Abstract
We discuss the higher Fock-state ($q\overline{q}g$) contributions to the nonzero value of the pion generalized parton distribution (GPD) at the crossover point $x=\ensuremath{\zeta}$ between the DGLAP and ERBL regions. Using the phenomenological light-front constituent quark model, we confirm that the higher Fock-state contributions indeed give a nonzero value of the GPD at the crossover point. Iterating the light-front quark model wave function of the lowest $q\overline{q}$ Fock state with the Bethe-Salpeter kernel corresponding to the one-gluon exchange, we include all possible time-ordered $q\overline{q}g$ Fock-state contributions and obtain the pion GPD satisfying necessary sum rules and continuity conditions.
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