Pioneers

20/05/2009

Jeffrey Mandula is a well-knwon theoretical physicist whose main result, Coleman-Mandula theorem, opened the road to the discovery of supersymmetry. But Mandula is also known for his pioneering works on lattice QCD. Looking back to old papers on the question of the Yang-Mills propagators, I have found two beautiful papers by Mandula and Ogilvie (see here and here) published in the eighties, where they arrive to the following conclusion

From the behavior of the gluon propagator reported here, it appears that in pure Yang-Mills theory, a dynamical Higgs phenomenon occurs. Our best estimate of the effective gluon mass, as determined at large distances, is about 600 MeV, with finite size effects, possible scaling violations, and statistical uncertainties of at least $\pm 25\%$. In analogy with the concept of a constituent quark mass, it may be useful to think of the mass in the gluon propagator as a constituent gluon mass. The massiveness of the gluon may be connected to the apparent suppression of many-gluon intermediate states in $J/\psi$ decay, and the relative absence of the mixing between the lowest quark model states and those with gluonic excitations.

They used small lattices due to the computer limitations at that time and ideas about infrared behavior of Yang-Mills theory were just beginning to flourish. But, with our hindsight, we should emphasize the deep intuition that these authors put forward when such analysis were just starting. Besides, $\sigma$ resonance was not yet seen and their estimate of the gluon mass appears really good.

As you may know, after these works, things took a different turn and for a long time since now we have been coping with a different scenario from that devised by Mandula and Ogilvie that took the scenes and not yet left them. This scenario appears today to be in a serious difficulty against lattice computations but people do not generally agree about what the right view should be, making painfully slow truth achievement .