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Analytical asymptotics for hard diffraction
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abstract
We show that the cross section for diffractive dissociation of a small onium off a large nucleus at total rapidity $Y$ and requiring a minimum rapidity gap $Y_{\text{gap}}$ can be identified, in a well-defined parametric limit, with a simple classical observable on the stochastic process representing the evolution of the state of the onium, as its rapidity increases, in the form of color dipole branchings: It formally coincides with twice the probability that an even number of these dipoles effectively participate in the scattering, when viewed in a frame in which the onium is evolved to the rapidity $Y-Y_{\text{gap}}$. Consequently, finding asymptotic solutions to the Kovchegov-Levin equation, which rules the $Y$-dependence of the diffractive cross section, boils down to solving a probabilistic problem. Such a formulation authorizes the derivation of a parameter-free analytical expression for the gap distribution. Interestingly enough, events in which many dipoles interact simultaneously play an important role, since the distribution of the number $k$ of dipoles participating in the interaction turns out to be proportional to $1/[k(k-1)]$.
Forward citations
Cited by 4 Pith papers
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Dipole-dipole scattering at high energy in the Pomeron field theory with Braun Hamiltonian and beyond
Deep in saturation, Braun-Hamiltonian pomeron calculus predicts S_dd = (S_BK)^4 for dipole-dipole scattering, four powers of the standard estimate, but the paper's own unitary toy model contradicts this prediction.
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Summing large Pomeron loops in the saturation region: dipole-nucleus collision beyond nonlinear equations
After summing large Pomeron loops, the dipole-nucleus amplitude has the same energy dependence as dipole-dipole scattering, limiting the BK equation to z' below roughly 2 sqrt(kappa c) A^{1/6}.
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Dipole-dipole scattering: summing large Pomeron loops in non-linear evolution with leading twist kernel
In a leading-twist kernel, matching the BK solution to fan-diagram series yields KNO multiplicity distributions and gluon entropy S_E = ln(xG) for dipole-nucleus and dipole-dipole scattering.
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Summing large Pomeron loops in the saturation region: nucleus-nucleus collision
The nucleus-nucleus scattering amplitude deep in the saturation region reduces to the single nucleon-nucleon term and therefore has the same energy dependence as dipole-dipole scattering.
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