Measurement of the e+e− → nn̄ cross section with the SND detector at the VEPP-2000 collider

New measurement of the e+e− → nn̄ cross section based on the data set recorded in 2017 with the SND detector at the VEPP-2000 e+e− collider is presented. In the energy range from the threshold up to 2 GeV the cross section is almost flat. Its average value is 0.5 nb. The polar angle distribution indicates dominance of the magnetic form factor GM .


Introduction
Measurement of e + e − annihilation into nucleon-antinucleon pairs allows to study the nucleons internal structure described by the timelike electromagnetic form factors, electric G E and magnetic G M . The nn production cross section is given by the following equation: where α is the fine structure constant, s = 4E 2 b = E 2 , E b is the beam energy, E is the centerof-mass (c.m.) energy, β = 1 − 4m 2 n /s, m n is neutron mass, τ = s/4m 2 n , and θ is the neutron polar angle. The |G E /G M | ratio can be extracted using this expression from the measured cos θ distribution.
The e + e − → nn cross section was measured previously in the FENICE [1] and SND [2] experiments. The value of the cross section obtained in these experiments below 2 GeV is about 1 nb. In this work we present the results from the new SND [3] measurement at VEPP-2000 collider [4] . Data have been taken in 9 energy points in the e + e − c.m. energy range from the nucleon threshold up to 2 GeV with an integrated luminosity of 19 pb −1 .

Backgrounds and events selection
The nn events are very different from events of other e + e − annihilation processes. Below 2 GeV the produced neutron has low energy and therefore gives low energy deposition in the SND electromagnetic calorimeter (EMC). The antineutron annihilates inside the EMC and produces pions with the total energy up to 2m n . In this analysis, the position of the calorimeter crystal with maximal energy deposition is taken as an estimate of the position of antineutron annihilation and used to determine the antineutron production angles, θ and ϕ.
Using the described specifics of nn events to suppress the physical background from other e + e − annihilation processes, we select events containing no charged tracks originated from the interaction region with a large unbalanced total event momentum measured in the calorimeter (P EMC > 0.5E b ). To reject the beam-induced background the condition on the total energy deposition in the EMC is applied (E EMC > 1.05E b ).
Under these conditions, we have significant cosmic background. For its suppression, we reject events with cosmic track in EMC and use the veto from the SND muon system. In addition, the energy deposition in the third layer of the calorimeter should be not large As a result of all applied conditions, we manage to make physical background negligibly small and reduce the beam background to the level of ∼ 10% of the nn signal. The rate of residual cosmic background is about 5 events/hour.

Detection efficiency
The detection efficiency ε is calculated using Monte Carlo simulation. The simulation includes emission of an additional photon by initial electron and positron and takes into account c.m. energy spread, which is about 1 MeV. The distribution over cos θ in Eq. (1) is taken to be uniform in the simulation. We also take into account spurious photons and charged tracks generated by beam background. They are simulated by using special background events recorded during data taking with a random trigger. These events are superimposed on simulated nn events.
The detection efficiency as a function of the c.m. energy is shown in Fig. 1. It varies from 13% to 18%. A drop in the efficiency close to the threshold is due to the radiative corrections and the rise of the antineutron annihilation rate in the central part of the SND detector and subsequent suppression of such events by our selection criteria. A slow decrease of the efficiency above 1.9 GeV is explained by the increase of the antineutron annihilation length in the EMC with the energy increase.

Determination of the number of nn events
The most of selected data events originate from the two sources, e + e − → nn signal and cosmic background, in approximately equal amounts. To separate signal and background, we analyze the distribution of the event trigger time with respect to the beam collision time. The data time distribution for the energy points from the range E b = 940.3 − 942.0 MeV is shown in Fig. 2. It consists of the uniform cosmic distribution and a peaked distribution, which contains signal nn events with a small contamination of beam background events. The latter is shown by the filled histogram. The vertical line in Fig. 2 indicates the position of zero delay time between the trigger and the beam collision. This position and the shape of the background distribution are determined using e + e − → γγ events. The effective cross section for the beam background events is determined using data recorded below the nn threshold. The special study shows that the number of beam background events is approximately proportional to the integrated luminosity.
One can see from the  The recoiled neutron can be also observed in EMC in the direction opposite to the antineutron direction as a photon or several photons. We construct the distribution of the angle between the photon direction and the expected neutron direction ∆θ n for photons with energy greater than 20 MeV. The ∆θ n distribution for the energy range E b = 970 − 1000 MeV is shown in Fig. 3. The peak in the distribution near zero is clearly seen. The data and simulated ∆θ n distributions are in good agreement. The efficiency of the recoiled neutron detection is about 30%.

The e + e − → nn cross section
The Born cross section σ 0 for the process e + e − → nn is related to the experimental data by the following expression: where 1+δ is the radiative correction factor (Fig. 4), calculated based on work [5], taking into account beam energy spread, N, ε, and L are the number of nn events, detection efficiency and luminosity in each energy point. The obtained Born cross section σ 0 is presented in Fig. 5 in comparison with the measurements by FENICE [1] and SND [2]. In average, σ 0 is about 0.5 nb, what is significantly lower than both previous measurements. In our previous work [2], the detection efficiency, and beam and physical background were not properly evaluated.
In Fig. 6 the data cosθ distribution for the energy range E b = 980 − 1000 MeV is shown. This distribution is fitted by the angular function from Eq. (1) with three fixed |G E /G M | values. The four histogram bins in Fig. 6 at cosθ = ±0.65, ±0.75, the most sensitive to |G E /G M |,   Figure 5. The e + e − → nn cross section measured in this work compared with the previous measurements [1,2]. The vertical line shows the nn threshold. are used in the fit. We obtained χ 2 /ND=3.9/3 for |G E |=0, χ 2 /ND=9.5/3 for the uniform cosθ distribution and χ 2 /ND=19.5/3 for |G M |=0, where ND=3 is the number of degrees of freedom. We conclude that the data strongly prefer dominant contribution of the |G M | term. The hypothesis of |G M |=0 is excluded at the level of 3.5σ.