Possible Multiparticle Ridge-like Correlations in Very High Multiplicity Proton-proton Collisions Page: 3 of 9
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bisectors of a triangle with the quarks at the vertices ("Y" diagrams). The idea of such flux
tubes goes back at least to the work of Isgur and Paton . Planar networks of strongly
interacting gluons connecting valence quarks are also natural in the higher Fock states of
the light-front wave functions of the proton as discussed by Mueller . Such saturating
configurations can lead to BFKL phenomena, color-glass models , and they could even
provide the color-confining potential of valence quarks as seen in the AdS/QCD soft-wall
model  using light-front holography [24-26] . We also note that 'H'-diagrams (e.g., two
vertical gluons, interacting via horizontal rungs, connecting a heavy quark and antiquark)
which enter the heavy-quark potential  have a similar origin.
II. CONSEQUENCES OF THE COLLISIONS OF ORIENTED QCD FLUX TUBES
A linear configuration of the proton has two valence quarks near one end of a gluon
flux tube and a third valence quark at the other end. We assume that the flux tube has a
transverse size no larger than a few tenths of a Fermi . The probability of finding such
a linear configuration is arguably quite considerable, especially given the phenomenological
success of quark-diquark models in spectroscopy and other QCD applications. We guess
the odds of having such a linear configuration as 20%, with an uncertainty either way of a
factor two or so. For the collisions of interest, we need the projection of the tube onto the
"impact-plane", and well over half of the linear configurations should survive this projection.
We are interested in the head-on collision of two such configurations. The overlap would
be significant as long as the impact parameter between the flux tubes were less than the
width of either flux tube. Just as with the elliptical overlap between two nuclei, this shape
would tend to produce larger momenta in the transverse direction perpendicular to the lines
than in the direction parallel to the lines. The cost in aligning them azimuthally is a factor
10 or 20, just from simple geometrical considerations. The impact parameter must of course
be small, with a transverse size of order of 0.2 fermi. Along the string direction we can loosen
this demand to, say, 0.5 fermi. This gives a cross-section of about 1 mb. After the penalty
factors which we have enumerated are included, the estimated cross-section for the collision
of aligned flux tubes is reduced to a value in the neighborhood of 1 microbarn. This is quite
similar to the cross section for events with a trigger of more than 110 charged-particle tracks
used in the CMS experimental 'ridge' analysis .
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Bjorken, James D.; Brodsky, Stanley J.; Goldhaber, Alfred Scharff & /SLAC. Possible Multiparticle Ridge-like Correlations in Very High Multiplicity Proton-proton Collisions, article, August 27, 2013; United States. (digital.library.unt.edu/ark:/67531/metadc830805/m1/3/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.