Michael Creutz has a remarkable new preprint out this evening, entitled The Saga of Rooted Staggered Quarks. It explains what has been going on in a rather bitter controversy within the lattice gauge theory community over the last few years.
While lattice gauge theory provides a quite beautiful way of discretizing gauge fields, preserving their geometric significance, fermions have always been much more problematic. Here the geometry is spin geometry, which doesn’t appear to have a natural formulation on a lattice. What does have a natural formulation is not a spinor field S, but End(S), the linear maps from S to itself, which can be identified with the exterior algebra, and naturally put on the lattice by assigning degrees of freedom to points, 1-simplices, 2-simplices, etc. The problem is that if you do this, you don’t get a theory of a single fermionic field, but instead multiple copies. This geometrical argument is just one aspect of the problem, which appears in other more convincing ways, but this all adds up to making chiral symmetry especially problematic on the lattice.
There are many possible ways of dealing with this, but one popular one has been “rooting” some of the fermionic degrees of freedom that have been staggered on neighboring vertices of the lattice. One ends up with four copies of what one wants, so the argument has been that the thing to do is to take the fourth root of this to get a calculation that tells one about a single fermion. The problem is that this is a quite non-analytic thing to do, and it is not clear that it gives one something sensible. A debate between Creutz and people using this method has raged for the last few years, with Creutz claiming that the rooting procedure gives the wrong answer, while proponents of rooting argue that the problems involved will go away in the continuum limit.
Creutz’s preprint describes the conclusion he has been led to about this, and his problems getting some of them published:
This led me to question whether there was some physical measurement one could make to determine if a quark mass was indeed zero. I could think of none, and proposed that a single vanishing quark mass might not be a physical concept. This paper was submitted to Physical Review D.
This is where the shit started hitting the fan. There was a common lore that if the up quark mass were to vanish, then the problem of why theta appeared to be phenomenologically very small would be solved. I was saying that this lore might be wrong. This drove the referees nuts, with statements like “I am somewhat concerned that the errors are so obvious.” After numerous similar scathing remarks the paper went to a divisional editor for PRD, who upheld their opinion. On rejection I took the paper and split it into two parts, one on the phase diagram and the second on the vanishing mass issue. These both appeared in Physical Review Letters, Phys.Rev.Lett.92:201601,2004 (hep-lat/0312018) and Phys.Rev.Lett.92:162003,2004 (hep-ph/0312225). I do derive some visceral pleasure from having turned a rejected PRD paper into two PRL’s…
Eventually the claims of the staggered advocates became so outrageous that I felt I had to be more aggressive. I was pushed further by statements that if someone had issues with staggered quarks, they needed to write them up. At the time I was too naive to appreciate how the stubborn nature of some personalities involved would mean that these arguments would be dismissed without serious discussion. As with the up quark mass issue, this is one of those situations where a person without tenure would be ill advised to challenge conventional lore.
So I submitted a paper (hep-lat/0603020) pointing out the inconsistencies between rooting and the expected chiral behavior. This was quickly rejected by PRL which has a policy of not publishing interesting and controversial papers. After transferring it to PRD, things got stuck, with numerous referees simply refusing to respond. After about a year and eight referee reports, some positive and some negative, PRD decided that they don’t publish interesting and controversial papers either. I did not take this delay kindly and rewrote the paper with the provocative title “The evil that is rooting.” This was fairly quickly accepted by Physics Letters (Phys.Lett.B649:230-234,2007; hep-lat/0701018), although the title was mollified at the editor’s suggestion…
The staggered community has continued to ignore these problems. I feel their stranglehold on the US lattice effort approaches scientific dishonesty. As an example of the prevailing vindictiveness, a recent paper of mine on a completely different topic was rejected from a prominent US journal on the basis of a single negative referee report stating that “It is puzzling that the author ignores all these highly relevant lessons that have been learned long ago in the context of the staggered fermion formalism.” It was overlooked because I wanted to avoid the ongoing controversy, of which the referee was certainly aware. After I did add remarks on the comparison with staggered, the paper was rejected without further review by a divisional associate editor representing the staggered community. He raised some symmetry issues based on comments by the Maryland group, to which I was never given a chance to respond. This paper was then submitted to a European journal where I hoped for a more equitable treatment. There it was quickly published.
Beyond the international ridicule this this controversy brings on the USQCD community, other aspects are particularly upsetting from a scientific point of view. First, enormous amounts of computer time continue to be wasted on generating lattice configurations from which any non-perturbative information will be questionable. About 38 percent of the current computer time allocated by the USQCD collaboration is going to continue these efforts. Second, young people associated with this project are taught to repeat, without question, the party line that all will be okay in the continuum limit. Third, the practitioners are such a powerful force that most outsiders are unwilling to look into the problems despite the fact that the underlying physics is so fascinating. And finally, I find it extremely unsettling that some physicists widely regarded as experts in chiral symmetry and lattice gauge theory can so casually and thoroughly delude themselves with bad science.
In short, the lattice has been very good to me. It is extremely painful to see it abused so blatantly
One would like to think that this issue will get sorted out over time as more work makes it clear whether or not rooting is as serious a problem as Creutz thinks it is. But the progress of science is not always smooth…