NNLO classical solution for Lipatov’s effective action for reggeized gluons

We consider the formalism of small-[Formula: see text] effective action for reggeized gluons[Formula: see text] and, following the approach developed in Refs. 11–17, calculate the classical gluon field to NNLO precision with fermion loops included. It is demonstrated that for each perturbative order, the self-consistency of the equations of motion is equivalent to the transversality conditions applied to the solution of the equations, these conditions allow to construct the general recursive scheme for the solution’s calculation. The one fermion loop contribution to the classical solutions and application of the obtained results are also discussed.

Exploratory studies for the position-space approach to hadronic light-by-light scattering in the muon g - 2

The well-known discrepancy in the muon g − 2 between experiment and theory demands further theory investigations in view of the upcoming new experiments. One of the leading uncertainties lies in the hadronic light-by-light scattering contribution (HLbL), that we address with our position-space approach. We focus on exploratory studies of the pion-pole contribution in a simple model and the fermion loop without gluon exchanges in the continuum and in infinite volume. These studies provide us with useful information for our planned computation of HLbL in the muon g − 2 using full QCD.

On isometry anomalies in minimal 𝒩 = (0,1) and 𝒩 = (0,2) sigma models

The two-dimensional minimal supersymmetric sigma models with homogeneous target spaces [Formula: see text] and chiral fermions of the same chirality are revisited. In particular, we look into the isometry anomalies in [Formula: see text] and [Formula: see text] models. These anomalies are generated by fermion loop diagrams which we explicitly calculate. In the case of [Formula: see text] sigma models the first Pontryagin class vanishes, so there is no global obstruction for the minimal [Formula: see text] supersymmetrization of these models. We show that at the local level isometries in these models can be made anomaly free by specifying the counterterms explicitly. Thus, there are no obstructions to quantizing the minimal [Formula: see text] models with the [Formula: see text] target space while preserving the isometries. This also includes [Formula: see text] (equivalent to [Formula: see text]) which is an exceptional case from the [Formula: see text] series. For other [Formula: see text] models, the isometry anomalies cannot be rescued even locally, this leads us to a discussion on the relation between the geometric and gauged formulations of the [Formula: see text] models to compare the original of different anomalies. A dual formalism of [Formula: see text] model is also given, in order to show the consistency of our isometry anomaly analysis in different formalisms. The concrete counterterms to be added, however, will be formalism dependent.

A WEYL DESCRIPTION OF GRAVITY INTERACTIONS

We compare the conventional description of the interaction of matter with the four known forces in the standard model with an alternative Weyl description in which the chiral coupling is extended to include gravity. The two are indistinguishable at the low energy classical level of equations of motion, but there are subtle differences at the quantum level when nonvanishing torsion and the Adler-Bell-Jackiw anomaly are taken into account. The spin current and energy-momentum of the chiral theory then contain non-Hermitian terms which are not present in the conventional theory. In the chiral alternative, CPT invariance is not automatic because chirality supersedes Hermiticity but full Lorentz invariance holds. New fermion loop processes associated with the theory are discussed together with a perturbative regularization which explicitly maintains the chiral nature and local symmetries of the theory.

γγ→γZ SCATTERING AND ITS RELATED PROCESSES

The analytic helicity amplitudes of Z→3γ, γγ→Zγ and γZ→γγ via W-loop and charged scalar-loop are presented. There is some difference between our results and those in Ref. 13 for Z→3γ via W-loop and fermion-loop, which has different physical meanings. We have calculated the unpolarized and polarized cross-sections for γγ→γZ process. We find that the total cross-section of γγ→γZ is larger than that of γγ→γγ at 500 GeV of γγ c.m.s. energy. In principle this process provides a test of the non-Abelian nature of the standard model.