Infrared and collinear safe event shape distributions and their mean values are determined in e+e- collisions at centre-of-mass energies between 45 and 202 GeV. A phenomenological analysis based on power correction models including hadron mass effects for both differential distributions and mean values is presented. Using power corrections, alpha_s is extracted from the mean values and shapes. In an alternative approach, renormalisation group invariance (RGI) is used as an explicit constraint, leading to a consistent description of mean values without the need for sizeable power corrections. The QCD beta-function is precisely measured using this approach. From the DELPHI data on Thrust, including data from low energy experiments, one finds beta_0 = 7.86 +/- 0.32 for the one loop coefficient of the beta-function or, assuming QCD, n_f = 4.75 +/- 0.44 for the number of active flavours. These values agree well with the QCD expectation of beta_0=7.67 and n_f=5. A direct measurement of the full logarithmic energy slope excludes light gluinos with a mass below 5 GeV.
1-THRUST distribution.
THRUST-MAJOR distribution.
THRUST-MINOR distribution.
Transverse mass spectra of protons emitted in Au+Au collisions at beam energies of 6, 8, and 10.8 GeV/nucleon have been measured as a function of collision centrality over a rapidity range 0.5<ylab<1.5. The spectra are well reproduced by Boltzmann distributions over the measured transverse mass region, which allows for extrapolation of the data to derive the rapidity density and apparent temperature of the emitting source. The shapes of the rapidity distributions suggest significant transparency or substantial longitudinal expansion in even the most central collisions at all three beam energies. The data are analyzed within a simple thermal source plus longitudinal expansion model.
The inverse slope, mean transverse mass and rapidity density values for centrality 0 to 5 PCT for 6 GeV/nucleon collisions. Statistical errors only.
The inverse slope, mean transverse mass and rapidity density values for centrality 5 to 12 PCT for 6 GeV/nucleon collisions. Statistical errors only.
The inverse slope, mean transverse mass and rapidity density values for centrality 12 to 23 PCT for 6 GeV/nucleon collisions. Statistical errors only.
Mid-rapidity spectra and yields of K$^-$ and K$^+$ have been measured for Au+Au collisions at 4, 6, 8, and 10.7 AGeV. The K$^-$ yield increases faster with beam energy than for K$^+$ and hence the K$^-$/K$^+$ ratio increases with beam energy. This ratio is studied as a function of both $\sqrt{s}$ and $\sqrt{s}$-$\sqrt{s_{th}}$ which allows the direct comparison of the kaon yields with respect to the production threshold in p+p reactions. For equal $\sqrt{s}$ - $\sqrt{s_{th}}$ the measured ratio K$^-$/K$^+$=0.2 at energies above threshold in contrast to the K$^-$/K$^+$ ratio of near unity observed at energies below threshold. The use of the K$^-$/K$^+$ ratio to test the predicted changes of kaon properties in dense nuclear matter is discussed.
Only statistical errors are presented.
Only statistical errors are presented.
Only statistical errors are presented.
Positive pion and kaon production from Au+Au reactions have been measured as a function of beam energy over the range 2.0-10.7~AGeV. Both the kaon and the pion production cross-sections at mid-rapidity are observed to increase steadily with beam kinetic energy. The ratio of K$^+$ to $\pi^+$ mid-rapidity yields increases from 0.0271$\pm0.0015\pm0.0014$ at 2.0~AGeV to 0.202$\pm0.005\pm0.010$ at 10.7~AGeV and is larger than the K$^+$/$\pi^+$ ratio from p+p reactions over the same beam energy region. There is no indication of an onset of any new production mechanism in heavy-ion reactions in this energy range beyond rescattering of hadrons.
The centrality selection at each beam energy is the most central 5% of the total interaction cross-section (SIG(C=interaction) = 6.8b). A single exponential function in MT was fit simultaneously to the two kaonspectra at each beam energy D2(N)/D(MT)/D(YRAP)/2/PI/MT=D(N)/D(YRAP)/2/PI/T/(T+ M(KAON))/EXP((MT-M(KAON))/T). The fits reproduce the spectra well with two free parameters, the inverse slope parameter T and the rapidity density, D(N)/D(YRAP)in that rapidity slice. The mid-rapidity range for 2, 4, 6, 8 AGeV is ABS((YRAP-Ynn)/Ynn) < 0.25, for 10.7 AGeV the width is ABS((YRAP-Ynn)/Ynn) < 0.125, where Ynn is mid-rapidity in the laboratory frame. The errors are statistical only. The 1.96, 4. and 10.74 GeV are E866 data, another - E917 data.
The centrality selection at each beam energy is the most central 5% of the total interaction cross-section (SIG(C=interaction) = 6.8b). A single exponential function in MT was fit simultaneously to the two kaonspectra at each beam energy D2(N)/D(MT)/D(YRAP)/2/PI/MT=D(N)/D(YRAP)/2/PI/T/(T+ M(KAON))/EXP((MT-M(KAON))/T). The fits reproduce the spectra well with two free parameters, the inverse slope parameter T and the rapidity density, D(N)/D(YRAP)in that rapidity slice. The mid-rapidity range for 2, 4, 6, 8 AGeV is ABS((YRAP-Ynn)/Ynn) < 0.25, for 10.7 AGeV the width is ABS((YRAP-Ynn)/Ynn) < 0.125, where Ynn is mid-rapidity in the laboratory frame. The errors are statistical only. The 1.96, 4. and 10.74 GeV are E866 data, another - E917 data.
The centrality selection at each beam energy is the most central 5% of the total interaction cross-section (SIG(C=interaction) = 6.8b). The spectra were fit with a scaled exponential, D2(N)/D(YRAP)/D(MT)/2/PI/MT=D(N)/D(YRAP)/2/PI/(T**(2-L))/GAMMA(2-L,M(PION)/T)/MT**L/EXP(MT/T), where GAMMA(2-L,M(PION)/T), the complementary incomplete gamma function, is introduced in the normalization so that D(N)/D(YRAP) is a fitted parameter (and other free parameters are L and T). The mid-rapidity range for 2, 4 (E866 data), 6, 8 AGeV (E917 data) beam energy is ABS((YRAP-Ynn)/Ynn) < 0.25, for 10.7 AGeV (E917 data) the width is ABS((YRAP-Ynn)/Ynn) <0.125, where Ynn is mid-rapidity in the laboratory frame. The errors are statistical only.
In this paper Au+Au collisions at 11.6A GeV/c are characterized by two global observables: the energy measured near zero degrees (EZCAL) and the total event multiplicity. Particle spectra are measured for different event classes that are defined in a two-dimensional grid of both global observables. For moderately central events (σ/σint<12%) the proton dN/dy distributions do not depend on EZCAL but only on the event multiplicity. In contrast the shape of the proton transverse spectra shows little dependence on the event multiplicity. The change in the proton dN/dy distributions suggests that different conditions are formed in the collision for different event classes. These event classes are studied for signals of new physics by measuring pion and kaon spectra and yields. In the event classes doubly selected on EZCAL and multiplicity there is no indication of any unusual pion or kaon yields, spectra, or K/π ratio even in the events with extreme multiplicity.
Table for event classification (from CLASS1 to CLASS8) where ZCAL energy solely used for event selection. Number of Projectile Participants Npp=197*(1-E(P=3)/EKIN(P=1)).
CLASS1 (see Table for event classification).
CLASS1 (see Table for event classification).
The multiplicity structure of the hadronic system X produced in deep-inelastic processes at HERA of the type ep -> eXY, where Y is a hadronic system with mass M_Y< 1.6 GeV and where the squared momentum transfer at the pY vertex, t, is limited to |t|<1 GeV^2, is studied as a function of the invariant mass M_X of the system X. Results are presented on multiplicity distributions and multiplicity moments, rapidity spectra and forward-backward correlations in the centre-of-mass system of X. The data are compared to results in e+e- annihilation, fixed-target lepton-nucleon collisions, hadro-produced diffractive final states and to non-diffractive hadron-hadron collisions. The comparison suggests a production mechanism of virtual photon dissociation which involves a mixture of partonic states and a significant gluon content. The data are well described by a model, based on a QCD-Regge analysis of the diffractive structure function, which assumes a large hard gluonic component of the colourless exchange at low Q^2. A model with soft colour interactions is also successful.
The multiplicity moment MULT as a function of the mass of the charged hadron system in the full phase space and separately in the forward and backward hemispheres.
The multiplicity moment DISPERSION as a function of the mass of the charged hadron system in the full phase space and separately in the forward and backward hemispheres.
The multiplicity moment R2 as a function of the mass of the charged hadron system in the full phase space and separately in the forward and backward hemispheres.
Previously published and as yet unpublished QCD results obtained with the ALEPH detector at LEP1 are presented. The unprecedented statistics allows detailed studies of both perturbative and non-perturbative aspects of strong interactions to be carried out using hadronic Z and tau decays. The studies presented include precise determinations of the strong coupling constant, tests of its flavour independence, tests of the SU(3) gauge structure of QCD, study of coherence effects, and measurements of single-particle inclusive distributions and two-particle correlations for many identified baryons and mesons.
Charged particle sphericity distribution.
Charged particle aplanarity distribution.
Charged particle Thrust distribution.
Inclusive charged particle and event shape distributions are measured using 321 hadronic events collected with the DELPHI experiment at LEP at effective centre of mass energies of 130 to 136 GeV. These distributions are presented and compared to data at lower energies, in particular to the precise Z data. Fragmentation models describe the observed changes of the distributions well. The energy dependence of the means of the event shape variables can also be described using second order QCD plus power terms. A method independent of fragmentation model corrections is used to determine αs from the energy dependence of the mean thrust and heavy jet mass. It is measured to be: $$←pha _s(133 {⤪ GeV})={0.116}pm {0.007}_{exp-0.004theo}^{+0.005}$$ from the high energy data.
mean values for event shape variables.
Integral of event shape distribution over the specified interval.
Integral of event shape distribution over the specified interval.
Event shape and charged particle inclusive distributions are measured using 750000 decays of the Z to hadrons from the DELPHI detector at LEP. These precise data allow a decisive confrontation with models of the hadronization process. Improved tunings of the JETSET, ARIADNE and HERWIG parton shower models and the JETSET matrix element model are obtained by fitting the models to these DELPHI data as well as to identified particle distributions from all LEP experiments. The description of the data distributions by the models is critically reviewed with special importance attributed to identified particles.
Transverse momentum PTIN w.r.t. the Thrust axis. For the first table Thrust axis definition is from seen charged particles corrected to final state particles. For the second table Thrust axis definition is from seen charged plus neutral particles corrected to final state charged plus neutral particles.
Transverse momentum PTOUT w.r.t. the Thrust axis. For the first table Thrust axis definition is from seen charged particles corrected to final state particles. For the second table Thrust axis definition is from seen charged plus neutral particles corrected to final state charged plus neutral particles.
Transverse momentum PTIN w.r.t. the Sphericity axis. For the first table Sphericity axis definition is from seen charged particles corrected to final state particles. For the second table Sphericity axis definition is from seen charged plus neutral particles corrected to final state charged plus neutral particles.
Hadronic decays of Z 0 bosons are studied in the Delphi detector. Global event variables and singel particles inclusive distributions are compared with QCD-based predictions. The mean charged multiplicity is found to be 20.6±1.0 (stat+syst). The mean values of the sphericity, aplanarity, thrust, minor value, p in T and p out T are compared with values found at lower energy e + e − colliders.
Corrected Sphericity distribution. Statistical errors only.
Corrected Aplanarity distribution. Statistical errors only.
Corrected Q3-Q2 distribution. Statistical errors only.
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