Progress and opportunities in backward angle (u-channel) physics

Abstract

Backward angle (u-channel) scattering provides complementary information for studies of hadron spectroscopy and structure, but has been less comprehensively studied than the corresponding forward angle case. As a result, the physics of u-channel scattering poses a range of new experimental and theoretical opportunities and questions. We summarize recent progress in measuring and understanding high energy reactions with baryon charge exchange in the u-channel, as discussed in the first Backward angle (u-channel) Physics Workshop. In particular, we discuss backward angle measurements and their theoretical description via both hadronic models and the collinear factorization approach, and discuss planned future measurements of u-channel physics. Finally, we propose outstanding questions and challenges for u-channel physics.

Appendix A: Missing mass reconstruction technique

Fig. 27

Example reconstructed missing mass ($m_{miss}$) distribution for $ep\rightarrow e^{\prime } p^{\prime } X$ at $Q^2 = 2.45$ GeV$^2$ (blue points) from Hall C of JLab [1, 3]. The simulated distributions for $\rho$ (blue), $\omega$ (red) and $\pi \pi$ (green) are used for the reaction channel separation

The missing mass $m_{miss}$ for a meson X ($X = \pi _0$, $\omega$, etc.) production interaction $^1$H$(e, e^{\prime }p)X$:

$$\begin{aligned} e (p_e) + p\,(p_p) \rightarrow e\,(p_{e^{\prime }})+p (p_{p^\prime }) + X. \end{aligned}$$

(A.1)

is calculated as:

$$\begin{aligned} \begin{aligned} m_{miss}&\!=\! \big \{\left( E_{e} \!+\! m_{p} \!-\! E_{e'} \!-\! E_{p'}\right) ^{2} \!-\! \left( \mathbf {p}_{e} \!-\! \mathbf {p}_{e'} \!-\! \mathbf {p}_{p'}\right) ^{2} \big \} ^{1/2} \end{aligned} \end{aligned}$$

(A.2)

For instance, in the case of $\omega$ electroproduction, the $\omega$ events sit on a broad background, shown in reconstructed missing mass spectrum for $ep\rightarrow e^{\prime } p X$ in Fig. 27. The final state particle X could be: $\omega$, $\rho$ or non-resonant $\pi \pi$. Various quality control criteria were introduced to validate the background subtraction procedure, as described in Ref. [1].