Following my exchange with Lubos Motl (see here) I try to explain what an unconventional view is for people working in QCD. Of course, I agree with Lubos sight that it does not matter how unconventional is your view and so more attracting. What really counts is that this view agrees finally with experiments. But for QCD we have an important goal to reach, a goal that can hit all QFT and whatever else will follow: Our ability to manage a strongly coupled theory and this is a thing that nobody is able to do today in its full generality. This would be a large impact technology as it could possibly apply to any field of physics.

Currently, people tries to approach Yang-Mills theory with lattice computations that grant a non-perturbative solution to such a theory. From a strict theoretical point of view we know from QFT that a tower of non-perturbative equations exists to obtain n-point functions of the theory and these are Dyson-Schwinger equations and can always be obtained for any QFT. What you need here is a proper truncation of the tower and you are done. But this is the most serious difficulty with this approach as it is generally hard to evaluate how good is the chosen truncation and one can also incur in a dramatic error.

So, unconventional views here are those that evade both approaches given above and are able to recover lattice results. I would like to cite the work of Sorella et al. ( see their latest preprint) where they consider an extended Yang-Mills Lagrangian to recover lattice results. Other works have been put forward e.g. by Cornwall as in a pioneering paper to be found here and this produced several interesting works by Aguilar, Natale and Papavassiliou that, numerically solving Dyson-Schwinger equations, are trying to support Cornwall’s view. Finally, I have modified Bender et al. approach that did not work changing it into a gradient expansion recovering straightforwardly lattice results. I apologize for any missing contribution but anyhow I would appreciate whoever would help me to enlarge this list and I will be happy to do it.

What is the most valued of these approaches? Surely one would appreciate the most general ones, those that are not just fitted for the specific aims but that can expand to a large extent to all fields of physics and this possibility exists. So, the stake is high and lattice computations defined the aims. Next years we will see what physicists creativity deserves to us.

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Hi,
I am just wondering if one can think of a QCD like theory with different lamda QCD, what would be its value, what does the value of lambda QCD depends on ? and generally can one put a lower bound on it from cosmology?

There is nothing in QCD like that lambda you are talking about and QCD-like theories are whatever gauge theories Nature adopted. Today we know electro-weak and strong interactions. So, you haveyour gauge group defined (SU(3) for QCD being 3 the numbers of charges) and eventually a running coupling. A running coupling is a parameter varying with continuity with respect energy giving a different coupled theory at a different energy. This is what I think is nearer your lambda and is a concept arisen with renormalization group and largely confirmed by experiments. For a Yang-Mills theory we have this running coupling going to zero at very large energies (asymptotic freedom) and also at very small energies passing for a maximum value. Cosmological consequences are that at the very beginning of the universe quarks and gluons were loosely bounded forming a plasma.

I am in vacation and somehow out of a correct tuning. Indeed, Lambda is generally taken to be about a few hundreds MeV. You can find something in my post

where you can see that is just an integration constant of Yang-Mills theory being determined experimentally. My view is that you can do perturbation theory and QFT also for this case, in agreement with such exact solution, and you can find a description of this in my papers

My view is that the behavior of QCD varying lambda does not change. Rather you should expect the set in of asymptotic freedom more later for a larger lambda and we would have serious difficulties to unveil it having been this parameter too large.

Hi,

I am just wondering if one can think of a QCD like theory with different lamda QCD, what would be its value, what does the value of lambda QCD depends on ? and generally can one put a lower bound on it from cosmology?

Thanks

Dan

So, what do you mean by a different lambda QCD? QCD has just one parameter, the coupling constant g, and the quark masses for the Higgs mechanism.

Marco

Hi,

I said lambda QCD of QCD like theory

Dan

There is nothing in QCD like that lambda you are talking about and QCD-like theories are whatever gauge theories Nature adopted. Today we know electro-weak and strong interactions. So, you haveyour gauge group defined (SU(3) for QCD being 3 the numbers of charges) and eventually a running coupling. A running coupling is a parameter varying with continuity with respect energy giving a different coupled theory at a different energy. This is what I think is nearer your lambda and is a concept arisen with renormalization group and largely confirmed by experiments. For a Yang-Mills theory we have this running coupling going to zero at very large energies (asymptotic freedom) and also at very small energies passing for a maximum value. Cosmological consequences are that at the very beginning of the universe quarks and gluons were loosely bounded forming a plasma.

Marco

Lambda QCD is the scale at which QCD becomes non perturbative

Thanks anyway

Dan

Dear Dan,

I am in vacation and somehow out of a correct tuning. Indeed, Lambda is generally taken to be about a few hundreds MeV. You can find something in my post

https://marcofrasca.wordpress.com/2008/07/15/classical-yang-mills-theory-and-mass-gap/

where you can see that is just an integration constant of Yang-Mills theory being determined experimentally. My view is that you can do perturbation theory and QFT also for this case, in agreement with such exact solution, and you can find a description of this in my papers

http://arxiv.org/abs/0807.4299

http://arxiv.org/abs/0807.2179

My view is that the behavior of QCD varying lambda does not change. Rather you should expect the set in of asymptotic freedom more later for a larger lambda and we would have serious difficulties to unveil it having been this parameter too large.

Marco

Ok, may be I was not clear

Assume that there exists a QCD-like theory, say another version of QCD with different details hence different lambda QCD or different mass gap

Is there a lower limit on the mass gap from cosmology?

Dan

No, currently I do not expect this. But lambda is fixed by experiments and an higher level theory may fix a link between this constant and cosmology.

Marco