Complete quartic (${\mathrm{\alpha }}_{\mathit{s}}^2$) correction to the deep-inelastic longitudinal structure function ${\mathit{F}}_{\mathit{L}}$ in QCD

The analytic next-to-leading-order correction [O(${\mathrm{\alpha }}_{\mathit{s}}^2$)] to the longitudinal structure function in QCD is presented in the form of kernels that give ${\mathit{F}}_{\mathit{L}}$ after convolution with the partonic densities. This final complete result, which corrects previous partial calculations, can be easily used for phenomenological applications, which are briefly discussed.