We calculate three-loop photon spectral density in QED with N different species of electrons. The obtained results were expressed in terms of iterated integrals, which can be either reduced to Goncharov’s polylogarithms or written in terms of one-fold integrals of harmonic polylogarithms and complete elliptic integrals. In addition, we provide threshold and high-energy asymptotics of the calculated spectral density. It is shown that the use of the obtained spectral density correctly reproduces separately calculated moments of corresponding photon polarization operator.
The decays KS,L → invisible have never been experimentally tested. In the Standard Model (SM), their branching ratios for the decay into two neutrinos are predicted to be extremely small, Br (KS,L → νν̄) ≲ 10−16. We consider several natural extensions of the SM, such as two-Higgs-doublet (2HDM), 2HDM and light scalar, and dark mirror sector models, that allow one to enhance the Br (KS,L → invisible) up to a measurable level. We briefly discuss the possible search for KS,L → invisible decays and KS,L oscillations into the dark sector at the NA64 experiment at CERN with the sensitivity to Br (KS,L → invisible) ≲ 10−7−10−5.
Using the generalized renormalisation group formalism, we calculate quantum corrections to the effective potential in α-attractor models describing the inflationary stage of the Universe evolution. We demonstrate that quantum corrections lead to a change in the initial classical potential, changing its value at the minimum, which can be interpreted as a manifestation of the cosmological constant or dark energy.
