Wave-like amplification of near-threshold two-particle reactions: from muon-catalyzed fusion to $Λ\barΛ$ production at $e^-e^+$ annihilation

Abstract

A simple model is proposed to explain the recently found wave-like enhancement of the $Λ\barΛ$ pair production near the threshold at the $e^-e^+$ annihilation, which allows extracting parameters of the $Λ\barΛ$ interaction and the $Λ$-hyperon rms-radius from the oscillatory nature of the measured cross section. In particular, it predicts a single bound state of $Λ\barΛ$ with a binding energy of $\varepsilon_{Λ\barΛ}=(36\pm5)$MeV. The model is a generalization of the formulas obtained in our earlier work [1] to explain the effect of wave-like amplification found in it near the threshold of fusion reactions screened by a muon or electron. The analysis allows us to conclude that the effect of wave-like amplification is an integral feature of any two-particle near-threshold reaction. In this regard, it seems promising to investigate, within the framework of our model, the oscillatory nature of the electromagnetic form factors of hyperons and nucleons extracted in experiments on $e^- e^+$ annihilation. A natural further development of the model could be its generalization to processes of producing various hadron pairs in $e^-e^+$ annihilation.

Figures (3)

• Figure 1: Dependence of the function $\mid f_0(E)\mid^{-2}$ (a), the s-wave elastic scattering cross section $\sigma_0^{(el)}(E)$ (b) and the corresponding scattering phase shift $\delta_0(E)$ (c) on the energy $E>0$ for a spherically symmetric potential wells $\hbar=M=V_0=1$. The dashed curves correspond to a potential well in which there are no bound states ($R_0=1, \nu=0$). In this case, the maxima of the crests of the function $\mid f_0(E)\mid^{-2}$ closest to zero and the next in energy are located at the points $E_0=0.23$ and $E_1=10.1$, respectively. When the well expands to $R_0=2.5$, a level with energy $\varepsilon_{\nu=1} =-0.540$ appears in it, and the positions of the first three maxima of the function $\mid f_0(E)\mid^{-2}$ closest to zero are at the points $E_1=0.78, E_2=3.93$ and $E_3=8.66$. This case is represented by solid curves.
• Figure 2: Points $\bar{\sigma}_0(E)v$ recalculated by formula (20) from the experimental cross sections $\sigma_0^{(exp)}(E)$ of reaction (13) [11], and the function $\mid f_0(E)\mid^{-2}$ calculated by formula (8) for a potential well with $V_0=58$ MeV and $R=3.1$ fm. The values $\bar{\sigma}_0(E)v$ are given in units $A_0=6.5\times 10^{-24}$cm$^3$/sec.
• Figure 3: Experimental cross sections $\sigma_0^{(exp)}(E)$ of annihilation of $e^-e^+$ into a pair $\Lambda\bar{\Lambda}$ (13) as a function of the $\Lambda\bar{\Lambda}$ kinetic energy together with theoretical curves $\sigma_0(E)$ for these cross sections calculated by formulas (20,16,8) for $\Delta=1.7$ GeV, $A_0=6.5\times 10^{-24}$ cm$^3$/sec, $V_0=58$ MeV,$R_0=3.1$ fm (solid curve); $\Delta=1.8$ GeV, $A_0=2.6\times 10^{-24}$ cm$^3$/sec, $V_0=50$ MeV, $R_0=3.2$ fm (dashed curve) and $\Delta=1.6$ GeV, $A_0=1.5\times 10^{-23}$cm$^3$/sec, $V_0=67$ MeV, $R_0=3.0$ fm (doted curve). The experimental points $\sigma_0^{(exp)}(E)\pm\Delta \sigma(E)$ are taken from [11] (Table 1).