arXiv subjects
Publications and source records attributed to F. V. Tkachov.
The fortran-77 code [hep-ph/9912415] of the jet algorithm based on the optimal jet definition [hep-ph/9901444] has been successfully verified (up to a few interface bugs) using an independently evolved code written in the object-oriented language Component Pascal [http://www.oberon.ch]. The final fortran code OJF_014 is available on the Web.
We describe an efficient implementation of the optimal jet definition derived in hep-ph/9901444 (revision of January, 2000) and implemented in Fortran 77. The algorithm handles both c.m.s. and hadron collision kinematics.
A new method of quasi-optimal observables allows one to approach the quality of data processing usually associated with the method of maximal likelihood within the simpler algorithmic context of generalized moments.
Reported is a factorization theorem for large-s behavior of total cross sections obtained in a straightforward fashion from ordinary perturbation theory. The theorem extends the standard factorization results for the Bjorken and Drell-Yan processes. The obtaining of useful evolution equations is found to be problematic. A by-product is a direct method for systematic calculations of the parton evolution kernels.
We report our experiences with the generalized integration-by-parts algorithm [hep-ph/9609429] in the context of calculations of a realistic one-loop subset of diagrams.
This postscriptum to the theory of jet definition [hep-ph/9901444] summarizes the points which did not find their way into the main text.
The evolution of the distribution-theoretic methods in perturbative quantum field theory is reviewed starting from Bogolyubov's pioneering 1952 work with emphasis on the theory and calculations of perturbation theory integrals.
We present an algebraic algorithm for analytical calculation of arbitrary dimensionally regulated massless two-loop forward-scattering diagrams that constitute the most cumbersome part of next-to-leading order calculations in the large-s/small-x regime.
The results of part I (hep-ph/9612284) are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS-scheme in the regimes when some of the masses and external momenta are large with respect to the others. The large momenta are Euclidean, and the expanded diagrams are regarded as distributions with respect to them. The small masses may be equal to zero. The asymptotic operation for integrals is defined and a simple combinatorial techniques is developed to study its exponentiation. The asymptotic operation is used to obtain the corresponding expansions of arbitrary Green functions. Such expansions generalize and improve upon the well-known short-distance operator-product expansions, the decoupling theorem etc.; e.g. the low-energy effective Lagrangians are obtained to all orders of the inverse heavy mass. The obtained expansions possess the property of perfect factorization of large and small parameters, which is essential for meaningful applications to phenomenology. As an auxiliary tool, the inversion of the R-operation is constructed. The results are valid for arbitrary QFT models.
The results of the mathematical theory of asymptotic operation developed in hep-th/9612037 are applied to problems of immediate physical interest. First, the problem of UV renormalizationis analyzed from the viewpoint of asymptotic behaviour of integrands in momentum representation. A new prescription for UV renormalization in momentum space representation is presented (generalized minimal subtraction scheme); it ensures UV convergence of renormalized diagrams by construction, makes no use of special (e.g. dimensional) regularizations, and comprizes massless renormalization schemes (including the MS scheme). Then we present formal regularization-independent proofs of general formulae for Euclidean asymptotic expansions of renormalized Feynman diagrams (inlcuding short-distance OPE, heavy mass expansions and mixed asymptotic regimes etc.) derived earlier in the context of dimensional regularization. This result, together with the new variant of UV renormalization, demonstrates the power of the new techniques based on a systematic use of the theory of distributions and establishes the method of As-operation as a comprehensive full-fledged---and inherently more powerful---alternative to the BPHZ approach.
We present a systematic description of the mathematical techniques for studying multiloop Feynman diagrams which constitutes a full-fledged and inherently more powerful alternative to the BPHZ theory. The new techniques emerged as a formalization of the reasoning behind a recent series of record multiloop calculations in perturbative quantum field theory. It is based on a systematic use of the ideas and notions of the distribution theory. We identify the problem of asymptotic expansion of products of singular functions in the sense of distributions as a key problem of the theory of asymptotic expansions of multiloop Feynman diagrams. Its complete solution for the case of Euclidean Feynman diagrams (the so-called Euclidean asymptotic operation for products of singular functions) is explicitly constructed and studied.
We discuss quantum-field-theoretic interpretation of the family of observables (the so-called C-algebra) introduced in [ F.V.Tkachov: Preprint FERMILAB-PUB-95/191-T] for a systematic description of multijet structure of multiparticle final states at high energies. We argue that from the point of view of general quantum field theory, all information about the multijet structure is contained in the values of a family of multiparticle quantum correlators that can be expressed in terms of the energy-momentum tensor.
An explicit example is presented (a one-loop triangle graph) where dimensional regularization fails to regulate the infra-red singularities that emerge at intermediate steps of studying large-$Q^2$ Sudakov factorization. The mathematical nature of the phenomenon is explained within the framework of the theory of the $As$-operation.