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V. A. Smirnov

Publications and source records attributed to V. A. Smirnov.

At least 55 records · Page 3Linked to original sources
arXiv2005

Next-to-Next-to-Leading Logarithms in Four-Fermion Electroweak Processes at High Energy

We sum up the next-to-next-to-leading logarithmic virtual electroweak corrections to the high energy asymptotics of the neutral current four-fermion processes for light fermions to all orders in the coupling constants using the evolution equation approach. From this all order result we derive finite order expressions through next-to-next-to leading order for the total cross section and various asymmetries. We observe an amazing cancellation between the sizable leading, next-to-leading and next-to-next-to-leading logarithmic contributions at TeV energies.

hep-ph↗
arXiv2005

Heavy Quarkonium Spectrum and Production/Annihilation Rates to order $β_0^3α_s^3$

We compute the third-order corrections to the heavy quarkonium spectrum and production/annihilation rates due to the leading renormalization group running of the static potential. The previously known complete ${\cal O}(m_qα_s^5)$ result for the heavy quarkonium ground state energy is extended to the exited states. After including the ${\cal O}(α_s^3)$ corrections the perturbative results are in surprisingly good agreement with the experimental data on the masses of the excited $Υ$ resonances and the leptonic width of the $Υ(1S)$ meson. The impact of the corrections on the $Υ$ sum rules and top quark-antiquark threshold production cross section is also discussed.

hep-ph↗
arXiv2004

Evaluating multiloop Feynman integrals by Mellin-Barnes representation

The status of analytical evaluation of double and triple box diagrams is characterized. The method of Mellin-Barnes representation as a tool to evaluate master integrals in these problems is advocated. New MB representations for massive on-shell double boxes with general powers of propagators are presented.

hep-ph↗
arXiv2003

Solving Recurrence Relations for Multi-Loop Feynman Integrals

We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, {\it i.e.}, the problem of expressing any Feynman integral from this class as a linear combination of master integrals. We show how the parametric representation invented by Baikov can be used to characterize the master integrals and to construct an algorithm for evaluating the corresponding coefficient functions. To illustrate this procedure we use simple one-loop examples as well as the class of diagrams appearing in the calculation of the two-loop heavy quark potential.

hep-ph↗
arXiv2003

Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple Box

The dimensionally regularized massless on-shell planar triple box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t in a Laurent expansion in the parameter \ep=(4-d)/2 of dimensional regularization up to a finite part. An explicit result is expressed in terms of harmonic polylogarithms, with parameters 0 and 1, up to the sixth order. The evaluation is based on the method of Feynman parameters and multiple Mellin-Barnes representation. The same technique can be quite similarly applied to planar triple boxes with any numerators and integer powers of the propagators.

hep-ph↗
arXiv2002

Analytical evaluation of certain on-shell two-loop three-point diagrams

An analytical approach is applied to the calculation of some dimensionally-regulated two-loop vertex diagrams with essential on-shell singularities. Such diagrams are important for the evaluation of QED corrections to the muon decay, QCD corrections to top quark decays t->W^{+}b, t->H^{+}b, etc.

hep-ph↗
arXiv2002

Evaluating double and triple (?) boxes

A brief review of recent results on analytical evaluation of double-box Feynman integrals is presented. First steps towards evaluation of massless on-shell triple-box Feynman integrals within dimensional regularization are described. The leading power asymptotic behaviour of the dimensionally regularized massless on-shell master planar triple-box diagram in the Regge limit $t/s \to 0$ is evaluated. The evaluation of the unexpanded master planar triple box is outlined and explicit results for coefficients at $1/\ep^j$, j=2,...,6, are presented.

hep-ph↗
arXiv2002

Potential NRQCD and Heavy-Quarkonium Spectrum at Next-to-Next-to-Next-to-Leading Order

The next-to-next-to-next-to-leading order (N^3LO) Hamiltonian of potential nonrelativistic QCD is derived. The complete matching of the Hamiltonian and the contribution from the ultrasoft dynamical gluons relevant for perturbative bound-state calculations is performed including one-, two-, and three-loop contributions. The threshold expansion is used to disentangle and match contributions of different scales in the effective-theory calculations. As a physical application, the heavy-quarkonium spectrum is obtained at N^3LO for the case of vanishing QCD beta function. Our results set the stage for a full N^3LO analysis of the heavy-quarkonium system.

hep-ph↗
arXiv2001

Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box

The dimensionally regularized master planar double box Feynman diagram with four massive and three massless lines, powers of propagators equal to one, all four legs on the mass shell, i.e. with p_i^2=m^2, i=1,2,3,4, is analytically evaluated for general values of m^2 and the Mandelstam variables s and t. An explicit result is expressed in terms of polylogarithms, up to the third order, depending on special combinations of m^2,s and t.

hep-ph↗
arXiv2001

E_\infty-structure and differentials of the Adams spectral sequence

The Adams spectral sequence was invented by J.F.Adams fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult problem of Algebraic Topology. Here we consider an approach to find inductive formulas for the differentials. It is based on the A_\infty-structures, E_\infty-structures and functional homology operations. As This approach it will be applied to the Kervaire invariant problem.

math.AT↗
arXiv2001

`Strategy of Regions': Expansions of Feynman Diagrams both in Euclidean and Pseudo-Euclidean Regimes

The strategy of regions [1] turns out to be a universal method for expanding Feynman integrals in various limits of momenta and masses. This strategy is reviewed and illustrated through numerous examples. In the case of typically Euclidean limits it is equivalent to well-known prescriptions within the strategy of subgraphs. For regimes typical for Minkowski space, where the strategy of subgraphs has not yet been developed, the strategy of regions is characterized in the case of threshold limit, Sudakov limit and Regge limit.

hep-ph↗
arXiv2000

Analytical Result for Dimensionally Regularized Massless Master Non-planar Double Box with One Leg off Shell

The dimensionally regularized massless non-planar double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with p_1^2=q^2\neq 0, and three legs on shell, p_i^2=0, i=2,3,4, is analytically calculated for general values of q^2 and the Mandelstam variables s,t and u (not necessarily restricted by the physical condition s+t+u=q^2). An explicit result is expressed through (generalized) polylogarithms, up to the fourth order, dependent on rational combinations of q^2,s,t and u, and simple finite two- and three fold Mellin--Barnes integrals of products of gamma functions which are easily numerically evaluated for arbitrary non-zero values of the arguments.

hep-ph↗
arXiv2000

Analytical Result for Dimensionally Regularized Massless Master Double Box with One Leg off Shell

The dimensionally regularized massless double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with non-zero q^2=p_1^2, and three legs on shell, p_i^2=0, i=2,3,4, is analytically calculated for general values of q^2 and the Mandelstam variables s and t. An explicit result is expressed through (generalized) polylogarithms, up to the fourth order, dependent on rational combinations of q^2,s and t, and a one-dimensional integral with a simple integrand consisting of logarithms and dilogarithms.

hep-ph↗
arXiv2000

Stasheff structures and differentials of the Adams spectral sequence

The Adams spectral sequence was invented by J.F.Adams almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult problem of Algebraic Topology. Here we consider an approach to solve this problem in the case of Z/2 coefficients and find inductive formulas for the differentials. It is based on the Stasheff algebra structures, operad methods and functional homology operations.

math.AT↗