Full two-loop electroweak corrections to the pole masses of gauge bosons
We discuss progress in SM two-loop calculations of the pole position of the massive gauge-boson propagators.
hep-ph↗
arXiv subjects
M. Yu. Kalmykov
Publications and source records attributed to M. Yu. Kalmykov.
MS vs. Pole Masses of Gauge Bosons: Electroweak Bosonic Two-Loop Corrections
The relationship between MS and pole masses of the vector bosons Z and W is calculated at the two-loop level in the Standard Model. We only consider the purely bosonic contributions which represents a gauge invariant subclass of diagrams. All calculations were performed in the linear $R_ξ$ gauge with three arbitrary gauge parameters utilizing the method of asymptotic expansions. The results are presented in analytic form as series in the small parameters $\sin^2θ_W$ and mass ratio $m_Z^2/m_H^2$. As a byproduct we obtain the bosonic two-loop contributions to the renormalization of the weak mixing parameter $\sin^2θ_W$ and of the Fermi constant. The running of Fermi constant will become important at high energy colliders.
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Geometrical approach to loop calculations and the epsilon-expansion of Feynman diagrams
Some problems related to the structure of higher terms of the epsilon-expansion of Feynman diagrams are discussed.
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ON-SHELL2: FORM based package for the calculation of two-loop self-energy single scale Feynman diagrams occurring in the Standard Model
A FORM based package (ON-SHELL2) for the calculation of two loop self-energy diagrams with one nonzero mass in internal lines and the external momentum on the same mass shell is elaborated. The algorithm, based on recurrence relations obtained from the integration-by-parts method, allows us to reduce diagrams with arbitrary indices (powers of scalar propagators) to a set of master integrals. The SHELL2 package is used for the calculation of special types of diagrams. Analytical results for master integrals are collected.
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Two-loop self-energy master integrals on shell
Analytic results for the complete set of two-loop self-energy master integrals on shell with one mass are calculated.
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Single mass scale diagrams: construction of a basis for the $ε$-expansion
Exploring the idea of Broadhurst on the ``sixth root of unity'' we present an ansatz for construction of a basis of transcendental numbers for the epsilon-expansion of single mass scale diagrams with two particle massive cut. As example, several new two- and three-loop master integrals are calculated.
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Single-scale diagrams and multiple binomial sums
The $ε$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.
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Some remarks on the epsilon-expansion of dimensionally regulated Feynman diagrams
Some problems related to construction of the epsilon-expansion of dimensionally regulated Feynman integrals are discussed. For certain classes of diagrams, an arbitrary term of the epsilon-expansion can be expressed in terms of log-sine integrals related to the polylogarithms. It is shown how the analytic continuation of these functions can be constructed in terms of the generalized Nielsen polylogarithms.
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Recursion relations for two-loop self-energy diagrams on-shell
A set of recurrence relations for on-shell two-loop self-energy diagrams with one mass is presented, which allows to reduce the diagrams with arbitrary indices (powers of scalar propagators) to a set of the master integrals. The SHELL2 package is used for the calculation of special types of diagrams. A method of calculation of higher order ε-expansion of master integrals is demonstrated.
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The one-loop divergences of the linear gravity with the torsion terms in tetrad approach
In this paper we discuss the connection between the geometric and tetrad approaches in the quantum affine-metric gravity. The corresponding transition formulas are obtained at the one-loop level. As an example, the one-loop counterterms are calculated in the tetrad formalism in the theory with terms quadratic in the torsion field. This model possesses the extra local symmetries connected with transformation of the connection field. It is shown that the special gauge can be chosen so that the corresponding additional ghosts do not contribute to the one-loop divergent terms.
gr-qc↗
Detailed analysis of the dependence of the one-loop counterterms on the gauge and parametrization in the Einstein gravity with the cosmological constant
In this paper, the dependence of the Einstein gravity with the cosmological constant as well as of this theory in the first-order formalism on the gauge and parametrization is been analyzed. The one-loop counterterms off the mass shell have been plainly calculated in arbitrary gauge and parametrization. The tensor package of analytic calculations, written in REDUCE, allowed all the calculations to be carried out. A method of renormalization group functions calculations off shell is discussed.
hep-th↗
Imaginary part of the electromagnetic lepton form factors
The charge $F_1(0)$ and the magnetic $F_2(0)$ form factors of heavy charged leptons have been shown in the framework of the perturbation theory to have imaginary part. The imaginary parts of the form factors for muon and tau lepton have been calculated at the two-loop level in the Standard Model. The effects where these imaginary parts could manifest themselves are discussed.
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Manifestation of metric renormalization in quantum $R^2$--gravity
The renormalization group method in $R^2$-gravity without matter fields is discussed. A criterion for the existence of the renormalization constant for the metric has been found, two-loop higher order poles have been calculated, a relation which allows us to find the one-loop renormalization constant of the Newtonian constant has been suggested.
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Large Mass Expansion versus Small Momentum Expansion of Feynman Diagrams
The method of the large mass expansion (LME) has the technical advantage that two-loop integrals occur only as bubbles with large masses. In many cases only one large mass occurs. In such cases these integrals are expressible in terms of $Γ$-functions, i.e. they can be handled completely analytically avoiding even recursions and therefore this approach may find a wide field of application. We consider it necessary to investigate the precision of this method and test it for several two-loop vertex functions ocurring in the $Z \to b\bar{b}$ decay by comparing it with the small momentum expansion. It turns out that in general high order approximants have to be taken into account for a sufficient accuracy.
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Towards Automatic Analytic Evaluation of Diagrams with Masses
A method to calculate two-loop self-energy diagrams of the Standard Model is demonstrated. A direct physical application is the calculation of the two-loop electroweak contribution to the anomalous magnetic moment of the muon ${{1/2}(g-2)}_μ$. Presently, we confine ourselves to a ``toy'' model with only $μ$, $γ$ and a heavy neutral scalar particle (Higgs). The algorithm is implemented as a FORM-based program package. For generating and automatically evaluating any number of two-loop self-energy diagrams, a special C-program has been written. This program creates the initial FORM-expression for every diagram generated by QGRAF, executes the corresponding subroutines and sums up the final results.
hep-ph↗
Pole masses of quarks in dimensional reduction
Pole masses of quarks in the quantum chromodynamics are calculated to the two-loop order in the framework of the regularization by dimensional reduction. For the diagram with a light quark loop, the non-Euclidean asymptotic expansion is constructed with the external momentum on the mass shell of a heavy quark.
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On calculation of the off-shell renormalization functions in the R^2 gravity
A new way how to calculate the off-shell renormalization functions within the $R^2$-gravity has been proposed. The one-loop renormalization group equations in the approach suggested have been constructed. The behaviour of effective potential for an massless scalar field interacting with the quantum gravitational field has been analyzed in this approach.
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The Affine-Metric Quantum Gravity with Extra Local Symmetries
We discuss the role of additional local symmetries related to the transformations of connection fields in the affine-metric theory of gravity. The corresponding BRST transformations connected with all symmetries (general coordinate, local Lorentz and extra) are constructed. It is shown, that extra symmetries give the additional contribution to effective action which is proportional to the corresponding Nielsen-Kallosh ghost one. Some arguments are given, that there is no anomaly associated with extra local symmetries.
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