## QCD and lattice computations

QCD in the infrared limit is generally not manageable for computations. We are not able to derive from it masses and other properties of hadrons. So, people thought to use computers to solve it in order to get exact results from it. Since the start, many difficulties were met by people working with this approach pioneered by K. G. Wilson (the Nobel prize winner for the introduction of renormalization group in statistical mechanics). The most serious ones are implied into the limitations of the resources of the computer one uses. On a lattice you have a spacing and you are interested in the continuum limit when the spacing goes to zero. But having the spacing going to zero implies more and more computational resources that are difficult to be found still today. The other question originates on how large is the volume you are using. One should be sure that small volume effects do not enter into our computations so that one is still not into the asymptotic limit is interested on. This latter problem is not so severe even if it has been advocated in computations of gluon and ghost propagators being theoretical expecations seriously at odd with those coming out from lattice.

In a comment about my analysis of quarkonia (see here) it was questioned by James Amundson at Fermilab that my potential does not seem to agree with the one emerging from lattice. People at Fermilab is doing a very good job for lattice QCD and so this comment should be taken rather seriously. Indeed, there is a point I did not emphaise in my answer. I have got an interquark potential

$V(r)=-\frac{\alpha_s}{r}+0.8762499705\alpha_s\sqrt{\sigma}$

but I do not take $\alpha_s$ to be a constant. Rather, it depends on the energy scale where I am doing computations and this is the key trick that does the job and I get the right answers.

But let me comment about the present situation of lattice QCD. I think that currently the most striking results are given in the following figure

This figure is saying to us that introducing quark sea the precision of computations improves dramatically. This computation was carried on by MILC, HPQCD, UKQCD and Fermilab Lattice Collaborations. In their paper they declare a spacing 1/8 fm and 1/11 fm. Quark masses are generally taken somewhat different from those of PDG as the proper ones require more computational resources. Indeed, the reached volumes are never that large for the reasons seen above. One can look at Gauge Connection to have an idea of the configurations generally involved. So, if volume effects enter in some physical quantity we cannot be aware of them. This is the situation seen on the computations of gluon and ghost propagators (see here). The situation in this case if far more simpler as there are no quarks. This is pure Yang-Mills theory and so people was able to reach volumes till $(128)^4$ that is a really huge volume.

But for the spectrum of pure Yang-Mills we are not that lucky as computations do not seem to hit the true ground state of the theory. Besides, we have $\sigma$ resonance seen at accelerator facilities but not with lattice computations at any level. Indeed, we know that there is an incongruence between lattice computations of pure Yang-Mills spectra and computations of the gluon propagator (see here and my paper for QCD 08). So, where is the $\sigma$ resonance on the lattice? Full QCD or pure Yang-Mills? In the latter case is a glueball. I think this is one of the main problem to be addressed in the very near future together with the computation of golden-plated quantities. There is too much involved in this to ignore it.

### 4 Responses to QCD and lattice computations

1. ervin says:

Dear Marco,

I am a constant visitor of your blog and, as an independent researcher in QFT, I must praise your individual efforts in understanding QCD outside lattice computations. It is too bad that too many field theorists are not really paying attention to your contributions and are instead focused on holographic QCD and similar techniques .
I happen to share a different view on nonperturbative QCD. I am now working on a paper where infrared QCD is developed from this novel viewpoint and hope to have it ready for submission by the end of the year.

Yours truly,

Ervin Goldfain

2. mfrasca says:

Dear Ervin,

Thank you for reading my blog and the praises to my work. I have also noticed your effort to communicate with me and I think that your comments here are widely appreciated. As for your work I cannot do anything about than suggesting to do what any researcher is currently doing, that is putting your papers on arxiv and then looking for publication in an archival journal. Another significant way to be considered is participation to conferences.

Theoretical situation is not that bad because there are several groups around the world that are doing studies in the field of QCD without recurring to AdS/CFT or other similar techniques that, in any case, are respectable as well. Future will say who is right. For this a lot of work on lattice must be accomplished yet and also on the side of the understanding the spectrum of light mesons a lot of questions are open.

For heavy quarks the question of quarkonia should be answered directly from QCD, a still “in fieri” thing. If you would be able to derive the potential to work out computations for higher excited states than you are done.

If your work is able to give an answer to these problems then it is interesting and worthwhile to be published in the way I have indicated you above.

Good luck,

Marco

3. ervin says:

Dear Marco,

Thanks for your feedback. Up to now I published mainly in journals devoted to nonlinear dynamics and complexity theory. One of the reasons is that I don’t have direct access to arxiv ( I am employed in the industry and not in the academia). The other reason is that few particle and field theorists are familiar with these novel topics. It is my view that computation of excited states for heavy quarks and the mass spectrum of light mesons requires a framework where non-unitary processes are allowed to develop. To me it is striking that (with few exceptions) almost nobody pays close attention to the combined effect of nonlinearity in Yang-Mills theory and undamped radiative corrections.

Yours truly,

Ervin Goldfain

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