Monday, July 31, 2006

Lattice 2006 -- Day Five

Hello from Regina, where I have now recovered from my flight back from Tucson, and hence am ready to report on the last day of this year's lattice meeting.

The last day consisted of plenary sessions only. The first plenary, chaired by Anna Hasenfratz, was right after another indoors breakfast. The first speaker was Richard Brower, who gave a non-lattice talk about QCD and string theory, or more specifically the search for a dual description of QCD in the form of string theory on an AdS background. He started out by giving a historical overview of the development of string theory from its beginnings as an attempt to describe the strong interactions based on the observed behaviour of Regge trajectories and s-t duality, recounting the well-known failure of string theory to capture the correct hard scattering behaviour in strong interactions, along with the need to incorporate gravity. The situation changed with the discovery of dualities and the AdS/CFT correspondence: now string theory on an AdS5 x S5 background is dual to N=4 Super-Yang-Mills theory in a 4d spacetime, with the strong coupling limit of SYM corresponding to the weak coupling limit of AdS. Of course we know that QCD is not a superconformal theory, so a description of QCD based on AdS/CFT has to break the conformal symmetry by introducing a boundary along the fifth-dimension of AdS5; there are a number of models of this kind, and while they manage to reproduce some qualitative features of the QCD glueball spectrum as seen on the lattice, other features are qualitatively different, and the quantitative agreement is usually rather poor. However, there is some hope that an exact string dual of QCD might still be found, returning string theory to its origins as a theory of the strong interactions.

The second talk was by Mark Alford, who spoke about colour superconductivity. Colour superconductivity arises via the BCS mechanism just like ordinary superconductivity, but instead of a weakly attractive phonon-mediated attraction, quarks attract via the much stronger strong interactions, making Cooper-pairing even more efficient. Hence we expect QCD matter to be colour superconducting at large chemical potentials, making this phase probably relevant for the study of the interior of neutron stars. Unfortunately, that region of the QCD phase diagram is not (yet) accessible on the lattice due to the sign problem. In the limit of infinite chemical potential, perturbative descriptions are possible; NJL models provide another qualitative description of this phase. What is found is that in this limit, for Nf=3 massless flavours, a curious phenomenon called colour-flavour locking (CFL) occurs: Light quarks of a given flavour only occur carrying a given colour charge, breaking the symmetry group from SU(3)c x SU(3)L x SU(3)R x U(1)B to SU(3)CFL x Z2. The electromagnetic gauge group U(1)Q, which was embedded in the SU(3)L x SU(3)R chiral group, is now changed into an U(1)Q' subgroup of SU(3)CFL due to photon-gluon mixing. This phase is therefore somewhat weird. It becomes complicated due to the fact that the strange mass isn't really zero, and also due to the weak interactions breaking flavour (while this is a weak effect, a compact star exists for a long time, giving the weak interactions time to act and affect the equilibrium); models indicate that this will lead to a complex phase structure in the regime of intermediate chemical potential. However, it is also known that a number of the phase found in the models, the so-called gapless phases, are artifacts and will not exist in full QCD; what will replace them is not known, and may not become known until a way to resolve the sign problem on the lattice is found.

After the coffee break the second plenary session was chaired by Peter Weisz, on behalf of the Local Organising Committee for next year's lattice meeting to be held in Regensburg, Germany. The session started with Tommy Burch extending a warm invitation to Regensburg to everyone and extolling its virtues as a lovely city and excellent conference venue. Lattice 2007 will be at Regensburg from 30th July to 4th August 2007, dates that should be in every lattice theorists diary. Peter Weisz thanked the Local Organizing Committe in Tucson for organizing such a splendid conference, which was met with lots of applause.

The first talk of the last session was Urs Heller speking about Lattice QCD at finite temperature (and zero chemical potential), concentrating especially on the nature of the transition as a function of the light quark masses, and on the QCD equation of state. On the first count, it seems conclusive by now that at the physical values of mu,d and ms the phase transition is in fact a crossover rather than a first-order transition. On the second count, the low-temperature description QCD matter by a hadron resonance gas and the high-temperature description by finite-temperature perturbation theory seem to match quite well onto the lattice data in their respective domains of validity. Some studies of non-static finite-temperature physics, such as transport coefficients, also are beginning to be undertaken on the lattice now.

The second speaker was Joel Giedt, who talked about lattice SUSY. Unfortunately this is a sufficiently technical field which is rather remote from my area of expertise, and thus I feel unable to give a reasonable summary of his talk. What I believed to understand was that a number of supersymmetric lattice theories are now known, that there is some problem with the Kähler potential being underconstrained by the symmetries and that actual lattice simulations might be helpful there, as well as in studying the AdS3/CFT2 correspondence.

The final talk was by Tom DeGrand, who was the only plenary (and probably simply the only) speaker to use foils and an overhead projector instead of a digital presentation to speak about the Nf=1 quark condensate. In the Nc --> &infinity; limit, it is found that Nf=1 QCD with quarks in the antisymmetric representation corresponds to N=1 Super-Yang-Mills theory. Nf=1 QCD is peculiar in that there are no light pions, only a massive η'. When overlap fermions are being used to simulate at a fixed gauge topology, it becomes possible to determine the quark condensate via the spectrum of the overlap Dirac operator; in this way, the 1/Nc corrections to the Nc --> &infinity; limit are found to be small even at Nc=3.

At noon, the symposium was adjourned, and the participants began to scatter.

Since my flight only left in the evening, I managed to go and sneak a look at a very interesting historical monument located near Tucson, the San Xavier de Bac mission church. This mission was founded by the Jesuits in the late 17th century and completed by Franciscans in the mid-18th century. The church itself is built in a colourful version of the baroque style with many elements of "naive" or peasant art in the ornamentation, suggesting that it was planned by the missionaries and executed by the local Natives, the Tohono O'odham, themselves. The white walls of the towers are visible from afar across the desert, giving this remarkable church the nickname "white dove of the desert".

As for the trip to Tucson, I feel little need to bore my readers with the details of our 15-hour zig-zag trip across the North American continent via L.A. and Toronto to Regina, and thus conclude my report on the Lattice 2006 meeting at this point. Thank you for reading; if and when I feel like it, I may follow-up with an overall summary of the conference later.

Friday, July 28, 2006

Lattice 2006 -- Day Four

Hello again from Tucson. Today started off somewhat unusual -- with rain, clouds and mist! So, no breakfast in the shade on the terrace; we didn't have to go hungry, though, as it was just relocated to the dining room instead.

The first plenary session of the morning was chaired by Anthony Williams. The first speaker was Kostas Orginos, who talked about recent lattice results on nucleon structure. Nucleons are tricky, because they have only light quarks, and it is known that the sea quarks actually play a bigger role than the valence quarks in determining the structure of the nucleons. However, with a lot of hard work and clever methods, people have made a lot of progress towards getting accurate results for the nucleon structure functions, momenta of generalised parton distributions, and various other structure-related quantities, and these results may one day soon help to lead to an understanding of e.g. the proton spin crisis.

The second speaker was Christian Schmidt, who spoke about lattice QCD at finite density. As mentioned yesterday, finite density QCD is hard on the lattice, because the action becomes complex and direct Monte Carlo simulations are no longer possible at non-zero chemical potential μ. The way to avoid this sign problem lies in one or another of a number of neat tricks such as reweighting configurations obtained at μ=0 to a finite value of μ, measuring Taylor expansions around μ=0 and resumming the series, simulations at imaginary μ (where the action remains real) with subsequent extrapolation to real μ, or some other method. A fair number of results exist now in this field, and while the quantitative precision still seems fairly low, there appears to be fair agreement on the qualitative features of the phase diagram. For large μ, however, new methods appear to be needed.

After the coffee break, the second plenary session, chaired by Sinya Aoki, had three speakers: First was Pilar Hernández, who reported on progress she and her collaborators had made towards understanding the ΔI=1/2 rule. This rule, which states that Kaon decays in which isospin changes by more than 1/2 are suppressed by a factor of approximately 20, is one of the longest-standing mysteries in QCD. Resolving it will require putting together a lot of work and know-how from both lattice QCD and chiral perturbation theory, and the people working on it seem to be far from a resolution in spite of a lot of recent progress.

Next was Michael Clark speaking about the Rational Hybric Monte Carlo (RHMC) algorithm. This algorithm is a variation on the well-known HMC algorithm and uses a rational approximation to maintain the exact nature of the HMC algorithm (which is needed in a many cases), while outperforming the Polynomial HMC (PHMC) algorithm through the better approximation properties of rational functions as opposed to polynomials. Apparently, with the proper implementation, this algorithm can push Wilson fermions into a speed range where they become competitive with staggered fermions.

Finally, Mikko Laine talked about warm dark matter (WDM) and hot QCD. One interesting candidate for a WDM particle are sterile right-handed neutrinos. These would have been created thermally in the early universe. As it turns out, for right-handed neutrino masses in the keV range, the production range peaks at temperatures of around the QCD scale, so that QCD contributions to the production rate, e.g. via u + d --> e- + νe, νe --> N1 might be dominant.

After lunch, there were parallel sessions again, featuring amongst others my talk (which went fine, thanks for asking) about our recent work on determining the QCD/NRQCD matching coefficients for leptonic widths of heavy quarkonia to O(αsv2) for realistic lattice NRQCD actions.

After the parallel sessions, we heard this year's keynote talk, delivered by Ann Nelson, who extended an invitation to all lattice theorists to work on beyond-the-Standard-Model physics, where models such as composite Higgs models could benefit from lattice simulations.

The day closed with dinner. There are going to be more plenary talks tomorrow, but you will have to wait for me to get back to Regina before I can report about them.

Thursday, July 27, 2006

Lattice 2006 -- Day Three

Hello again from Tucson.

Day three was the odd one out in that the program today was arranged a little differently from the other days. As usual, the day started off with a plenary session, chaired by Philippe de Forcrand. The first speaker was Misha Stephanov, who talked about the QCD phase diagram. The general features of the phase diagram (confinement at low temperature and density, quark-gluon plasma at high temperature, colour superconductivity and colour-flavour locked phase at high density, and the phase transition lines separating these phases) are fairly well known by now. What is a lot less well known is the location of the critical point at which the phase transition line from the confined phase terminates and the transition turns into a crossover. A number of models have given wilfly different predictions for its location, and since working at finite chemical potential on the lattice is only possible by some ingenious tricks (the action is no longer real with a real chemical potential, so Monte Carlo methods won't work directly), the lattice predictions are somewhat in disagreement with each other as well. On the experiments at RHIC are able to scan some region of the phase diagram by varying the center-of-mass energy in heavy ion collisions, so there is some hope of nailing it down in the near future, though.

Next came a much-expected talk by Stephen Sharpe, who summarized the debate on the validity of the fourth-root trick for staggered fermions. The options which he put up initially were "good" (works as desired without any problems), "bad" (wrong continuum limit, hence wrong physics) and "ugly" (right continuum limit, hence ultimately right physics, but lots of complications and unexpected features). Since rooted staggered fermions have been shown to be non-local, the "good" option was ruled out right away, which might seem worrying given that the stakes are so high with the best ensembles of configurations (by MILC) currently in existence relying on rooted staggered fermions. However, he pointed out that non-locality does not mean the theory is sick; an example were certain non-local Ising models which turn out to lie in the same universality class as the local model if the locality falls off fast enough at large separations. The replica trick and renormalisation group analysis elaborated in the parallel talks by Bernard, Golterman and Shamir were explained again, and Mike Creutz's objections to a number of features of rooted staggered fermions were answered in the next sections of this talk. The summary was that rooted staggered fermions were not "bad" (as shown by the Bernard-Golterman-Shamir analysis), but that they were "ugly" (as pointed out by Creutz's criticisms).

After the coffee break, the program changed from its usual format: a parallel session replaced the usual second plenary session. That plenary session took place after lunch instead, with Shoji Hashimoto in the chair. The first speaker was Anthony Duncan, who spoke about applications of methods from lattice field theory to problems in the theory of Coulomb gases appearing in biophysics. These problems can be transformed into Feynman path integrals defined with a lattice cutoff by some ingenious transformations, and Monte Carlo methods developed for lattice QCD can then be used to treat them.

The second talk was the traditional experimental talk, delivered by Alessandro Cerri, who gave an overview of recent advances in flavour physics. I had to sneak out of the room at the end of this talk, and hence I cannot report anything on the third talk, entitled Search for gluonic excitations in light unconventional mesons by Paul Eugenio.

In the later afternoon and evening we had an excursion to the Arizona Sonoran Desert Museum, which was much, much better than the excursion on the first day. The desert museum is a combination of botanical garden and zoo, which features the astounding variety, breathtaking beauty and sheer strangeness of this most extraordinary landscape. There were dozens of different kinds of cacti, agaves and other desert plants, mountain lions, wolves, coyotes, javelinas, coati, hummingbirds and (yes, that is not a typo) otters and beavers, colourful minerals and fossils and the scorching heat of the sun, all of which combined to leave a remarkable impression (besides making me scold myself again for being stupid enough to forget my camera). The day closed with the banquet, which was held in the grounds of the desert museum and was very pleasant, even if the chocolate cake for desert was a little too delicious.

Tuesday, July 25, 2006

Lattice 2006 -- Day Two

Hello again from the Lattice 2006 conference in Tucson, Arizona.

The second day started with plenary sessions again. The first session was chaired by Julius Kuti, and began with a talk by Leonardo Giusti about simulating light dynamical fermions on the lattice; the main focus of the talk was on new development using Wilson fermions, although some results on Ginsparg-Wilson and twisted mass fermions were mentioned as well, but staggered quarks were missing almost completely. Important areas covered were the need to control all systematic errors in a truly "first principles" approach, and the problems that Wilson fermions face because their spectral gap is not always positive, along with some proposals as to how this problem might be resolved, as well as direct comparisons with chiral perturbation theory results for the finite-size errors (which seem to show some significant discrepancies in many cases).

Next was a talk by Hank Thacker, who spoke about new types of extended topological objects: If the topological charge density is determined from the spectrum of the overlap operator via the index theorem, what is found is that there appear to be no instantons, but instead thin extended three-dimensional sheets of coherent topological charge, with two sheets of opposite topological charge always next to each other. Two-dimensional CPN-1 (toy) models show similar structure for N>3. These sheets may be identical to domain walls that appear in certain AdS/CFT models as the remnant of D6-branes wrapped around a 4-sphere, where they separate so-called k-vacua whose θ-parameter differs by 2πk. They may also be suggestive of some kind of relation between N=1 SYM and Nf=1 QCD. A point that was raised during questions was that, since the width of these sheets appears to be on the order of the lattice spacing, they don't scale and in this kind of picture the continuum limit would either not exist or at least look very weird.

After the tea break, the second plenary session of the morning had Maria Lombardo in the chair. The first talk was by Tetsuo Hatsuda, who spoke about RHIC physics and hot QCD. At the center was the possibility of using heavy flavours as probes to look into the RHIC fireball. Relevant lattice results concern the temperature dependence of the Debye screening mass and the spectral functions of charmonia, which can be reconstructed via MEM. What is found there is that the J/ψ and ηc persist well up to temperature of about 1.5 TC, whereas their orbital excitations disappear around TC.

The last talk of the morning was by Tetsuya Onogi and was a review of progress in heavy flavour physics from the lattice. This is such a large and active field that he actually had to apologize to all the people (including myself) who had sent him materials which he had no time to include in his talk. The physics goal in this area is largely to overconstrain the elements of the CKM matrix through determinations of heavy meson decay constants and mixing parameters; this is exciting because it might lead to the discovery of new physics beyond the Standard Model, and also because the errors on these quantities are currently dominated by the theoretical errors. So the results presented were largely determinations of fB, fBs, fD, fDs, BB etc. and various ratios and combinations thereof. Other results included determinations of mb and various parameters in HQET.

After lunch there are going to be parallel sessions. Stay tuned.

Update: The afternoon parallel sessions are over now. One of them was almost entirely devoted to talks aiming to resolve the debate about staggered fermions outlined earlier on this blog. Essentially, as far as I understand the argument, what is claimed is that firstly, rooted staggered fermions are non-local because of taste-breaking, but that secondly, the continuum limit exists nevertheless and is in the right universality class by renormalisation group arguments, and that thirdly, the correct chiral perturbation theory for rooted staggered fermions can be obtained from staggered chiral perturbation theory using a "replica trick" whereby one consider nR copies of the theory and takes nR=1/4 in the end. The speakers (Maarten Golterman, Yigal Shamir and Claude Bernard) got into some almost heated argument with Mike Creutz about the whole issue.

Still upcoming today: the poster session. Stay tuned.

Update: The poster session was only moderately exciting, which was probably due to the fact that there were a lot of posters that really were 20-page papers pinned to a wall, which I find rather deterring since you would have to read them in full before talking to the presenter. A good poster (at least in my opinion) is very different from a good paper; the poster should minimize the amount of unnecessary text and use figures and other graphical layout elements to emphasize the main point, since the details can always be filled in by the presenter.

There also was a little problem with the food, which was served only during the first hour of the session; this meant that people who presented their posters int the "A" section got nothing to eat.

The most unusual poster was a live presentation of the ILDG by people from the ILDG working group. Mike Creutz's poster on "diseases" with rooted staggered fermions also got a lot of attention. And the posters by the people from Regina were also nice, although I may of course be biased in their favour.

Lattice 2006 -- Day One

Hello from Tucson, Arizona, where I am at the Lattice 2006 conference.

Unfortunately, I am facing a similar technical problem to that Matt experience last year in Dublin: the wireless age is not quite upon us yet (at least not unless one is willing to pay outrageous internet fees to the hotel), so I will have to report after the event, rather than blog live.

This year the lattice conference takes place here in the middle of the very picturesque Arizona desert (sorry, I forgot my camera at home -- I'm already kicking myself for it, so you don't need to) at the extremely luxurious Starr Pass resort. Getting here from Regina was more than a little tedious, but I won't bore you with tales of endless lineups at US customs or long-delayed flights. Instead I'll jump medias in res:

After a welcome message from the President of the University of Arizona and a number of announcements (such as that we should remember to drink plenty of water), the first plenary session (chaired by Junko Shigemitsu) started with a talk by Weonjong Lee about recent progress in Kaon physics on the lattice. The main point of his talk was to emphasize how essential improvement is in order to reduce the impact of lattice artifacts, and to advertize HYP smearing over ASQTAD. The results presented included demonstrations of how taste-breaking effects in the pion spectrum with staggered fermions get supressed by improvement, determinations of fπ and fK in full QCD, of BK in quenched QCD with an outlook towards full QCD results that should become available next year, and of K->ππ and Kl3 decays. He closed by suggesting that the MILC collaboration should create a set of Fat7bar configurations in addition to their ASQTAD configurations to allow people to investigate the better suppression of lattice spacing artifacts expected there.

Next was a talk by Stefan Schaefer about algorithms for dynamical simulations with overlap fermions. While overlap fermions have the advantages of preserving chiral symmetry exactly, possess automatic O(a) improvement and their spectrum has an exact relation to gauge field topology via the index theorem, they are extremely expensive to simulate, due to the appearance of the operator sign function in the overlap Dirac operator. One cause of this is that the exact link with topology implies that the overlap operator is discontinuous at the surfaces in the space of gauge connections that separate different topological sectors. Three possibilities to treat this have been proposed: the first is to modify the time evolution algorithm that generates the configurations by taking the existence of these surface into account and to properly reflect or refract a trajectory that would cross them; this has the advantage of being exact, but is very expensive because it requires a full inversion of the overlap operator each time a sector boundary is crossed. The second possibility is to approximate the sign function by some smooth function; this is much easier to implement, but has to deal with large forces near sector boundaries where the approximation becomes steep, and also needs a good approximation of the determinant function to work. The third alternative are topology-preserving gauge actions, which are set up so as to disallow transitions between topological sectors. In summary, while a lot of progress has been made, large volumes are still unattainable with overlap fermions at this time.

After a tea break there was a second plenary session, chaired by Mike Peardon. The first talk, by Kim Splittorf, was about the sign problem in the epsilon regima of QCD at finite chemical potential. The problem there is that at finite chemical potential, the discontinuity of the chiral condensate at zero quark mass cannot be understood in the same terms (via the Banks-Casher relation) as at zero chemical potential, because the eigenvalues can now be complex. Instead, the spectral density also becomes complex and develops oscillations that lead to the discontinuity.

The next speaker was Carlos Pena, who talked about determinations of weak matrix elements using twisted mass lattice QCD, especially about results that the ALPHA collaboration has obtained for BK, and results for BB that are expected next year.

The session was rounded off by Karl Jansen presenting the status of the ILDG. For those not active in the field, the International Lattice Data Grid is a grid framework that allows lattice theorists to share and access their configurations between countries and collaborations by linking the different national grids into a global grid. This requires agreeing on some common data format, a way to describe metadata (such as lattice size, actions used etc.) by means of an XML schema defining a language known as QCDml, and various layers of software linking it all together. The people working on this have done a lot of hard work for the benefit of the lattice community, and by giving people outside the large collaborations access to unquenched configurations on large lattices using their action of choice, this should help a lot to advance the state of the field.

In the afternoon there were two parallel session with a break for refreshments and informal conversations in between. I see little point in recounting which talks I went to, since that would at most reflect my biases rather than anything about the work being done by others in general.

In the evening there was an excursion dinner to Old Tucson, which is a movie set outside Tucson, where Westerns have been produced since the 1930s. The excursion featured some nice food, almost unbearable heat, a staged shootout between Western actors, some fairly bizarre and allegedly funny goings-on on the stage of the local Saloon, and a bit of stargazing. If that sounds odd, it doesn't half reflect how odd it really was (or at least how odd I thought it to be, which again may simply reflect my cultural biases). I might try and obtain some pictures from those who managed to bring their cameras, and if I succeed, some pictures may be posted on this blog.