- #1
Anashim
- 38
- 1
The directed percolation dynamical universality class is characterized by just three independent critical exponents. These exponents are (in a 3d space):
$$\beta=\beta'=0.813(9)$$
$$\nu_\perp=0.584(5)$$
$$\nu_\parallel=1.110(10)$$
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.
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. The directed percolation universality class (this time in d=2), has the following independent critical exponent values:
$$\beta=\beta'=0.5834(30)$$
$$\nu_\perp=0.7333(75)$$
$$\nu_\parallel=1.2950(60)$$
Again, the latter value is very close to the accepted "hard Pomeron" intercept value. 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, 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 there is a third Regge trajectory (the Odderon) needed to explain the difference between ##pp## and ##p\bar p## total cross-sections, the (soft) Odderon intercept value should be close to the third critical exponent ##0.813(9)##.
$$\beta=\beta'=0.813(9)$$
$$\nu_\perp=0.584(5)$$
$$\nu_\parallel=1.110(10)$$
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.
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. The directed percolation universality class (this time in d=2), has the following independent critical exponent values:
$$\beta=\beta'=0.5834(30)$$
$$\nu_\perp=0.7333(75)$$
$$\nu_\parallel=1.2950(60)$$
Again, the latter value is very close to the accepted "hard Pomeron" intercept value. 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, 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 there is a third Regge trajectory (the Odderon) needed to explain the difference between ##pp## and ##p\bar p## total cross-sections, the (soft) Odderon intercept value should be close to the third critical exponent ##0.813(9)##.