Separated response functions in exclusive, forward<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mo>±</mml:mo></mml:msup></mml:math>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 ${\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\ensuremath{\pi}}^{+}$ 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.Purpose: We perform the first complete separation of the four unpolarized electromagnetic structure functions $L/T/LT/TT$ in forward, exclusive ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ electroproduction on deuterium above the dominant resonances.Method: Data were acquired with 2.6--5.2-GeV electron beams and the $\mathrm{HMS}+\mathrm{SOS}$ spectrometers in Jefferson Lab Hall C at central ${Q}^{2}$ values of 0.6, 1.0, and 1.6 ${\text{GeV}}^{2}$ at $W=1.95$ GeV, and ${Q}^{2}=2.45$ ${\text{GeV}}^{2}$ at $W=2.22$ GeV. There was significant coverage in $\ensuremath{\phi}$ and $\ensuremath{\epsilon}$, which allowed separation of ${\ensuremath{\sigma}}_{L,T,LT,TT}$.Results: ${\ensuremath{\sigma}}_{L}$ shows a clear signature of the pion pole, with a sharp rise at small $\ensuremath{-}t$. In contrast, ${\ensuremath{\sigma}}_{T}$ is much flatter versus $t$. The longitudinal/transverse ratios evolve with ${Q}^{2}$ and $t$ and at the highest ${Q}^{2}=2.45$ ${\text{GeV}}^{2}$ show a slight enhancement for ${\ensuremath{\pi}}^{\ensuremath{-}}$ production compared to ${\ensuremath{\pi}}^{+}$. The ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ 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 ${\ensuremath{\sigma}}_{TT}/{\ensuremath{\sigma}}_{T}$ ratio also drops rapidly with ${Q}^{2}$, qualitatively consistent with $s$-channel helicity conservation. The ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ 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.Conclusions: The separated cross sections are compared to a variety of theoretical models, which generally describe ${\ensuremath{\sigma}}_{L}$ but have varying success with ${\ensuremath{\sigma}}_{T}$. Further theoretical input is required to provide a more profound insight into the relevant reaction mechanisms for longitudinal and transverse photons, such as whether the observed transverse ratio is indeed attributable to a transition from pion to quark knockout mechanisms and provide useful information regarding the twist-3 transversity generalized parton distribution, ${H}_{T}$.

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