A multidimensional study of the structure function ratio ${\sigma }_{L{T}^{\mathrm{\prime }}}\mathrm{/}{\sigma }_0$ from hard exclusive ${\pi }^{+}$ electro-production off protons in the GPD regime

A multidimensional extraction of the structure function ratio ${\sigma }_{L{T}^{\mathrm{\prime }}}\mathrm{/}{\sigma }_0$ from the hard exclusive $\vec{e}p\to e^{\mathrm{\prime }}n{\pi }^{+}$ 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 ($t\mathrm{/}{Q}^2$ $\ll$ 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 $Q^2$.