The $\hat{I}›$-parameter in 3-flavour QCD and $\hat{I}{\pm }_s(m_Z)$ by the ALPHA collaboration

Abstract

We present results by the ALPHA collaboration for the $\hat{I}›$-parameter in 3-flavour QCD and the strong coupling constant at the electroweak scale, $\hat{I}{\pm }_s(m_Z)$, in terms of hadronic quantities computed on the CLS gauge configurations. The first part of this proceedings contribution contains a review of published material \cite{Brida:2016flw,DallaBrida:2016kgh} and yields the $\hat{I}›$-parameter in units of a low energy scale, $1/L_{\mathrm{had}}$. We then discuss how to determine this scale in physical units from experimental data for the pion and kaon decay constants. We obtain $\hat{I}{›}_{\overline{\mathrm{MS}}}^{(3)}=332(14)$ MeV which translates to $\hat{I}{\pm }_s(M_Z)=0.1179(10)(2)$ using perturbation theory to match between 3-, 4- and 5-flavour QCD.

21 pages. Collects contributions of A. Ramos, S. Sint and R. Sommer to the 34th annual International Symposium on Lattice Field Theory; LaTeX input encoding problem fixed