Observation of a $J^{\mathrm{PC}}=1^{-+}$ Exotic Resonance in Diffractive Dissociation of $190\mathrm{GeV}/c$ ${\pi }^{-}$ into ${\pi }^{-}{\pi }^{-}{\pi }^{+}$

The COMPASS experiment at the CERN SPS has studied the diffractive dissociation of negative pions into the ${\pi }^{-}{\pi }^{-}{\pi }^{+}$ final state using a $190\mathrm{GeV}/c$ pion beam hitting a lead target. A partial wave analysis has been performed on a sample of 420 000 events taken at values of the squared 4-momentum transfer $t^{\prime }$ between 0.1 and $1{\mathrm{GeV}}^2/c^2$. The well-known resonances $a_1(1260)$, $a_2(1320)$, and ${\pi }_2(1670)$ are clearly observed. In addition, the data show a significant natural-parity exchange production of a resonance with spin-exotic quantum numbers $J^{\mathrm{PC}}=1^{-+}$ at $1.66\mathrm{GeV}/c^2$ decaying to $\rho \pi$. The resonant nature of this wave is evident from the mass-dependent phase differences to the $J^{\mathrm{PC}}=2^{-+}$ and $1^{++}$ waves. From a mass-dependent fit a resonance mass of $(1660\pm {10}_{-64}^{+0})\mathrm{MeV}/c^2$ and a width of $(269\pm {21}_{-64}^{+42})\mathrm{MeV}/c^2$ are deduced, with an intensity of $(1.7\pm 0.2)\%$ of the total intensity.

Figure 1

Invariant mass of the $3\pi$ system for $0.1{\mathrm{GeV}}^2/c^2<t^{\prime }<1.0{\mathrm{GeV}}^2/c^2$ (histogram), and intensity of the background wave with a flat distribution in three-body phase space (triangles), obtained from a partial wave analysis in $40\mathrm{MeV}/c^2$ bins of the $3\pi$ mass and rescaled to the binning of the histogram. Both the invariant mass spectrum and the background distribution are not acceptance corrected.

Figure 2

Intensities of major waves $1^{++}{0}^{+}\rho \pi S$ (a), $2^{-+}{0}^{+}{f}_2\pi S$ (b), and $2^{++}{1}^{+}\rho \pi D$ (c), as well as the intensity of the exotic wave $1^{-+}{1}^{+}\rho \pi P$ (d), as determined in the fit in mass bins (data points with error bars). The lines represent the result of the mass-dependent fit (see text).

Figure 3

Phase differences of the exotic $1^{-+}{1}^{+}\rho \pi P$ wave to the $1^{++}{0}^{+}\rho \pi S$ (a) and the $2^{-+}{0}^{+}{f}_2\pi S$ (b) waves. The data points represent the result of the fit in mass bins; the lines are the result of the mass-dependent fit.