A comment on the impact of CMD-3 e+e−→π+π−e^+e^- \to \pi^+\pi^- cross section measurement on the SM gμ−2g_\mu-2 value

We estimated an impact of the recent CMD-3 measurement of the $e^+e^- \to \pi^+\pi^-$ total cross section at $0.3 < \sqrt{s} < 1.2$ GeV on the leading order hadronic contribution $a_\mu^{had,LO}$ to the muon anomalous magnetic moment $a_\mu = (g_\mu-2)/2$, in presence of comparably precise ISR measurements of the cross section by BaBar and KLOE experiments being in significant tension with the CMD-3. Assuming that all the experiments are affected by yet unidentified systematic effects, to account for the latter, we scaled the experimental uncertainties following the PDG prescription, thus facilitating a consistent joint fit of the world data on the $e^+e^- \to \pi^+\pi^-$ total cross section. The same procedure was applied in all $e^+e^- \to hadrons$ channels contributing to the dispersive estimate of $a_\mu^{had,LO}$. Despite an inclusion of the new CMD-3 $\pi^+\pi^-$ data, our estimate $a_\mu^{had,LO}(e^+e^-) = (696.2 \pm 2.9) \times 10^{-10}$ is consistent with $a_\mu^{had,LO}(e^+e^-)$ values obtained by other authors before publication of the CMD-3 result. Including our $a_\mu^{had,LO}$ value into the SM prediction for $a_\mu$, we obtain $a_\mu^{SM} = (11~659~184 \pm 4_{\mathrm{tot}}) \times 10^{-10}$ which is by $4.7\sigma$ smaller than the world average for the experimental value $a_\mu^{exp} = (11~659~205.9 \pm 2.2) \times 10^{-10}$. We confirm the observation by the CMD-3 authors that their $\sigma(e^+e^- \to \pi^+\pi^-)$ measurement, when taken alone, implies the $a_\mu^{SM}$ prediction consistent with the $a_\mu^{exp}$ at $\sim 1\sigma$ level.Comment: The note contains a comprehensive bibliography on the total e+e- --> hadrons cross section measurements at sqrt(s) < 12 Ge

Two-loop renormalization group restrictions on the standard model and the fourth chiral family

In the framework of the two-loop renormalization group, the global profile of the Standard Model (SM) in its full parameter space is investigated up to the scale of the gauge singularity. The critical Higgs masses bordering the strong coupling, unstable and the safe regions are explicitly found. Restrictions on the Higgs boson mass as a function of a cutoff scale are obtained from the stability of the electroweak vacuum and from the absence of the strong coupling both in the Higgs and Yukawa sectors. The cutoff being equal to the Plank scale requires the Higgs mass to be M=(161.3+-20.6)+4-10 GeV and M>=140.7+-10 GeV, where the M corridor is the theoretical one and the errors are due to the top mass uncertainty. The SM two-loop beta-functions are generalized to the massive neutrino case. Modification of the two-loop global profile of the SM extended by one new chiral family is studied, and bounds on the masses of the family are found. The requirement of self-consistency of the perturbative SM as an underlying theory up to the Planck or GUT scale excludes the fourth chiral family with the mass up to 250 GeV depending on the Higgs mass and the cutoff scale. Under precision experiment restriction M<=200 GeV, the fourth chiral family, taken alone, is excluded. Nevertheless a pair of the chiral families constituting the vector-like one could still exist.Comment: 22 LaTeX pages, 17 PostScript figures. In the 2nd version of the e-print a typo in the 2-loop beta function of a charged lepton is correcte

Black Hole Shadows: How to Fix the Extended Gravity Theory

The first images of black hole shadows open new possibilities to develop modern extended gravity theories. We discuss the shadow calculations in non-rotating case both when $g_{11} = - g_{00}^{-1}$ and $g_{11} \neq - g_{00}^{-1}$. We demonstrate the application to few different models: Horndesky theory with Gauss-Bonnet invariant, loop quantum gravity and conformal gravity. The difference of these theories from shadow models with the theory of general relativity is shown. In addition we show that when the rotation is taken into account the requirements to the observational accuracy decrease