The SF running coupling with four flavours of staggered quarks

Understand

In order to study the running coupling in four-flavour QCD, we review the set-up of the Schr\"odinger functional (SF) with staggered quarks.

• Staggered quarks require lattices which, in the usual counting, have even spatial lattice extent $L/a$ while the time extent $T/a$ must be odd.
• Setting $T=L$ is therefore only possible up to ${\rm O}(a)$, which introduces different cutoff effects already in the pure gauge theory.
• We re-define the SF such as to cope with this situation and determine the corresponding classical background field.