Observation of a Fine Structure in $e^+e^- \to$ hadrons Production at the Nucleon-antinucleon Threshold

A study of hadron production at the nucleon-antinucleon threshold has been performed with the CMD-3 detector at the VEPP-2000 $e^+e^-$ collider. A very fast rise with about 1 MeV width has been observed in the $e^+e^- \to p\bar p$ cross section. A sharp drop in the $e^+e^- \to 3(\pi^+\pi^-)$ cross section has been confirmed and found to have a less than 2 MeV width, in agreement with the observed fast rise of the $e^+e^- \to p\bar p$ cross section. For the first time a similar sharp drop is demonstrated in the $e^+e^- \to K^+K^-\pi^+\pi^-$ cross section. The behavior of the $e^+e^- \to 3(\pi^+\pi^-),~ K^+K^-\pi^+\pi^-$ cross sections cannot be explained by an interference of any resonance amplitude with continuum, therefore this phenomenon cannot be due to a narrow near-threshold resonance. No such structure has been observed in the $e^+e^- \to 2(\pi^+\pi^-)$ cross section.


INTRODUCTION
Production of six pions in e + e − annihilation, studied at DM2 [1], showed a "dip" in the cross section at about 1.9 GeV, confirmed later by the FOCUS Collaboration in photoproduction [2,3], and with a much larger effective integrated luminosity at BaBar [4] using initial-state radiation (ISR). Even earlier, a narrow structure near the proton-antiproton threshold has been also observed in the total cross section of e + e − annihilation into hadrons in the FENICE experiment [5]. The measurement of the CMD-3 Collaboration [6] confirmed these observations and demonstrated that the drop in the e + e − → 3(π + π − ) cross section occurred in the narrow energy range of less than 10 MeV width. The origin of the "dip" remains unclear, but one of the explanations suggests a presence of the below-threshold proton-antiproton (pp) resonance [7].
Alternatively, in Ref. [8,9] the "dip" is due to the strong interaction in virtual nucleon-antinucleon (NN ) production, and is related to fast rise of the e + e − → NN cross section and NN annihilation to hadrons. This hypothesis is supported by the fast increase of the pp [10,11] and nn [12] form factors near threshold, and explains a similar drop in the η (958)π + π − spectrum, observed by the BES-III Collaboration [13]. The authors of Ref. [8] consider the two-step process e + e − → NN → multipions and evaluate the total reaction amplitude for various intermediate mechanisms of the e + e − → 5π, 6π reactions.
In Ref. [9] the authors go even further taking into account the proton-neutron mass difference andpp Coulomb interaction.
However, mass-energy resolution of the previous experiments does not allow to study a fine structure of the "dip" or the rise of the e + e − → NN cross section. In this paper we present the analysis of the data sample based on 50 pb −1 of the integrated luminosity collected with the CMD-3 detector [14] in the 1.5-2.0 GeV center-ofmass energy (E c.m. ) range. These data were collected in the energy scan at 29 c.m. energy points, performed at arXiv:1808.00145v2 [hep-ex] 2 Aug 2018 the VEPP-2000 collider with the upgraded injection complex [15]. The scan of the NN -threshold energy range was performed with a fine step, corresponding to the c.m. energy spread. The beam energy and energy spread have been monitored by the back-scattering-laser-light system [16]. During data taking the E c.m. stability was at the level of 0.1 MeV at each energy point, while the energy spread, σ Ec.m. , was 1.2 MeV at the NN threshold.
The luminosity was measured using events of Bhabha scattering at large angles [17]. The analysis of the e + e − → 3(π + π − ) process was described in detail in Ref. [6]. and that with one missing track to 17822 (5069) events.
The cross section obtained from the new data is shown in Fig. 1 by squares, while the BaBar [4] and previous CMD-3 [6] data are shown by open and closed circles, respectively. Our previous result is confirmed with better statistical accuracy, while a systematic uncertainty is estimated at the same 6% level. The "dip" at the NN threshold is also confirmed and is studied in more detail (see below). The analysis of the e + e − → K + K − π + π − process was described in detail in Ref. [18]. The "dip" at the NN threshold is observed for the first time in this channel, and is studied in more detail below.
The analysis procedure is described in our previous publication [11]. At the energies near threshold, Ec.m.

,
where σ fγ (E c.m. ) is a convolution of the Born cross section with the radiator function F(E c.m. , E γ ) [20]: where E γ is the radiative photon energy, and E max γ is a maximum allowed photon energy for the reaction.
For a demonstration of very fast change of the cross section, σ Born (E c.m. ) is described with an exponentially saturated function, where E thr (E c.m. > E thr ) and σ thr are the energy threshold and a variation scale of the Born cross section change, respectively. Parameters A, B are the cross section values below and above the pp threshold.  The results of the fit are summarized in Table I, and demonstrate that the observed behavior of the cross sections has similar origin, and the "dip" in the hadron cross section can be interpreted as due to opening of the direct production of the NN channel. Unfortunately, the accelerator-induced energy spread and relatively low statistical accuracy do not allow us to directly observe a possible structure of this rise (drop) due to the protonneutron interaction, which could be expected in the studied reactions.
In a recently published paper [9], the authors use the optical potential to make a prediction of the pp and nn cross section behavior at very small energies above the production thresholds. Figure 4 for the e + e − → pp VI. THE e + e − → 2(π + π − ) CROSS SECTION AT THE NN THRESHOLD As suggested in Ref. [9], the total hadronic cross sec- To test that, we analyze data at the NN threshold selecting events for the reaction e + e − → 2(π + π − ) according to the procedure described in Ref. [21], and show the obtained cross section in Fig. 5 together with the most precise measurement by BaBar [22]. No structure exceeding the level of 0.1 nb is observed at the NN threshold in both measurements. According to Ref. [23], the pp annihilation probability (with isospin one) to four charged pions is 14.6%, while for six charged pions it is about 6%.
If a cross section drop in the hadronic channel is related to virtual NN annihilation [9], for four-pion production one could expect an about 0.5-0.8 nb drop in the cross section, which is not supported by our data. Note that according to Ref. [23] the probability of NN annihilation to the K + K − π + π − final state is very low.