Monday, June 11, 2007

Unquenching meets improvement

In a recent post, I explained how the fact that the vacuum in quantum field theory is anything but empty affects physical calculations by means of Feynman diagrams with loops, and specifically how one has to take account of these contributions in lattice field theory via perturbative improvement. In this post, I want to say some words about the relationship between perturbative improvement and unquenching.

To obtain accurate results from lattice QCD simulations, one must include the effects not just of virtual gluons, but also of virtual quarks. Technically, this happens by including the fermionic determinant that arises from integrating over the (Grassman-valued) quark fields. Since the historical name for omitting this determinant is "quenching", its inclusion is called "unquenching", and since quenching gives rise to an uncontrollable systematic error, unquenched simulations are absolutely crucial for the purpose of precise predictions and subsequent experimental tests of lattice QCD.

However, the perturbative improvement calculations that have been performed so far correct only for the effects of gluon loops. This leads to a mismatch in unquenched calculations using the perturbatively improved actions: while the simulation includes all the effects of both gluon and quark loops (including the discretisation artifacts they induce), only the discretisation artifacts caused by the gluon loops are removed. Therefore the discretisation artifacts caused by the quark loops remain uncorrected. Now, for many quantities of interest these artifacts are small higher-order effects; however, increased scaling violations in unquenched simulations (when compared with quenched simulations) have been seen by some groups. It is therefore important to account for the effects of the quark loops on the perturbative improvement of the lattice actions used.

This is what a group of collaborators including myself have done recently. For details of the calculations, I refer you to our paper. The calculation involved the numerical evaluation of a number of lattice Feynman diagrams (using automated methods that we have developed for the purpose) on a lattice with twisted periodic boundary conditions at a number of different fermion masses and lattice sizes, and the extrapolation of the results to the infinite lattice and massless quark limits. The computing resources needed were quite significant, as were the controls employed to insure the correctness of the results (which involved both repeated evaluations using independent implementations by different authors and comparison with known physical constraints, giving us great confidence in the correctness of our results). The results show that the changes in the coefficients in the actions needed for O(αsa2) improvement caused by unquenching are rather large for Nf=3 quark flavours, which is the case relevant to most unquenched simulations.