Nonperturbative Effects in Gluon Radiation and Photoproduction of Quark Pairs

TL;DR

This work develops a nonperturbative framework for light-cone fluctuations involving quarks and gluons, introducing a confining quark–antiquark potential and a stronger nonperturbative quark–gluon interaction. Using a Green-function approach, the authors compute photon-induced fluctuations, diffractive processes, and gluon radiation, calibrating the interaction strengths with data on diffraction and photoabsorption. They find that gluon shadowing in nuclei is weaker and slower to appear than quark shadowing, and that nonperturbative effects substantially suppress gluon bremsstrahlung at small transverse momentum, while maintaining a semi-hard scale that preserves near scale invariance up to moderate $Q^2$. The results have implications for high-energy nuclear physics, including shadowing phenomena, diffraction, and the dynamics of gluons in nuclei, with potential relevance to quark–gluon plasma formation in heavy-ion collisions.

Abstract

We introduce a nonperturbative interaction for light-cone fluctuations containing quarks and gluons. The $\bar qq$ interaction squeezes the transverse size of these fluctuations in the photon and one does not need to simulate this effect via effective quark masses. The strength of this interaction is fixed by data. Data on diffractive dissociation of hadrons and photons show that the nonperturbative interaction of gluons is much stronger. We fix the parameters for the nonperturbative quark-gluon interaction by data for diffractive dissociation to large masses (triple-Pomeron regime). This allows us to predict nuclear shadowing for gluons which turns out to be not as strong as perturbative QCD predicts. We expect a delayed onset of gluon shadowing at $x \leq 10^{-2}$ shadowing of quarks. Gluon shadowing turns out to be nearly scale invariant up to virtualities $Q^2\sim 4 GeV^2$ due to presence of a semihard scale characterizing the strong nonperturbative interaction of gluons. We use the same concept to improve our description of gluon bremsstrahlung which is related to the distribution function for a quark-gluon fluctuation and the interaction cross section of a $\bar qqG$ fluctuation with a nucleon. We expect the nonperturbative interaction to suppress dramatically the gluon radiation at small transverse momenta compared to perturbative calculations.

Figures (11)

• Figure 1: Illustration for the Green function $G_{\bar{q}q}(z_1,\vec{\rho}_1=0;z_2,\vec{\rho}_2=\vec{\rho})$ for an interacting $\bar{q}q$ fluctuation of a photon, as defined by Eq. (\ref{['2.1']}).
• Figure 2: Feynman diagrams for diffractive radiation of a gluon in a quark-nucleon interaction, $qN\to qGN$.
• Figure 3: Contributions from projectile valence quarks to the amplitude of diffractive gluon emission in $NN$ collisions. Six additional graphs resulting from the permutation $\{1\rightleftharpoons2\}$ and $\{1\rightleftharpoons3\}$ have not been plotted.
• Figure 4: Diagrams for the diffractive radiation of a gluon in photon-nucleon interaction, $\gamma^* N\to\bar{q}qGN$.
• Figure 5: Ratio of the gluon distribution functions in nuclei (carbon, copper and lead) and nucleons at small Bjorken $x$ and $Q^2 = 4\,GeV^2$ (solid curves) and $40\,GeV^2$ (dashed curves).