  The new experimental measurements of beam spin asymmetry were performed for
the deeply virtual exclusive $\pi^0$ production in a wide kinematic region with
the photon virtualities $Q^2$ up to 8 GeV$^2$ and the Bjorken scaling variable
$x_B$ in the valence regime. The data were collected by the CEBAF Large
Acceptance Spectrometer (CLAS12) at Jefferson Lab with longitudinally polarized
10.6 GeV electrons scattered on an unpolarized liquid-hydrogen target. Sizable
asymmetry values indicate a substantial contribution from transverse virtual
photon amplitudes to the polarized structure functions.The interpretation of
these measurements in terms of the Generalized Parton Distributions (GPDs)
demonstrates their sensitivity to the chiral-odd GPD $\bar E_T$, which contains
information on quark transverse spin densities in unpolarized and polarized
nucleons and provides access to the proton's transverse anomalous magnetic
moment. Additionally, the data were compared to a theoretical model based on a
Regge formalism that was extended to the high photon virtualities.
