Constraints between Δαhad(MZ2) and (gμ-2)HVP

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 1/pi Im Delta(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 1/pi Im Delta(t) is a constant in a finite t-region and show that in this case, up to a t(max) less than or similar to 5 GeV2, the size of the total delta Delta alpha((5))(had)(M-Z(2))-shift, remains below or of the order of the present error value on Delta alpha((5))(had)(M-Z(2)).