Phenomenologically relevant electroweak precision pseudo-observables related to Z-boson physics are discussed in the context of the strong experimental demands of future $e^+e^-$ colliders. The recent completion of two-loop Z-boson results is summarized and a prospect for the 3-loop Standard Model calculation of the Z-boson decay pseudo-observable is given.
For the search for electroweak (EW) particles in the Minimal Supersymmetric Standard Model (MSSM) as well as for future precision analyses of these particles an accurate knowledge of their production and decay properties is mandatory. We evaluate the
cross sections for the chargino, neutralino and slepton production at e+e- colliders in the MSSM with complex parameters (cMSSM). The evaluation is based on a full one-loop calculation of all possible production channels including soft and hard photon radiation. The dependence of the cross sections on the relevant cMSSM parameters is analyzed numerically. We find sizable contributions to many production cross sections. They amount to roughly 15% of the tree-level results but can go up to 40% or higher in extreme cases. Also the dependence on complex parameters of the one-loop corrections for many production channels was found non-negligible. The full one-loop contributions are thus crucial for physics analyses at a future linear e+e- collider such as the ILC or CLIC.
Electroweak radiative corrections to the cross section of the process $e^+ e^- to Z H$ are considered. The complete one-loop electroweak radiative corrections are evaluated with the help of the SANC system. Higher-order contributions of the initial s
tate radiation are computed in the QED structure function formalism. Numerical results are produced by a new version of the ReneSANCe event generator and MCSANCee integrator for the conditions of future electron-positron colliders. The resulting theoretical uncertainty in the description of this process is estimated.
We present Standard Model predictions for the complete set of phenomenologically relevant electroweak precision pseudo-observables related to the Z-boson: the leptonic and bottom-quark effective weak mixing angles $sin^2theta_{rm eff}^ell$, $sin^2the
ta_{rm eff}^b$, the Z-boson partial decay widths $Gamma_f$, where $f$ indicates any charged lepton, neutrino and quark flavor (except for the top quark), as well as the total Z decay width $Gamma_Z$, the branching ratios $R_ell$, $R_c$, $R_b$, and the hadronic cross section $sigma_{rm had}^0$. The input parameters are the masses $M_Z$, $M_H$ and $m_t$, and the couplings $alpha_s$, $alpha$. The scheme dependence due to the choice of $M_W$ or its alternative $G_mu$ as a last input parameter is also discussed. Recent substantial technical progress in the calculation of Minkowskian massive higher-order Feynman integrals allows the calculation of the complete electroweak two-loop radiative corrections to all the observables mentioned. QCD contributions are included appropriately. Results are provided in terms of simple and convenient parameterization formulae whose coefficients have been determined from the full numerical multi-loop calculation. The size of the missing electroweak three-loop or QCD higher-order corrections is estimated. We briefly comment on the prospects for their calculation. Finally, direct predictions for the $Z{bar f}f$ vector and axial-vector form-factors are given, including a discussion of separate order-by-order contributions.
The calculation of the full electroweak O(alpha) corrections to the charged-current four-fermion production processes e+e- --> nu_tau tau+ mu- anti-nu_mu, u anti-d mu- anti-nu_mu, and u anti-d s anti-c is briefly reviewed. The calculation is performe
d using the complex-mass scheme for the gauge-boson resonances. The evaluation of the occurring one-loop tensor integrals, which include 5- and 6-point functions, requires new techniques. The effects of the complete O(alpha) corrections to the total cross section and to the production-angle distribution are discussed and compared to predictions based on the double-pole approximation, revealing that the latter approximation is not sufficient to fully exploit the potential of a future linear collider in an analysis of W-boson pairs at high energies.
By using the GRACE-Loop system, we calculate the full $mathcal{O}(alpha)$ electroweak radiative corrections to the process $e^+e^- rightarrow e^+e^- gamma$, which is important for future investigations at the International Linear Collider (ILC). With
the GRACE-Loop system, the calculations are checked numerically by three consistency tests: ultraviolet finiteness, infrared finiteness, and gauge-parameter independence. The results show good numerical stability when quadruple precision is used. In the phenomenological results, we find that the electroweak corrections to the total cross section range from $sim -4%$ to $sim -21%$ when $sqrt{s}$ varies from $250$ GeV to $1$ TeV. The corrections also significantly affect the differential cross sections, which are a function of the invariant masses and angles and the final-particle energies. Such corrections will play an important role for the high-precision program at the ILC.