Study of the hadronic contributions to the running of the QED coupling and the weak mixing angle

Abstract

The electromagnetic coupling receives significant contributions to its running from nonperturbative QCD effects. We present an update of a lattice QCD study of the Adler function and of its application to the determination to the running of the QED coupling. We perform a high-statistics computation with two flavours of O(a) improved Wilson fermions in a large range of momentum transfer Q 2 . The running of the electromagnetic coupling, including contributions from u, d, s and c valence quarks, is compared to phenomenological determinations at intermediate Q 2 values. An extension of this study to the determination of the hadronic contributions to the running of the weak mixing angle is also described.

The hadronic contribution to the running of the electromagnetic coupling and the electroweak mixing angle

“…Around this Q 2 and above, D(Q 2 ) can be computed reliably in perturbative QCD. Crucially, ∆α had (−Q 2 ) at space-like momenta Q 2 > 0 is accessible to non-perturbative lattice techniques defined in Euclidean space-time [3,4,5]. It is given by…”

“…As in the electromagnetic case,Π Zγ (Q 2 ) is directly accessible to lattice computations [3,4,18,19].…”