Recoil Polarization for $\Delta$ Excitation in Pion Electroproduction

We measured angular distributions of recoil-polarization response functions for neutral pion electroproduction for $W=1.23\mathrm{GeV}$ at $Q^2=1.0(\mathrm{GeV}/c{)}^2$, obtaining 14 separated response functions plus 2 Rosenbluth combinations; of these, 12 have been observed for the first time. Dynamical models do not describe quantities governed by imaginary parts of interference products well, indicating the need for adjusting magnitudes and phases for nonresonant amplitudes. We performed a nearly model-independent multipole analysis and obtained values for $\mathrm{Re}(S_{1+}/M_{1+})=-(6.84\pm 0.15)\%$ and $\mathrm{Re}(E_{1+}/M_{1+})=-(2.91\pm 0.19)\%$ that are distinctly different from those from the traditional Legendre analysis based upon $M_{1+}$ dominance and ${\ell }_{\pi }\le 1$ truncation.

Figure 1

Data for response functions at $W=1.23\mathrm{GeV}$ and $Q^2=1.0(\mathrm{GeV}/c{)}^2$ are compared with recent models and with fits. The labeling distinguishes L, T, LT, and TT contributions to the unpolarized (0) cross section and to transverse (t), normal (n), or longitudinal (l) components of recoil polarization with an h to indicate helicity dependence, if any. Linear combinations that cannot be resolved without Rosenbluth separation are identified by $\mathrm{L}+\mathrm{T}$. Black dash-dotted, dotted, short-dashed, and long-dashed curves represent the MAID2003, DMT, SAID, and SL models, respectively. The green mid-dashed curves show a Legendre fit while the solid red curves show a multipole fit.

Figure 2

Red circles, present results from multipole analysis; open squares, MAMI [9, 27]; open triangles, LEGS [28]; filled triangles, MIT [29]; crosses, ELSA [30]; open circles, CLAS [26]. Small horizontal displacements are used to reduce clutter. Inner error bars with end caps show statistical and systematic errors; where available, outer error bars without end caps include model error. Red, green dashed, blue dash-dotted, and cyan dotted curves represent MAID2003, DMT, SAID, and SL, respectively. Magenta bars show lattice QCD results [5].