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 $\Delta {\alpha }_{\mathrm{had}}^{(5)}(M_Z^2)$.

Version to appear as Rapid Communication in Physical Review D

References in corpus (4)

• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• The muon $g$-2 and $\Delta \alpha$ connection
• The muon g-2 and the bounds on the Higgs boson mass
• Moment Analysis of Hadronic Vacuum Polarization - Proposal for a lattice QCD evaluation of $g_{\mu }-2$

Cited by in corpus (10)

• The muon $g$-2 and $\Delta \alpha$ connection
• Electroweak Precision Fit and New Physics in light of $W$ Boson Mass
• Hadronic Uncertainties versus New Physics for the $W$ boson Mass and Muon $g-2$ Anomalies
• Pion and Kaon box contribution to $a_{\mu }^{\text{HLbL}}$
• $(g-2{)}_{\mu }$ and SUSY Dark Matter: Direct Detection and Collider Search Complementarity
• Interdependence of the new "MUON G-2" Result and the $W$-Boson Mass
• 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