Rosenbluth Separation of the ${\pi }^0$ Electroproduction Cross Section Off the Neutron

We report the first longitudinal-transverse separation of the deeply virtual exclusive ${\pi }^0$ electroproduction cross section off the neutron and coherent deuteron. The corresponding four structure functions $d{\sigma }_L/dt$, $d{\sigma }_T/dt$, $d{\sigma }_{LT}/dt$, and $d{\sigma }_{TT}/dt$ are extracted as a function of the momentum transfer to the recoil system at $Q^2=1.75{\mathrm{GeV}}^2$ and $x_B=0.36$. The $ed\to ed{\pi }^0$ cross sections are found compatible with the small values expected from theoretical models. The $en\to en{\pi }^0$ cross sections show a dominance from the response to transversely polarized photons, and are in good agreement with calculations based on the transversity generalized parton distributions of the nucleon. By combining these results with previous measurements of ${\pi }^0$ electroproduction off the proton, we present a flavor decomposition of the $u$ and $d$ quark contributions to the cross section.

Figure 1

Diagram of the coherent ${\pi }^0$ electroproduction reaction on the nucleon ($M=M_N$, $x_B=0.36$) or deuteron ($M=M_d$, $x_B=0.18$) with the dominant ${\pi }^0\to \gamma \gamma$ decay mode. The minimal $|t|$ value is $t_{\min }=(Q^2+m_{{\pi }^0}^2{)}^2/(4W^2)-(|{\overrightarrow{q}}^{\mathrm{c}.\mathrm{m}.}|-|{\overrightarrow{q}}^{\prime \mathrm{c}.\mathrm{m}.}|{)}^2$, where $m_{{\pi }^0}$ is the ${\pi }^0$ mass, $q^{\prime }=q_1+q_2$, and the c.m. superscript refers to the target $-{\pi }^0$ center-of-mass frame.

Figure 2

Corrected missing mass squared $M_X^{\prime 2}$ for $D(e,e^{\prime }{\pi }^0)X$ (solid circles) and normalized Fermi-smeared $H(e,e^{\prime }{\pi }^0)X$ events (open circles). Bars show statistical uncertainties. The difference between the two distributions (squares) is scaled by a factor 10 for clarity. The blue and magenta bands (both scaled $\times 10$), show the simulated $n(e,e^{\prime }{\pi }^0)n$ and $d(e,e^{\prime }{\pi }^0)d$ yields, respectively, fit to the data by minimizing Eq. (6). These bands include the statistical uncertainty of the fit. The total fit to the open squares distribution is shown by the solid (red) histogram.

Figure 3

Total cross section $2\pi [d^2{\sigma }^n/dtd\varphi +r(d^2{\sigma }^d/dtd\varphi )]$ as a function of $\varphi$ at $E=4.45\mathrm{GeV}$ (left) and $E=5.55\mathrm{GeV}$ (right), in the bin $⟨t^{\prime }⟩=0.025{\mathrm{GeV}}^2$ (neutron kinematics), equivalently $⟨t^{\prime }⟩=0.021{\mathrm{GeV}}^2$ (deuteron kinematics), with $r=1.27$ (left) and $r=1.33$ (right) being the ratio deuteron-neutron of the virtual photon flux convoluted with the experimental acceptance. The error-bars show the statistical uncertainty. The boxes around the points show the total systematic uncertainties. The blue and magenta bands represent the contributions of $2\pi (d^2{\sigma }^n/dtd\varphi )$ and $2\pi (d^2{\sigma }^d/dtd\varphi )$, respectively, including the statistical uncertainty of the fit.

Figure 4

The $\varphi$-independent photoproduction cross sections extracted from the fit, as functions of $t^{\prime }$, and separated into quasifree neutron and coherent deuteron contributions: $d{\sigma }_T^n/dt+\epsilon (d{\sigma }_L^n/dt)$ and $d{\sigma }_T^d/dt+\epsilon (d{\sigma }_L^d/dt)$. The data in the left and right panels were obtained at $E=4.45$ and $E=5.55\mathrm{GeV}$, respectively. The error bars show the statistical uncertainty from the fit. The blue and magenta bands represent the systematic errors. The solid lines are theoretical calculations for the neutron from Ref. [14].

Figure 5

Structure functions $d{\sigma }_T/dt$, $d{\sigma }_L/dt$, $d{\sigma }_{TL}/dt$, and $d{\sigma }_{TT}/dt$ as a function of $t^{\prime }=t_{\min }-t$ for the neutron (blue) and the deuteron (red). The filled bands around the points show systematic uncertainties. The solid lines are theoretical calculations for the neutron from Ref. [14].

Figure 6

Magnitude of the nucleon helicity-flip $⟨H_T⟩$ (top) and nonflip $⟨{\overline{E}}_T⟩$ (bottom) transversity terms for $u$ (squares) and $d$ (circles) quarks assuming no relative phase between them. The boxes around the points represent the variation of the results when their relative phase varies between 0 and $\pi$. Bars show the quadratic sum of the statistical and systematic uncertainties of the data. Solid (dashed) lines are calculations from the Goloskokov-Kroll model [14] for $u$ ($d$) quark.