Two-Loop Bosonic Electroweak Corrections to the Muon Lifetime and M_Z-M_W Interdependence

The two-loop electroweak bosonic correction to the muon lifetime and the M_W-M_Z interdependece is computed using analytical methods of asymptotic expansion. Combined with previous calculations this copmletes the full two-loop correction to $\Delta r$ in the Standard Model. The shift to the prediction of W-boson mass due to two-loop bosonic corrections does not exceed 1 MeV for the range of the Higgs mass from 100 to 1000 GeV.Comment: 8 pp, 3 figs, LaTeX, replaced with journal versio

Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM

In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in $\mathcal{N}=4$ SYM with arbitrary number of off-shell gluons or equivalently Wilson line operator insertions. We make a conjecture for the Grassmannian integral representation for such objects and verify our conjecture on several examples. It is remarkable that in our formulation one can consider situation when on-shell particles are not present at all, i.e. we have Grassmannian integral representation for purely off-shell object. In addition we show that off-shell amplitude with arbitrary number of off-shell gluons could be also obtained using quantum inverse scattering method for auxiliary $\mathfrak{gl}(4|4)$ super spin chain.Comment: 38 pages, 9 figures; v4: typos corrected, comment in section 3.2 adde

Ambitwistor strings and reggeon amplitudes in N=4 SYM

We consider the description of reggeon amplitudes (Wilson lines form factors) in N=4 SYM within the framework of four dimensional ambitwistor string theory. The latter is used to derive scattering equations representation for reggeon amplitudes with multiple reggeized gluons present. It is shown, that corresponding tree-level string correlation function correctly reproduces previously obtained Grassmannian integral representation of reggeon amplitudes in N=4 SYM.Comment: 18 page