c

Volume 103B, number 3

PHYSICS LETTERS

23 July 1981

MEASUREMENT OF THE REAL-TO-IMAGINARY RATIO OF THE ~p FORWARD AMPLITUDE AT BEAM MOMENTA BETWEEN 400 AND 730 MeV/c ~" H. IWASAKI, H. A I H A R A , J. CHIBA, H. FUJII, T. FUJII, T. KAMAE, K. NAKAMURA, T. SUMIYOSHI, Y. T A K A D A a, T. TAKEDA and M. YAMAUCHI Department of Physics, University of Tokyo, Tokyo 113, Japan and H. FUKUMA 2 Department of Physics, Hiroshima University, Hiroshima 730, Japan Received 14 May 1981

Differential cross sections of pp forward elastic scattering were measured between 400 and 730 MeV/c, and the real-toimaginary ratio, p, of the forward amplitude was deduced. We found that p increases from ~0.1 to ~0.4 in this momentum range. A dispersion-relation analysis shows the existence of a pole-like structure in the real part of the ~p amplitude near threshold.

Measurement of the real-to-imaginary ratio, p, of the ~p forward elastic amplitude at low momenta is interesting for the following reasons. A straightforward search for the characteristic resonant structure is related to the baryonium states near threshold. On the other hand, the global behavior of p is sensitive to the imaginary part o f the ~p amplitude in the unphysical region, via the forward dispersion relation. Thus systematic measurement of the real part o f the ~p amplitude offers an imp o r t a n t means to investigate the behavior of the scattering amplitude in the unphysical region, where as yet no strictly quantitative theory exists. The real-to-imaginary ratio is also compared with the predictions of potential models such as the one proposed by Bryan and Phillips [ 1 ], and therefore offers a means to test or to constrain these models. In this letter we report the first systematic measurem e n t o f p at low momenta ( 4 0 0 - 7 3 0 MeV/c). Previous Work supported in part by the Grant-in-Aid from the Japanese Ministry of Education, Science and Culture. 1 Present address: Institute of Applied Physics, University of Tsukuba, Sakura, lbaraki 305, Japan. 2 Present address: National Laboratory for High Energy Physics (KEK), Oho, Ibaraki 305, Japan. 0 031

measurements [ 2 - 5 ] o f p have been performed above 1 GeV/c except one bubble-chamber measurement [6] at 700 MeV/c. The experiment was performed in a lowm o m e n t u m separated beam (K3) of the National Laboratory for High Energy Physics (KEK). By tracing the trajectories of every incoming antiproton and outgoing charged particle in the forward direction, using multiwire proportional chambers (MWPC), we concurrently measured the ~p total cross section and the differential cross section of forward elastic scattering. The result of the total cross section, showing negative evidence for the existence o f the narrow S-resonance, has been published elsewhere [7]. Fig. 1 shows the apparatus used in the present experiment. The incoming antiprotons were momentumanalyzed by a hodoscope H1 placed at a dispersive intermediate focus of the K3 beam channel and were identified by pulse-height (dE/dx) and time-of-flight (TOF) information from three trigger counters C 1 - C 3 . The absolute beam momentum was calibrated to +0.5% and continuously monitored by use of a magnet D3 whose magnetic fields were accurately known. Contamination of misidentified pions in the beam was carefully studied and found to be about 1/5000. A 8.6 cm

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Volume 103B, number 3

PHYSICS LETTERS

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Fig. 1. Plan view of the experimental apparatus. D1 -D3, bending magnets; Q1 -Q10, quadrupole magnets; C1 -C5, scintillation counters; H1 -H3 and TH, scintillation counter hodoscopes; and MWPC1-MWPC5, multiwire proportional chambers. long liquid hydrogen target and an empty target having the same structure were placed at a final focus of the beam channel. At 500 MeV/e, the mass resolution of the ~p system was 1.5 MeV/e 2 (rms). The normalization constant related to the target was known to ± 1%. About 95% of the solid angle around the target was surrounded by a scintillation counter hodoscope TH which has holes to allow the incoming and forward outgoing antiprotons to pass through. This hodoscope was used to detect the annihilation events. Trajectories of charged particles were determined by the MWPCs with bidimensional readout [8]. Further details of the apparatus are described in ref. [9]. Data were taken at 25 beam momentum settings in a step of 2% between 413 and 715 MeV/c. For the present analysis, no attempt was made to further resolve the beam momentum using H1. Since the momentum bite transmitted by the beam channel was +-2%, each 248

23 July 1981

momentum bin has 50% overlap with the neighbouring bins. The trigger condition was a three-fold coincidence of C1 • C2 • C3 timed to the antiprotons, with the C1 threshold set high enough to reject pions. No other selection was made at the trigger level. For the analysis of ~p elastic scattering, MWPCs 1 - 4 were used to reconstruct the trajectories of charged particles. The events used in the analysis were required to have a charged particle traversing a 3 mm thick scintillator C4 and to have a single hit in each of MWPC 1 - 4 . The dE/dx information from C4 was used for ~/Tr discrimination. The hodoscope TH was also helpful. To determine the dE/dx cut of C4, the counter C5 behind the magnet D3 was conveniently used. Since the distance between C1 and C5 was long enough (13.5 m), the TOF provided unambiguously identified samples of antiprotons and minimum-ionizing pions. The elastic scattering events were also required to have a vertex point within the target region (target cut). Before applying this cut, however, we artificially smeared, by a Monte Carlo technique, the reconstructed outgoing trajectories in the empty-target runs, in order to take into account the different amount of multiple scattering in the full- and empty-target runs. The raw data of the differential cross section were obtained by subtracting the empty-target counts from the full-target counts corrected for the beam attenuation in the liquid hydrogen. The following corrections were subsequently made to obtain the final results. (i) Reconstruction efficiency. In the extreme forward direction, this was estimated by use of antiprotons transmitted to C5. It was 87% at 413 MeV/c, decreasing to 70% at 715 MeV/c. A study of the local efficiencies of the MWPCs established the uniformity of the reconstruction efficiency within 7% over the acceptance of MWPC 3 and 4. (ii) Geometrical acceptance (almost 100% for the scattering angle 0 ~< 5 °, decreasing to 70% for 0 = 10°). (iii) Pion misidentification ( - 1.5 +- 0.5%). (iv) Absorption of the beam and scattered antiprotons by the materials other than liquid hydrogen (1.4 -+ 0.3%). (v) Backward elastic scattering ( - 4 . 3 -+ 0.2% at 504 MeV/c and - 0 . 9 ± 0.1% at 701 MeV/c). (vi) Inefficiency due to the single-hit requirement in each MWPC (1.5 ± 1.0%). Fig. 2 shows the forward elastic differential cross section at two momenta. The error bars show the total errors. The statistical errors dominate over the systematic errors except the two smallest-angle data points,

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Fig. 3. Tide real-to-imaginary ratio of the ~p forward amplitude obtained in this experiment. The solid curve shows the best-fit result of the dispersion-relation calculation with an additional pole term near threshold. well as the theoretical curves corresponding to p = -+ 1.0. The best-fit values o f p are insensitive to the uncertainties in b, but sensitively d e p e n d e n t on Oto t. Here we note that our values o f Oto t [7] are about 6% smaller than the results r e p o r t e d by other experiments [ 1 1 ]. If Oto t from these experiments are used, the values o f p decrease by 0 . 1 - 0 . 1 5 . A dispersion-relation analysis o f the real part of the ~p forward amplitude was p e r f o r m e d including the present results. Here we closely followed Grein's ap-

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Volume 103B, number 3

PHYSICS LETTERS

proach [12]. The ~p and pp total cross sections were taken from the existing data. The imaginary part of the ~p forward amplitude in the unphysical region was approximated by a sum of the two-pion contribution [ 12] ,2 and the pole terms accounting for dominant contributions from known mesons. The parameters for these pole terms were taken from ref. [12]. To take into account the contribution from other meson states far below the ~p threshold, a constant term was added and fitted to the data of p above 1 GeV/c. The result of this dispersion-relation calculation is shown by the dashed curve in fig. 4. Below 600 MeV/c, this result completely disagrees with the data. We then introduced an additional pole term with a variable mass rn. The best fit was obtained for m = 1884 + 9 MeV/c 2 with residue = 0.97 -+ 0.08, slightly above the threshold. However, for the lack of data below 400 GeV/c, the exact position of this pole is not very significant as seen in fig. 4, where the best-fit result as well as the results with rn = 1850 and 1830 MeV/c 2 are shown. It should be remarked that this additional pole term negligibly changes the real-to-imaginary ratio of the pp forward amplitude (at most 0.02). The necessity of an effective pole term near the ~p threshold was previously pointed out by Grein [12] and Kaseno [ 13]. Our new results have confirmed their conclusions. The origin of this effective pole term is as yet not very clear. One possibility is unusual threshold behavior caused by the strong annihilation effect [12]. To further clarify the structure of the ~p amplitude in the unphysical region, measurement of/) down to the threshold is clearly very important. 4-2 We thank Dr. W. Grein for supplying us with the numerical values of the two-pion contribution.

250

23 July 1981

Finally, we note the non-static version of the Bryan Phillips potential model [1] gives +3 p = 0.103 at 500 MeV/c and 0.212 at 700 MeV/c, in rather good agreement with the data, considering the present ambiguity in O'tot . We would like to thank all the staff of KEK for tile machine operation and various help given to us throughout this experiment. *3 These results are based on somewhat different parameters from those in the original paper [ 1]. We thank Dr. R.J.N. Phillips for sending us the results of the calculation. R eferen ces [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

[ 13]

R.A. Bryan and R.J.N. Phillips, Nucl. Phys. B5 (1968) 201. K.J. Foley et al., Phys. Rev. Lett. 19 (1967) 857. P. Jenni et al., Nucl. Phys. B94 (1975) 1. P. Jenni et al., Nucl. Phys. B129 (1977) 232. L.A. Fajardo et al., Fermilab preprint FERMILAB-Pub80/27-Exp, submitted to Phys. Rev. D. H. Kaseno et al., Phys. Lett. 61B (1976) 203; 68B (1977) 487 (E). T. Kamae et al., Phys. Rev. Lett. 44 (1980) 1439. H. lwasaki et al., Japan. J. Appl. Phys. 20 (1981) 189. H. lwasaki, thesis submitted to Univ. of Tokyo (1981), unpublished. J.E. Entstrom et al., Particle Data Group, NN and Nd interactions - a compilation, LBL-58 (1972). A.S. Carroll et al., Phys. Rev. Lett. 32 (1974) 247; R.P. Hamilton et al., Phys. Rev. Lett. 44 (1980) 1182. W. Grein, Nucl. Phys. B131 (1977) 255; W. Grein, Proc. 4th European Antiproton Symp. (Bari, 1978) (Centre National de la Recherche Scientifique, Paris, 1979) Vol. 1, p. 35. H. Kaseno, Nuovo Cimento 43A (1978) 119.