Separated Response Functions in Exclusive, Forward $π^{\pm}$ Electroproduction on Deuterium
Background: Measurements of forward exclusive meson production at different squared four-momenta of the exchanged virtual photon, $Q^2$, and at different four-momentum transfer, t, can be used to probe QCD's transition from meson-nucleon degrees of freedom at long distances to quark-gluon degrees of freedom at short scales. Ratios of separated response functions in $π^-$ and $π^+$ electroproduction are particularly informative. The ratio for transverse photons may allow this transition to be more easily observed, while the ratio for longitudinal photons provides a crucial verification of the assumed pole dominance, needed for reliable extraction of the pion form factor from electroproduction data. Method: Data were acquired with 2.6-5.2 GeV electron beams and the HMS+SOS spectrometers in Jefferson Lab Hall C, at central $Q^2$ values of 0.6, 1.0, 1.6 GeV$^2$ at W=1.95 GeV, and $Q^2$=2.45 GeV$^2$ at W=2.22 GeV. There was significant coverage in $ϕ$ and $ε$, which allowed separation of $σ_{L,T,LT,TT}$. Results: $σ_L$ shows a clear signature of the pion pole, with a sharp rise at small -t. In contrast, $σ_T$ is much flatter versus t. The longitudinal/transverse ratios evolve with $Q^2$ and t, and at the highest $Q^2$=2.45 GeV$^2$ show a slight enhancement for $π^-$ production compared to $π^+$. The $π^-/π^+$ ratio for transverse photons exhibits only a small $Q^2$-dependence, following a nearly universal curve with t, with a steep transition to a value of about 0.25, consistent with s-channel quark knockout. The $σ_{TT}/σ_T$ ratio also drops rapidly with $Q^2$, qualitatively consistent with s-channel helicity conservation. The $π^-/π^+$ ratio for longitudinal photons indicates a small isoscalar contamination at W=1.95 GeV, consistent with what was observed in our earlier determination of the pion form factor at these kinematics.