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O. L. Veretin

Publications and source records attributed to O. L. Veretin.

26 records · Page 2Linked to original sources
arXiv1999

Techniques for Calculating two-loop Diagrams

Methods developed by the Bielefeld-DESY-Dubna collaboration in recent years are: DIANA (DIagram ANAlyser), a program to produce ``FORM input'' for Feynman diagrams, starting from the Feynman rules; methods to calculate scalar diagrams: Taylor expansion in small momenta squared in connection with a mapping and the Padé method to sum the series. Recently program packages for the large mass expansion were written and applied to the $Z \to b\bar{b}$ decay. Reviews of these activities were presented in the proceedings of the Ustroń '97 and Rheinsberg '98 conferences. Here we concentrate on recent developements in the large mass expansion, applied to the two-loop contribution of the $Z \to b\bar{b}$ decay in the $m_b=0$ approximation, taking into account higher order terms of the expansion in $M_W^2/m_t^2$.

hep-ph↗
arXiv1998

Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass

For a large class of two-loop selfenergy- and vertex-type diagrams with only one non-zero mass ($M$) and the vertices also with only one non-zero external momentum squared ($q^2$) the first few expansion coefficients are calculated by the large mass expansion. This allows to `guess' the general structure of these coefficients and to verify them in terms of certain classes of `basis elements', which are essentially harmonic sums. Since for this case with only one non-zero mass the large mass expansion and the Taylor series in terms of $q^2$ are identical, this approach yields analytic expressions of the Taylor coefficients, from which the diagram can be easily evaluated numerically in a large domain of the complex $q^2-$plane by well known methods. It is also possible to sum the Taylor series and present the results in terms of polylogarithms.

hep-ph↗
arXiv1998

Applications of the Large Mass Expansion

The method of the large mass expansion (LME) is investigated for selfenergy and vertex functions in two-loop order. It has the technical advantage that in many cases the expansion coefficients can be expressed analytically. As long as only one non-zero external momentum squared, $q^2$, is involved also the Taylor expansion (TE) w.r.t. small $q^2$ yields high precision results in a domain sufficient for most applications. In the case of only one non-zero mass $M$ and only one external momentum squared, the expansion w.r.t. $q^2/M^2$ is identical for the TE and the LME. In this case the combined techniques yield analytic expressions for many diagrams, which are quite easy to handle numerically.

hep-ph↗
arXiv1998

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.

hep-ph↗
arXiv1997

Multi-Loop Calculations in the Standard Model: Techniques and applications

We present a review of the Bielefeld-Dubna activities on the multiloop calculations. In the first part a C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented, in the second part various techniques for the evaluation of scalar diagrams are described, based on the Taylor expansion method and large mass expansion.

hep-ph↗
arXiv1997

Dispersive Approach to the Trace Anomaly

In the scalar $ϕ^4$ field model the dispersive approach to the trace anomaly is proposed. It is shown that it is impossible to get dispersion representation for all formfactors so that preserve both the translation and dilatation Ward identities. Subtractions which preserve energy-momentum conservation violate the classical trace Ward--Takahashi identity and give rise to an anomalous contribution to the matrix element of stress tensor $θ_μ^ν$. This contribution coincides with one-loop $β$-function in accordance with previous analyses based on RG technique.

hep-ph↗
arXiv1996

Quark Mass Corrections to the Bjorken and Gross--Llewellyn-Smith Sum Rules

Quark mass corrections to the spin partonic structure function g_1(x,Q^2) and function F_3(x,Q^2) are obtained at the order O(alpha_s) along with the coefficient functions C^{(A)} and C^{(V)} related to the Bjorken and Gross--Llewellyn-Smith sum rules. In the massless limit the difference between F_3 and g_1 is encountered to be (alpha_s/π)*CF*(1-x). The results for the functions C^{(A)} and C^{(V)} at m=0 agree with the previous MS-scheme calculations C^{(A)}=C^{(V)}=1-(3*alpha_s/4π)*CF.

hep-ph↗