On Constraints Between $\Delta {\alpha }_{\mathrm{had}}(M_Z^2)$ and $(g_{\mu }-2{)}_{\mathrm{HVP}}$

Abstract

I discuss the possibility of estimating the shift $\delta \Delta \alpha (M_Z^2)$ on the running of the EM-coupling to the $M_Z$ scale, induced by the discrepancy $\Delta a_{\mu }$ between two precise determinations of the hadronic vacuum polarization contribution to $g_{\mu }-2$. It is shown that the size of $\Delta a_{\mu }$ implies rigorous bounds on the $\delta \Delta \alpha (M_Z^2)$-shift. Any extra contribution to this minimal shift necessarily depends on the specific shape of the underlying spectral function $\frac{1}π\ImmΔ(t)$ responsible for the $\Delta a_{\mu }$-discrepancy. I show that, in the case of a quark model, the total $\Delta \alpha (M_Z^2)$-shift remains small. I also discuss the scenario where $\frac{1}π\ImmΔ(t)$ is a constant in a finite $t$-region and show that in this case, up to a $t_{\rm max}\precsim 5~\GeV^2$, the size of the total $\delta \Delta {\alpha }_{\mathrm{had}}^{(5)}(M_Z^2)$-shift, remains below or of the order of the present error value on $\Delta {\alpha }_{\mathrm{had}}^{(5)}(M_Z^2)$.

arXiv commentVersion to appear as Rapid Communication in Physical Review D

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• Constraints on the two-pion contribution to hadronic vacuum polarization
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• Impact of correlations between $a_{\mu }$ and ${\alpha }_{QED}$ on the EW fit
• Effective field theory interpretation of lepton magnetic and electric dipole moments
• The new "MUON G-2" Result and Supersymmetry
• New $\tau$-based evaluation of the hadronic contribution to the vacuum polarization piece of the muon anomalous magnetic moment
• Muon $g-2$: A review
• The Tiny (g-2) Muon Wobble from Small-$\mu$ Supersymmetry
• Hadronic Uncertainties versus New Physics for the $W$ boson Mass and Muon $g-2$ Anomalies
• Improved $(g-2{)}_{\mu }$ Measurements and Wino/Higgsino Dark Matter
• Pion and Kaon box contribution to $a_{\mu }^{\text{HLbL}}$
• The new $(g-2{)}_{\mu }$ result and the $\mu \nu$SSM
• $(g-2{)}_{\mu }$ and SUSY Dark Matter: Direct Detection and Collider Search Complementarity
• Hints of Natural Supersymmetry in Flavor Anomalies?
• Interdependence of the new "MUON G-2" Result and the $W$-Boson Mass
• Studying the $b\to s{\ell }^{+}{\ell }^{-}$ anomalies and $(g-2{)}_{\mu }$ in $R$-parity violating MSSM framework with the inverse seesaw mechanism
• Explaining Atomki anomaly and muon $g-2$ in $U(1{)}_X$ extended flavour violating two Higgs doublet model
• The new $(g-2{)}_{\mu }$ and Right-Handed Sneutrino Dark Matter
• Explaining anomalies of $B$-physics, muon $g-2$ and $W$ mass in $R$-parity violating MSSM with seesaw mechanism
• The Muon Magnetic Moment and Physics Beyond the Standard Model
• Neutrinophilic DM annihilation in a model with $U(1{)}_{L_{\mu }-L_{\tau }}\times U(1{)}_H$ gauge symmetry
• Semi-Visible Dark Photon Phenomenology at the GeV Scale
• Muon $g-2$, dark matter, and neutrino mass explanations in a modular $A_4$ symmetry