Critical correlations of Wilson lines in SU(3) and the high energyγ*pcross section

Abstract

We discuss deep inelastic scattering at high energies as a critical phenomenon in 2 + 1 space -time dimensions. In the limit of Bjorken x → 0, QCD SU (3) with quark fields becomes a critical theory with a diverging correlation length ξ(x) ∝ x − 1 2λ 2 where the exponent λ 2 = 2.52 is obtained from the center group Z(3) of SU (3). We conjecture that the dipole wave function of the virtual photon for transverse sizes 1/Q < x ⊥ < ξ obeys correlation scaling Ψ ∝ (x ⊥ ) −(1+n) before exponentially decaying for distances larger than the correlation length. Using this behavior combined with different x -independent dipole proton cross sections we calculate the proton structure function and compare with the experimental data. We take the good agreement with the measured proton structure function F 2 (x, Q 2 ) as an indication that at high energies dimensional reduction to an effective three dimensional theory with a critical point occurs. *

Gluons and the quark sea at high energies: distributions, polarization, tomography

“…On a more fundamental level, we have analysed correlations of Wilson lines in vacuum as one approaches the light cone from space-like distances [817]. The dominant terms of the near light cone Hamiltonian for the Wilson lines define a field theory in 2+1 dimensions.…”

“…In the low momentum limit, xG(x, k t ) · k t converges towards a constant independent of x, related to the size of the hadron. The cross-over from the non-perturbative region to the perturbative region occurs at around k t = 1 GeV at x-values 10 −4 < x < 10 −2 .On a more fundamental level, we have analysed correlations of Wilson lines in vacuum as one approaches the light cone from space-like distances [817]. The dominant terms of the near light cone Hamiltonian for the Wilson lines define a field theory in 2+1 dimensions.…”

Hamiltonian Lattice QCD near the Light Cone

“…(2). Having a parameterization of the ground state wave functional in dependence of the nlc parameterη at hand, we plan to extrapolate to the light cone and finally calculate hadronic cross sections by simulating how a color dipole moving near the light cone hits a neutral hadron localized at x − = 0 [12]. The color dipole can be represented by a longitudinal-transversal Wilson loop elongated in x − direction and the simplified target by a transverse plaquette.…”

QCD — NLC

“…The reduced calculation in SU(2) [5] was done without the inclusion of transverse gluons, so we still have to prove that this procedure works. Phenomenologically [7] we have conjectured that the increase of the high-energy electron-proton cross section is due to this critical point s * . At infinite energies when this point is approached, the correlation length of near-light-like Wilson lines of the partons increases with a critical index from Z(3) symmetry.…”

“…We have analyzed QCD approaching the light-cone with a tilted near-lightcone coordinate reference system [5,6,7] containing a parameter η = 0 giving the distance away from the light-cone. The constraint equations appear in the nearlight-cone Hamiltonian as terms proportional to 1/η 2 .…”