arXiv subjects

M. Faisst

Publications and source records attributed to M. Faisst.

6 recordsLinked to original sources

arXiv2006

Standard and epsilon-finite Master Integrals for the rho-Parameter

We have constructed an epsilon-finite basis of master integrals for all new types of one-scale tadpoles which appear in the calculation of the four-loop QCD corrections to the electroweak rho-parameter. Using transformation rules from the epsilon-finite basis to the standard minimal-number-of-lines basis, we obtain as a by-product analytical expressions for few leading terms of the epsilon-expansion of all members of the standard basis. The new master integrals have been computed with the help of the Pade method and by use of difference equations independently.

hep-ph↗

arXiv2006

Four-Loop QCD Corrections to the Rho Parameter

The four-loop QCD corrections to the electroweak $ρ$-parameter arising from top and bottom quark loops are computed. Specifically we evaluate the missing ``non-singlet'' piece. Using algebraic methods the amplitude is reduced to a set of around 50 new master integrals which are calculated with various analytical and numerical methods. Inclusion of the newly completed term halves the final value of the four-loop correction for the minimally renormalized top-quark mass. The predictions for the shift of the weak mixing angle and the W-boson mass is thus stabilized.

hep-ph↗

arXiv2006

ep-Finite Basis of Master Integrals for the Integration-By-Parts Method

It is shown that for every problem within dimensional regularization, using the Integration-By-Parts method, one is able to construct a set of master integrals such that each corresponding coefficient function is finite in the limit of dimension equal to four. We argue that the use of such a basis simplifies and stabilizes the numerical evaluation of the master integrals. As an example we explicitly construct the ep-finite basis for the set of all QED-like four-loop massive tadpoles. Using a semi-numerical approach based on Pade approximations we evaluate analytically the divergent and numerically the finite part of this set of master integrals. The calculations confirm the recent results of Schröder and Vuorinen. All the contributions found there by fitting the high precision numerical results have been confirmed by direct analytical calculation without using any numerical input.

hep-ph↗

arXiv2004

Pole- versus MS-mass definitions in the electroweak theory

Two different two-loop relations between the pole- and the MS-mass of the top quark have been derived in the literature which were based on different treatments of the tadpole diagrams. In addition, the limit M_W^2/m_t^2 \to 0 was employed in one of the calculations. It is shown that, after appropriate transformations, the results of the two calculations are in perfect agreement. Furthermore we demonstrate that the inclusion of the non-vanishing mass of the W-boson leads to small modifications only.

hep-ph↗

arXiv2003

Three Loop Top Quark Contributions to the rho Parameter

We present results for the three-loop top quark contributions to the rho parameter in the limit of large top quark mass. The simultaneous dependence on the mass of the Higgs boson M_H and the mass of the top quark m_t is obtained from expansions in the range of M_H around m_t and in the limit M_H >> m_t. In combination with the previous result for M_H = 0 the dependence of the rho parameter on the leading Yukawa contributions, i.e. on m_t and M_H, is well under control for all mass values of practical importance. The effects lead to a shift in the W mass in the order of 5 MeV and are relevant for precision measurements at TESLA.

hep-ph↗

arXiv2000

Three-Loop Leading Top Mass Contributions to the rho Parameter

We present analytical results for the leading contributions of the top quark to the electroweak rho parameter at order GF^3 Mt^6 and GF^2 Mt^4 alpha_s. The Higgs boson and the gauge bosons are taken to be massless in this limit. The correction of order GF^3 Mt^6 is found to be sizeable in comparison to the the leading two-loop GF^2 Mt^4 correction, however it is much smaller than the subleading GF^2 Mt^2 MZ^2 correction.

hep-ph↗