Pion pair production in photon-photon collisions at spear

Abstract We report a measurement of the cross section for the process γγ → π + π − at invariant masses 500 MeV/ c 2 m ππ c 2 . A value for the radiative width of the f(1270) tensor meson Γ f→ γγ = 3.6 ± 0.3 ± 0.5 KeV (helicity λ = 2) has been obtained from a fit to the observed ππ mass spectrum.

The process 77 + lrn is an ideal place to study the properties ofJ c = even + resonances [1] and, at high masses, it becomes a testing ground for QCD [2]. In this letter we present a study of the process Work supported in part by Department  e+e --+ e+e-rr+n-, at invariant masses 500 MeV/c 2 ~< m~r~r ~< 2000 MeV/c 2 A strong signal at the well-known f(1270) resonance occurs midway in this region. Below the resonance the cross section for reaction (1) is found to be large (~ 100 nb) while at higher masses it falls rapidly. The data presented here were taken with the SLAC-LBL Mark II detector [3,4] at SPEAR with center-ofmass energies between 4.5 GeV/c 2 and 6.5 GeV/c 2-The accumulated luminosity was 13 200 nb-1. Events were selected that contained two detected tracks of opposite charge and no other detected charge particles. Separation of reaction (1) from the large background of two-photon initiated QED processes e+e --~ e+e -+ (e+e -or/a+/a -) (2) has been done using the signals from the Mark II liquid argon system. To ensure that each track was within the fiducial acceptance of the liquid argon calorimeters, 304 0 031-9163/81/0000-0000/$ 02.75 © 1981 North-HoUand the laboratory polar angle of each track was required to satisfy Ices OL I <~ 0.6. The outgoing small-angle beam electrons were not detected. Backgrounds to process (1), other than the QED processes (2), include beam-gas events, higher multiplicity two-photon processes, and events from the e+e -annihilation channel. The beam-gas contamination was minimized by requiring the vertex of each event to be in the measured interaction region. Sideband subtractions were then made to correct the data for the remaining beam-gas background. Separation of the desired two-prong final state from beambeam backgrounds was achieved by accepting only those events for which the net transverse momentum of the observed prongs, I~PT l, was less than 100 MeV/c. The two-photon production of the 7/'(958) and of the four-plan £mal state (p0p0) produce a cluster of events near the rho mass. Since these processes have previously been observed in the same detector [3,5], a direct computation of the feed-down from these sources that survives the PT cut has been made with a Monte Carlo. Remaining backgrounds were determined by fitting the observed I ]~PT ] distributions in various mass bins with a combination of the shape expected from the photon-photon processes (1) and (2) and the shape expected from events produced in the annihilation channel. The two distributions were determined by Monte Carlo simulations. The detected two-prong mass spectrum is shown in fig. 1 along with the various contributions as they have been calculated or measured. The non-QED backgrounds are only a few percent of the total two-prong sample, but they become 5-30% in the raw 7rTr signal that we will present below.
The QED curve shown in fig. 1 was computed by Monte Carlo [6] and normalized by the measured luminosity of the experiment. Because this normalization is uncertain by +6%, the extraction of the 7rTr signal by a direct subtraction of the expected QED from the observed spectrum is impossible. To enhance the mr signal relative to the QED background, we make use of the relatively large probability that a low-momentum plan will interact in the magnet coil which is positioned between the central drift chamber and the liquid argon calorimeters. Unlike the electromagnetic interactions of electrons and muons, the hadronic na-"ture of these plan interactions leads to a substantial probability that a pion will not deposit any energy in the liquid argon along the track trajectory. According- ly, we identify a particle as a pion if it is assigned less energy by the liquid argon tracking programs than would be expected from a minimum ionizing particle. The event selection criteria include geometrical cuts to guarantee that all accepted events contain two-prongs within the fiducial acceptance of the calorimeters. Sources of pions, muons, and electrons that have been unambiguously identified without the use of the liquid argon signals have been used to calibrate the resulting plan identification probability and the electron and muon misidentification probabilities. The results are given in fig. 2a. The pion efficiency for momenta below 400 MeV/c was checked using a large sample of two-prong beam-gas events. These events are relatively free of contamination b~, electrons and muons. Events containing protons, identified by time of flight, were removed. The agreement of the pion efficiency obtained from these events with that in fig. 2a was found to be better than 10%. The pion identification criteria have been applied to each event in the two-prong sample ( fig. 1). The histogram in fig. 2b shows the number of these events that contain at least one identified plan. The points with errors in this figure are the numbers of events that would have satisfiedthese criteria if the two-  I  I  I  I  I  I  I  I  I  I  I  I  prong sample consisted of only electron and muon pairs [reactions (2) above]. To compute these points the QED Monte Carlo [6] was used to determine the expected rario of detected electron pairs to detected rouen pairs and then each event in the two-prong sample was weighted by the probability that it is a rotsidentified electron pair plus the corresponding probability that is is a misidentified muon pair. A definite excess of events at m~ >~ 750 MeV/c 2 is seen from which we extract the n+~ -signal. This analysis has been carried out in a completely parallel manner with events that have been required to consist of two identified pions. This latter sample contains negligible QED background at m~ >~ 700 MeV/c 2. The two-photon cross section ovv_~÷~-is related to the measured cross section aee_,eelrl r by [7] daeo..eeTr~ r (~)2 f(Eb,S~r~r) d°'ry~*r~r  fig. 3. The cross section o~/9-~r~r integrated over the range of c.m. angles I cos e* I < 0.35. The solid curve is from the Born cross section [8], the dashed-dotted curve is from a QCD calculation [2], and the dashed curves is from the f(1270) calculation.
range Icos 0* I ~< 0.35. The agreement between the resuits extracted with the two levels of pion identification indicates that the lrrr £mal state has been accurately separated from the QED background. Also included in fig. 3 is a data point at high mass that was measured using the Mark II muon and liquid argon systems to directly reject muon and electron pairs. This point has been corrected for all backgrounds with previously described techniques, and the pion efficiencies and electron and muon misidentification probabilities have been studied with the test samples previously described.
The data tend to fall below the Born cross section [8] at masses >~ 1.5 GeV/c 2 . The prediction of a recent QCD calculation [2] also shown in the figure, indicates that data from higher beam energies will be needed in order to reach the interesting region at masses above the tail of the f(1270).
The two-prong sample ( fig. 1) exhibits a large enhancement over the QED background in the mass region of the f(1270) meson. We have previously reported [9] that this structure is not consistent with the dwave Breit-Wigner expected from parameters of the f determined in hadronic reactions [10] ; Since we now have a more complete measurement of the rr~r mass spectrum it is possible to investigate the hypothesis that the Breit-Wigner for the resonance amplitude is modified by interference with the non-f background [ 11 ]. Although it contains a large QED component, the spectrum in fig. 1 gives the best accuracy for this study. We use the detected spectrum of identified lrTr events (with l eos 0L I <0.6 ) to normalize the QED curve in fig. 1 ; this normalization is determined so that the excess of two-prong events over QED in the region 700 MeV/c 2 ~< m~r~r ~< 950 MeV/c 2 is consistent with the measured number of ~rlr events in the same mass region. Shown in fig. 4 is the resulting non-QED spectrum in the vicinity of the f. Errors in the measured Ir~r yield result in a +4% uncertainty in the QED normalization which is taken into account in the fitting procedure described below.

• [(~ C(m) f(m)] 1/2 + f'(m). (4)
In this expression f(m) is the contribution to the rate appropriate for a relativistic d-wave Breit-Wigner with resonance mass and width equal to 1271 MeV/c 2 and I  I  I  I  i  I  i  I  I  I   ~'lO0  l~ n°ne  interference  180 MeV/c 2, respectively. All relevant photon flux factors have been included, and we assume that the f is only produced with helicity +2. Two extreme cases for the shape of the non.f rtrt production C(m), were considered. The first was the simple Born term at all masses, and the second consisted of using the Born term at masses below 1 GeV/c 2, but replacing it with the QCD prediction at higher masses. (See fig. 3.) The third term in eq. (4) is an interference between the first two terms. We take the non-f amplitude to be real (like the Born term) so that the relative phase of these two terms is equal to the resonant phase shift 8 (m), modulo n. Since we are not able to do a partial wave analysis for the lrrt spectrum, the parameter/3 has been included and we do fits for various values -1 ~</3 <1. The last term in eq. (4) represents the contribution made by the process 77~ f'(1515) ~ K+K -where the kaons have been misidentified as pions. If we use the SU(3) expectation for the ratio Pf'-+~/Pf--,'r~ (= 0.14 assuming an m 3 phase-space correction) and take the branching ratio f' ~ K+K -to be 50%, then a Monte Carlo calculation, which includes losses due to kaon decays, gives this term to be 3.8% of the f. The yield f' events is shown in fig. 4 for the "Y7 partial width of the f obtained below. The fitted parameters are the normalization of the non-f background (o 0 and the 77 partial width of the f(1270). Although a varies by a factor of ~1.5 as the QED normalization is varied, the 77 partial width of the f depends very little on either the QED normalization, the value of/3, or the choice for the continuum