Symanzik improvement

In lattice QCD with Wilson quarks the continuum limit is approached with a rate roughly proportional to the lattice spacing "a". On the lattices currently accessible through numerical simulations, the lattice spacing is often not very much smaller than the relevant physical scales, and it has been observed that the residual discretization errors can be quite large.

Many years ago Symanzik pointed out that the convergence to the continuum limit can be accelerated by including counterterms of order "a" (and higher orders) in the lattice action and the local operators of interest. The ALPHA collaboration has set out to implement Symanzik's improvement programme to order "a" in a systematic manner. The aim is to cancel all order "a" corrections in the correlation functions considered, at the non-perturbative level. So far the coefficients multiplying the counterterms to the action and the isovector axial current have been determined non-perturbatively in the quenched approximation.

For a recent account of the order "a" improvement of lattice QCD see

"Chiral symmetry and O(a) improvement in lattice QCD",

Nucl. Phys. B478 (1996) 365, hep-lat/9605038

The non-perturbative calculation of the improvement coefficients
c_sw and c_A is described in 

"Non-perturbative O(a) improvement of lattice QCD",

CERN preprint CERN-TH/96-218, hep-lat/9609035

Non-perturbative improvement of the axial current for dynamical Wilson fermions,
DESY-05-026, HU-EP-05-08, SFB-CPP-05-07, hep-lat/0503003

Non-perturbative improvement of the axial current with three dynamical flavors and the Iwasaki gauge action,
JHEP0704:092,2007 [hep-lat/0703006]