Precision Determination of the $d\pi \leftrightarrow NN$ Transition Strength at Threshold

An unusual but effective way to determine at threshold the $d\pi \leftrightarrow NN$ transition strength $\alpha$ is to exploit the hadronic ground-state broadening ${\Gamma }_{1s}$ in pionic deuterium, accessible by x-ray spectroscopy. The broadening is dominated by the true absorption channel $d{\pi }^{-}\to nn$, which is related to $s$-wave pion production $pp\to d{\pi }^{+}$ by charge symmetry and detailed balance. Using the exotic atom circumvents the problem of Coulomb corrections to the cross section as necessary in the production experiments. Our dedicated measurement finds ${\Gamma }_{1s}=({1171}_{-49}^{+23})\mathrm{meV}$ yielding $\alpha =({252}_{-11}^{+5})\mu \mathrm{b}$.

Figure 1

Threshold parameter $\alpha$. Points are shown in the same order as listed in Table .

Figure 2

Sum spectrum of the $\pi \mathrm{D}(3p\mathrm{\text{−}}1s)$ transition measured at 10 and 17.5 bar equivalent density in first order with a silicon (111) Bragg crystal having a bending radius of $R=2982.2\pm 0.3\mathrm{mm}$. The narrow structure inside the $\pi \mathrm{D}$ line represents the spectrometer response function.