Separated response functions in exclusive, forward π [superscript ±] electroproduction on deuterium

Abstract

Background: Measurements of forward exclusive meson production at different squared four-momenta of the exchanged virtual photon, Q[superscript 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 [superscript −] and π [superscript +] 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 π [superscript ±] electroproduction on deuterium above the dominant resonances. 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 [superscript 2] values of 0.6, 1.0, and 1.6 GeV [superscript 2] at W=1.95 GeV, and Q [superscript 2] = 2.45 GeV [superscript 2] at W = 2.22 GeV. There was significant coverage in ϕ and ε, which allowed separation of σ [subscript L,T,LT,TT]. Results: σ [subscript L] shows a clear signature of the pion pole, with a sharp rise at small −t. In contrast, σ [subscript T] is much flatter versus t. The longitudinal/transverse ratios evolve with Q [superscript 2] and t and at the highest Q [superscript 2] = 2.45 GeV [superscript 2] show a slight enhancement for π [superscript −] production compared to π [superscript +]. The π [[superscript -] over π [superscript +]] ratio for transverse photons exhibits only a small Q [superscript 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 [[subscript TT] over σ[subscript T]] ratio also drops rapidly with Q [superscript 2], qualitatively consistent with s-channel helicity conservation. The [π [superscript −] over π [superscript +]] 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 σ [subscript L] but have varying success with σ [subscript 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 [subscript T].