## Gluon condensate: The situation

Stephan Narison agreed to contribute to my blog with the following lines describing the current situation about the gluon condensate. It is a pleasure for me to put them here.

The gluon condensate $\alpha_s G^2$  introduced by Shifman-Vainshtein-Zakharov (SVZ) [see also Zakharov, contribution at Sakurai’s prize 1999: Int. J. Mod. Phys A14 (1999)4865 (here)] within the framework of QCD spectral sum rules  (QSSR) plays also an important role in gluodynamics. The original value of $0.04 GeV^4$  obtained by SVZ from charmonium sum rules has been shown by Bell-Bertlmann (BB) to be underestimated by about a factor 2 from their analysis of the non-relativistec version of heavy quark sum rules. The BB result has been confirmed later on from QSSR analyzes of  different channels including  $e^+e^-$  into hadrons, tau-decay and charmonium by different groups, where the most recent value of  $(0.07\pm 0.01) GeV^4$ has been obtained [see for a review my 2 books (here and here) and the last paper on tau-decay: PLB673(2009)30 (here) ]. However, in order to extract reliably this (small) quantity one should work with sum rule which can properly disentangle its contribution where some possible competing contributions due to perturbative radiative corrections and to quark mass should not appear. This feature may explain some results in the literature. The non-vanishing of the gluon condensate and its positive sign has been seen in the lattice by  the Pisa group [A. Di Giacomo, G.C. Rossi, PLB100(1981)481 (here);  M. Campostrini, A. Di Giacomo, Y. Gunduc, PLB225(1989)393 (here)] and more recently by P.E. Rakow (here). Its positive sign is expected in a model with a magnetic confinement (H. Nambu), while phenomenologically, its eventual negative value would leave to serious inconsistencies in the QSSR approach. Its negative and non-universal values obtained from some tau-decays analysis can indicate the difficulty to extract its value among the competitive parameters present there where in the tau-decay width the gluon condensate contribution acquires an extra $\alpha_s$ contribution compared to some other non-perturbative contributions. In fact, this peculiar properties have been the most important observation that non-perturbative contributions are small in this observable, then allowing an accurate determination of $\alpha_s$ from tau-decays.

### 2 Responses to Gluon condensate: The situation

1. Homi says:

Hello Marco

Thanks for your nice note on the gluon condensate. I have still a question about the physical meaning (role) of the gluon condensate. It is not clear to me what does mean it physically. From sum rules we know that it somehow parametrize the nonperturbative part of the QCD vacuum, but what more? Is it a constituent of the QCD vacuum? If so, what is its effective potential (specially nonperturbative form)?

• mfrasca says:

Dear Homi,

A gluon condensate describes gluon excitations in a Yang-Mills field representing observable degrees of freedom. It gives the mass to particles, mostly built from glue, that can be observed at accelerator facilities. Indeed, some examples could be f0(500) or f0(980) or both but, in any case, if you want to understand glueballs from sum rules, a gluon condensate is needed.

It is interesting to note that, being this a gauge invariant quantity, it enters into observables. The situation is rather different for the $\langle A^2\rangle$ condensate that, being not gauge invariant, just enters into the formation of the mass gap of the theory. Evidence of this can be found in the work of D. Dudal, H. Verschelde, J. A. Gracey, V. E. R. Lemes, M. S. Sarandy, R. F. Sobreiro, S. P. Sorella as in http://arxiv.org/abs/hep-th/0311194.

Marco