  A multidimensional extraction of the structure function ratio
$\sigma_{LT'}/\sigma_{0}$ from the hard exclusive $\vec{e} p \to e^\prime n
\pi^+$ reaction above the resonance region has been performed. The study was
done based on beam-spin asymmetry measurements using a 10.6 GeV incident
electron beam on a liquid-hydrogen target and the CLAS12 spectrometer at
Jefferson Lab. The measurements focus on the very forward regime ($t/Q^{2}$
$\ll$ 1) with a wide kinematic range of $x_{B}$ in the valence regime (0.17 $<$
$x_{B}$ $<$ 0.55), and virtualities $Q^{2}$ ranging from 1.5 GeV$^{2}$ up to 6
GeV$^{2}$. The results and their comparison to theoretical models based on
Generalized Parton Distributions demonstrate the sensitivity to chiral-odd GPDs
and the directly related tensor charge of the nucleon. In addition, the data is
compared to an extension of a Regge formalism at high photon virtualities. It
was found that the Regge model provides a better description at low $Q^{2}$,
while the GPD model is more appropriate at high $Q^{2}$.
