Calculation of fermionic two-loop contributions to muon decay

Abstract

The computation of the correction ∆r in the W-Z mass correlation, derived from muon decay, is described at the two-loop level in the Standard Model. Technical aspects which become relevant at this level are studied, e.g. gauge-parameter independent mass renormalization, ghost-sector renormalization and the treatment of γ 5 . Exact results for ∆r and the W mass prediction including O(α 2 ) corrections with fermion loops are presented and compared with previous results of a next-to-leading order expansion in the top-quark mass.

Becchi-Rouet-Stora symmetry restoration of chiral Abelian Higgs-Kibble theory in dimensional renormalization with a nonanticommutingγ5

“…Most of them involve theories without a chiral gauge symmetry [18], where there is no room for the introduction of spurious anomalies but subtleties related with evanescent operators [5] appear, or quantities related with axial currents [12,19], where it gives correctly the essential axial current anomalies. Several practical computations, taking care of the fulfillment of Slavnov Taylor Identities (STI), but involving only some restricted set of diagrams, have been done in the case of the Standard Model [20,21,22] or in Supersymmetric QED [23]. In [22], the authors report a relevant finite difference between the results of NDR and BMHV in two-loop diagrams of the Standard Model containing triangle subdiagrams.…”

“…Several practical computations, taking care of the fulfillment of Slavnov Taylor Identities (STI), but involving only some restricted set of diagrams, have been done in the case of the Standard Model [20,21,22] or in Supersymmetric QED [23]. In [22], the authors report a relevant finite difference between the results of NDR and BMHV in two-loop diagrams of the Standard Model containing triangle subdiagrams.…”

Adequacy of Effective Born for electroweak effects and TauSpinner algorithms for LEP, Tevatron, HL-LHC and FCC simulated samples

“…• Switch for Hadronic vacuum polarization corrections ∆α (5) had : IHVP = 1 parametrization of [33] IHVP = 5 parametrization of [31] • Switch for re-summation of the leading O(G f m 2 t ) electroweak corrections: IAMT4 = 4 with two-loop sub-leading corrections and re-summation [34,35,36,37] IAMT4 = 5 with fermionic two-loop corrections to M W [38,39,40] IAMT4 = 6 with complete two-loop corrections to M W [41] and fermionic two-loop corrections to sin 2 θ e f f lep W [42] IAMT4 = 7 with complete two-loop corrections to sin 2 θ e f f lep W and sin 2 θ e f f lb W [43,44] IAMT4 = 8 with complete two-loop corrections to sin 2 θ e f f W [45] • Switch for three-loop corrections O(αα 2 s ) to the electroweak ρ parameter:…”

Application of Methods of Computer Algebra for Doing Physical Sums

“…Further improvement of Δr was achieved in (Degrassi, G. et al, 1996;Degrassi, G. et al, 1997) where the leading and subleading large t-quark corrections were computed at O(α 2 ) order. Other two-loop fermionic corrections were considered in a series of papers (Freitas, A. et al, 2000a;Freitas, A. et al, 2000b;Freitas, A. et al, 2002). The calculation at the two loop level has been completed recently with the evaluation of the electroweak bosonic corrections (Awramik, M. & Czakon, M., 2002;Awramik, M. & Czakon, M., 2003a;Onishchenko, A.…”