Small- b expansion of the DOZZ formula for light operators

We present a systematic asymptotic small-[Formula: see text] expansion of the Liouville DOZZ three-point structure constant in the light-operator regime [Formula: see text] in the limit [Formula: see text]. In this limit the DOZZ structure constant admits the asymptotic representation [Formula: see text] where [Formula: see text] is an explicitly determined prefactor. Using Thorn’s asymptotic expansion of the [Formula: see text]-function, we derive explicit closed-form expressions for the first coefficients [Formula: see text] and show that they form a symmetric polynomial structure in the variables [Formula: see text]. The resulting asymptotic expansion provides explicit finite-[Formula: see text] corrections to the leading light-limit Liouville three-point data and furnishes a practical framework for applications in celestial holography. In particular, it provides Liouville data relevant for a perturbative program aimed at studying finite-[Formula: see text] corrections to celestial Yang–Mills amplitudes. Finally, we formulate such a perturbative Liouville framework and discuss several directions for its future development.