Chiral behaviour of the pion decay constant in $N_f=2$ QCD

Abstract: As increased statistics and new ensembles with light pions have become available within the CLS effort, we complete previous work by inspecting the chiral behaviour of the pion decay constant. We discuss the validity of Chiral Perturbation Theory ($\chi$PT) and examine the results concerning the pion decay constant and the ensuing scale setting, the pion mass squared in units of the quark mass, and the ratio of decay constants $f_K/f_\pi$; along the way, the relevant low-energy constants of SU(2) $\chi$PT are estimated. All simulations were performed with two dynamical flavours of nonperturbatively O(a)-improved Wilson fermions, on volumes with $m_\pi L \geq 4$, pion masses $\geq$ 192 MeV and lattice spacings down to 0.048 fm. Our error analysis takes into account the effect of slow modes on the autocorrelations.