Abashian-Booth-Crowe Effect in Basic Double-Pionic Fusion: A New Resonance?

We report on an exclusive and kinematically complete high-statistics measurement of the basic double-pionic fusion reaction $pn\to d{\pi }^0{\pi }^0$ over the full energy region of the ABC effect, a pronounced low-mass enhancement in the $\pi \pi$-invariant mass spectrum. The measurements, which cover also the transition region to the conventional $t$-channel $\Delta \Delta$ process, were performed with the upgraded WASA detector setup at COSY. The data reveal the Abashian-Booth-Crowe effect to be uniquely correlated with a Lorentzian energy dependence in the integral cross section. The observables are consistent with a narrow resonance with $m=2.37\mathrm{GeV}$, $\Gamma \approx 70\mathrm{MeV}$ and $I(J^P)=0(3^{+})$ in both $pn$ and $\Delta \Delta$ systems. Necessary further tests of the resonance interpretation are discussed.

Figure 1

Distribution of the spectator proton momenta in the $pd\to d{\pi }^0{\pi }^0+p_{\mathrm{spectator}}$ reaction. Data are given by solid dots. The dashed line shows the expected distribution for the quasifree process based on the CD Bonn potential [19] deuteron wave function. For comparison the dotted line gives the pure phase-space distribution as expected for a coherent reaction process. It extends up to momenta of $1.5\mathrm{GeV}/c$ and peaks around $0.7\mathrm{GeV}/c$. For the data analysis only events with $p_{\mathrm{spectator}}<0.16\mathrm{GeV}/c$ (vertical line) have been used.

Figure 2

Total cross sections obtained from this experiment on $pd\to d{\pi }^0{\pi }^0+p_{\mathrm{spectator}}$ for the beam energies $T_p=1.0\mathrm{GeV}$ (triangles), 1.2 GeV (dots), and 1.4 GeV (squares) normalized independently. Shown are the total cross section data after acceptance, efficiency and Fermi motion corrections. The hatched area indicates systematic uncertainties. The drawn lines represent the expected cross sections for the Roper excitation process (dotted) and the $t$-channel $\Delta \Delta$ contribution (dashed) as well as a calculation for a $s$-channel resonance with $m=2.37\mathrm{GeV}$ and $\Gamma =68\mathrm{MeV}$ (solid).

Figure 3

Energy dependence of the cross section as a function of the ${\pi }^0{\pi }^0$ invariant mass $M_{{\pi }^0{\pi }^0}$ shown by a 3D plot of the cross section versus $M_{{\pi }^0{\pi }^0}$ and $\sqrt{s}$.

Figure 4

Top: Dalitz plots of $M_{d{\pi }^0}^2$ versus $M_{{\pi }^0{\pi }^0}^2$ at $\sqrt{s}=2.38\mathrm{GeV}$ (peak cross section) (left) and at $\sqrt{s}=2.5\mathrm{GeV}$ (right). Bottom: Dalitz plot projections $M_{d{\pi }^0}^2$ (left) and $M_{{\pi }^0{\pi }^0}^2$ (right) axes at $\sqrt{s}=2.38\mathrm{GeV}$. The curves denote calculations for a $s$-channel resonance decaying into $\Delta \Delta$ with $J^P=3^{+}$ with (solid) and without (dash-dotted) form factor as well as for $J^P=1^{+}$ (dashed). Hatched and shaded areas represent systematic uncertainties and phase-space distributions, respectively.

Figure 5

Same as Fig. 4, but for angular distributions at the peak cross section ($\sqrt{s}=2.38\mathrm{GeV}$). Top: $\Delta$ (left) and deuteron (right) c.m.s. distributions, bottom: pion distribution in c.m.s. (left) and Jackson frame (right).