXiv2003

Optimal Jet Finder

We describe a FORTRAN 77 implementation of the optimal jet definition for identification of jets in hadronic final states of particle collisions. We discuss details of the implementation, explain interface subroutines and provide a usage example. The source code is available from http://www.inr.ac.ru/~ftkachov/projects/jets/

hep-ph↗
arXiv2003

Towards a standard jet definition

In a simulated measurement of the $W$-boson mass, evaluation of Fisher's information shows the optimal jet definition to be physically equivalent to the $k_\mathrm{T}$ algorithm while being much faster at large multiplicities.

hep-ph↗
arXiv2002

From novel mathematics to efficient algorithms. Do we have proper SD foundation to build future?

Computer implementation of sophisticated algorithms for physics applications is greatly facilitated by the new generation of component-oriented SD technologies pioneered by Wirth's Oberon and embraced by the software industry (Sun's Java and Microsoft's C#). In a stark contrast with the deeply flawed C++, the Oberon technologies (specifically, the Component Pascal and the BlackBox development environment) offer an unparalleled SD platform for building scientific applications from sophisticated data processing to demanding symbolic calculations. Specific examples are discussed.

hep-ph↗