Measurement of the e+e- -->p anti-p cross section in the energy range from 3.0 to 6.5 GeV

The e+ e- -->p anti-p cross section and the proton magnetic form factor have been measured in the center-of-mass energy range from 3.0 to 6.5 GeV using the initial-state-radiation technique with an undetected photon. This is the first measurement of the form factor at energies higher than 4.5 GeV. The analysis is based on 469 fb-1 of integrated luminosity collected with the BABAR detector at the PEP-II collider at e+e- center-of-mass energies near 10.6 GeV. The branching fractions for the decays J/psi -->p anti-p and psi(2S) -->p anti-p have also been measured.


INTRODUCTION
In this paper we analyze the initial-state-radiation (ISR) process e + e − → ppγ represented by Fig. 1. This analysis is a continuation of our previous studies [1,2], where the ISR technique was used to measure the cross section of the nonradiative process e + e − → pp over the center-of-mass (c.m.) energy range from pp threshold, 2m p c 2 = 1.88 GeV, up to 4.5 GeV. In Refs. [1,2] it is required that the ISR photon be detected (large-angle ISR). In this paper, we analyze events in which the ISR photon is emitted along the e + e − collision axis (smallangle ISR) and is therefore not detected. This allows us to increase the detection efficiency for ISR events with pp invariant mass above 3.2 GeV/c 2 , to select ppγ events with lower background, and, therefore, to extend the en- * Now at the University of Tabuk ergy range for measurement of the e + e − → pp cross section. A discussion of the difference between the largeand small-angle ISR techniques is given in Ref. [3]. The Born cross section for the ISR process integrated over the nucleon momenta and the photon polar angle is given by where M pp is the pp invariant mass, s is the e + e − c.m. energy squared, x ≡ E * γ / √ s = 1−M 2 pp /s, and E * γ is the ISR photon energy in the e + e − c.m. frame 1 . The function [3] W (s, x) = α πx (ln s m 2 e − 1)(2 − 2x + x 2 ) (2) specifies the probability of ISR photon emission, where α is the fine structure constant and m e is the electron mass. Equations (1) and (2) describe ISR processes at lowest QED order. To calculate the function W (x) more precisely, taking into account higher-order diagrams involving loops and extra photon emission, we make use of the analytic techniques described in Refs. [4][5][6] and the Monte Carlo (MC) generator of ISR events, Phokhara [7]. The cross section for e + e − → pp is given by is the Coulomb correction factor [8], and y = πα(1 + β 2 )/β. The Coulomb factor makes the cross section nonzero at threshold. The cross section depends on the magnetic (G M ) and electric (G E ) form factors. At large pp invariant masses the second term in Eq. (3) is suppressed as 2m 2 p /M 2 pp , and therefore the measured total cross section is not very sensitive to the value of the electric form factor. The value of the magnetic form factor can be extracted from the measured cross section with relatively small model uncertainty using, for example, the assumption that |G M | = |G E | [9][10][11].
The existing experimental data on |G M (M pp )| at high pp invariant masses were obtained in e + e − [2,[9][10][11] and pp annihilation [12,13]. At energies higher than 3 GeV the value of the magnetic form factor decreases rapidly with increasing energy. The energy dependence measured in Refs. [2,10,12,13] agrees with the dependence α 2 s (M 2 pp )/M 4 pp predicted by QCD for the asymptotic proton form factor [14]. However, the two precision measurements of Ref. [11] based on CLEO data indicate that the decrease of the form factor at energies near 4 GeV is somewhat slower.
In this work we improve the accuracy of our measurements of the e + e − → pp cross section and of the proton magnetic form factor for pp invariant masses greater than 3 GeV/c 2 , and extend the range of measurement up to 6.5 GeV/c 2 .

II.
THE BABAR DETECTOR, DATA AND SIMULATED SAMPLES We analyse a data sample corresponding to an integrated luminosity of 469 fb −1 [15] recorded with the 1 Throughout this paper, the asterisk denotes quantities in the e + e − c.m. frame; all other variables are given in the laboratory frame.
Charged-particle tracking is provided by a five-layer silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH), operating in the 1.5 T magnetic field of a superconducting solenoid. The transverse momentum resolution is 0.47% at 1 GeV/c. The position and energy of a photon-produced cluster are measured with a CsI(Tl) electromagnetic calorimeter. Charged-particle identification (PID) is provided by specific ionization measurements in the SVT and DCH, and by an internally reflecting ring-imaging Cherenkov detector. Muons are identified in the solenoid's instrumented flux return.
The events of the process under study and the background processes e + e − → π + π − γ, K + K − γ, and µ + µ − γ are simulated with the Phokhara [7] event generator, which takes into account next-to-leading-order radiative corrections. To estimate the model uncertainty of our measurement, the simulation for the signal process is performed under two form-factor assumptions, namely |G M | = |G E | and |G E | = 0. To obtain realistic estimates of pion and kaon backgrounds, the experimental values of the pion and kaon electromagnetic form factors measured by the CLEO Collaboration at √ s = 3.67 GeV [10] are used in the event generator. The invariant-mass dependence of the form factors is assumed to be 1/m 2 , according to the QCD prediction for the asymptotic behavior of the form factors [17]. The e + e − → e + e − γ process is simulated with the BHWIDE [18] event generator. Background from the two-photon process e + e − → e + e − pp is simulated with the GamGam event generator [19]. In addition, possible background contributions from e + e − → qq, where q represents a u, d or s quark, are simulated with the JETSET [20] event generator. Since JETSET also generates ISR events, it can be used to study background from ISR processes with extra π 0 's, such as e + e − → ppπ 0 γ, ppπ 0 π 0 γ, etc. The most important non-ISR background process, e + e − → ppπ 0 , is simulated separately [1].
The detector response is simulated using the Geant4 [21] package. The simulation takes into account the variations in the detector and beam-background conditions over the running period of the experiment.

III. EVENT SELECTION
We select events with two charged-particle tracks with opposite charge originating from the interaction region. Each track must have transverse momentum greater than 0.1 GeV/c, be in the polar angle range 25.8 • < θ < 137.5 • , and be identified as a proton or antiproton. The pair of proton and antiproton candidates is fit to a common vertex with a beam-spot constraint, and the χ 2 probability for this fit is required to exceed 0.1%. The final event selection is based on two variables: the pp transverse momentum (p T ) and the missing-masssquared (M 2 miss ) recoiling against the pp system. The p T distribution for simulated e + e − → ppγ events is shown in Fig. 2. The peak near zero corresponds to ISR photons emitted along the collision axis, while the long tail is due to photons emitted at large angles. We apply the condition p T < 0.15 GeV/c, which removes large-angle ISR events, and strongly suppresses background from the process e + e − → ppπ 0 and from ISR processes with extra π 0 's. The process e + e − → ppπ 0 was the dominant background source at large invariant masses in our previous studies of the e + e − → ppγ process with large-angle ISR [1,2].
In the e + e − c.m. frame protons with low pp invariant masses are produced in a narrow cone around the vector opposite to the ISR photon direction. Due to limited detector acceptance, the low-mass region cannot be studied with small-angle ISR. A pp pair with p T < 0.15 GeV/c is detected in BABAR when its invariant mass is larger than 3.0 (4.5) GeV/c 2 for an ISR photon emitted along the electron (positron) beam direction. The corresponding average proton or antiproton momentum in the laboratory frame is about 2 (5) GeV/c. The difference between the two photon directions arises from the energy asymmetry of the e + e − collisions at PEP-II. Since particle misidentification probability strongly increases at large momentum, we reject events with the ISR photon emitted along the positron beam. This condition decreases the detection efficiency by about 20% for signal events with invariant masses above 5 GeV/c 2 .
The missing-mass-squared distribution for simulated e + e − → ppγ events is shown in Fig. 3. We select events with |M 2 miss | < 1 GeV 2 /c 4 . This condition suppresses background from two-photon and ISR events, which have large positive M 2 miss , and background from e + e − → e + e − γ, µ + µ − γ events, which have negative M 2 miss . Sideband regions in M 2 miss and in p T for ISR background are used to estimate remaining background contributions from these sources.
The pp invariant-mass spectrum for the selected data candidates is shown in Fig. 4. The total number of selected events is 845. About 80% of selected events originate from J/ψ → pp and ψ(2S) → pp decays. We do not observe events with invariant mass above 6 GeV/c 2 .

IV. BACKGROUND ESTIMATION AND SUBTRACTION
The processes e + e − → π + π − γ, K + K − γ, µ + µ − γ, and e + e − γ in which the charged particles are misidentified as protons, are potential sources of background in the sample of selected data events. In addition, the two-photon process e + e − → e + e − pp, and processes with protons and neutral particles in the final state, such as e + e − → ppπ 0 and e + e − → ppπ 0 γ, may yield background contributions.
In Ref. [2] it was shown that the BABAR MC simulation reproduces reasonably well the probability for a pion or a kaon to be identified as a proton. Consequently, the simulation is used to estimate the e + e − → π + π − γ and e + e − → K + K − γ background contributions in the present analysis. No events satisfying the selection criteria for ppγ are observed in the π + π − γ and K + K − γ MC samples. Since these MC samples exceed those expected for pion and kaon events in data by about an order of magnitude, we conclude that these background sources can be neglected.
To estimate possible electron and muon background a method based on the difference in the M 2 miss distributions for signal and background events is used. For e + e − → µ + µ − γ events the ratio of the number of events with |M 2 miss | < 1 GeV 2 /c 4 to the number with M 2 miss < −1 GeV 2 /c 4 varies from 0.03 to about 0.1 in the M pp range of interest. Smaller values are expected for e + e − → e + e − γ events. In data we observe 15 events with M 2 miss < −1 GeV 2 /c 4 , of which 6 events are expected to originate from signal (of these, 5 are from J/ψ → pp and ψ(2S) → pp decays). From the ratio values given above, we estimate that muon and electron background in our selected event sample does not exceed 1 event. The estimated background contributions for different invariantmass intervals are listed in Table I. B. Two-photon background Figure 5 shows the M 2 miss distribution for data events selected using all the criteria described in Sec. III except |M 2 miss | < 1 GeV 2 /c 4 . Events with large recoil mass arise from the two-photon process e + e − → e + e − γ * γ * → e + e − pp. The two-photon background in the region |M 2 miss | < 1 GeV 2 /c 4 is estimated from the number of data events with M 2 miss > d using the scale factor R γγ = N γγ (|M 2 miss | < 1)/N γγ (M 2 miss > d) obtained from the e + e − → e + e − pp simulation. Since the M 2 miss distribution for two-photon events changes with pp invariant mass, the parameter d is changed from 40 GeV 2 /c 4 for the invariant-mass interval 3.0-3.2 GeV/c 2 I: The number of selected ppγ candidates (N data ) and the estimated numbers of background events from the processes e + e − → µ + µ − γ and e + e − → e + e − γ (N ℓℓγ ), e + e − → e + e − pp (N2γ ), and the ISR processes with extra neutral particle(s), such as e + e − → ppπ 0 γ, pp2π 0 γ (N ISR bkg ). In the invariant-mass intervals 3.0-3.2 GeV/c 2 and 3.6-3.8 GeV/c 2 the contribution of the J/ψ → pp and ψ(2S) → pp decays are subtracted (see Sec. VI), with related statistical uncertainties reported. to 15 GeV 2 /c 4 for the interval 5.5-6.5 GeV/c 2 . To determine a realistic value of the scale factor, the simulated events are reweighted according to the proton angular distribution observed in data. The value of the scale factor is found to increase from 5 × 10 −4 in the 3.0-3.2 GeV/c 2 interval to 2 × 10 −2 in the 5.5-6.5 GeV/c 2 interval. Fortunately, the number of observed two-photon events decreases significantly over this same range. The estimated number of two-photon background events for each invariant-mass interval is listed in Table I. The background is found to be small, at the level of 1%.

C. ISR background
To estimate background from ISR processes with at least one extra neutral particle, such as e + e − → ppπ 0 γ, e + e − → ppηγ, e + e − → ppπ 0 π 0 γ, etc., we use differences in the p T and M 2 miss distributions for signal and background events. Figure 6 shows the two-dimensional distributions of M 2 miss versus p T for data events with M pp > 3.2 GeV/c 2 , and for simulated signal and ISR background events. The ISR background is simulated using the JETSET event generator. It should be noted that most of the background events (about 90%) shown in Fig. 6 arise from e + e − → ppπ 0 γ. The lines in Fig. 6 indicate the boundaries of the signal region (bottom left rectangle) and of the sideband region (top right rectangle). The number of data events in the sideband (N 2 ) is used to estimate the number of background events in the signal region by using where N 1 is the number of data events in the signal region, and β sig and β bkg are the N 2 /N 1 ratios for the signal and background, respectively. These ratios are determined from MC simulation to be β sig = 0.043 ± 0.002 and β bkg = 5 ± 1. Both coefficients are found to be practically independent of pp invariant mass. The estimated numbers of ISR background events for different invariantmass regions are listed in Table I. This is the main source of background for the process under study.
The background from the process e + e − → ppπ 0 , which was the dominant background source in our previous large-angle studies [1,2], is found to be negligible in the data sample selected with the criteria for small-angle ISR events.

V. DETECTION EFFICIENCY
The detection efficiency determined using MC simulation is shown in Fig. 7 as a function of pp invariant mass. The efficiency is calculated under the assumption that |G E | = |G M |. To study the model dependence of the detection efficiency, we analyze a sample of MC events produced using a model with G E = 0. The ratio of the efficiencies obtained in the two models is shown in Fig 8. The deviation of this ratio from unity is taken as an estimate of the model uncertainty on the detection efficiency.
The efficiency determined from MC simulation (ε MC ) must be corrected to account for data-MC simulation dif-  ferences in detector response according to where the δ i are the efficiency corrections listed in Table II. The corrections for data-MC simulation differences in track reconstruction, nuclear interaction, and PID were estimated in our previous publications [1,2]. Systematic effects on p T and M 2 miss may bias the estimated efficiency through the selection criteria. This is studied using e + e − → J/ψγ → ppγ events. In Sec. VI the number of J/ψ events is determined with the requirements p T < 1 GeV/c and −2 < M 2 miss < 3 GeV 2 /c 4 , which are significantly looser than our standard criteria. The double data-MC simulation ratio of the numbers of J/ψ events selected with the standard and looser criteria, 1.043 ± 0.026, is used to estimate the efficiency correction. The corrected values of the detection efficiency are listed in Table III.

VI. J/ψ AND ψ(2S) DECAYS INTO pp
The pp invariant-mass spectra for selected events in the J/ψ and ψ(2S) invariant-mass regions are shown in  To determine the number of resonance events, both spectra are fitted using the sum of a probability density function (PDF) for resonance events and a linear background function. The resonance PDF is a Breit-Wigner function convolved with a double-Gaussian function describing detector resolution. The parameters of the resolution function are determined from simulation. To account for possible differences in detector response between data and simulation, the simulated resolution function is modified by allowing an additional σ G to be added in quadrature to both σ's of the double-Gaussian function and by introducing the possibility of an invariant-mass shift. The free parameters in the fit to the J/ψ invariant-mass region are the number of resonance events, the total number of nonresonant background events, the slope of the background function, σ G , and the mass shift parameter. In the ψ(2S) fit, σ G is fixed to the value obtained from the J/ψ fit. The result of the fit for the J/ψ region is shown by the solid curve in Fig. 9(a), and the corresponding signal yield is 918 ± 31 events. Similarly, the solid curve in Fig. 9(b) shows the fit result for the ψ(2S) region, with signal yield of 142 ± 13 events.
The detection efficiency is estimated from MC simulation. The event generator uses the experimental data on the polar-angle distribution of the proton in ψ → pp decay. The distribution is described by the function 1 + a cos 2 ϑ with a = 0.595 ± 0.019 for J/ψ [22] and 0.72 ± 0.13 for ψ(2S) [23,24]. The model error on the detection efficiency due to the uncertainty of a is estimated to be 1.5% for the J/ψ and 5% for the ψ(2S). The efficiencies (ε MC ) are found to be (2.20 ± 0.02)% for the J/ψ and (6.86 ± 0.04)% for the ψ(2S). The data-MC simulation differences discussed earlier are used to correct the above efficiency values by (−0.8 ± 2.1)% (Table II, corrections 1-3).
The value of the cross section for the production of the J/ψ or ψ(2S) followed by its decay to pp is given by N/(εL), where N is the number of signal events extracted in the fit shown in Fig. 9(a) or Fig. 9(b), ε is the relevant detection efficiency, and L is the nominal integrated luminosity. The cross section values obtained in this way are (89.5 ± 3.0 ± 2.8) fb and (4.45 ± 0.41 ± 0.25) fb for the J/ψ and ψ(2S), respectively, where the first error is statistical and the second systematic.
These values correspond to the integral of the righthand side of Eq. (1) over the resonance lineshape, i.e. for resonance R where m runs over the resonance region. For a narrow resonance is a very good approximation, where x R = 1−m 2 R /s, and m R is the resonance mass.
From the measured values of the cross section we thus obtain: The systematic error includes the uncertainties of the detection efficiency, the integrated luminosity (1%), and the theoretical uncertainty on the production cross section (1%).
Using the nominal values of the e + e − widths [25], the ψ → pp branching fractions are calculated to be B(J/ψ → pp) = (2.33 ± 0.08 ± 0.09) × 10 −3 , B(ψ(2S) → pp) = (3.14 ± 0.28 ± 0.18) × 10 −4 . The cross section for e + e − → pp in each pp invariantmass interval i is calculated as N i /(ε i L i ). The number of selected events (N i ) for each pp invariant-mass interval after background subtraction is listed in Table III. The values of the L i (Table III) have been obtained by integration of W (s, x) from Refs. [4,5] over each invariantmass interval. They can be calculated also using the Phokhara event generator [7]. The results of the two calculations agree within 0.5%, which coincides with the estimated theoretical accuracy of the Phokhara generator [7]. The obtained values of the e + e − → pp cross section are listed in Table III. For the invariant-mass intervals 3.0-3.2 GeV/c 2 and 3.6-3.8 GeV/c 2 we quote the nonresonant cross sections with the respective J/ψ and ψ(2S) contributions excluded. The quoted errors are statistical, as obtained from the uncertainty in the number of selected ppγ events. The systematic uncertainty is independent of invariant mass and is equal to 4%. It includes the statistical error of the detection efficiency (2%), the uncertainty of the efficiency correction (3.3%), the uncertainty in the integrated luminosity (1%), and an uncertainty in the ISR luminosity (0.5%). The model uncertainty due to the unknown |G E /G M | ratio (see Fig. 8) is about 15% at 3 GeV/c 2 , decreases to 5% at 4.5 GeV/c 2 , and does not exceed 5% at higher values. The measured e + e − → pp cross section is shown in Fig. 10 together The pp invariant-mass interval (Mpp), number of selected events (N ) after background subtraction, detection efficiency (ε), ISR luminosity (L), measured e + e − → pp cross section (σpp), and the proton magnetic form factor (|GM |). The quoted uncertainties are statistical. The systematic uncertainty is 4% for the cross section, and 2% for the form factor. The model uncertainty for the cross section (form factor) is 15 (8)% at 3 GeV, decreases to 5 (3)% at 4.5 GeV, and does not exceed 5(3)% at higher values.  BES [9], CLEO [10], NU [11], E835 [13], E760 [12], BABAR (LA ISR) [2] with the results of previous e + e − measurements. The values of the proton magnetic form factor are obtained using Eq. (3) under the assumption that |G E | = |G M |. They are listed in Table III and shown in Fig. 11 (linear scale) and in Fig. 12 (logarithmic scale). It is seen that our results are in good agreement with the results from other experiments. The curve in Fig. 12 is the result of a fit of the asymptotic QCD dependence of the proton form factor [14], |G M | ∼ α 2 s (M 2 pp )/M 4 pp ∼ D/(M 4 pp log 2 (M 2 pp /Λ 2 )), to all the existing data with M pp > 3 GeV/c 2 , excluding the two points from Ref. [11]. Here Λ = 0.3 GeV and D is a free fit parameter. The data are well described by this function, with χ 2 /ν = 17/24, where ν is the number of degrees of freedom. Including the points from Ref. [11] in the fit increases χ 2 /ν to 54/26.
In Fig. 12 we also show the space-like |G M | data BES [9], CLEO [10], NU [11], E835 [13], E760 [12], BABAR (LA ISR) [2]. Points denoted by "SLAC 1993" represent data on the space-like magnetic form factor obtained in ep scattering [26] as a function of −q 2 , where q 2 is the momentum transfer squared. The curve is the result of the QCDmotivated fit described in the text.
("SLAC 1993" points) obtained in Ref. [26]. The QCD prediction is that the space-and time-like asymptotic values be the same. In the region from 3.0 to 4.5 GeV/c 2 the value of the time-like form factor is about two times larger than that of the space-like one. Our points above 4.5 GeV/c 2 give some indication that the difference between time-and space-like form factors may be decreasing, although our measurement uncertainties are large in this region.