We present the first results of an experiment at the CERN intersecting storage rings, which measures the total cross-section in proton-proton collisions. The equivalent laboratory momenta are 291, 496, 1068 and 1480 GeV/c. We have made a direct measurement of αT as the ratio between the total interaction rate and the machine luminosity. The present paper gives a detailed description of the experimental apparatus and of the analysis procedure. We find that αT increases by about 10% in the energy region studied.
No description provided.
Data, obtained from p-p collisions at centre-of-mass energies between 31 and 63 GeV, are presented on inclusive and semi-inclusive correlations between forward emitted neutrons and charged particles observed in an omnidirectional hodoscope. A total absorption spectrometer was used to detect the neutrons and to measure their energy. Significant correlations are observed over the whole rapidity range. The data suggest that neutrons result from the decay of clusters emitted in the fragmentation region.
No description provided.
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Data obtained from p-p collisions at centre-of-mass energies between 31 and 63 GeV are presented on correlations between momentum analysed forward π − , K − and p and charged particles observed in an omnidirectional hodoscope. The data show that significant correlations are present over the whole rapidity range for all three types of negative particles. The dependence on various kinematic variables suggests a cluster mechanism for the production of particles. In this picture, pions would be produced in clusters emitted in the fragmentation region while K − and p emanate from non-leading clusters.
No description provided.
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We present a measurement of the total cross section σ t in proton-proton collisions at the CERN ISR. The method involves determination of the total interaction rate and machine luminosity. A two-arm scintillation hodoscope observes ∼ 90% of the total interaction rate, while a streamer chamber is employed for event topologies missed by the main trigger. An increase of about 10% in σ t is observed in the energy range √ s = 23.6 to √ s = 62.8 GeV/ c in agreement with previous experiments.
VAN DER MEER METHOD.
We present a study of the transverse momentum spectrum of π 0 's produced at c.m. angles θ = 90° and 53° in pp collisions at √ s = 23.6, 30.8, 45.1, 53.2, and 62.9 GeV. The experiment was performed with a lead-glass detector. The data can be described with the usual parametrization p T −n ƒ;(x T , θ) , with n = 7.2 ± 0.2. Comparison between the 90° and 53° data further indicates no appreciable dependence on θ , at least for x T < 0.3. Two-particle inclusive cross sections for π 0 's produced alongside are also presented. They are observed to have a dependence upon the transverse momentum of the dipion similar to that of single-particle cross sections and with the same value of n . Two-photon decays of η mesons are observed between 3 and 4 GeV/ c transverse momentum with a production cross section half of that of π 0 .
No description provided.
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Measurements of the proton-proton total cross section have been made with increased precision (±0.6%) over the ISR energy range s =23.5−62.7 GeV . Two different experimental methods gave consistent results, showing that the total cross section increases 10% over the ISR range and in addition that the absolute value of the ISR luminosity can be measured to ±0.9%.
CROSS SECTIONS ARE A WEIGHTED AVERAGE OF THOSE OBTAINED BY THE PISA-STONY BROOK METHOD AND BY THE CERN-ROME (OPTICAL THEOREM) METHOD.
We have performed a simultaneous measurement of the large transverse momentum (1.6 to 3.8 GeV/ c ) yields of single photons and of photon pairs at 90° production angle in pp collisions at ISR energies. Production cross sections for each of these two processes are compared.
No description provided.
No description provided.
Results are reported for the invariant differential cross-section of charged pions produced at x = 0 in proton-proton collisions at the CERN ISR. The range covered is 40 to 400 MeV/c in transverse momentum and 23 to 63 GeV in collision energy. The inclusive cross-section for π + and π − are increasing by 36 ± 2% and 41 ± 2%, respectively over the ISR energy range with a somewhat stronger increase at the lowest transverse momenta. The transverse momentum distribution is well described by an exponential in the transverse energy.
No description provided.
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The inclusive production of low-momentum charged pions, kaons, and protons has been measured at x = 0 over the ISR energy range 23 < √ s < 63 GeV. The average increase in the invariant differential cross section is 36 ± 2% for π + , 41 ± 2% for π − , 52 ± 8% for K + , 69 ± 8% for K − , 8 ± 5% for p, and 84 ± for p ̄ . Pions have been measured in the range 0.04 < p T < 0.4 GeV/ c , kaons over 0.1 < p T < 0.3 GeV/ c , and nucleons over 0.1 < p T < 0.5 GeV/ c .
No description provided.
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The real part of the proton proton elastic scattering amplitude has been determined from its interference with the Coulomb amplitude at total centre-of-mass energies up to 62 GeV. The observed steady increase of ϱ with energy indicates that the total proton proton cross section continues to increase well beyond this energy.
No description provided.
USING SIG AND SLOPE OBTAINED FROM INTERPOLATIONS OF PREVIOUS MEASUREMENTS.
The Split Field Magnet facility at the CERN ISR has been used to measure inclusive resonance production in inelastic p-p collisions at a c.m. energy of 53 GeV. The mass spectrum of pairs of oppositely charged hadrons shows a strong correlation, which can be explained as a consequence of dominant vector meson production, accounting for more than 60% of all pions and kaons produced.
No description provided.
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We present the first direct measurements of charged-particle multiplicity distributions for pp collisions at ISR energies. The measurements are performed by means of a streamer chamber detector with large solid-angle coverage and excellent multitrack efficiency. Particle densities are observed to rise in the central region as s increases. The multiplicity distributions in this region deviate from a Poisson Law, thus giving evidence for correlations. These correlations are of the same type as those obtained from clustering of the collision products. The mean charged multiplicity over the full rapidity range increases faster than log s . Our data do not support an early onset of KNO multiplicity scaling.
Pseudorapidity distribution at 23.6 GeV.
Pseudorapidity distribution at 45.2 GeV.
Pseudorapidity distribution at 62.8 GeV.
We report on measurements of inclusive π 0 production at c.m. energies of 53 and 63 GeV, θ ≅90°, from p-p collisions at the CERN ISR. In the range 0.2< x t <0.45 the data can be described by a form: Ed 3 σ d p 3 ∝p − (6.6±0.8) t (1−x t ) (9.6±1.0) .
No description provided.
No description provided.
Measurements are presented of the inclusive π 0 production cross section, in the transverse momentum range 2.3 ⪅ p T ⪅4.5 GeV/c, for dd and dp interactions at total c.m. energies of √ s = 52.7 GeV and √ s = 63.2 GeV and for pp interactions at √ s = 52.7 GeV. The produced π 0 's are detected by identifying both protons from the decay π 0 → γγ . As in pp interactions, the data can be adequately described by a p T −n ƒ(x T ) dependence with n ≌ 8 . The data are approximately consistent with the expectations of free nucleon scattering. No significant differenceare observed in either the charged or the neutral particle distributions associated with π 0 , for dd, dp and pp interactions.
GLOBAL NORMALIZATION UNCERTAINTY = 12 PCT. RELATIVE NORMALIZATION UNCERTAINTY = 5 PCT.
GLOBAL NORMALIZATION UNCERTAINTY = 10 PCT. RELATIVE NORMALIZATION UNCERTAINTY = 6 PCT.
GLOBAL NORMALIZATION UNCERTAINTY = 15 PCT. RELATIVE NORMALIZATION UNCERTAINTY = 7 PCT.
The measurement of the proton-proton total cross section performed by the CERN-Pisa-Rome-Stony Brook Collaboration at the CERN ISR is discussed in detail. The total interaction rate, the elastic scattering rate in the forward direction, and the machine luminosity were measured simultaneously to obtain three different determinations of the total cross section. Consistent results were found, which made it possible to prove the reliability of the Van der Meer luminosity calibration within +-0.9% and to achieve a precision of +-0.6% in the measurement of the total cross section.
No description provided.
Inclusive cross sections are presented for 2π and 3π systems with large longitudinal x at the highest intersecting storage ring energies (s=53 GeV for 2π; s=53 and 62 GeV for 3π). The ratio π+π−π−π− rises sharply with increasing x similar to the ratio K+K−, as expected in a quark-model interpretation.
The differential cross section is fitted by the equation : E*D3(SIG)/D3(P) = CONST*(1-XL)**POWER*EXP(-SLOPE*PT**2).
The differential cross section is fitted by the equation : E*D3(SIG)/D3(P) = CONST*(1-XL)**POWER*EXP(-SLOPE*PT**2).
Inclusive measurements of Λ 0 , Λ 0 , Ξ − , Σ(1385) ± ) production in the forward direction at the CERN intersecting storage rings are presented. A signal for simulataneous Λ 0 Λ 0 production is also observed with total x > 0.6, 2.3 < M Λ Λ < 2.5 GeV and with a cross section of (1.7 ± 0.2) μb.
No description provided.
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The inclusive production of π 0 at large values of p T in pp collisions at the ISR has been studied. In this experiment the two photons are resolved and separately measured for p T values of up to 6 GeV/ c , giving confidence that the desired signal has been separated from various backgrounds.
No description provided.
Inclusive π 0 production at 90° has been studied at the ISR at s 1 2 = 52.7 and 62.4 GeV over the p T range from 7 to 15 GeV/ c . The two photons from π 0 decay yielded overlapping electromagnetic showers in the liquid-argon-Pb plate calorimeter detector system. Any direct photon production is included in these measurements. For large values of p T , the cross section is observed to decrease with p T more slowly than the p T −8 behaviour which has been observed at lower values of p T .
No description provided.
The inclusive η production cross section at the CERN ISR has been measured for p T values of up to 11 GeV/ c . We find that the η π 0 cross-section ratio has an average value of 0.55 ± 0.07 and varies little with p T .
No description provided.
Single photon production in pp collisions at 30 < √ s < 62 GeV has been measured with liquid-argon-lead calorimeters at the CERN ISR. This process remains approximately constant with increasing √ s . For fixed √ s , the single photon to π 0 ratio increases strongly with increase in p T . The γ π 0 ratio is about 0.2 for p T above 4.5 GeV/c.
No description provided.
We have measured direct photon production in pp collisions at the CERN intersecting storage rings for c.m. energies 31 < √ s < 63 GeV and transverse momenta up to 9GeV/ c , using segmented lead/liquid-argon calorimeters. The ratio of direct photon to π 0 production is significantly larger than zero, starting at p T ≈ 4 GeV/ c and increasing to values of about 0.4 at 9GeV/ c . No significant √s dependence is seen.
No description provided.
Data from a study of electron pairs produced in pp collisions (√ s = 5 and 63 GeV) are used to extend measurements of the scaling function down to m /√ s ≈ 0.07 (4.5 < m < 19 GeV). The dilepton continuum can be described by the scaling formula (fx475-1)
No description provided.
No description provided.
We present the B( d θ d y ) y=0 for J /ψ over thefull range of ISR energies and for ϒ at √ s = 53 and 63 GeV, using their dielectron decay mode. The average transverse momentum and the decay angles are presented. We found ( p T ) = 1.75 ± 0.19 GeV for ϒ, being higher than ( p T ) of the continuum and rising with √s. We present a comparison of the cross sections of J/ψ and ϒ with those of the continuum, at the same masses, as a function of √s. An appropriate scaling of the hadronic production of quark-antiquark narrow bound states involving ⋉, J/ψ, ψ′, ϒ, and ϒ′ is presented as a function of m /√ s at y = 0, and is compared with Drell-Yan scaling.
No description provided.
UPSILON HERE = UPSILON+UPSILON PRIME.
The inclusive cross-section for π0 production near 90° inpp collisions at the CERN Intersecting Storage Rings has been studied for thepT range 3<pT<16GeV/c at four different centre-of-mass energies (\(\sqrt s = 30.6\), 44.8, 52.7, and 62.8 GeV). In this experiment the two photons from the π0→yy decay were resolved and measured separately forpT values up to 10 GeV/c. Results indicate an agreement with thepT−8 behaviour for the lower values ofpT and a slower decrease of the cross-section for the higher values ofpT. The high-pT data deviate from the scaling expressionpT−nF(xT), which holds for the lowerpT values (pT<8GeV/c).
USING RETRACTED GEOMETRY.
USING SUPER-RETRACTED GEOMETRY.
USING SUPER-RETRACTED GEOMETRY.
The π0 inclusive cross section for c.m. production angles θ=90° and 22°>~θ>~5° at c.m. energies of s=23 and 53 GeV has been measured. This cross section is strongly dependent on both θ and s at small angles. The hypothesis of radial scaling is shown to be incapable of incorporating both θ and s dependence of the cross section. A recent quantum-chromodynamics calculation is in qualitative agreement with our results.
No description provided.
No description provided.
No description provided.
By using three different c.m. energies in pp interactions,\(\sqrt s \), 44, 62 GeV, it is shown that the average charged-particle multiplicity <nch> sclaes with\(\sqrt s \) once the correct hadronic energy available for multiparticle production,Ehad, is used as basic parameter. The pp data, analysed in this way, are compared with e+e− data at equivalent energies. The agreement is very satisfactory.
WITH SQRT(S) OF 30 GEV.
WITH SQRT(S) OF 44 GEV.
WITH SQRT(S) OF 62 GEV.
Measurements of pp→μ+μ−+X at s=44 and 62 GeV are compared. The data are taken under identical conditions utilizing clean proton-proton collisions from the CERN intersecting storage rings and confirm scaling to 5%. The observed μ+μ− yield is a factor of 1.6±0.2 larger than estimated from a simple parton model but is consistent with QCD. The pT dependence of the muon pairs agrees well with expectations from QCD.
No description provided.
The inclusive production cross sections of pions, kaons, protons, and antiprotons in p p and pp interactions at √ s =53 GeV are compared in the kinematic range | y | < 0.8 and p T < 1.5 GeV/ c . We observe differences in the K + /K − and p /p ratios for the two data samples. Although the bulk of the particles are produced with the same momentum and rapidity distributions in p p and pp collisions, we observe difference in these distributions for produced protons and antiprotons.
No description provided.
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We measured the total cross section for p p scattering at √ s = 53 GeV at the CERN ISR. The method was based on the measurement of the total interaction rate and of the ISR luminosity. The result obtained, σ tot = 44.1 ± 2.0 mb, suggests that σ tot ( p p) starts increasing at ISR energies. A measurement of the p p differential cross section was also performed: the results show a change in the slope at | t | ≈ 0.1 GeV 2 , similar to that observed in pp scattering.
No description provided.
No description provided.
Results are presented from the first p p colliding beam runs at the CERN ISR, using the UA5 streamer chamber detector. p p interactions at s = 53 GeV are compared with pp data taken in the same experiment. The results are in good agreement with extrapolations of low-energy p p data.
No description provided.
MOMENTS OF MULTIPLICITY DISTRIBUTIONS FOR P P AND P AP. MULT(NAME=DQ) IS <(N-<N>)**Q>**1/Q. MULT(NAME=NQ) IS <N**Q>.
Data read from plot.
We measured the total cross section for p p scattering at s = 52.8 GeV at the CERN ISR, using the direct, total-rate method. The result obtained, σ tot ( p p ) = 44.70 ± 0.53 mb , shows that, in common with σ tot (pp), this cross section also starts to rise in the ISR energy range. We remeasured the total cross section for pp scattering at the same energy, obtaining σ tot (pp) = 43.26 ± 0.33 mb, and found for the difference, Δσ tot = σ tot ( p p ) − σ tot ( pp ) , a value of 1.44±0.45 mb.
No description provided.
No description provided.
We measured the differential cross section for p̄p and pp elastic scattering in the momentum-transfer range 0.01 <| t | < 1.0 GeV 2 at the CERN Intersecting Storage Rings with center-of-mass energy s = 52.8 GeV . Fitting the differential cross section with an exponential [ A exp ( bt )], we found b p p = 13.92 ± 0.59 GeV −2 for | t | < 0.05 GeV 2 , whilst for | t | > 0.09 GeV 2 , b p p = 10.68 ± 0.26 GeV −2 . Using the optical theorem, we obtained for the total cross section σ tot ( p p)= 44.86 ± 0.78 mb and, by integrating the differential cross section, we obtained for the total elastic cross section σ el ( p p) = 7.89 ± 0.28 mb . Calculations of σ tot combining elastic-rate and total-rate measurements are also given. All of these measurements were also performed for pp scattering at the same energy, and the results for both reactions are compared.
NUMERICAL VALUES OF DATA IN FIGURE TAKEN FROM PREPRINT CERN-EP/82-65.
NUMERICAL VALUES OF DATA ON FIGURES TAKEN FROM PREPRINT CERN-EP/82-65.
No description provided.
Measurements of charged particle multiplicity distributions in the central rapidity region in p-p and p-α, and α-α collisions are reported. They are better fitted to the “wounded nucleon” than to the “gluon string” model. The average transverse momenta, for all three reactions, are identical (and almost independent of multiplicity) up to very high multiplicities.
THE FIRST PP DATA IS AT 44 GEV, THE SECOND AT 63 GEV.
No description provided.
We have studied the inclusive production of the hadrons π ± , K ± , p, p , Λ, Λ , ρ and ⋉ in the central region at the ISR s = 53 GeV , in both pp and p p collisions. Differences are observed only for K ± , p, and p production. We then study also correlations between low- p T pp and p p pairs in the two types of collisions, separating the contribution from baryon pair production and from the incident particles (stopping protons). We observe a positive correlation between two stopping protons; between the production of two pairs, and between a stopping proton and a pair production, there are negative correlations.
No description provided.
Measurements are presented of inclusive distributions in pp and p p interactions at √ s = 53 GeV. The data were obtained at the CERN ISR using the Split Field Magnet spectrometer with a minimum bias trigger. The inclusive distributions are analyzed as functions of the transverse momentum, the rapidity and the Feynman- x variable.
No description provided.
No description provided.
No description provided.
The multiplicities of charged secondaries in proton-proton collisions were determined using the split-field-magnet detector at the CERN Intersecting Storage Rings (ISR). Measurements are presented on multiplicity distributions both for inelastic and non-single-diffractive events at four different energies s=30.4, 44.5, 52.6, and 62.2 GeV. The results reported here represent the first high-statistics measurement of charged multiplicity distributions at ISR energies with a magnetic detector covering nearly the full solid angle.
INELASTIC EVENTS.
NON-SINGLE-DIFFRACTIVE EVENTS.
Moments of the multiplicity distributions for Inelastic events.
We have measured the differential cross section for pp and p̄p elastic scattering at √ s = 31, 53 and 62 GeV in the interval 0.05 < | t | < 0.85 GeV 2 at the CERN ISR using the Split Field Magnet detector. At 53 and 62 GeV, for 0.17 < | t | < 0.85 GeV 2 both pp and p̄p data show simple exponential behaviour in t ; at √ s = 31 GeV the data for 0.05 < | t | < 0.85 GeV 2 are consistent with a change in slope near | t | = 0.15 GeV 2 .
ERRORS CONTAIN BOTH STATISTICAL AND T-DEPENDENT SYSYEMATIC ERRORS.
No description provided.
LOCAL SLOPE PARAMETERS BASED ON QUADRATIC EXPONENTIAL FIT.
A detailed account is given of high-precision measurements of the total hadronic cross sections of proton-antiproton and proton-proton interactions at centre-of-mass energies of 30.6, 52.8 and 62.7 GeV. The experiment was performed at the CERN Intersecting Storage Rings (ISR) using the total interaction-rate method, in which additive correction terms for trigger losses were held to less than 6% of the final result. An experimental determination of the vertical beam-displacement scale permitted luminosity-monitor calibrations to be made with high intrinsic accuracy. The overall precision (systematic and statistical errors combined) achieved in the total cross sections was ± 1.1% for proton-antiproton reactions and 0.7% for proton-proton reactions. In the proton-proton case the measurement was the most precise such measurement made at the ISR.
No description provided.
ERRORS CONTAIN BOTH STATISTICS AND SYSTEMATICS.
ERRORS CONTAIN POINT-TO-POINT AND THE ERROR-INDEPENDANT ERRORS.
We have measured the differential cross section for p¯p and pp elastic scattering at s=53 GeV in the interval 0.5<|t|<4.0 (GeV/c)2 at the CERN intersecting storage rings using the split-field magnet detector. The shape of the differential cross section differs significantly between p¯p and pp scattering in the region 1.1<|t|<1.5 (GeV/c)2, with p¯p data showing a less pronounced dip structure than pp data.
No description provided.
No description provided.
We have measured the production of direct photons, π 0 's, and η's in p p and pp collisions at √ s =53 GeV in the range 2≈ p T ≈6 GeV/ c for the central rapidity region | y | 0.4. No statistically significant difference between pp̄ and pp interactions is observed.
No description provided.
No description provided.
No description provided.
Results are presented from a study of the reaction p p→ Λ Λ near threshold. Over 3000 events recorded at s values 14.6 and 25.5 MeV above the Λ Λ threshold (2231.2 MeV) have been analysed. Results for the production cross section, differential cross section, and the Λ and Λ polarization are given at both energies and are compared with recent theoretical calculations of this process.
Statistical errors only.
No description provided.
No description provided.
The total cross section for the process of the e + e - annihilation into hadrons has been measured at the centre-of-mass energies of 50 GeV and 52 GeV and a search has been made for new heavy quarks. The ratios R = σ ( e + e - → hadrons )/ σ point ( e + e - → μ + μ - ) obtained are 4.4±0.5 at 50 GeV and 4.7±0.3 at 52 GeV, respectively. An additional systematic uncertainty is 10%. From the event shape analysis we found no evidence for a new quark with charge 2 3 e .
No description provided.
The ratio R of the cross section for e+e− annihilation into hadronic final states to the QED cross section for muon-pair production is measured to be 4.34±0.45±0.30 and 4.23±0.20±0.21 at c.m. energies of 50 and 52 GeV, respectively. From these values of R and an analysis of the event shapes we deduce a 95%-confidence-level upper limit for the production rate of new heavy charge +23e or −13e quarks to be 0.19 units of R.
No description provided.
We searched for possible signatures of top-quark production in 508 e+e− hadronic annihilation events collected at s=52 GeV by the TOPAZ detector at the KEK e+e− collider TRISTAN. The observed hadronic cross section and shape of hadronic events are consistent with the standard-model predictions without top quarks. A lower limit (95% confidence level) on the mass of the lightest top meson is set at 25.8 GeV.
No description provided.
Differential cross sections for the processes e + e − → e + e − (Bhabha scattering) and e + e − → γγ have been measured with the TOPAZ detector at s =52 GeV . The results agree with the predictions of quantum electrodynamics (QED). The lower limits for the QED cut-off parameters have been obtained to be Λ + ⩾115 GeV and Λ − ⩾236 GeV for Bhabha scattering, and Λ + ⩾94 GeV and Λ − ⩾59 GeV for the reaction e + e − → γγ .
Statistical errors only.
Statistical errors only.
Ratio of experimental data to prediction for lowest order QED. Statistical errors only.
The reactions e + e − → μ + μ − and τ + τ − were measured at s =52 GeV and 55 GeV by using the TOPAZ detector at TRISTAN. For the combined data, the observed charge asymmetry is −0.29±0.13 and the total cross section is 27.9±3.0 (stat.)±0.8 (syst.) pb for μ + μ − production, and those for τ + τ − production are −0.20±0.14 and 35.7±4.3 (stat.)±2.4 (syst.)pb, respectively. These values are consistent with predictions by the standard model of electroweak interactions.
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We have studied inclusive lepton production in e + e − annihilations into multihadrons in the energy range between √ s =50 and 55 GeV using the VENUS detector at TRISTAN, KEK. Though MARK-J and JADE groups at PETRA found an excess of isolated muon events at √ s ⩾46.3 GeV, we have not observed such an anomaly in muon nor in electron production. The observed rates of isolated leptons are consistent with the production and decay of five known quarks.
Observed rates for whole event sample.
No description provided.
No description provided.
Measurements of the differential cross sections for e + e − →μ + μ − and e + e − →τ + τ − at values of s from 52 to 57 GeV are reported. The forward-backward asymmetries and the total cross sections for these reactions are found to be in agreement with predictions of the standard model of the electro-weak interactions. These measurements are used to extract values of the weak coupling constant g v e g v l and g A e g A l , where l = μ or τ .
Axis error includes +- 5/5 contribution (Included in the quoted errors for the total cross sections. The main contribution to SYS-ERR are the systematic uncertainty in the luminosity measurement and the uncertainty in the computer modeling of the various efficiencies and backgrounds).
Axis error includes +- 5/5 contribution (Included in the quoted errors for the total cross sections. The main contribution to SYS-ERR are the systematic uncertainty in the luminosity measurement and the uncertainty in the computer modeling of the various efficiencies and backgrounds).
No description provided.
The total cross section for e + e − annihilation into hadrons has been measured for CM energies ranging from 50 to 57 GeV. We fit the predictions of the standard model to these measurements and those at lower energies. The mass of the Z 0 boson, M Z , and the QCD scale parameter, Λ MS , are derived from the fit. The results are M Z =88.6 −1.8 +2.0 GeV/ c 2 , and Λ MS =0.15 −0.11 +0.16 GeV .
No description provided.
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