On Hard Coherent Processes

A factorization theorem for the hard coherent processes involving high-energy scattering of photons is derived. We elaborate the treatment for the case of the longitudinally polarized photons and extend the treatment to the case of the processes initiated by transversely polarized photons, as well as to the coherent photo-production of heavy quarkonia. A wave function of a hadron being the solution of the Schrödinger equation is presented in the space-time evolution of initially zero-size and zero-color charge wave packet of bare quarks and gluons. The increase of the running coupling constant in QCD with the distance leads to the coexistence of two phases within the hadron wave function. One phase is the pQCD phase, the second phase is dominated by the phenomenon of spontaneously broken chiral symmetry. The critical line at \(r=r_{\mathrm {c}}\) follows from the gauge symmetry, asymptotic freedom, causality, quantum diffusion, and from the cancellation of soft color fields outside the wave packet. The distinctive properties of QCD are the significant probability of a high-momentum tail of the minimal Fock component (MFC) of the hadron wave function and the strong suppression of the soft part of MFC of hadron WF in the strong coupling regime of QCD. The factorization theorems predict hard coherent processes, color transparency, color fluctuations phenomena, <span class="it">etc</span>. We argue that the value of the radius of the region occupied by the pQCD phase, \(r_{\mathrm {c}}\), is restricted by the radius of the onset of spontaneously broken chiral symmetry \(r_{\mathrm {c}}\gg r_{\mathrm {CS}}\). The success of the constituent quark model for a baryon suggests that the radius of the confinement of color is significantly larger than \(r_{\mathrm {c}}\). The presence of a color core in hadrons matches well with preQCD field theories at distances larger than the critical line for the onset of the regime of spontaneously broken chiral symmetry. It substitutes Landau nullification of the interaction within preQCD field theories, the preQCD Feynman model at the distances smaller than \(r_{\mathrm {c}}\). Abstract Published by the Jagiellonian University 2025 authors