mitchell porter said:
I am less than an amateur with respect to this topic. You're helping
me out. However, I did have one thought. Chew hoped to create an alternative to field theory, the bootstrap theory. Something called bootstrap has been revived and
applied to Ising model. Meanwhile,
you pointed out that the reggeon description of pp and ppbar scattering resembles 3d directed percolation. So maybe the answers are in that area.
What I am about to write is purely speculative. They are just a set of ideas that some researchers are working with and some ideas that I have in mind. They are just phenomenological models that try to fit the experimental hadronic interactions and speculations of my own. If any of these models turns out to be fully successful (my own ideas will probably be wrong), it should later be derived from first principles (QCD). I am not trying to confuse anybody.
OK, yes there might be a connection between hadron scattering and the 2+1 directed percolation model. However, that connection has been stablished through a "Reggeon Field Theory" used in hadronic interactions, as you can see in (and references therein) (I do not know if it is paywalled):
http://iopscience.iop.org/article/10.1088/0305-4470/13/12/002/pdf
That, IMO,
might mean that the relationship has been enforced from the very beginning and might not be relevant (I have to think a lot more about it because there are other issues to be considered that I am not mentioning for the moment, see point 4).
Let us assume that there
might (speculation) be a relationship between the 2+1 DP model and elastic hadron interactions:
1.- In the directed percolation model you have to fix a single relevant operator to be at the critical point (there is a single reduced relevant variable). Once you are there (critical point) (or, at least not too far from it), every relevant physical quantity is related to the reduced operator by a non-trivial critical exponent. There are only three independent critical exponents. Any other relevant operator MUST be null at the critical point. Other critical exponents are related by scaling relations to the three independent ones.
2.- Is all this related to elastic hadron interactions?
To be honest I do not know. I have a few "crazy" hypothesis in mind: for example, elastic ##pp## and ##p\bar p## elastic scattering are clearly ##s##-channel interactions and the average diffraction angles are tiny. Perhaps, only perhaps, it may not be unreasonable to think that ##t=0## (zero momentum transfer) could be a critical condition and ##s\gt 4m^2## the relevant operator, maybe, there might be a conection between the 1+2 DP and elastic hadron interactions.
3.- The simplest (and, to the best of my knowledge,
only) model that
fully explains the experimental results (so far) of elastic ##pp## and ##p\bar p## scattering is published here:
https://arxiv.org/pdf/1711.03288.pdf. Here ##t=0## (total cross-sections).
https://arxiv.org/abs/1808.08580. Here ##t\lt0## (elastic differential cross-sections).
Where three different "particles" (I do not really know how to call them) are used: several "Reggeons" (collectively secondary Reggeons), several "Pomerons" (collectively called Froissaron) and a several "Odderons" (collectively called maximal Odderon). That means 3 different "critical exponents" at ##t=0## and 6 at ##t\leq 0##. We know of a Regge trajectory for the "secondary Reggeons". If there happens to be Regge trajectories for the "Pomeron" and "Odderon" it could be argued that there are only THREE independent "critical exponents" like in the 1+2 DP even at ##t\leq 0##. Or, maybe, the scaling relationships of the 1+2 DP model could be used as a guide to look for the missing Regge trajectories.
These ideas are purely speculative but they can be checked. If ##\alpha_R\big(t=0\big)##, ## \frac{d\alpha_R\big ( t\big )}{dt}\Big|_{t=0}##, ##\alpha_P\big(t=0\big)##, ## \frac{d\alpha_P\big ( t\big )}{dt}\Big|_{t=0}##,##\alpha_O\big(t=0\big)## and ## \frac{d\alpha_O\big ( t\big )}{dt}\Big|_{t=0}## are all contained in the list of 1+2 DP critical exponents, then there must be a
deep relationship between this model and, at least,the ##pp## and ##p\bar p## elastic scattering amplitude functions ##T(s,t)_{pp}##, ##T(t,s)_{p\bar p}## and ##T(u,t)_{p\bar p}##.
If not the relationship has been artificially enforced. At the time when:
http://iopscience.iop.org/article/10.1088/0305-4470/13/12/002/pdf
was written, to the best of my knowledge, the Odderon was not included as an interacting field.
4.- The quark-gluon plasma seems to behave like a superfluid liquid (almost free of viscosity).
https://arxiv.org/pdf/1802.04801.pdf
The directed percolation models seems to describe the critical transition from laminar flow to turbulent flow in incompressible fluids (where viscosity just limits the minimum size of the eddies and otherwise is negligeable outside the tiny boudary layer)(paywalled):
https://www.nature.com/collections/rxsztdqblr/
The 3+1 Ising Model is a very "nice" Field theory (it is a conformal field theory) "too nice for my taste" but, of course, that's just a prejudice and I will take a close look at it. Thank you for the information.
