## predictions from Lattice QCD

*May 30, 2006 at 1:23 pm* *
8 comments *

Georg from Life on the Lattice recommended a couple of papers which show the success of LQCD.

*He is right!* The post- and pre-dictions of real experimentally accessible quantities are confirmed now at the couple percent level – something which is not generally appreciated in the HEP community.

For example, in hep-lat/0304004 show that computations with staggered quarks correctly reproduce the known values for nine diverse and independent non-perturbative quantities, after the quarks masses and lattice spacing (equivalent to the strong coupling constant) have been tuned. As pointed out in the paper, this result is important not only for the impressive level of agreement for those nine quantities, but also for the way LQCD physics is inextricably linked to B-physics. To put it bluntly, we have a confirmed *theory* here, not just a clevel phenomenological model. (Not that clever phenomenology is bad – it does help us to think about the physics, at least at an early stage of the game.)

Even more impressive are the successes discussed briefly in hep-lat/0509169. These are true predictions – LQCD was used to obtain precise values for three quantities which were first published and then subsequently confirmed by actual measurements in real experiments. These quantities are, specifically:

- the q
^{2}-dependence of the form-factor in semileptonic*D*-decays - the decay constants for D
^{+}and D_{s}mesons - the mass of the B
_{c}-meson

I consider Fig.1 in Kronfeld et al. (hep-lat/0509169) to be especially striking.This is a big deal for particle physics. There are many places in which fundamental quantities such as elements of the CKM matrix cannot be extracted reliably from measurements due to poorly known “phenomenological” constants. For example, we would like to extract precise values for third-generation CKM matrix elements from the recent measurements of B_{s}-mixing (D0: hep-ex/0603029 and CDF: FERMILAB-CONF/06-076-e) and lattice will play a key role. It’s time to start paying closer attention to LQCD, at least for me!

Thanks, Georg, for the info!!

Entry filed under: Particle Physics.

1.David | May 31, 2006 at 6:29 amWhile these lattice results are impressive, it should be remembered that there is a controversial theoretical issue regarding the staggered lattice quark formulation used in these lattice simulations. See Georg’s post “A debate about staggered fermions” on the `life on the lattice’ blog.

2.Michael Schmitt | May 31, 2006 at 7:37 amDear David, thanks very much for pointing this out. Indeed, Georg, in his usual clear and careful manner, outlines a controversy concerning the staggered quark formulation. As a naive outsider, this strikes me as a serious issue – if LQCD is to be a real theory, then all methods of calculation ultimately must be free of such controversies. If it were just a phenomenological model, then this kind of problem would serve only to limit the applicability of the model. I hope the experts will resolve this issue soon, since I believe that LQCD will be soon an indispensible tool in particle physics.

3.Stefan Scherer | May 31, 2006 at 4:36 pmDear Michael,

there is another important application of lattice QCD: some years ago, several clever techniques have been developped to do calculations at finite chemical potential of the quarks. Using these techniques, one can try to figure out how the phase diagram of QCD matter looks like, i.e. study whether and where there is a phase transition between hadrons and the quark gluon plasma as a function of temperature and chemical potential (see e.g. hep-lat/0510087,

hep-lat/0601013). There is a prediction that the transition is a cross-over at zero chemical potential and that there is a critcal point in the phase diagram. This is quite important as an input to the analysis of heavy ion collision experiments.

Best, Stefan.

PS: You have opened a very interesting blog!

4.Michael Schmitt | June 2, 2006 at 8:41 pmHi Stefan,

thanks for pointing this out – I had no idea that LQCD was already exploring this ground. I have to be honest and admit that I know little about QGP physics and I could not understand much of the two papers that you recommend. Nonetheless it is plain that this work is important and exciting – and results will soon be well tested at RHIC and the LHC!

thanks again,

Michael

5.Stefan Scherer | June 4, 2006 at 11:22 amHi Michael,

sorry about the references – actually I do not know some good overview covering this recent “LQCD at finite mu” stuff.

Maybe as a more general reference about lattice calculations of bulk QCD matter and the QCD phase diagram, you may find hep-ph/0303042 more useful:

LATTICE QCD AT FINITE TEMPERATUREby E. Laermann and O. Philipsen, published as Ann.Rev.Nucl.Part.Sci. 53 (2003) 163-198. The paper discusses progress concerning finite baryon density in the last chapter.Best, Stefan

6.Michael Schmitt | June 4, 2006 at 11:38 amExcellent! thank you – I will take a look and see if I can understand a little bit more.

7.Alexey Petrov | June 13, 2006 at 10:48 pmThe post- and pre-dictions of real experimentally accessible quantities are confirmed now at the couple percent level – something which is not generally appreciated in the HEP community.Why is it not appreciated? It is very much appreciated. For example, lattice QCD results are incorporated in all analyses of the CKM Unitarity triangle — from all (theoretical) collaborations providing CKM angles from a variety of measurements (like UTfit etc.). Of course, post-dictions are somewhat easier than pre-dictions… and also lattice people had this reputation of providing numbers with nice and relatively small error bars, which would however not include quenching errors — kinda important systematic error… and their up and down quark masses are not physical… but what the heck!

While lattice will certainly be THE source of results for certain nonperturbative quantities in the nearest future, there are also other methods that are useful now. Like QCD sum rules for example…

8.Michael Schmitt | June 14, 2006 at 9:42 amHi Alexey,

Perhaps you misunderstood what I meant. If you stop your average experimenter in particle physics, and ask for his/her opinion on lattice QCD, you’ll find that most people don’t know anything about it (I certainly know very little, unfortunately) and they believe that “they can’t even get the proton mass right” – which is no longer true. There is a similar misperception among particle theorists, especially those whose work never touches non-perturbative QCD. An additional problem comes from the fact that few people understand LQCD beyond the basic idea, so when someone gives a talk at a conference, it is difficult to learn much. I hope that the blog “Life on the Lattice” will help with that, at least for people who read blogs.

I think the recent successes of LQCD are wonderful which is why I wrote about them, and people like you who understand these things are to be admired and encouraged to inform the rest of us what we’re missing!