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Pions from the reaction γ + p → π + + n were analysed in the backward direction by a magnetic spectrometer. The photon energy region of 0.394 GeV to 1.397 GeV was covered by 19 different momentum settings. Data reduction resulted in 74 measured differential cross sections with statistical uncertainties typically from 4% to 8%. The systematic uncertainty was estimated to be ±5%. The data are compared to other recent experiments and predictions of phenomenological analyses.

New results are presented on the differential cross-section for the reaction α+p→π0+p, at energies between 600 and 1000 MeV, and c.m. pion angles Θ*π=40° and Θ*π=60°. The present data, together with that at Θ*π=40° already published (11), show an angle-independent position of the second resonance at about 750 MeV. Rather flat angular distributions in the forward c.m. hemisphere are also favoured by these data. On comparing the cross-sections obtained when detecting both the neutral pion and the recoil proton, and when detecting only the latter, estimates of the background of «ghost protons» are obtained, in agreement with the empirical curve proposed in ref. (11).

The polarization of the recoil proton in the photoproduction process γ+p→p+π0 has been measured with the beam of the Frascati electrosynchrotron at an angle of 90° in the c.m. system, in the energy interval (500÷900) MeV. A counter technique has been used, and the polarization of the proton was revealed by the left to right asymmetry in the elastic scattering of the protons in a carbon target. The experimental results are given in Table III and in Fig. 10. A definite polarization is found, always of the same sign and equal to −0.4±.14, −0.63±.23, −0.6±.25, −0.57±.12, −0.38±.09, −0.5±.17, −0.5±.22 at the γ-ray energies of 560, 610, 650, 700, 750, 800, 850 MeV respectively. The discussion of these experimental results, together with the data of angular dstributions, allows to conclude that they are in agreement with the hypothesis that the second resonance is a transition (E 1,d 3/2) and the third one is a transition (E 2,f 3/2).

Results are presented on the elastic scattering of photons by protons. The incident photon energy ranged from 0.55 GeV to 4.5 GeV, and the four-momentum transfer t ranged from 0.12 to 1.0 (GeV/c)2. The data at large angles, 60°<θ*<115°, are characterized by a pronounced excitation of the D13(1518) resonance, a shoulder in the 1688-MeV mass region, and a precipitous drop thereafter in the cross section as a function of incident energy. The low-t data are characterized by a diffraction slope of 5 (GeV/c)−2. The data are inconsistent with the predictions of the vector-dominance model if the latter is restricted to ρ0, ω, and φ vector mesons.

The reaction γ V p → p π + π − was studied in the W , Q 2 region 1.3–2.8 GeV, 0.3–1.4 GeV 2 using the streamer chamber at DESY. A detailed analysis of rho production via γ V p→ ϱ 0 p is presented. Near threshold rho production has peripheral and non-peripheral contributions of comparable magnitude. At higher energies ( W > 2 GeV) the peripheral component is dominant. The Q 2 dependence of σ ( γ V p→ ϱ 0 p) follows that of the rho propagator as predicted by VDM. The slope of d σ /d t at 〈 Q 2 〉 = 0.4 and 0.8 GeV 2 is within errors equal to its value at Q 2 = 0. The overall shape of the ϱ 0 is t dependent as in photoproduction, but is independent of Q 2 . The decay angular distribution shows that longitudinal rhos dominate in the threshold region. At higher energies transverse rhos are dominant. Rho production by transverse photons proceeds almost exclusively by natural parity exchange, σ T N ⩾ (0.83 ± 0.06) σ T for 2.2 < W < 2.8 GeV. The s -channel helicity-flip amplitudes are small compared to non-flip amplitudes. The ratio R = σ L / σ T was determined assuming s -channel helicity conservation. We find R = ξ 2 Q 2 / M ϱ 2 with ξ 2 ≈ 0.4 for 〈 W 〉 = 2.45 GeV. Interference between rho production amplitudes from longitudinal and transverse photons is observed. With increasing energy the phase between the two amplitudes decreases. The observed features of rho electroproduction are consistent with a dominantly diffractive production mechanism for W > 2 GeV.

The rates for forward electroproduction of single charged pions from deutrium have been measured in the resonance region, at a virtual photon mass squared ≈−0.5( GeV/ c 2 ) 2 . Results are presented in the form of a π − to π + cross-section ratio.

The ratio of π - to π + electroproduction cross sections from deuterium has been measured in the resonance region, at a four-momentum transfer squared close to −1.0 (GeV/ c ) 2 . Results in the forward direction are presented and a comparison is made with predictions based on SU(6) W and the Melosh transformation.

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The differential cross section for photoproduction of π° on hydrogen has been measured in a photon energy range of 560-690 MeV and for production angles in the interval 90°-105° in the centre of mass system. The experiment detects the recoil proton and a π°-decay photon in coincidence, using optical spark chambers and a lead glass Cerenkov counter. Presented cross sections, based on 35 000 events recorded on film, are in good agreement with recent phase shift analysis.

We have identified 262 doubly tagged two-photon events. A subset of the data shows an enhancement of 21 events in the inclusive two-photon mass squared distribution between 0.8 and 2.2 GeV 2 . If these events result from spin 2 resonance production then Γ γγ = 9.5 ± 3.9 ± 2.4 keV (statistical and systematic). From another subset of 58 events in which the final state could be classified we determine the two-photon hadron to muon cross section ratio R γγ = 1.1 ± 0.3 ± 0.3.

To complete data on resonance electroproduction we constructed an electron spectrometer with large angular and momentum acceptance. As a first result inclusive cross sections for an invariant hadronic mass 1.2<W<1.7 GeV and a four momentum transfer squared 0.5<Q2<1.5 (GeV/c)2 and for values of the polarization parameter 0.1<ɛ<0.25 are presented. Combining our results with the SLAC 4°-data we obtain σL/σT in the specified kinematical range.

We present a measurement of the cross section for the reaction e + e − → e + e − π + π − π + π − at SPEAR. This channel is found to be large and dominated by the process γγ → ϱ 0 ϱ 0 → π + π − π + π − . The cross section, which is small just above the four-pion threshold, exhibits a large enhancement near the ϱ 0 ϱ 0 threshold.

We present the first data on photon-photon annihilation into hadrons for CM energies > 1 GeV obtained with the detector PLUTO at the e + e − storage ring PETRA. Cross sections are extracted using an inelastic eγ scattering formalism. The results are compared to expectations from Regge-like models.

We present new high statistics data on hadron production in photon-photon reactions. The data are analyzed in terms of an electron-photon scattering formalism. The dependence of the total cross section of Q 2 , the four-momentum transfer squared of the scattered electron, and on the mass W of the hadronic system is investigated. The data are compared to predictions from Vector-Meson Dominance and the quark model.

We have measured the production cross section for K s 0 in e + e − annihilation from 3.6 to 5.0 GeV center of mass energy. A substantial increase of the K s 0 yield is observed around 4 GeV in qualitative agreement with the charm hypothesis.

The ratio of π − to π + electroproduction cross sections from deuterons has been measured in the resonance region at an average four-momentum transfer squared of 0.5 (GeV/ c ) 2 . Results are presented over a wide range of pion production angles and comparisons are made with theoretical predictions based on SU(6) w symmetry and the Melosh transformation.

The asymmetry parameter A in π−p elastic scattering at incident pion laboratory kinetic energies Tπ of 98, 238, and 2922 MeV and in π−p charge-exchange scattering π−p→π0n at Tπ=238, 292, and 310 MeV have been measured over a wide range of scattering angles (typically from about 60° to 130° c.m.) with a polarized proton target. The data have been used in an energy-independent phase-shift analysis to improve the precision of the pion-nucleon phase shifts, to set new limits on violation of isospin conservation in the pion-nucleon S wave, and to confirm significant charge dependence in the P32 wave.

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We investigate the four-photon final state produced in γγ colissions. In the π 0 π 0 channel we observe f(1270) production with predominantly helicity 2 and measure a partial width Γ γγ 2.9 +0.6 −0.4 ± keV (independent of assumptions on the helicity). We observe A 2 (1310) production in the π 0 η channel and find a partial width Γ γγ = 0.77 ± 0.18 ± 0.27 KeV (assuming helicity 2). We give an upper limit for f ≈ ηη .

The production of thef0 in two photon collisions, with the subsequent decayf0→π+π− has been observed in the CELLO detector at PETRA. Thef0 peak was found to lie on a dipion continuum and to be shifted downwards in mass by ≃50 MeV/c2. The ππ mass spectrum from 0.8 to 1.5 GeV/c2 was well fitted by the model of Mennessier using only a unitarised Born amplitude and helicity 2f0 amplitude. The previously observed mass shift and distortion of thef0 peak are explained by strong interference between the Born andf0 amplitudes. The only free parameter in the fit of the data to the model is the radiative widthΓγγ(f0). It was found that:Γγγ(f0)=2.5±0.1±0.5 keV where the first (second) quoted errors are statistical (systematic).

We have determined the cross section for γγ→π+π+π−π− in a way free of assumptions about the relative contributions fromρ0ρ0,ρ02π and 4π (uncorrelated phase space). We find a sharp onset above threshold and a rather high cross section of about 200 nb aroundWγγ=1.5 GeV which consists to about 40% ofρ0ρ0 production with sizeable contributions fromρ02π and 4π (PS). The total cross section as well as theρ0ρ0 content fall rather fast at higher c.m. energies. Attempts to explain this behaviour in terms of production of known resonances are not successful so far. The angular distributions do not show any significant structure pointing to resonance formation in the 4π-system. Only theρ0-meson is observed in the moment analysis. The decay distributions of theρ0 for forward produced rhos are fairly consistent with helicity conservation of the produced rhos in accordance with the VDM picture.

We have observed exclusive production of K + K − and K S O K S O pairs and the excitation of the f′(1515) tensor meson in photon-photon collisions. Assuming the f′ to be production in a helicity 2 state, we determine Λ( f ′ → γγ) B( f ′ → K K ) = 0.11 ± 0.02 ± 0.04 keV . The non-strange quark of the f′ is found to be less than 3% (95% CL). For the θ(1640) we derive an upper limit for the product Λ(θ rarr; γγ K K ) < 0.03 keV (95% CL ) .

Results are presented of an untagged e + e − → e + e − + π + π − experiment performed at PEP with the DELCO detector. In the invariant-mass range 0.7 ⩽ W ππ < 2.0 GeV/ c 2 , the QED e + e − background is identified and eliminated, and both the π + π − predictions and the μ + μ − and K + K − background substractions are normalized to the measurement of the e e + e − events. The results agree with a simple model of superposition and interference of the f 0 (1270) resonance, produced with helicity 2, with a Born-term continuum. From a fit of the model to the data, the radiative width of the f 0 is determined to be Γ f 0 → γγ = 2.70 ± 0.21 keV.

An analysis of the production ofKS0KS0 andK±Ks0π∓ by two quasi-real photons is presented. The cross section forγγ→K0\(\overline {K^0 } \), which is given for the γγ invariant mass range fromK\(\bar K\) threshold to 2.5 GeV, is dominated by thef′(1525) resonance and an enhancement near theK\(\bar K\) threshold. Upper limits on the product of the two-photon width times the branching ratio intoK\(\bar K\) pairs are given forΘ(1700),h(2030), and ξ(2220). For exclusive two-photon production ofK±Ks0π∓ no significant signal was observed. Upper limits are given on the cross section ofγγ→K+\(\overline {K^0 } \)π− orK−K0π+ between 1.4 and 3.2 GeV and on the product of the γγ width times the branching ratio into theK\(\bar K\)π final states for theηc(2980) and the ι(1440), yieldingΓ(γγ)→i(1440))·BR(i(1440)→K\(\bar K\)π<2.2 keV at 95% C.L.

We report measurements of the two-photon processes e+e−→e+e−π+π− and e+e−→e+e−K+K−, at an e+e− center-of-mass energy of 29 GeV. In the π+π− data a high-statistics analysis of the f(1270) results in a γγ width Γ(γγ→f)=3.2±0.4 keV. The π+π− continuum below the f mass is well described by a QED Born approximation, whereas above the f mass it is consistent with a QCD-model calculation if a large contribution from the f is assumed. For the K+K− data we find agreement of the high-mass continuum with the QCD prediction; limits on f′(1520) and θ(1720) formation are presented.

This paper gives a detailed description of an experiment which studies the interactions of muon-type neutrinos in hydrogen and deuterium. The experiment was performed at the Zero Gradient Synchrotron using the wide-band neutrino beam incident on the Argonne 12-foot bubble chamber filled with hydrogen and deuterium. The neutrino energy spectrum peaks at 0.5 GeV and has a tail extending to 6 GeV. The shape and intensity of the flux is determined using measurements of pion yields from beryllium. The produced pions are focused by one or (for the latter part of the experiment) two magnetic horns. A total of 364000 pictures were taken with a hydrogen filling of the bubble chamber and 903 000 with a deuterium filling. The scanning and other analyses of the events are described. The most abundant reaction occurs off neutrons and is quasi-elastic scattering νd→μ−pps. The separation of these events from background channels is discussed. The total and differential cross sections are analyzed to obtain the axial-vector form factor of the nucleon. Our result, expressed in terms of a dipole form factor, gives an axial-vector mass of 0.95±0.09 GeV. A comparison is made to previous measurements using neutrino beams, and also to determinations based upon threshold pion electroproduction experiments. In addition, the data are used to measure the weak vector form factor and so check the conserved-vector-current hypothesis.

We have used the momentum spectrum of leptons produced in semileptonic B-meson decays to set a 90%-confidence-level upper limit on Γ(b→ulν)Γ(b→clν) of 4%. We also measure the semileptonic branching fractions of the B meson to be (12.0±0.7±0.5)% for electrons and (10.8±0.6±1.0)% for muons.

Results are presented on the exclusive production of four-prong final states in photon-photon collisions from the TPC/Two-Gamma detector at the SLAC e+e− storage ring PEP. Measurement of dE/dx and momentum in the time-projection chamber (TPC) provides identification of the final states 2π+2π−, K+K−π+π−, and 2K+2K−. For two quasireal incident photons, both the 2π+2π− and K+K−π+π− cross sections show a steep rise from threshold to a peak value, followed by a decrease at higher mass. Cross sections for the production of the final states ρ0ρ0, ρ0π+π−, and φπ+π− are presented, together with upper limits for φρ0, φφ, and K*0K¯ *0. The ρ0ρ0 contribution dominates the four-pion cross section at low masses, but falls to nearly zero above 2 GeV. Such behavior is inconsistent with expectations from vector dominance but can be accommodated by four-quark resonance models or by t-channel factorization. Angular distributions for the part of the data dominated by ρ0ρ0 final states are consistent with the production of JP=2+ or 0+ resonances but also with isotropic (nonresonant) production. When one of the virtual photons has mass (mγ2=-Q2≠0), the four-pion cross section is still dominated by ρ0ρ0 at low final-state masses Wγγ and by 2π+2π− at higher mass. Further, the dependence of the cross section on Q2 becomes increasingly flat as Wγγ increases.

In the analysis of the reactione+e−→e+e−KS0Ks0 clear evidence for exclusive γγ→f2′ resonance production is observed. The productΓγγ ·B(f2′→K\(\bar K\)) is measured to be 0.10−0.03−0.02+0.04+0.03 keV independent of ana priori assumption on the helicity structure. Our data are consistent with a pure helicity 2 contribution and we derive an upper limit for the ratioΓγγ(0)/Γγγ. The absence of events in the mass region around 1.3 GeV clearly proves destructivef2−a2 interference and allows to measure the relative phases betweenf2,a2 andf2′. Upper limits on the production of the glueball candidate statesf2(1720) andX(2230) as well as theKS0KS0-continuum are given.

We have measured the cross section of four charged pion production in photon-photon interactions in the invariant mass range 1.0≦Wγγ≦3.2 GeV and up toQ2=16 GeV2. For 1.2 GeV≦Wγγ≦1.7 GeV the process is dominated by ρ0ρ0 production with a rapid rise in cross section around 1.2 GeV, well below the nominal ρ0ρ0 threshold. The observed distributions in the two particle masses and in the production and decay angles are well described by an incoherent sum of the phase-space subprocesses γγ →ρ0ρ0, →ρ0π+π−, and →π+π−π+π−. A spin-parity analysis of the ρ0ρ0 system showsJP=2+ to dominate, although 0+ is also possible forWγγ≦1.4 GeV. Negative partity states are excluded.

The reactione+e−→e+e− A2 (1320) has been observed by detecting the decayA2→π+,π-π0. The two-photon width of theA2 has been measured to be Г(A2→γγ)=(0.09±0.27 (stat)±0.16 (syst)) keV. The cross section σ(γγ→π+,π-π0 has been determined outside theA2 resonance region.

The e + e − → ηπ + π − reaction has been measured in the center of mass energy interval 1350–2400 MeV by the magnetic detector DM2 at the Orsay storage ring DCI. Under the hypothesis of only one large resonance the cross section is not fit in a satisfactory way. The branching ratio τ − → η − π 0 ν τ =(0.13 ± 0.02)% is deduced via CVC from the above measurement.

Result of cross section measurements for the reaction π − p → π − π + n are presented. They cover a range of incident pion momenta between 295 and 450 MeV/ c . It is the first time that the cross section has been measured so close to threshold. The experiment was performed with Omicron, a large-solid-angle spectrometer, which enables a measurement of the full set of kinematic variables. In the region of overlap there is a good agreement with other experiments. The extracted value for the chiral-symmetry-breaking parameter ξ is seen to be largely extrapolition dependent but the measured value of -0.5±0.8 leaves Weinberg's prediction of ξ =0 the only remaining choice.

The e + e − → π + π − cross section has been measured from about 280 events (an order of magnitude more than the previous world statistics) in the energy interval 1.35 ⩽ s ⩽ 2.4 GeV with the DM2 detector at DCI. The pion squared form factor | F π | 2 shows a deep minimum around 1.6 GeV/ c 2 and is better fit under the hypothesis of two ϱ-like resonance ⋍0.25 GeV/ c 2 wide with 1.42 and 1.77 GeV/ c 2 masses.

A full-kinematics measurement of the π − p→ π − p π 0 reaction in the incident π − momentum region from 295 to 450 MeV/ c is presented. The measurement was performed with the OMICRON spectrometer at the CERN synchrocyclotron.

Resonance production in the γγ reactionse+e−→e+e+e−π0π0 ande+e−π0η has been studied with the JADE detector at PETRA. The decay widths into γγ of thef2(1270),a0(980) anda2(1320) were measured to be\(\Gamma _{\gamma \gamma } (f_2 (1270)) = 3.19 \pm 0.09_{ - 0.38}^{ + 0.22} \) Kev,Γλλ(a0(980))=0.28±0.04±0.10 KeV/BR(a0(980)→π0η) andΓλλ(a2(1320))=1.01±0.14±0.22KeV. For thef0(975) andf4(2050) upper limits of the widths were obtained,Γλλ(f0(975))<0.6 KeV, andΓλλ(f4(2050))<1.1 KeV, both at the 95% C.L. Assuming that the spin 0 background under thef2(1270) is small, thef2(1270) was found to be produced exclusively in a helicity 2 state. The helicity 0 contribution is <15% at the 95% C.L. The cross section forλλ→π0π0 in the mass range 2.0–3.5 GeV/c2 was measured for the first time. Since the cross section forλλ→π+π− is a factor ∼2 larger, ππ production in this range can be interpreted as taking place via isospin 0 production.

An analysis has been performed of neutrino and antineutrino interactions with protons and neutrons in a deuterium bubble chamber. The interactions under study are quasielastic neutrino-neutron scattering and one-, two- and three-pion production reactions. Results are presented on cross sections, effective mass distributions, resonance production, momentum transfer distributions and coefficients of the decay angular distributions. Where possible, comparisons are made with existing theoretical models and predictions.

Using data onvp and\(\bar vp\) charged current interactions from a bubble chamber experiment with BEBC at CERN, the average multiplicities of charged hadrons and pions are determined as functions ofW2 andQ2. The analysis is based on ∼20000 events with incidentv and ∼10000 events with incident\(\bar v\). In addition to the known dependence of the average multiplicity onW2 a weak dependence onQ2 for fixed intervals ofW is observed. ForW>2 GeV andQ2>0.1 GeV2 the average multiplicity of charged hadrons is well described by〈n〉=a1+a2ln(W2/GeV2)+a3ln(Q2/GeV2) witha1=0.465±0.053,a2=1.211±0.021,a3=0.103±0.014 for thevp anda1=−0.372±0.073,a2=1.245±0.028,a3=0.093±0.015 for the\(\bar vp\) reaction.

We present a measurement of the polarization of Antilambda hyperons produced in nu_mu charged current interactions. The full data sample from the NOMAD experiment has been analyzed using the same V0 identification procedure and analysis method reported in a previous paper for the case of Lambda hyperons. The Antilambda polarization has been measured for the first time in a neutrino experiment. The polarization vector is found to be compatible with zero.

The production of charged kaon pairs in two-photon interactions has been studied with the ARGUS detector and the topological cross section has been measured. The γγ-widths and interference parameters have been determined for the tensor mesonsf2 (1270),a2 (1318) andf′2 (1525). The helicity structure assumed for the continuum contribution has a significant effect on the result. Upper limits have been obtained for the γγ-widths of the glueball candidate statesf2 (1720) andX (2230).

The process γγ→π+π−π+π− has been investigated in reactions of the typee+e−→e+e−π+π−π+π− in the single tag mode. The range of the four momentum squared of one of the virtual photons was 0.28 GeV2/c2≦Q2≦3.6 GeV2/c2, the average being 〈Q2〉=0.92 GeV2/c2; the other photon was quasi real. The reaction is mainly described by the channels γγ→ρ0ρ0 and γγ→4π (phase space), occuring with about equal probability. TheQ2-dependence of the cross section is in agreement with the ρ form factor.

In the reaction γγ→KS0KS0 resonance production of thef2− is observed. For the radiative with\(\Gamma _{\gamma \gamma } .B(f'_2\to K\bar K) = 0.11_{ - 0.02}^{ + 0.03}\pm 0.02keV\) is found. The small number of events in thef2,a2 mass region is consistent with the assumption of destructivef2−a2 interference. From the mass distribution we determine the relative phases between the tensor mesons. Upper limits on the radiative widths of the glueball candidatesf2(1720) andX (2220) are derived.

The cross section for exclusive π+ electroproduction on the proton has been measured near threshold for the first time at two different values of the virtual photon polarization (ɛ∼0.2 and ɛ∼0.7). Using the low energy theorem for this reaction we deduce the axial and pseudoscalar weak form factors GA and GP at ‖t‖=0.073, 0.139, and 0.179 (GeV/c)2. The slope of GA agrees with the value obtained in neutrino experiments. GP satisfies the pion pole dominance hypothesis, which is thus verified for the first time in this range of transfer.

The total cross sections for the three γp → Nππ reactions have been measured for photon energies from 400 to 800 MeV. The γ p → p π 0 π 0 and γ p → n π + π 0 cross sections have never been measured before while the γ p → p π + π − results are much improved compared to earlier data. These measurements were performed with the large acceptance hadronic detector DAPHNE, at the tagged photon beam facility of the MAMI microtron in Mainz.

The reactionγγ→π+π−π+π− has been studied with the ARGUS detector. The rate in the invariant mass region below 1.8 GeV/c2 is found to be largely due toρ0ρ0 production. A spin-parity analysis shows a dominance of the partial wave (JP,Jz)=(2+, 2) with a small admixture fromJP=0+. The contribution of negative parity states is consistent with zero. The large ratio of cross sectionsσ(γγ→ρ0ρ0)/σ(γγ→ρ+ρ−)≃4, and the dominance of theJP=2+ wave in the reactionγγ→ρ0ρ0 is a signature consistent with the production of an exotic (I=2) resonance.

We have investigated the elastic scattering of high energy $\Sigma^-$ off electrons from carbon and copper targets using the CERN hyperon beam. Scattering events a

The\(e^ +e^ -\to K_s^0 K^ \pm\pi ^ \mp\) andK+K−π0 cross sections have been measured in the energy interval\(1350 \leqq \sqrt s\leqq 2400\) with the DM2 detector at DCI. The\(K_s^0 K^ \pm\pi ^ \mp\) cross section shows the contribution of an isoscalar vector meson at ≈1650 MeV/c2 in agreement with a previous experiment. The low statisticsK+K−π0 measurement is consistent with the above result.

The Sigma^- mean squared charge radius has been measured in the space-like Q^2 range 0.035-0.105 GeV^2/c^2 by elastic scattering of a Sigma^- beam off atomic electrons. The measurement was performed with the SELEX (E781) spectrometer using the Fermilab hyperon beam at a mean energy of 610 GeV/c. We obtain <r^2> = (0.61 +/- 0.12 (stat.) +/- 0.09 (syst.)) fm^2. The proton and pi^- charge radii were measured as well and are consistent with results of other experiments. Our result agrees with the recently measured strong interaction radius of the Sigma^-.