## A wonderful confirmation

Contributions to proceedings to Ghent conference “The many faces of QCD” are starting to appear on arxiv and today appeared one of the most striking one I have heard of at that conference: Orlando Oliveira, Pedro Bicudo and Paulo Silva published their paper (see here). This paper represents a true cornerstone for people doing computations of propagators as the authors for the first time try to connect a gauge-dependent quantity as the gluon propagator is to a gauge-independent one as is the spectrum of Yang-Mills theory, mostly in the way I advocated here and in my papers. The results are given in the following figure

and the data are the following

[0.57{3.535(64),0.5907(86)}1.4]
[1.52{17(3),0.797(17)}{−17(3),1.035(31)}1.5]
[6.46{31(6),0.851(16)}{−52(11),1.062(26)}{22(9),1.257(40)}1.6]
[7.77{33(9),0.900(26)}{−54(12),1.163(49)}{33(14),1.65(12)}{−11(11),2.11(24)}1.1]

for one, two, three and four masses respectively. The form of the propagator they consider is the following one

$D(p)=\sum_{n=0}^N\frac{Z_n}{p^2+m^2_n}$

and so the first number above is the maximum momentum considered in the fit, then you have the pairs $\{m_n,Z_n\}$ and the last number is the goodness of the fit as $\chi^2/d.o.f.$. As you can see from the picture above, the fit goes excellently well on all the range with four masses! The masses they obtain are values that are consistent with hadronic physics and can represent true glueball masses. The series has alternating signs signaling that the match with a true Källén-Lehmann spectral representation is not exact. Finally, the authors show how all the lattice computations performed so far agree well with a value $D(0)\approx 8.3-8.5$.

Why have I reasons to be really happy? Because all this is my scenario! The paper you should refer to are this and this. The propagator I derive from Yang-Mills theory is exactly the one of the fit of these authors. Besides, this is a confirmation from the lattice that a tower of masses seems to exist for these glue excitations as I showed. The volumes used by these authors are quite large, $80^4$, and will be soon accessible also from my CUDA machine (so far I reached $64^4$ thanks to a suggestion by Nuno Cardoso), after I will add a third graphics card. Last but not least the value of D(0). I get a value of about 4, just a factor 2 away from the value computed on the lattice, for a string tension of 440 MeV. As my propagator is obtained in the deep infrared, I would expect a better fit in this region.

The other beautiful result these authors put forward is the dependence of the mass on momentum. I have showed that the functional form they obtain is to be seen in the next to leading order of my expansion (see here). Indeed, they show that the fit with a single Yukawa propagator improves neatly with a mass going like $m^2=m^2_0-ap^2$ and this is what must be in the deep infrared from my computations.

I have already said in my blog about the fine work of these authors. I hope that others will follow these tracks shortly. For all my readers I just suggest to stay tuned as what is coming out from this research field is absolutely exciting.

O. Oliveira, P. J. Silva, & P. Bicudo (2011). What Lattice QCD tell us about the Landau Gauge Infrared Propagators arxiv arXiv: 1101.5983v1

FRASCA, M. (2008). Infrared gluon and ghost propagators Physics Letters B, 670 (1), 73-77 DOI: 10.1016/j.physletb.2008.10.022

FRASCA, M. (2009). MAPPING A MASSLESS SCALAR FIELD THEORY ON A YANG–MILLS THEORY: CLASSICAL CASE Modern Physics Letters A, 24 (30) DOI: 10.1142/S021773230903165X

Marco Frasca (2008). Infrared behavior of the running coupling in scalar field theory arxiv arXiv: 0802.1183v4