Study of $e^+ e^- \to p \bar p$ via initial state radiation at BESIII

The Born cross section for the process $e^+ e^- \to p \bar p $ is measured using the initial state radiation technique with an undetected photon. This analysis is based on data sets corresponding to an integrated luminosity of 7.4 fb$^{-1}$, collected with the BESIII detector at the BEPCII collider at center of mass energies between 3.773 and 4.600 GeV. The Born cross section for the process $e^+ e^- \to p \bar p $ and the proton effective form factor are determined in the $p\bar p$ invariant mass range between 2.0 and 3.8 GeV/$c^2$ divided into 30 intervals. The proton form factor ratio ($|G_E|/|G_M|$) is measured in 3 intervals of the $p\bar p$ invariant mass between 2.0 and 3.0 GeV/$c^2$.

The Born cross section for the process e + e − → pp is measured using the initial state radiation technique with an undetected photon. This analysis is based on data sets corresponding to an integrated luminosity of 7.4 fb −1 , collected with the BESIII detector at the BEPCII collider at center of mass energies between 3.773 and 4.600 GeV. The Born cross section for the process e + e − → pp and the proton effective form factor are determined in the pp invariant mass range between 2.0 and 3.8 GeV/c 2 divided into 30 intervals. The proton form factor ratio (|GE|/|GM |) is measured in 3 intervals of the pp invariant mass between 2.0 and 3.0 GeV/c 2 . Electromagnetic form factors (FFs) are fundamental quantities that describe the internal structure of hadrons. The proton (spin 1/2) is characterized by the electric FF G E and the magnetic FF G M . They are experimentally accessible through the measurements of cross sections for elastic electron-proton scattering in the space-like region (momentum transfer squared q 2 < 0) and annihilation processes e + e − ↔ pp in the time-like region (q 2 > 0) [1,2]. At low momentum transfer, space-like FFs provide information on the distributions of the electric charges and magnetization within the proton. In the time-like region, electromagnetic FFs can be associated with the time evolution of these distributions [3]. The unpolarized cross section for elastic electron-proton scattering has been measured for decades with improved accuracy. However, the recent data on the elastic electron-proton scattering, based on the polarization transfer method [4,5], showed that the ratio µ p G E /G M (where µ p is the proton magnetic moment) decreases almost linearly with Q 2 = −q 2 . This result is in disagreement with the previous measurements of unpolarized elastic ep scattering [6].
In the time-like region, the proton FFs have been measured with the annihilation channels e + e − ↔ pp using the energy scan technique [7][8][9][10][11][12][13][14][15][16][17][18][19], in which the center of mass (c.m.) energy ( √ s) of the collider is varied systematically, and at each c.m. energy point a measurement of the associated cross section is carried out. The radiative return channel e + e − → ppγ, where γ is a hard photon emitted by initial state radiation (ISR), allows for a complementary approach to the energy scan technique in proton FF measurements. It has been used by the BaBar collaboration to measure the time-like proton FF ratio and the effective FF |G eff (q 2 )| (see Eq. (12)) in a continuous range of q 2 [20,21]. The BaBar data shows some oscillations in the measured |G eff (q 2 )|. The origin of these oscillations has recently been the subject of several theoretical studies [22,23], but has not yet been well understood. The precision of the proton FF measurements in the time-like region has been limited by the statistics collected at the e + e − and pp annihilation experiments.
In this paper we study the ISR process e + e − → ppγ to measure the Born cross section of the process e + e − → pp and to determine the proton FFs in the time-like region. We use data sets, corresponding to an integrated luminosity of 7.4 fb −1 , collected with the Beijing Spectrometer III (BESIII) [24] at the Beijing Electron-Positron Collider II (BEPCII) at c.m. energies between 3.773 and 4.600 GeV. We analyze the e + e − → ppγ events in which the ISR photon can not be detected because it is emitted at small polar angles, into the region not covered by the acceptance of the BESIII detector. The differential cross section of the reaction e + e − → ppγ as a function of the ISR polar angle, reaches its highest values at small angles relative to the direction of the electron (or positron) beam [25]. The measurement of the reaction e + e − → ppγ in this region benefits from the availability of a large number of signal events.
The cross section for the ISR process e + e − → ppγ represented by Fig. 1, can be written as [25]: where α is the electromagnetic coupling constant, E * γ is the energy of the ISR photon in the e + e − c.m. system. The momentum transfer q (q 2 = M 2 pp , M pp is the pp invariant mass) is the momentum carried by the exchanged virtual photon. The function W (s, x) [26] is the probability for the emission of a hard ISR photon with energy fraction x, and m e is the electron mass. In Eq. (1), integration over the proton momenta and the photon polar angle is performed. Equation 1 describes ISR processes at the lowest QED order. The Born cross section for the non radiative process σ pp (q 2 ) is given by: where M p is the proton mass and C is the Coulomb correction factor [27] which makes the cross section for the pp production non zero at threshold. The paper is organized as follows. The BESIII detector, the data and the Monte Carlo (MC) samples used in this analysis are described in Sec. II. The procedure to identify the signal and to estimate the number of remaining background events is explained in Sec. III and Sec. IV. In Sec. VI we present the results on the measurements of the Born cross section for the e + e − → pp channel and the proton effective FF. The measured values of the proton FF ratio and the branching fractions for the J/ψ, ψ(3686) to pp decays are reported in Sec. VII and in Sec. VIII, respectively. The conclusion section contains a summary and an outlook.

II. THE BESIII DETECTOR AND EVENT SAMPLES
BEPCII is a double ring e + e − collider running at c.m. energies between 2.0 and 4.6 GeV. It has a peak luminosity of 1.0 × 10 33 cm −2 s −1 at √ s = 3773 MeV. The BESIII detector is a general purpose spectrometer with an effective geometrical acceptance of 93% of 4π. It consists of a small cell, helium-based (60% He, 40% C 3 H 8 ) main drift chamber (MDC), a time-of-flight (TOF) system, a CsI(Tl) electromagnetic calorimeter (EMC) and a muon system (MUC). The MDC provides momentum measurement of charged particles with a resolution of 0.5% at 1 GeV/c in a 1 Tesla magnetic field. The energy loss measured by the MDC has a resolution better than 6%. The TOF is based on 5-cm-thick plastic scintillators with a time resolution of 80 ps in the barrel and 110 ps in the end caps. The EMC is used to measure the energies of photons and electrons. The EMC provides an energy resolution (for 1 GeV photons) of 2.5% in the barrel region and 5.0% in the end caps. The MUC system consists of resistive plate chambers. It is used to identify muons and provides a spatial resolution better than 2 cm. The data samples used in this analysis were collected at 7 c.m. energy points between 3.773 and 4.600 GeV. Table I summarizes the integrated luminosity collected at each c.m. energy point [28,29]. MC samples for signal and background channels are simulated using a geant4based [30] simulation software package BESIII BOOST (BESIII Object Oriented Simulation Tool) [31]. The MC samples are produced with large amounts of generated events to determine the signal efficiencies and to estimate the potential background contamination. The signal process e + e − → ppγ is generated with the phokhara event generator [32], which takes into account next-toleading order radiative corrections. The critical background channels e + e − → ppπ 0 (γ) and the two-photon process (e + e − → e + e − f + f − , where f can be leptons, or quarks which hadronize using jetset [33]) are simulated using the generator software package conexc [34] and the event generator bestwogam [35], respectively. The ISR background processes e + e − → µ + µ − γ, π + π − γ and K + K − γ are simulated with the phokhara event generator [36] up to the next-to-leading order of radiative corrections. The inclusive hadronic channels e + e − → qq (q = u, d, s) are studied with the kkmc event generator [37,38]. The e + e − → e + e − γ channel is simulated with the babayaga event generator [39]. The ISR processes e + e − → γJ/ψ, γψ(3686), γψ(3773) and γψ(4040) are generated with besevtgen [35] using the vectorisr model [26,40].

III. EVENT SELECTION
Charged tracks of polar angles | cos θ| < 0.93 are identified by the MDC. The distance between the interaction point (IP) and the point of closest approach for each charged track is required to be within 1 cm in the plane perpendicular to the beam direction and within ±10 cm along the beam direction. The energy loss in the MDC and the flight time measured by the TOF system are used to calculate the particle identification (PID) probabilities for the electron, muon, pion, kaon and proton hypotheses. The particle type of highest PID probability is assigned to the charged track. The ratio of the shower energy deposited in the EMC (E EMC ) to the reconstructed momentum (p rec ) of the positively charged track associated with the shower is required to be less than 0.5. The events with only two charged tracks, identified as proton and antiproton, are selected.
In this analysis, the ISR photon is not detected. The final event selection is based mainly on two variables, the missing momentum p miss and the missing mass squared M 2 miss recoiling against the pp system. The missing momentum is defined as: where k 1 ( k 2 ) and p 1 ( p 2 ) are the momentum vectors in the laboratory frame of the initial state electron (positron) and final state antiproton (proton), respectively. The angular distribution of the missing momentum is used to suppress the hadronic background, in particular the process e + e − → ppπ 0 . Figure 2 shows the distribution of the polar angle (θ miss ) of the missing momentum in the laboratory frame for the MC signal and e + e − → ppπ 0 background events. θ miss is required to be in the region: The missing mass squared is defined by: where K 1 (K 2 ) and P 1 (P 2 ) are the four-momenta of the initial state electron (positron) and final state antiproton (proton), respectively. Figure 3 shows the distributions of M 2 miss for the simulated signal and background events at √ s = 4.226 GeV. The events are required to have a M 2 miss in the interval: for the data samples collected at √ s > 4 GeV, and for the data sample collected at √ s = 3.773 GeV. This condition mainly suppresses the background from e + e − → e + e − γ, µ + µ − γ, ppπ 0 (γ), KKγ and π + π − γ channels. At √ s = 3.773 GeV, a narrower window of the M 2 miss interval is needed to reject the remaining background from the resonance (J/ψ, ψ(3686)) decays into the ppγ final state. The polar angles of the proton and the antiproton in the pp c.m. system are required to be within | cos θ pp p,p | < 0.75. Due to the conditions applied on the distributions of θ miss and M 2 miss (Eqs. (4), (6) and (7)), the efficiency of the signal in the region | cos θ pp p,p | > 0.75 is very small. The condition | cos θ pp p,p | < 0.75 is used to suppress the remaining background from the process e + e − → e + e − γ.
The distribution of M pp for the selected data candidates is shown in Fig. 4. The total number of events, from the data samples collected at the 7 c.m. energies, is around 9100. Selected events from J/ψ → pp and ψ(3686) → pp decays are clearly seen at M pp ∼ 3.1 and 3.7 GeV/c 2 , respectively.

IV. BACKGROUND ESTIMATION AND SUBTRACTION
The background events in the MC samples of e + e − → e + e − γ, µ + µ − γ, π + π − γ and KKγ are suppressed by the selection criteria described in Sec. III. The amount of generated events in each MC sample exceeds the number of expected events for these background channels according to their cross sections and luminosities, and they can consequently be safely neglected. The ISR channels e + e − → γR (R → ppγ), R = J/ψ, ψ(3686), ψ(3773), ψ(4040) are suppressed to below 0.5% of the total selected events and they can also be neglected. In the following the numbers of background events from e + e − → γR (R → pp), R = J/ψ, ψ(3686), e + e − → ppπ 0 and the two-photon channel are estimated and subtracted from the selected data events.  The selected events with M pp falling in the regions of J/ψ resonance are shown in Figs. 5 and 6 and those in ψ(3686) resonance in Fig. 7. The selected events for the different data samples are fitted using the sum of a Gaussian function (for resonance events) and a linear or exponential function (for signal and possible remaining background channels). The fit parameters are the number of resonance events, the number of non-resonance events, the constant of the linear/exponential function, the mean and the sigma of the Gaussian function. The numbers of resonance and non-resonance events are calculated for each data sample separately. The numbers of events for the J/ψ → pp and ψ(3686) → pp decays are listed in Table II.  The process e + e − → ppπ 0 (γ) is a critical background to the signal process since it contains the same detected charged particles, proton and antiproton, as the signal. To estimate the background from the process e + e − → ppπ 0 (γ), we use the difference of the θ miss distributions between signal and background events. The MC samples generated based on the measured angular distributions of the process e + e − → ppπ 0 [41,42] are used. Figure 8 shows the distributions of θ miss , the polar angle of the missing momentum, for data events and simulated signal and e + e − → ppπ 0 background events. The red (blue) area in Fig. 8 represents the signal (sideband) region. The number of data events in the sideband region (N 2 ) and the number of background events in the signal region The dashed green curve represents the exponential fit function and the solid blue curve represents the sum of the Gaussian (for resonance events) and the exponential (for signal (Fig. 1) and background events) functions.
(N bkg ) are related by: where N 1 is the number of data events in the signal region. N 1 and N 2 are determined from data after applying the event selection conditions except the θ miss requirement. β sig and β bkg are the N 2 /N 1 ratios from the MC signal and background events, respectively. ISR effects (e + e − → ppπ 0 γ) are simulated with the generator software package conexc and they are used to correct β bkg . The number of background events N ppπ 0 (γ) is deter- mined for each data sample separately. This background source constitutes 2.3% of the selected data events.

C. Background from two-photon channel
The number of background events from the two-photon channel N 2γ is estimated using the same method described in Sec. IV B. Figure 9 shows the two-dimensional distributions of M 2 miss versus M pp for the MC signal and two-photon events, and for the data events at √ s = 4.226 GeV. The region of large M 2 miss values (| p miss | < 0.2 GeV/c at √ s > 3.773 GeV and | p miss | < 0.25 GeV/c at √ s > 4 GeV) is chosen as the sideband region. The black lines in Fig. 9 show the borders of the signal region at √ s=4.226 GeV. The total number of background events from the two-photon channel constitutes 1.0% of the total selected data events. The remaining background events are in the M pp region below 3.0 GeV/c 2 .
The sum of the background events over the 7 c.m. energy points for the e + e − → ppπ 0 (γ) and two-photon channels in each M pp interval is given in Table III.

V. SIGNAL EFFICIENCY
The collected events at the 6 c.m. energies for √ s > 4 GeV are analyzed in M pp intervals between 2.0 and 3.8 GeV/c 2 . In the low M pp region (M pp < 2 GeV/c 2 ), the proton and antiproton are produced in a narrow cone around the vector opposite to the direction of the ISR photon. The signal events at low M pp region are suppressed due to the limited acceptance of the BESIII tracking system. The events collected at √ s = 3.773 GeV are analyzed in a smaller M pp range between 2.0 and 2.9 GeV/c 2 . Above 2.9 GeV/c 2 (3.8 GeV/c 2 ), the number of signal events from √ s = 3.773 GeV ( √ s > 4 GeV) is small and it is comparable to the number of remaining background events. The integrated signal efficiency at √ s = 3.773 GeV is equal to 17.8%. It decreases to 12.6% at the highest c.m. energy ( √ s = 4.600 GeV). The signal efficiency is determined in each M pp interval using the MC events of the process e + e − → ppγ generated up to the next-to-leading order radiative corrections. The parametrizations for G E and G M from Ref. [32] are used to calculate the efficiency of the signal. The M pp dependence of the signal efficiency is shown in Fig. 10 for √ s = 3.773, 4.226, and 4.600 GeV.

VI. CROSS SECTION FOR THE e + e − → pp CHANNEL AND THE PROTON EFFECTIVE FF
The Born cross section for the process e + e − → pp is calculated in each M pp interval i and for each data sample j (j = 1, 2, ..., 7) as follows: where N ij is the number of selected e + e − → ppγ events after background subtraction, ǫ ij is the detection efficiency, (1 + δ ij ) is the radiative correction factor and L ij is the ISR differential luminosity. The index j runs over the 7 c.m. energies. The detection efficiency ǫ ij is determined in each M pp interval using the MC events of the process e + e − → ppγ generated up to the next-to-leading order radiative corrections. The radiative correction factor (1 + δ ij ) describes the distortion of the e + e − → ppγ cross section due to contribution of higher order diagrams. It is calculated using the generated MC events of the signal and takes into account vacuum polarization and photon emissions from the initial and final states. The differential  luminosity L i is calculated as: where W (s j , x ij ) (Eq. (1)) is a function of the c.m. energy squared s j (j = 1, 2, ..., 7) and the energy fraction x ij . L j is the integrated luminosity collected at the c.m. energy √ s j (Table I) The Born cross sections σ ij are combined using the error weighted combination method [43]: where ∆σ i and ∆σ ij are the statistical errors of σ i and σ ij , respectively. The indices j and l run over the 7 c.m. energies.
The obtained values of the Born cross section for the process e + e − → pp are listed in Table IV. The quoted uncertainties are statistical and systematic. The systematic uncertainties of the measured cross section include uncertainties from tracking, PID, E EMC /p rec requirement, background estimation, M 2 miss and θ miss requirements, and luminosity determination. The contributions of the uncertainties from the tracking of the two charged particles (2.0%), PID (2.0%) and E EMC /p rec requirement (1.0%) are uniform over the considered M pp range [17]. To determine the uncertainty from the background estimation of the e + e − → ppπ 0 and two-photon channels, we calculate the number of selected events (before efficiency correction) with and without background subtraction. The difference between the two cases (1.0-7.3% for the e + e − → ppπ 0 channel and less than 5.4% for the two-photon channel) is taken as systematic uncertainty from the background estimation. We associate 0.5% systematic uncertainty to the possible background contribution from e + e − → γR (R → ppγ), R = J/ψ, ψ(3686).
To study the systematic uncertainties from the θ miss and M 2 miss requirements, the Born cross section for the process e + e − → pp is recalculated using reduced selection windows of about 20% compared to the original values. The uncertainties from the θ miss (M 2 miss ) requirements are found to be less than 6% (5%). The uncertainty in the measurements of the integrated luminosity at different c.m. energies is less than 1.0% [28,29]. In addition, we associate 0.5% systematic uncertainty to the radiator function W (s, x) [25] and 1.0% to the calculation of the III. The differential luminosity (Li), the numbers of background events (N bkg ) from e + e − → ppπ 0 and two-photon channel, and the numbers of selected events after background subtraction (N data ) at each Mpp interval, from the combined data collected at the 7 c.m. energies. The numbers of events in the Mpp intervals [3.0 -3.2] GeV/c 2 and [3.6 -3.8] GeV/c 2 are determined from the fits described in Sec. IV A and do not include the background events from the J/ψ → pp and ψ(3686) → pp decays. The uncertainties are statistical. final state radiation [32]. At low M pp region, the uncertainty of the Born cross section is dominated by the uncertainty in the measured FF ratio The values of the signal efficiency depend on the model of the proton FFs used in the event generator. The model error due to the uncertainty in the measured R is determined by varying R within its statistical uncertainty (see Sec. VII). It decreases from 8% at 2 GeV/c 2 to 3-4% in the M pp region below 3.0 GeV/c 2 . For M pp > 3 GeV/c 2 , where R is not measured, the model uncertainty (∼ 9%) is estimated as the difference between the detection efficiencies obtained with |G E | = 0 and |G M | = 0, divided by two. In each M pp interval, the systematic uncertainties listed above are added in quadrature.
Knowing the Born cross section for the process e + e − → pp, one can determine the effective FF of the proton by .
The obtained values of |G eff | are reported in Table IV for each M pp interval. The results on the Born cross section and the proton effective FF are shown in Fig. 11 and Fig. 12, respectively. The results are consistent with previous experiments. In particular, we reproduce the structures seen in the measurements of the proton effective FF by the BaBar collaboration [20,21]. Refs. [9,[44][45][46] provide several parametrizations of the time-like proton FFs. For example, the blue dashed curve in Fig. 12 represents the Quantum ChromoDynamics (QCD) inspired parameterization of |G eff | from Refs. [23,46]: where the parameters A QCD = 72 (GeV/c) 4 and Λ QCD = 0.52 (GeV/c) are obtained from a fit to the previous experimental data [47]. The data on the time-like effective FF are best reproduced by the function proposed in Ref. [45], where A = 7.7 and m 2 a = 14.8 (GeV/c) 2 are the fit parameters obtained previously in Ref. [47]. It is illustrated in Fig. 12 by the solid black curve.
The two functions (Eqs. (13) and (14)) reproduce the behavior of the effective FF over the long q 2 range. However, the measurements indicate some oscillating structures and therefore a more complex behavior than the smooth decrease predicted by QCD as a function of q 2 . These oscillations are clearly seen when the data are plotted as a function of the 3-momentum p of the relative motion of the final proton and antiproton [23]. Figure 13a shows the values of the proton effective FF as a function of p after subtraction of the smooth function described by Eq. (14). The black solid curve in Fig. 13a describes the periodic oscillations and has the form [23]: where A osc = 0.05, B osc = 0.7 (GeV/c) −1 , C osc = 5.5 (GeV/c) −1 and D osc = 0.0 are obtained previously from a fit to the BaBar data [47]. The origin of these oscillating structures can be attributed to an interference effect involving rescattering processes in the final state [23] or to independent resonant structures, as in Ref. [22]. The structure seen around M pp = 2.15 GeV/c 2 (Fig. 13b) can be for example attributed to the ρ(2150) resonance [48]. Other possible interpretations of these structures are not excluded here. The proton FF ratio R is determined by fitting the distribution of the helicity angle θ p for the selected data events. θ p is the angle between the proton momentum in the pp rest frame, and the momentum of the pp system in the e + e − c.m. system. The distribution of θ p is given by [49]: , DM1 [13], DM2 [14,15], BES [16], BESIII [17], CLEO [18], BaBar [20,21], CMD-3 [19] and ADONE73 [7].  [8,9], Fenice [10], PS170 [11], E760 [12], DM1 [13], DM2 [14,15], BES [16], BESIII [17], CLEO [18], BaBar [20,21] and ADONE73 [7]. The blue dashed curve shows the QCD inspired parametrisation [23,46] based on Eq. (13). The solid black curve shows the parametrisation (Eq. (14)) suggested in Ref. [45].
are studied in three M pp intervals between 2.0 and 3.0 GeV/c 2 . The background events are subtracted from the selected data events in each cos θ p interval. After background subtraction, the data events are corrected by the efficiency of the signal. The signal efficiency is determined from the MC simulations of the signal by di- viding the number of selected events by the number of generated events. The signal efficiency depends on the distributions of θ p , M pp , and √ s. The data collected at the 7 c.m. energies are combined after efficiency correction. The proton FF ratio is determined by fitting the cos θ p distributions (Fig. 14) using Eq. (16) and taking into account the relative normalization between H E and H M .
The obtained values of R are listed in Table V. The total uncertainty is dominated by the statistical uncertainties. The main contributions to the systematic uncertainty in the R measurements come from the fit range, background estimation, and from the M 2 miss and θ miss requirements. A comparison of R measured in this work and other experiments is shown in Fig. 15.

VIII.
BRANCHING FRACTIONS OF J/ψ, ψ(3686) → PP The measured numbers of resonance decays N R (R = J/ψ, ψ(3686)) (Sec. IV A) are used to determine the branching fractions, J/ψ → pp and ψ(3686) → pp, as where M R is the mass of the resonance, W (s, x R ) is the ISR function (Eq. (1)), and Γ R→e + e − is the electronic width of R. The radiative correction factor (1 + δ R ) is determined using the MC events of the signal process e + e − → ppγ. L is the integrated luminosity collected at the c.m. energy √ s (Table I). For the electronic widths of J/ψ and ψ(3686), the nominal values from Ref. [48] are used. MC samples for J/ψ → pp and ψ(3686) → pp are generated at the different c.m. energies between 3.773 and 4.6 GeV to determine the detection efficiency ǫ R . The MC events are produced with proton angular distributions described by the function 1 + C cos 2 θ with C = 0.595 ± 0.012 ± 0.015 for J/ψ [52] and C = 1.03±0.06±0.03 for ψ(3686) [53]. The branching fractions of J/ψ → pp and ψ(3686) → pp are calculated for each data sample individually. The systematic uncertainties of the measured branching fractions include uncertainties from tracking (2.0%), PID (2.0%), E EMC /p rec requirement (1.0%), M 2 miss and θ miss requirements, luminosity determination (0.8%), and radiator function W (s, x) (0.5%). The uncertainties from the θ miss (M 2 miss ) requirements are found to be 1.3% (1.0%) for ψ(3686) and negligible for J/ψ. The model error in the detection efficiency due to the uncertainty of the C value is negligible. The difference between the fit output using a linear and an exponential fit function for the non-peaking events is added to the systematic uncertainties (1.8% for ψ(3686) and negligible for J/ψ). The obtained average value of B(J/ψ → pp) = (2.08±0.04±0.07)×10 −3 , where the quoted uncertainties are statistical and systematic, respectively, is in good agreement with the world average value of (2.12 ± 0.03) × 10 −3 [48]. For B(ψ(3686) → pp), the obtained average value (3.01 ± 0.23 ± 0.12) × 10 −4 is consistent with the world average value of (2.88 ± 0.09) × 10 −4 [48] and with the latest measurement of BESIII B(ψ(3686) → pp) = (3.05 ± 0.02 ± 0.12) × 10 −4 [53] based on 1.07 × 10 8 ψ(3686) events [54].  FIG. 15. The values of the proton FF ratio R measured in this analysis and in previous experiments: BaBar [20,21], PS170 (LEAR) [11], BESIII [17], CMD-3 [19] and from Ref. [50]. The previous BESIII results (black crosses) were obtained using the energy scan technique where the precision on q 2 is given by the precise determination of √ s.

IX. SUMMARY
Based on data samples corresponding to an integrated luminosity of 7.4 fb −1 collected with the BESIII detector at c.m. energies between 3.773 and 4.600 GeV, the proton FFs have been measured using the ISR technique. In this work, the e + e − → ppγ events in which the ISR photons cannot be detected have been analyzed. The Born cross section of the e + e − → pp channel and the proton effective FF have been measured in 30 M pp intervals between 2.0 and 3.8 GeV/c 2 . The results are consistent with previous measurements and provide better precision in different M pp intervals. The total relative uncertainty of the Born cross section is between 8% and 41%. We have confirmed the structures seen in the measurements of the proton effective FF by the BaBar collaboration [20,21]. The proton angular distributions have been also analyzed to determine the proton FF ratio in 3 M pp intervals between 2.0 and 3.0 GeV/c 2 . The uncertainty on the measured proton FF ratio is dominated by the statistical uncertainty due to limited range of the proton angular distribution. The possibility to access the low M pp region below 2 GeV/c 2 with ISR technique and undetected photon will be investigated in the future using the data samples collected at c.m. energies below 3.773 GeV. In addition, the branching fractions of the J/ψ, ψ(3686) to pp decays are also measured. The results are in good agreements with the world average values. BESIII is an excellent laboratory for the measurement of baryon timelike FFs. Both ISR and scan methods can be performed, and the kinematical threshold for different baryon pair production is covered by the energy range of BEPCII. In 2015, BESIII performed high luminosity scan in 22 energy points between 2.0 and 3.08 GeV. Based on these data samples, more measurements of the nucleon electromagnetic FFs will be available in this kinematical region.