A BRST perturbative analysis of SU (N ) Yang-Mills theory in a class of maximal Abelian gauges is presented. We point out the existence of a new nonintegrated renormalizable Ward identity which allows to control the dependence of the theory from the diagonal ghosts. This identity, called the diagonal ghost equation, plays a crucial role for the stability of the model under radiative corrections implying, in particular, the vanishing of the anomalous dimension of the diagonal ghosts. Moreover, the Ward identity corresponding to the Abelian Cartan subgroup is easily derived from the diagonal ghost equation. Finally, a simple proof of the fact that the beta function of the gauge coupling can be obtained from the vacuum polarization tensor with diagonal gauge fields as external legs is given. A possible mechanism for the decoupling of the diagonal ghosts at low energy is also suggested.

We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them.

Elaborating on the four-dimensional helicity scheme, we propose a pure four-dimensional formulation (FDF) of the d-dimensional regularization of one-loop scattering amplitudes. In our formulation particles propagating inside the loop are represented by massive internal states regulating the divergences. The latter obey Feynman rules containing multiplicative selection rules which automatically account for the effects of the extra-dimensional regulating terms of the amplitude. We present explicit representations of the polarization and helicity states of the four-dimensional particles propagating in the loop. They allow for a complete, four-dimensional, unitarity-based construction of d-dimensional amplitudes. Generalized unitarity within the FDF does not require any higher-dimensional extension of the Clifford and the spinor algebra. Finally we show how the FDF allows for the recursive construction of d-dimensional one-loop integrands, generalizing the fourdimensional open-loop approach.

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Ghost condensates of dimension two are analyzed in a class of nonlinear gauges in pure Yang–Mills theories. These condensates are related to the breaking of the SL (2, R) symmetry, present in these gauges.

The lightest Higgs boson mass of the Minimal Supersymmetric Standard Model has been recently computed diagrammatically at the three-loop order in the whole supersymmetric parameters space of the SUSY-QCD sector. The code FeynHiggs combines one-and two-loop fixed-order with the effective-fieldtheory calculations for the same Higgs mass. The two numerical predictions agree considering the scenario of only one SUSY-scale and vanishing stop mixing parameter below 10 TeV. The agreement is improved by introducing an additional supersymmetric scale and a non-zero stop mixing. Additionally, the combined CMS/ATLAS Higgs mass value was used to derive an upper bound on the needed SUSY scale. In the considered scenario, values above the scale 12.5±1.2 TeV are excluded.

We present a novel set of Feynman rules and generalised unitarity cut-conditions for computing one-loop amplitudes via d-dimensional integrand reduction algorithm. Our algorithm is suited for analytic as well as numerical result, because all ingredients turn out to have a four-dimensional representation. We will apply this formalism to NLO QCD corrections.

We are investigating if the double copy structure as product of scattering amplitudes of gauge theories applies to cosmological correlators computed in a class of theories for inflation by the operatorial version of the In-In formalism of Schwinger-Keldysh. We consider tree level momentum-space correlators involving primordial gravitational waves with different polarizations and the scalar curvature fluctuations on a three dimensional fixed spatial slice. The correlators are sum of terms factorized in a time dependent scalar factor, which takes into account the curved background where energy is not conserved, and in a so-called tensor factor, constructed by polarization tensors. In the latter we recognize scattering amplitudes in four dimensional Minkowski space spanned by three points gravitational amplitudes related by double copy to those of gauge theories. Our study indicates that gravitational waves are double copy of gluons and the primordial scalar curvature is double copy of a scalar with Higgs-like interactions.