Antiproton-proton annihilation into light neutral meson pairs within an effective meson theory

Antiproton-proton annihilation into light neutral mesons in the few GeV energy domain is investigated in view of a global description of the existing data and predictions for future work at the Antiproton Annihilation at Darmstadt (PANDA) experiment at the Facility for Antiproton and Ion Research (FAIR). An effective meson model earlier developed, with mesonic and baryonic degrees of freedom in $s, t$, and $u$ channels, is applied here to ${\pi }^0{\pi }^0$ production. Form factors with logarithmic $s$ and $t\left(u\right)$ dependencies are applied. A fair agreement with the existing angular distributions is obtained. Applying SU(3) symmetry, it is straightforward to recover the angular distributions for ${\pi }^0\eta$ and $\eta \eta$ production in the same energy range. A good agreement is generally obtained with all existing data.

Figure 1

Feynman diagrams for different exchanged particles for the reaction $\overline{p}+p\to {\pi }^0+{\pi }^0$.

Figure 2

$f_0$ and $f_2$ decay into a pion pair.

Figure 3

Energy dependence of the logarithmic form factors without (red, dashed line) and with (black, solid line) exponential correction.

Figure 4

Angular distribution for the reaction $\overline{p}p\to {\pi }^0{\pi }^0$ in CMS in the energy range 2.911 $\le \sqrt{s}\le$ 3.686 GeV. The data (open circles) are from Ref. [14]: $\sqrt{s}=2.911$ GeV (a); 2.950 GeV (b); 2.975 GeV (c); 2.979 GeV (d); 2.981 GeV (e); 2.985 GeV (f); 2.990 GeV (g); 2.994 GeV (h); 3.005 GeV (i); 3.050 GeV (j); 3.097 GeV (k); 3.524 GeV (l); 3.526 GeV (m); 3.556 GeV (n); 3.591 GeV (o); 3.595 GeV (p); 3.613 GeV (q); 3.616 GeV (r); 3.619 GeV (s); 3.621 GeV (t), 3.586 GeV (u). The calculation is the solid, red line.

Figure 5

Integrated cross section for the reaction $\overline{p}p\to {\pi }^0{\pi }^0$. The data are obtained by the integration of the partial differential cross section in the available range: $0<cos\theta <0.48$ up to $\sqrt{s}=3.2$ GeV, and $0<cos\theta <0.66$ above $\sqrt{s}=3.6$ GeV, Ref. [14]. The present calculation covering the range $0<cos\theta <0.48$ (blue dash-dotted line) and $0<cos\theta <0.66$ (red dashed line) is also shown. The integration in the whole angular range is shown as a black, solid line.

Figure 6

Parameter dependence of the cross section for the reaction $\overline{p}p\to {\pi }^0{\pi }^0$, integrated for $|cos\theta |\le$ 0.66. The calculation with the nominal parameter is shown (black solid line), together with the calculation corresponding to 10% decrease of the $f_0$ parameters (red dashed line) and to 10% decrease of the logarithmic form factor parameters (blue dash-dotted line).

Figure 7

Angular distribution for reaction $\overline{p}p\to {\pi }^0{\pi }^0$ at $\sqrt{s}$ = 4.274 GeV [14] with the different components. The parameters are listed in Table 3.

Figure 8

Angular distribution for $\overline{p}p\to \eta \eta$ in CMS in the energy range 2.911 $\le \sqrt{s}\le$ 3.617 GeV. The data (open circles) are from Ref. [14]: $\sqrt{s}=2.911$ GeV (a); 2.950 GeV (b); 2.975 GeV (c); 2.979 GeV (d); 2.981 GeV (e); 2.985 GeV (f); 2.990 GeV (g); 2.994 GeV (h); 3.005 GeV (i); 3.097 GeV (j); 3.526 GeV (k); 3.592 GeV (l); 3.617 GeV (m). The calculation is the solid, red line.

Figure 9

Same as Fig. 8, but for the reaction $\overline{p}p\to \eta {\pi }^0$.