  Single pseudoscalar and vector mesons inclusive photoproduction $\gamma
h\rightarrow MX$ via higher twist mechanism is calculated using the QCD running
coupling constant method. It is proved that in the context of this method a
higher twist contribution to the photoproduction cross section cannot be
normalized in terms of the meson electromagnetic form factor. The structure of
infrared renormalon singularities of the higher twist subprocess cross section
and the resummed expression (the Borel sum) for it are found. Comparisons are
made with earlier results, as well as with leading twist cross section.
Phenomenological effects of studied contributions for $\pi, K, \rho$-meson
photoproduction are discussed.
