Measurement of gamma gamma ->p p-bar production at Belle

A high precision study of the process gamma gamma ->p p-bar has been performed using a data sample of 89/fb collected with the Belle detector at the KEKB e+e- collider. The cross section of p p-bar production has been measured at two-photon center-of-mass (c.m.) energies between 2.025 and 4.0 GeV and in the c.m. angular range of |cos(theta^*)|<0.6. Production of gamma gamma ->eta_c ->p p-bar is observed and the product of the two-photon width of the eta_c and its branching ratio to p p-bar is determined.


Introduction
Two-photon collisions provide a clean environment for baryon pair production and such events can be produced in great abundance at a high luminosity electron-positron collider.Accurate measurements of such processes, in particular γγ → pp, is important to test existing theoretical predictions.
General theories of hard exclusive processes in QCD [1,2] (see also [3] for a review) predict that the differential cross section for γγ → h 1 h 2 at large energies and fixed c.m. angle (θ * ) has the form dσ/dt ∝ s 2−nc f (θ * ) (as s → ∞). ( Here n c is the number of elementary constituents participating in the hard interaction, f (θ * ) is a specific function expressed via definite integrals over hadron wave functions, s is the square of the c.m. energy of the two-photon system, and t is the square of the four-momentum transfer from a photon to hadron.The first estimate of the cross section for γγ → pp was obtained in the three-quark picture (n c = 8) [4,5], using the proton wave function based on QCD sum rules [6].Previous measurements [7,8,9,10,11] in the W γγ (≡ √ s) range between 2.5 and 3.0 GeV gave cross sections one order of magnitude larger than this expectation.To explain these experimental observations, various model-dependent approaches were suggested.For example, in the diquark model [12,13,14] the proton is considered to be a quark-diquark system.In this case n c = 6 and a diquark form factor is introduced, so that Eq. ( 1) becomes dσ/dt ∝ s −4 |F | 2 , where F may depend on s.Asymptotically, F → f (θ * )/s [12], and the behavior dσ/dt ∝ s −6 is recovered.These results exhibit better agreement with measurements of the absolute size of the cross section for W γγ = 2.5 -3.0 GeV.
Other approaches have been developed recently.The handbag model [15] has been developed for large momentum transfers, and the calculations have been applied at medium energies (W γγ > 2.55 GeV) with large uncertainty bands.In Ref. [16], the Veneziano model is applied in an unmodified form to the process, and fair agreement with data is obtained without adjustable parameters.
Recently, the measured energy range for γγ → pp has been extended to W γγ = 4 GeV and above [10,11], but with very limited statistics for W γγ > 3 GeV.Furthermore, pp → γγ experiments give the cross section for the inverse process at W γγ = 3.2 -3.7 GeV [17].To test QCD predictions, it is very important to improve the statistics at higher energies.Moreover, an accurate measurement with higher statistics for γγ → pp is crucial in the study of the interactions involved.This paper presents the Belle measurement of the γγ → pp cross section for W γγ between 2.025 to 4.0 GeV and | cos θ * | < 0.6, using a data sample corresponding to an integrated luminosity of 89 fb −1 .

Experimental apparatus and event selection
Experimental data are recorded with the Belle detector [18] at KEKB [19], which is an asymmetric e + e − collider running at 10.58 GeV c.m. energy.In the laboratory frame, the direction of the positron beam is taken to define the −z direction.For the analyses in this paper, the following Belle subsystems are of importance: the central drift chamber (CDC), the aerogel Cherenkov counters (ACC), the time-of-flight scintillation counters (TOF) and the CsI electromagnetic calorimeter (ECL), all of which are located in a 1.5 T solenoidal magnetic field.The CDC measures the momenta of charged particles and provides particle identification information by precise (6%) dE/dx measurement, allowing separation of protons from other particles for momentum up to 1 GeV/c.The TOF measures the time of flight of particles with a 0.1 ns timing resolution, which is powerful for p/K separation for momentum up to 2 GeV/c.The ECL detects photons and is used to reject electrons by measuring the deposited energy with a resolution of σ E /E = 1.5% (2.0%) at 1 GeV (0.1 GeV).Using the number of photoelectrons observed, the ACC extends particle identification beyond that of the CDC dE/dx and TOF and is effective in the suppression of highly relativistic π ± , µ ± and e ± up to a momentum of 3.5 GeV/c.
Through the process e + e − → e + e − γ * γ * → e + e − pp, exclusive pp pairs are produced in quasi-real two-photon collisions, where the scattered e + and e − are lost down the beam-pipe, and only the p and p can be detected.The γγ axis thus approximates the beam direction in the e + e − c.m. frame.Candidate events are searched for in a data stream where the sum of the magnitudes of momentum of all charged tracks and the total ECL energy are restricted to 6 GeV/c and 6 GeV, respectively.Events are required to have exactly two tracks of opposite charge satisfying the following conditions in the laboratory frame: p t > 0.35 GeV/c, dr < 1 cm and |dz| < 5 cm.Here p t is the transverse momentum and dr and dz are the radial and axial coordinates of the point of closest approach to the nominal collision point, respectively.Both tracks are required to hit the TOF counters.The invariant mass of the two tracks and the squared missing mass of the event, assuming the two tracks are massless, are required to be smaller than 4.5 GeV/c 2 and larger than 2 GeV 2 /c 4 , respectively.A good transverse momentum balance in the e + e − c.m. frame is also required: , where p * t 1 and p * t 2 denote the transverse momenta of the two tracks in that frame, with respect to the e + e − beam-axis.
The selected events are dominated by γγ → e + e − , µ + µ − , π + π − and K + K − up to this stage.Events with pp are separated from the others by a particle iden- Fig. 1.Two-dimensional distribution of the normalized likelihood for pp identification, for the events passing all selection criteria except the cuts on the normalized likelihood indicated by the arrows.The dark parts show the events satisfying λ x ≡ L x /(L p + L K + L π + L µ + L e ) > 0.01 for both tracks using the same x, where x is K, π, µ or e. tification (PID) algorithm, which is applied to each individual track under the following conditions: 1) the difference between the measured and the expected CDC dE/dx is less than 4 times the resolution: χ 2 dE/dx ≡ [∆(dE/dx)/σ dE/dx ] 2 < 4 2 ; 2) the ratio of the associated ECL energy to the momentum is less than 0.9, which is only applied to the positively charged track; 3) the number of the photoelectrons in ACC counters associated with the track is less than 4, and this condition removes a large part of high-momentum π ± , µ ± and e ± ; 4) the likelihoods for each particle assignment are combined to determine the normalized likelihood, λ p ≡ L p /(L p + L K + L π + L µ + L e ), which has to be larger than 0.8 (Fig. 1).In these likelihoods, L ≡ exp[− 1 2 (χ 2 dE/dx + χ 2 T )] is calculated using information from the CDC (dE/dx) and the TOF (time of flight T ).Here χ 2 T ≡ (∆T /σ T ) 2 , ∆T is the difference between the measured and the expected values for T , and σ T is the timing resolution.A combined use of CDC and TOF allows p(p) separation from other particles, in particular K ± , for momentum up to 2 GeV/c.For W γγ = 2 -4 GeV a total 36094 events survive all of the selection criteria.Their distribution in W γγ is shown in Fig. 2. A peak around 2.98 GeV can be identified as the η c (2980) resonance [20].A much narrower peak at 3.08 -3.10 GeV, corresponding to an excess of 26 ± 8 events relative to the continuum, could be attributed to backgrounds from radiative return to J/ψ, and the enhancement is in agreement with expectations based on this assumption [21].Fitting the data from 2.6 to 3.7 GeV with a smooth (exponential of a fifthorder polynomial) function for the continuum, a Breit-Wigner function for the η c and a Gaussian for the J/ψ, a total η c yield of 156.9 ± 33.3 events is obtained.The statistical significance of the η c signal is 5.3 σ, defined as −2 ln(L 0 /L S ), where L S and L 0 denote the maximum likelihoods of the fits with and without a signal component, respectively.

Monte Carlo simulation
Monte Carlo samples for the following channels have been generated: e + e − → e + e − X where X is pp, K + K − , π + π − , µ + µ − , e + e − and ppπ 0 .Hadron pair, lepton pair and γγ → ppπ 0 events are generated by the codes TREPS [22], AAFH [23] and GGLU [24], respectively.Event generation is followed by a detector simulation based on GEANT3 [25] and a trigger simulation.The selection criteria described in Section 2 are then applied to these Monte Carlo events.
Because the acceptance depends on both W γγ and | cos θ * |, the signal (γγ → pp) efficiencies are determined for a number of two-dimensional bins of the two variables.Other channels are generated for the study of residual backgrounds.Similar to γγ → pp, the selection efficiencies for γγ → K + K − and γγ → ppπ 0 are evaluated within each narrow bin.For the γγ → π + π − , µ + µ − and e + e − channels, realistic distributions are generated [23,26,27].Events from those samples that survive the selection criteria are referred to as the expected residual backgrounds.
From Monte Carlo simulation, the overall efficiency of γγ → pp for | cos θ * | < 0.1 ranges from ∼ 3% at W γγ = 2 GeV to ∼ 32% at W γγ = 4 GeV (Fig. 3).and 100 MeV (for 3 -4 GeV), the number of events selected from the data, ∆N(W γγ , | cos θ * |), is determined for each of the two-dimensional bins.The efficiency ε(W γγ , | cos θ * |) is also evaluated from Monte Carlo simulation for each bin.The ratio of ∆N to ε is then converted to the differential cross section, according to the formula: where f is the fraction of residual background in the data, L int is the integrated luminosity and dLγγ dWγγ is the luminosity function.Here L int = 88.96fb −1 , with a systematic uncertainty of 1.4%.The luminosity function dLγγ dWγγ , as a function of W γγ , is defined by and is calculated by TREPS [22] using the equivalent photon approximation method [21].For the calculation of the luminosity function, the effects from longitudinal photons are neglected.For simulation in TREPS, the maximum virtuality of each of the two photons, Q 2 1 and Q 2 2 , is limited to 1 GeV 2 .Moreover, a form factor term is introduced for the high-Q 2 suppression effect, Fig. 4. Measured cross sections for γγ → pp.For the Belle, CLEO [8] and VENUS [9] results, the error bars are purely statistical; while for OPAL [10] and L3 [11], both statistical and systematic uncertainties are included.Theoretical prediction curves shown are from [14] (diquark) and [4] (three-quark).
function is estimated by comparing the kinematic distributions of the twophoton system for the events generated with TREPS to those from a QED calculation that includes all order α 4 diagrams [23].Within the range W γγ = 2 -4 GeV agreement within 3 -5% was reported [22,28].
The cross section σ γγ→pp (W γγ ) is obtained by a summation over | cos θ * |: to polar angular coverage limits of the TOF system.The results are summarized in Table 1 and Fig. 4. The contribution from γγ → η c → pp is included in these results.For the two cross section measurements in the lowest W γγ bins (2.025 -2.075 GeV), the efficiencies are extremely small at larger | cos θ * | and data are only available up to | cos θ * | = 0.4 and 0.5, respectively.We thus fit a second-order polynomial function of cos 2 θ * to these differential cross sections and arrive at a result by integrating the fit over | cos θ * | up to 0.6.For comparison, we also show in Fig. 4 the results from previous measurements [8,9,10,11].Fig. 5 shows the angular dependence of the differential cross sections measured in 11 ranges of W γγ separately.The η c region (2.9 -3.1 GeV) is skipped.For W γγ < 2.4 GeV, the differential cross sections decrease as | cos θ * | increases; while for W γγ > 2.6 GeV, the opposite trend is observed.The transition occurs around W γγ = 2.5 GeV.Similar results are shown in Fig. 6 for three larger ranges of W γγ and are summarized in Table 2.For comparison, previous measurements [8,10,11] are also shown in Fig. 6.Further discussion is given in Section 6.
Based on studies from Monte Carlo and data, residual backgrounds due to particle misidentification and non-exclusive events are subtracted from the data.Corrections are based on ∆N multiplied by (1 − f ) as shown in Eq.( 2).Complete details are given in Section 5, and the systematic errors are shown in Table 3.All measured cross sections and differential cross sections shown in this paper have been corrected in this way.The excess caused by the J/ψ background described at the end of Section 2 is estimated in each | cos θ * | bin separately and subtracted from ∆N before the other corrections above.The systematic uncertainty due to this subtraction is 8% for the measured cross section in the 3.0 -3.1 GeV W γγ bin, taking into account the fluctuation of the estimated number of J/ψ.The total η c yield, N ηc = 156.9± 33.3, can be converted to the product of the two-photon width of η c and the branching fraction of η c → pp: .20 ± 1.53(stat.)+0.67 −0.75 (syst.)eV, using the luminosity function dL γγ /dW γγ determined at the energy of the η c mass (m ηc ) and the efficiency ε from Monte Carlo.For the systematic error, effects from the uncertainties of the continuum background shape and the signal width are taken into account, in addition to all other sources listed in Table 3.The above result gives Γ γγ (η c ) = 5.5±1.2(stat.)+0.5 −0.6 (syst.)±1.7(norm.)keV, where the last error comes from the branching fraction B(η c → pp) uncertainty [20].Since observations of the η c in the pp channel are scarce and suffer from low statistics, current measurements for B(η c → pp) available in Ref. [20] are not very consistent with each other.Our result is the first measurement of Γ γγ (η c ) × B(η c → pp) in two-photon collisions and, together with the observation of the η c in pp collisions in its γγ decay mode [29], will help to decrease the errors on both the η c two-photon width and branching fraction.

Corrections and major sources of systematic error
The accuracy of the Monte Carlo trigger efficiency has been checked from the two-track trigger, which requires at least two CDC tracks with an opening angle larger than 135 • , two or more TOF hits as well as the ECL timing signal, using experimental events passing the high energy trigger based on a 1 GeV threshold for an ECL total energy sum [18,30].The trigger efficiency depends on the average transverse momentum of the two tracks in the laboratory frame, , where the latter is the transverse momentum of p(p) in the γγ c.m. frame.We determine the trigger efficiency as a function of p γγ t , since each of the two-dimensional bins in W γγ and | cos θ * |, where the number of events is measured, is associated with a p γγ t value using the relation above.From the data, the trigger efficiency is 0.83 ± 0.02 at p γγ t = 0.55 GeV/c and 0.95 ± 0.05 at p γγ t = 0.95 GeV/c.Corrections for the Monte Carlo trigger efficiency are implemented according to the data, with a systematic error within 5%.
The accuracy of the PID efficiencies has been checked by comparing Monte Carlo estimates to those based on data.The efficiency associated with each of the four PID conditions (Section 2) is studied, using events passing all selection criteria except the condition in question.The overall PID efficiency is ∼ 92%, ∼ 88% and down to ∼ 78% at W γγ = 2, 3 and 4 GeV respectively, with a systematic error less than 6% in the whole W γγ range.The fake rate is ∼ 0.01% -0.3% for W γγ = 3 -4 GeV, respectively.
Monte Carlo studies indicate that the PID requirements are very efficient in rejecting electrons and other relativistic particles, so that events from γγ → π + π − , µ + µ − and e + e − do not survive the selection, leaving those from γγ → K + K − as the main residual background.From Monte Carlo simulation and the measured cross sections for γγ → K + K − [27,31], the fraction of data that can be attributed to residual K + K − background, f m , is evaluated.Based on Monte Carlo studies, the dependence of f m on | cos θ * | is negligible and f m (W γγ ) = 0.8 ± 0.3%, 3.2 ± 0.5% and 7.7 ± 0.8% at W γγ = 3.2, 3.6 and 4.0 GeV, respectively.For W γγ < 3.0 GeV, f m is negligible.The values of f m have been checked in the data, using events passing all selection criteria except that on the normalized likelihood, λ p > 0.8.The number of signal events that would pass all selection criteria is estimated from the ∆T distribution of one of the two tracks, after requiring the other to satisfy λ p > 0.8.The values of f m inferred in this way are in good agreement with those above.The contribution from this source of background is subtracted from the data, using the expected f m from the Monte Carlo studies.The systematic uncertainty due to this source is ∼ 1% or less in the whole W γγ range.
Possible non-exclusive backgrounds (ppX), most of them from γγ → ppπ 0 events, have been searched for in the data.Monte Carlo studies show that a high purity sample of such background can be derived from events with larger |Σp * t | and smaller |Σp * t (ppπ 0 )|, the latter being the transverse momentum balance of the three particles.By comparing Monte Carlo and data distributions of these parameters we obtain the fraction of the data attributed to this background type, f n .We find that the dependence of f n on | cos θ * | is negligible, and it ranges from 5 ± 2% to 17 ± 8% for W γγ from 2 to 4 GeV, respectively.Corrections are made using the f n (W γγ ) obtained above, and in total 7±1% of the selected data are subtracted.The systematic error from this source is 2 -12% for W γγ from 2 to 4 GeV, respectively.The fraction of the data attributed to γγ → ppπ 0 events is also obtained as a function of |Σp * t |.Before the cor-rection, a comparison of the |Σp * t | distribution between data and Monte Carlo exhibits a total difference of ∼ 9% between the two samples, while it is reduced to less than 3% for any W γγ range after the correction (Fig. 7).Since the residual excess in the |Σp * t | distribution could be attributed to residual nonexclusive backgrounds and a broader nature of the signal distribution than the Monte Carlo, the systematic uncertainty due to other possible non-exclusive backgrounds is limited to 3% after the correction.

Theoretical approaches
From the asymptotic QCD prediction of Eq.( 1) and after integration over cos θ * , the cross section for γγ → pp is proportional to W −10 γγ for asymptotically large W γγ .All models based on this framework behave asymptotically as σ ∝ W −10 γγ .For the diquark scenario, two curves are provided [14]: from the complete diquark model and from the same model with only helicity conserved amplitudes, where p and p are in opposite helicity states.The scale of the diquark predictions matches the data for W γγ = 2.5 -3.0 GeV, but the deviation becomes larger as W γγ increases (Fig. 4).At higher energies, the data fall below the diquark predictions and exhibit a gradual approach to the three-quark model predictions [4].At medium energies between 2.5 and 4.0 GeV, a steeper fall of the total cross section in W γγ is observed.
If we fit the data with a power law σ ∝ W −n γγ with n floating (Fig. 8(a)), taking into account both statistical and systematic uncertainties as well as possible correlations between the latter, we obtain n = 15.1 +0.8 −1.1 and 12.4 +2.4 in the range of W γγ = 2.5 -2.9 GeV and 3.2 -4.0 GeV, respectively (the charmonium region between 2.9 and 3.2 GeV is excluded).For completeness, we also show in Fig. 8(b) the results of the fits with n fixed at 10 and 15.
Although for both ranges a good fit to the data can be obtained at n = 15, a smaller power, n = 10, describes the data above 3.2 GeV reasonably well.This may imply that lower power terms become dominant at higher enegies, which is an indication for the transition to the asymptotic predictions.
The angular differential cross section in | cos θ * | is another observable most important to the study of the nature of the interactions involved in the process γγ → pp.All existing models based on the constituent scattering picture [4,5,12,13,14,15], as expected, predict an ascending trend, which is in agreement with the data for W γγ > 2.5 GeV.This is due to the factor 1/ √ tu ∝ 1/ √ 1 − cos 2 θ * contained in the hard scattering amplitudes.The same trend is obtained from naive QED [32] estimates: dσ/d| cos θ * | ∝ (1 + cos 2 θ * )/(1 − cos 2 θ * ), in the massless limit.A simplified picture with diquarks would follow the naive QED expectation above [10,12], if all quark masses are neglected and only scalar diquarks are considered.In Fig. 9 we plot the differential cross section normalized to that averaged within | cos θ * | < 0.3, and compare various predictions to the data.We observe that the data rise more sharply in | cos θ * | at higher energy (see also Fig. 5).In comparison, all current models predict a flatter trend in | cos θ * |.Theoretical predictions are from [14] (diquark), [5] (three-quark) and [15] (handbag).
The deviation of the leading term QCD calculations [4,5] from the data at W γγ = 2.5 -4.0 GeV implies that power corrections are still significant at these intermediate energies.It is not surprising since the very threshold of pp production corresponds to W γγ ∼ 2 GeV.However, the diquark and handbag models [12,13,14,15] were developed in order to describe the intermediate energy region at the price of introducing model form factors, etc..The disagreement of the data at W γγ = 2.5 -4.0 GeV with their predictions (see Fig. 4 and 9) obviously necessitates their improvement.
The descending trend of the differential cross section in | cos θ * | observed at low energies (W γγ < 2.5 GeV) cannot be understood within the hard scattering picture (Fig. 6(a)).In a recent study based on non-perturbative QCD sum rules [33], this trend was proposed as a general feature for hadron pair production from two-photon collisions.The behavior is very natural if low partial waves are involved.In Ref. [16] it was shown that even a simple model based on pole-and resonance-dynamics can reproduce this behavior.

Conclusion
Using the Belle detector at the high-luminosity KEKB collider, the cross sections for γγ → pp have been measured for W γγ from 2.025 to 4.0 GeV and | cos θ * | < 0.6, with systematic uncertainties ranging from 7% to 14%.These results represent a great improvement in precision compared to all previous measurements and allow more accurate tests of various theoretical models.We also observed the production of γγ → η c → pp and determined the product of the two-photon width of the η c and its branching ratio to pp.
Fitting to a power law σ ∝ W −n γγ shows that the best fit value of n decreases as energy increases, and n = 10 cannot be rejected at energies above 3.2 GeV, implying the gradual transition to the expectation from asymptotic predictions.The ascending trend for the differential cross section in | cos θ * | predicted by the hard scattering picture is in agreement with the data for W γγ > 2.5 GeV; however, the data rise more sharply in | cos θ * | as W γγ increases.The descending trend in | cos θ * | at lower energies W γγ < 2.5 GeV can be reproduced by non-perturbative approaches [16].The descending trend of the differential cross section in | cos θ * | changes to an ascending one with the increase of energy, which could be an indication for the transition from a soft resonance regime to the beginning of a hard regime.Existing models suggested for the intermediate energies [12,13,14,15] can not provide satisfactory description of the observed energy and angular dependence in the studied energy range.

Fig. 3 .
Fig. 3. Overall detection efficiency of γγ → pp as a function of W γγ and | cos θ * |. 4 Measurement of the cross sections for γγ → pp

6 Fig. 5 .
Fig. 5. Measured differential cross sections in 11 ranges of W γγ as a function of | cos θ * |.The error bars are statistical only.

Fig. 6 .
Fig. 6.Measured differential cross sections as a function of | cos θ * | for three ranges of W γγ .The error bars are statistical only.

W γγ = 2 Fig. 7 .
Fig. 7. |Σp * t | distributions for the data before (left column) and after (right column) the subtraction of residual non-exclusive backgrounds (γγ → ppπ 0 ).The Monte Carlo distributions are scaled with the first bin normalized to the data.

Fig. 8 .
Fig. 8. Separate fits of σ ∝ W −n γγ to the data in the range of W γγ = 2.5 -2.9 GeV and 3.2 -4.0 GeV, with (a) n floating; (b) n = 10 and n = 15.The error bars include statistical and systematic errors.The χ 2 /ndf values for each fit are indicated in the figure.

Table 1 Measured
cross sections for γγ → pp (| cos θ * | < 0.6).The first error is statistical and the second is systematic.

Table 2 Measured
differential cross sections versus | cos θ * | for different W γγ ranges.The first error is statistical and the second is systematic.

Table 3
Systematic errors for the measured cross sections of γγ → pp.Some uncertainties are W γγ -dependent and shown as ranges.