Friday, June 29, 2007

Lattice 2007 abstracts online

The list of abstracts for the Lattice 2007 conference is now online. The JavaScript popup feature -- hover your mouse over a title and see the abstract as a tooltip -- is very nice.

Wednesday, June 13, 2007

Vexillology and the Moon Hare

A friend of mine recently asked me a question regarding the moon, and I thought it might be good to share the answer with my readers.

The question was whether the fact that Europeans tend to see the face of a man in the moon (with the Mare Imbrium and Mare Serenitatis forming the eyes, and the Mare Nubium and/or Mare Humorum forming the Mouth), whereas Asians tend to see a hare or rabbit (with the Mare Foecunditatis and Mare Nectaris forming the ears), had any astronomical basis.

Now, longitude is of course a largely arbitrary quantity (for which reason it was historically so hard to determine that a large prize was offered for the development of a method to determine it reliably while at sea) and should not have any effect on the appearance of celestial bodies (except for the time at which they transit, some parallax and effects following from those, such as visibility of eclipses etc., but certainly not the size or orientation of a disc). Latitude, on the other hand, has a true astronomical meaning, and a moment's thought should show you that the angle that the crescent moon (which always points towards the sun, which moves accross the sky at different angles to the horizon at different latitudes) forms with the horizon varies with latitude -- in fact, it is something of a cliché that this is reflected in the flags of islamic countries at different latitudes: compare the flags of Turkey, Pakistan and Mauritania.

Since the part of the moon turned towards the sun is of course independent of the observer's latitude, it follows that from the point of view of an observer close to the equator the orientation of the moon disk is such that the rabbit in the moon is quite clearly visible, whereas an observer in the temperate zone sees the moon under an angle at which he would likely prefer the face, unless being told about the rabbit (which, at least for me, easily supersedes the face). I therefore hypothesize that the tradition of the moon rabbit spread into East Asia from South Asia, whereas the tradition of the face in the moon comes from Nothern Europe. Does anyone know whether that would appear to agree with the historical record? It seems rather plausible to me.

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.