Chiral dynamics and the growth of the nucleon's gluonic transverse size at small x

We study the distribution of gluons in transverse space in the nucleon at moderately small x (∼10^-2). At large transverse distances (impact parameters) the gluon density is generated by the "pion cloud" of the nucleon, and can be calculated in terms of the gluon density in the pion. We investigate the large-distance behavior in two different approaches to chiral dynamics: (i) phenomenological soft-pion exchange; (ii) the large-N_c picture of the nucleon as a classical soliton of the pion field, which corresponds to degenerate N and Δ states. The large-distance contributions from the "pion cloud" cause a ∼20% increase in the overall transverse size of the nucleon if x drops significantly below M _π/M_N. This is in qualitative agreement with the observed increase of the slope of the t dependence of the J/ψ photoproduction cross section at DESY HERA compared to fixed-target energies. We argue that the glue in the pion cloud could be probed directly in hard electroproduction processes accompanied by "pion knockout," γ*+ N→γ (or ρ,J/ψ) + π+N′, where the transverse momentum of the emitted pion is large while that of the outgoing nucleon is restricted to values of order M_π.