The directed percolation dynamical universality class is characterized by just three independent critical exponents. These exponents are (in a 3d space):

$$\beta=\beta'=0.813(9)$$ $$\nu_\perp=0.584(5)$$ $$\nu_\parallel=1.110(10)$$

See, for example, https://arxiv.org/abs/cond-mat/0001070, page 56.

The latter two numbers are in close agreement with the (soft) Reggeon and Pomeron intercept values used to fit the total cross-sections of all known stable hadrons.

See, for example, https://arxiv.org/abs/hep-ph/9209205, pages 10-14.

In the low $x$ limit of deep inelastic scattering, a different Pomeron seems to be needed: the "hard Pomeron", whereas the Reggeon does not play any role.

See, for example, https://indico2.riken.jp/event/2729/attachments/7480/8729/PomeronRIKEN.pdf, slide 44.

The directed percolation universality class (this time in d=2), has the following independent critical exponent values:

$$\beta=\beta'=0.5834(30)$$ $$\nu_\perp=0.7333(75)$$ $$\nu_\parallel=1.2950(60)$$

See, again, https://arxiv.org/abs/cond-mat/0001070, page 56.

The latter value is very closed to the accepted "hard Pomeron" intercept value.

See, again, https://indico2.riken.jp/event/2729/attachments/7480/8729/PomeronRIKEN.pdf, slide 44.

Could this mean that the number of relevant spatial dimensions has decreased from 3 to 2?

Since Pomerons are explained in QCD as 'reggeized' colorless glueballs,

See, for example, https://en.wikipedia.org/wiki/Pomeron .

it could be that this universality class (The Directed Percolation) is related to the collective bahavior of 'reggeized gluons'.

This hypothesis, admittedly weak, comes, however, with a prediction. Since a third Regge trajectory is needed (the Odderon) to explain the difference between $pp$ and $p\bar p$ cross-sections, the (soft) Odderon intercept value should be close to the third critical exponent $0.813(9)$.

Quote from the following lectures:

The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical approximation relevant at high energies is a peculiar branching-diffusion process, and parton branching supplemented by saturation effects (such as gluon recombination) is a reaction-diffusion process. In these lectures, we first introduce the basic concepts in the context of simple toy models, we study the properties of the latter, and show how the results obtained for the simple models may be taken over to quantum chromodynamics.


This idea is, unfortunately, not mine.


closed as off-topic by ACuriousMind Jul 25 at 10:17

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  • 2
    $\begingroup$ Sourcing the statements about critical exponents and pomeron theory does not seem to me to make this question any less about a personal theory. What you'd need to find is a mainstream reference that establishes some sort of connection between the critical exponents of directed perlocation and the regge theory intercepts of QCD, because otherwise you're just matching values because they look similar, which is numerology. $\endgroup$ – ACuriousMind Jul 25 at 11:18
  • $\begingroup$ For future reference, please link to the arXiv abstract page, rather than the PDF page (consider, for instance, mobile users). $\endgroup$ – Kyle Kanos Jul 25 at 11:44