Wonderful QCD!

On Science this week appeared a milestone paper showing two great achievements by lattice QCD:

  • QCD gives a correct description of low energy phenomenology of strong interactions.
  • Most of the ordinary mass (99%) is due to the motion of quarks inside hadrons.

The precision reached has no precedent. The authors are able to get a control of involved  errors in such a way to reach an agreement of about 1% into the computation of nucleon masses. Frank Wilczek gives here a very readable account of these accomplishments and is worthwhile reading. These results open a new era into this kind of method to extract results to be compared with experiments for QCD and give an important confirmation to our understanding of strong interactions. But I would like to point out Wilczek’s concern: Until we will not have a theoretical way to obtain results from QCD in the low energy limit, we will miss a great piece of understanding of physics. This is a point that I discussed largely with my posts in this blog but it is worthwhile repeating here coming from such an authoritative voice.

An interesting point about these lattice computations can be made by observing that again no \sigma resonance is seen. I would like to remember that in these computations entered just u, d and s quarks as the authors’ aims were computations of bound states of such quarks. Some authoritative theoretical physicists are claiming that this resonance should be a tetraquark, that is a combination of u and d quarks and their antiparticles. What we can say about from our point of view? As I have written here some time ago, lattice computations of the gluon propagator in a pure Yang-Mills theory prove that this can be fitted with a Yukawa form

G(p)=\frac{A}{p^2+m^2}

being m\approx 500 MeV. This is given in Euclidean form. This kind of propagators says to us that the potential should be Yukawa-like, that is

V(r)=-A\frac{e^{-mr}}{r}

if this is true no tetraquark state can exist for lighter quarks. The reason is that a Yukawa-like potential heavily damps any van der Waals kind of residual potential. But, due to asymptotic freedom, this is no more true for heavier quarks c and b  as in this case the potential is Coulomb-like and, indeed, such kind of states could have been seen at Tevatron.

We expect that the glueball spectrum should display itself in the observed hadronic spectrum. This means that a major effort in lattice QCD computations should be aimed in this direction now that such a deep understanding of known hadronic states has been reached.

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2 Responses to Wonderful QCD!

  1. […] But the point to be emphasized here is the proposal of von Smekal arriving to present a modification of lattice computations. His proposal relies on a recent work done with Andre Sternbeck (see here) where they study the limit of the Yang-Mills theory. Indeed, in this limit they recover the results obtained by functional methods that disagree with lattice computations. Again, they simply freeze the dynamics and get meaningless results as also happens when one compares D=1+1 Yang-Mills theory with no dynamics and the D=4 case. Besides, recent QCD computations on the lattice, relying on known formulations of the Yang-Mills side, give too striking results to go to look for reformulations (see my post). […]

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