We present the results of a lattice study of the second moment of the light-cone pion distribution amplitude using two flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to $m_pisim 150 , mathrm {MeV}$. At la
ttice spacings between $0.06 , mathrm {fm}$ and $0.08 , mathrm {fm}$ we find for the second Gegenbauer moment the value $a_2 = 0.1364(154)(145)$ at the scale $mu=2 , mathrm {GeV}$ in the $overline{mathrm{MS}}$ scheme, where the first error is statistical including the uncertainty of the chiral extrapolation, and the second error is the estimated uncertainty coming from the nonperturbatively determined renormalization factors.
We study the spectra of heavy-light and heavy-heavy mesons containing charm quarks, including higher spin states. We use two sets of $N_f = 2 + 1$ gauge configurations, one set from QCDSF using the SLiNC action, and the other configurations from the
Budapest-Marseille-Wuppertal collaboration, using the HEX smeared clover action. To extract information about the excited states, we choose a suitable basis of operators to implement the variational method.
We consider the Schrodinger functional with staggered one-component fermions on a fine lattice of size $(L/a)^3 times (T/a)$ where $T/a$ must be an odd number. In order to reconstruct the four-component spinors, two different set-ups are proposed, co
rresponding to the coarse lattice having size $(L/2a)^3 times (T/2a)$, with $T = T pm a$. The continuum limit is then defined at fixed $T/L$. Both cases have previously been investigated in the pure gauge theory. Here we define fermionic correlation functions and study their approach to the continuum limit at tree-level of perturbation theory.
In order to study the running coupling in four-flavour QCD, we review the set-up of the Schrodinger functional (SF) with staggered quarks. Staggered quarks require lattices which, in the usual counting, have even spatial lattice extent $L/a$ while th
e 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. A perturbative calculation yields the coefficient of the pure gauge ${rm O}(a)$ boundary counterterm to one-loop order.
