First Measurement of Chiral Dynamics in ${\pi }^{-}\gamma \to {\pi }^{-}{\pi }^{-}{\pi }^{+}$

The COMPASS Collaboration at CERN has investigated the ${\pi }^{-}\gamma \to {\pi }^{-}{\pi }^{-}{\pi }^{+}$ reaction at center-of-momentum energy below five pion masses, $\sqrt{s}<5m_{\pi }$, embedded in the Primakoff reaction of 190 GeV pions impinging on a lead target. Exchange of quasireal photons is selected by isolating the sharp Coulomb peak observed at smallest momentum transfers, $t^{\prime }<0.001{\mathrm{GeV}}^2/c^2$. Using partial-wave analysis techniques, the scattering intensity of Coulomb production described in terms of chiral dynamics and its dependence on the $3\pi$-invariant mass $m_{3\pi }=\sqrt{s}$ were extracted. The absolute cross section was determined in seven bins of $\sqrt{s}$ with an overall precision of 20%. At leading order, the result is found to be in good agreement with the prediction of chiral perturbation theory over the whole energy range investigated.

Figure 1

(a) Leading-order, i.e., tree-level ChPT diagrams for ${\pi }^{-}\gamma \to {\pi }^{-}{\pi }^{-}{\pi }^{+}$, embedded in the Primakoff reaction ${\pi }^{-}\mathrm{Pb}\to {\pi }^{-}{\pi }^{-}{\pi }^{+}\mathrm{Pb}$. (b) Dalitz plots corresponding to the leading-order ChPT cross section, normalized to the respective maximum of the distribution. The left plot is for $m_{3\pi }=0.475\mathrm{GeV}/c^2$, the right one for $0.642\mathrm{GeV}/c^2$, i.e., at the lower and upper ends of the investigated region. The quantities $m_{13}^2$ and $m_{23}^2$ are the squared masses of the ${\pi }^{-}{\pi }^{+}$ subsystems.

Figure 2

Invariant mass spectrum of the final-state $3\pi$ system observed in the Primakoff region ($t^{\prime }<0.001{\mathrm{GeV}}^2/c^2$), with the interaction point observed in the target region. The kaon decay into ${\pi }^{-}{\pi }^{-}{\pi }^{+}$ is seen as sharp peak at $m_K\approx 0.493\mathrm{GeV}$. The low-mass region of interest for this Letter is highlighted.

Figure 3

Momentum transfer distribution of events in the investigated low-mass region. The Primakoff region ($t^{\prime }<0.001{\mathrm{GeV}}^2/c^2$) is highlighted. In order to suppress the kaon contribution, $m_{3\pi }>0.51\mathrm{GeV}/c^2$ is required.

Figure 4

PWA intensities summed separately for the $M=0$ and $M=1$ components. Total uncertainties are shown. Fluctuations of the systematic uncertainties, as discussed along with Fig. 6, were smoothed in the range $0.5<m_{3\pi }/(\mathrm{GeV}/c^2)<1$, and the obtained uncertainties were added quadratically to the statistical ones.

Figure 5

PWA intensities for the investigated low-mass range. Each $t^{\prime }$ bin represents an independent fit to the data, yielding simultaneously the two values for the $M=0$ and the chiral intensity.

Figure 6

Cross section for ${\pi }^{-}\gamma \to {\pi }^{-}{\pi }^{-}{\pi }^{+}$ as a function of the total collision energy $\sqrt{s}=m_{3\pi }$. The error bars show only the statistical error. The evolution of the systematic uncertainty, as discussed in the text and smoothed over the bins, is indicated as a dashed line.