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The hadronic final states observed with the ALEPH detector at LEP in ${\rm e}^ + {\rm e}^-$ annihilation
Mean charged particle multiplicities at different c.m. energies.
XP distribution at c.m. energy 133.0 GeV.
XP distribution at c.m. energy 161.0 GeV.
XP distribution at c.m. energy 172.0 GeV.
XP distribution at c.m. energy 183.0 GeV.
XP distribution at c.m. energy 189.0 GeV.
XP distribution at c.m. energy 196.0 GeV.
XP distribution at c.m. energy 200.0 GeV.
XP distribution at c.m. energy 206.0 GeV.
Peak position in XI distribution for different c.m. energies.
XI distribution at c.m. energy 133.0 GeV.
XI distribution at c.m. energy 161.0 GeV.
XI distribution at c.m. energy 172.0 GeV.
XI distribution at c.m. energy 183.0 GeV.
XI distribution at c.m. energy 189.0 GeV.
XI distribution at c.m. energy 196.0 GeV.
XI distribution at c.m. energy 200.0 GeV.
XI distribution at c.m. energy 206.0 GeV.
XE distribution at c.m. energy 133.0 GeV.
XE distribution at c.m. energy 161.0 GeV.
XE distribution at c.m. energy 172.0 GeV.
XE distribution at c.m. energy 183.0 GeV.
XE distribution at c.m. energy 189.0 GeV.
XE distribution at c.m. energy 196.0 GeV.
XE distribution at c.m. energy 200.0 GeV.
XE distribution at c.m. energy 206.0 GeV.
PTIN distribution at c.m. energy 133.0 GeV.
PTIN distribution at c.m. energy 161.0 GeV.
PTIN distribution at c.m. energy 172.0 GeV.
PTIN distribution at c.m. energy 183.0 GeV.
PTIN distribution at c.m. energy 189.0 GeV.
PTIN distribution at c.m. energy 196.0 GeV.
PTIN distribution at c.m. energy 200.0 GeV.
PTIN distribution at c.m. energy 206.0 GeV.
PTOUT distribution at c.m. energy 206.0 GeV.
RAPIDITY W.R.T THRUST AXIS distribution at c.m. energy 133.0 GeV.
RAPIDITY W.R.T THRUST AXIS distribution at c.m. energy 161.0 GeV.
RAPIDITY W.R.T THRUST AXIS distribution at c.m. energy 172.0 GeV.
RAPIDITY W.R.T THRUST AXIS distribution at c.m. energy 183.0 GeV.
RAPIDITY W.R.T THRUST AXIS distribution at c.m. energy 189.0 GeV.
RAPIDITY W.R.T THRUST AXIS distribution at c.m. energy 196.0 GeV.
RAPIDITY W.R.T THRUST AXIS distribution at c.m. energy 200.0 GeV.
RAPIDITY W.R.T THRUST AXIS distribution at c.m. energy 206.0 GeV.
RAPIDITY W.R.T. SPHERICITY AXIS distribution at c.m. energy 133.0 GeV.
RAPIDITY W.R.T. SPHERICITY AXIS distribution at c.m. energy 161.0 GeV.
RAPIDITY W.R.T. SPHERICITY AXIS distribution at c.m. energy 172.0 GeV.
RAPIDITY W.R.T. SPHERICITY AXIS distribution at c.m. energy 183.0 GeV.
RAPIDITY W.R.T. SPHERICITY AXIS distribution at c.m. energy 189.0 GeV.
RAPIDITY W.R.T. SPHERICITY AXIS distribution at c.m. energy 196.0 GeV.
RAPIDITY W.R.T. SPHERICITY AXIS distribution at c.m. energy 200.0 GeV.
RAPIDITY W.R.T. SPHERICITY AXIS distribution at c.m. energy 206.0 GeV.
Combined results for ALPHAS.
Event shape means.
THRUST distribution at c.m. energy 91.20 GeV.
1-THRUST distribution at c.m. energy 133.00 GeV.
1-THRUST distribution at c.m. energy 161.00 GeV.
1-THRUST distribution at c.m. energy 172.00 GeV.
1-THRUST distribution at c.m. energy 183.00 GeV.
1-THRUST distribution at c.m. energy 189.00 GeV.
1-THRUST distribution at c.m. energy 200.00 GeV.
1-THRUST distribution at c.m. energy 206.00 GeV.
Heavy Jet Mass (RHO) distribution at c.m. energy 91.20 GeV.
Heavy Jet Mass (RHO) distribution at c.m. energy 133.00 GeV.
Heavy Jet Mass (RHO) distribution at c.m. energy 161.00 GeV.
Heavy Jet Mass (RHO) distribution at c.m. energy 172.00 GeV.
Heavy Jet Mass (RHO) distribution at c.m. energy 183.00 GeV.
Heavy Jet Mass (RHO) distribution at c.m. energy 189.00 GeV.
Heavy Jet Mass (RHO) distribution at c.m. energy 200.00 GeV.
Heavy Jet Mass (RHO) distribution at c.m. energy 206.00 GeV.
Total jet broadening distribution at c.m. energy 91.20 GeV.
Total jet broadening distribution at c.m. energy 133.00 GeV.
Total jet broadening distribution at c.m. energy 161.00 GeV.
Total jet broadening distribution at c.m. energy 172.00 GeV.
Total jet broadening distribution at c.m. energy 183.00 GeV.
Total jet broadening distribution at c.m. energy 189.00 GeV.
Total jet broadening distribution at c.m. energy 200.00 GeV.
Total jet broadening distribution at c.m. energy 206.00 GeV.
Wide jet broadening distribution at c.m. energy 91.20 GeV.
Wide jet broadening distribution at c.m. energy 133.00 GeV.
Wide jet broadening distribution at c.m. energy 161.00 GeV.
Wide jet broadening distribution at c.m. energy 172.00 GeV.
Wide jet broadening distribution at c.m. energy 183.00 GeV.
Wide jet broadening distribution at c.m. energy 189.00 GeV.
Wide jet broadening distribution at c.m. energy 200.00 GeV.
Wide jet broadening distribution at c.m. energy 206.00 GeV.
C-PARAMETER distribution at c.m. energy 91.20 GeV.
C-PARAMETER distribution at c.m. energy 133.00 GeV.
C-PARAMETER distribution at c.m. energy 161.00 GeV.
C-PARAMETER distribution at c.m. energy 172.00 GeV.
C-PARAMETER distribution at c.m. energy 183.00 GeV.
C-PARAMETER distribution at c.m. energy 189.00 GeV.
C-PARAMETER distribution at c.m. energy 200.00 GeV.
C-PARAMETER distribution at c.m. energy 206.00 GeV.
Thrust Major distribution at c.m. energy 91.20 GeV.
Thrust Major distribution at c.m. energy 133.00 GeV.
Thrust Major distribution at c.m. energy 161.00 GeV.
Thrust Major distribution at c.m. energy 172.00 GeV.
Thrust Major distribution at c.m. energy 183.00 GeV.
Thrust Major distribution at c.m. energy 189.00 GeV.
Thrust Major distribution at c.m. energy 200.00 GeV.
Thrust Major distribution at c.m. energy 206.00 GeV.
Thrust Minor distribution at c.m. energy 91.20 GeV.
Thrust Minor distribution at c.m. energy 133.00 GeV.
Thrust Minor distribution at c.m. energy 161.00 GeV.
Thrust Minor distribution at c.m. energy 172.00 GeV.
Thrust Minor distribution at c.m. energy 183.00 GeV.
Thrust Minor distribution at c.m. energy 189.00 GeV.
Thrust Minor distribution at c.m. energy 200.00 GeV.
Thrust Minor distribution at c.m. energy 206.00 GeV.
Jet Mass Difference distribution at c.m. energy 91.20 GeV.
Jet Mass Difference distribution at c.m. energy 133.00 GeV.
Jet Mass Difference distribution at c.m. energy 161.00 GeV.
Jet Mass Difference distribution at c.m. energy 172.00 GeV.
Jet Mass Difference distribution at c.m. energy 183.00 GeV.
Jet Mass Difference distribution at c.m. energy 189.00 GeV.
Jet Mass Difference distribution at c.m. energy 200.00 GeV.
Jet Mass Difference distribution at c.m. energy 206.00 GeV.
Aplanarity distribution at c.m. energy 91.20 GeV.
Aplanarity distribution at c.m. energy 133.00 GeV.
Aplanarity distribution at c.m. energy 161.00 GeV.
Aplanarity distribution at c.m. energy 172.00 GeV.
Aplanarity distribution at c.m. energy 183.00 GeV.
Aplanarity distribution at c.m. energy 189.00 GeV.
Aplanarity distribution at c.m. energy 200.00 GeV.
Aplanarity distribution at c.m. energy 206.00 GeV.
Planarity distribution at c.m. energy 133.00 GeV.
Planarity distribution at c.m. energy 161.00 GeV.
Planarity distribution at c.m. energy 172.00 GeV.
Planarity distribution at c.m. energy 183.00 GeV.
Planarity distribution at c.m. energy 189.00 GeV.
Planarity distribution at c.m. energy 200.00 GeV.
Planarity distribution at c.m. energy 206.00 GeV.
Oblateness distribution at c.m. energy 91.20 GeV.
Oblateness distribution at c.m. energy 133.00 GeV.
Oblateness distribution at c.m. energy 161.00 GeV.
Oblateness distribution at c.m. energy 172.00 GeV.
Oblateness distribution at c.m. energy 183.00 GeV.
Oblateness distribution at c.m. energy 189.00 GeV.
Oblateness distribution at c.m. energy 200.00 GeV.
Oblateness distribution at c.m. energy 206.00 GeV.
Sphericity distribution at c.m. energy 91.20 GeV.
Sphericity distribution at c.m. energy 133.00 GeV.
Sphericity distribution at c.m. energy 161.00 GeV.
Sphericity distribution at c.m. energy 172.00 GeV.
Sphericity distribution at c.m. energy 183.00 GeV.
Sphericity distribution at c.m. energy 189.00 GeV.
Sphericity distribution at c.m. energy 200.00 GeV.
Sphericity distribution at c.m. energy 206.00 GeV.
LN(Y12) distribution at c.m. energy 91.20 GeV.
LN(Y12) distribution at c.m. energy 133.00 GeV.
LN(Y12) distribution at c.m. energy 161.00 GeV.
LN(Y12) distribution at c.m. energy 172.00 GeV.
LN(Y12) distribution at c.m. energy 183.00 GeV.
LN(Y12) distribution at c.m. energy 189.00 GeV.
LN(Y12) distribution at c.m. energy 200.00 GeV.
LN(Y12) distribution at c.m. energy 206.00 GeV.
LN(Y23) distribution at c.m. energy 91.20 GeV.
LN(Y23) distribution at c.m. energy 133.00 GeV.
LN(Y23) distribution at c.m. energy 161.00 GeV.
LN(Y23) distribution at c.m. energy 172.00 GeV.
LN(Y23) distribution at c.m. energy 183.00 GeV.
LN(Y23) distribution at c.m. energy 189.00 GeV.
LN(Y23) distribution at c.m. energy 200.00 GeV.
LN(Y23) distribution at c.m. energy 206.00 GeV.
LN(Y34) distribution at c.m. energy 91.20 GeV.
LN(Y34) distribution at c.m. energy 133.00 GeV.
LN(Y34) distribution at c.m. energy 161.00 GeV.
LN(Y34) distribution at c.m. energy 172.00 GeV.
LN(Y34) distribution at c.m. energy 183.00 GeV.
LN(Y34) distribution at c.m. energy 189.00 GeV.
LN(Y34) distribution at c.m. energy 200.00 GeV.
LN(Y34) distribution at c.m. energy 206.00 GeV.
LN(Y45) distribution at c.m. energy 91.20 GeV.
LN(Y45) distribution at c.m. energy 133.00 GeV.
LN(Y45) distribution at c.m. energy 161.00 GeV.
LN(Y45) distribution at c.m. energy 172.00 GeV.
LN(Y45) distribution at c.m. energy 183.00 GeV.
LN(Y45) distribution at c.m. energy 189.00 GeV.
LN(Y45) distribution at c.m. energy 206.00 GeV.
LN(Y56) distribution at c.m. energy 91.20 GeV.
LN(Y56) distribution at c.m. energy 133.00 GeV.
LN(Y56) distribution at c.m. energy 161.00 GeV.
LN(Y56) distribution at c.m. energy 172.00 GeV.
LN(Y56) distribution at c.m. energy 183.00 GeV.
LN(Y56) distribution at c.m. energy 189.00 GeV.
LN(Y56) distribution at c.m. energy 206.00 GeV.
1-jet fraction at c.m. energy 91.20 GeV.
1-jet fraction at c.m. energy 133.00 GeV.
1-jet fraction at c.m. energy 161.00 GeV.
1-jet fraction at c.m. energy 172.00 GeV.
1-jet fraction at c.m. energy 183.00 GeV.
1-jet fraction at c.m. energy 189.00 GeV.
1-jet fraction at c.m. energy 200.00 GeV.
1-jet fraction at c.m. energy 206.00 GeV.
2-jet fraction at c.m. energy 91.20 GeV.
2-jet fraction at c.m. energy 133.00 GeV.
2-jet fraction at c.m. energy 161.00 GeV.
2-jet fraction at c.m. energy 172.00 GeV.
2-jet fraction at c.m. energy 183.00 GeV.
2-jet fraction at c.m. energy 189.00 GeV.
2-jet fraction at c.m. energy 200.00 GeV.
2-jet fraction at c.m. energy 206.00 GeV.
3-jet fraction at c.m. energy 91.20 GeV.
3-jet fraction at c.m. energy 133.00 GeV.
3-jet fraction at c.m. energy 161.00 GeV.
3-jet fraction at c.m. energy 172.00 GeV.
3-jet fraction at c.m. energy 183.00 GeV.
3-jet fraction at c.m. energy 189.00 GeV.
3-jet fraction at c.m. energy 200.00 GeV.
3-jet fraction at c.m. energy 206.00 GeV.
4-jet fraction at c.m. energy 91.20 GeV.
4-jet fraction at c.m. energy 133.00 GeV.
4-jet fraction at c.m. energy 161.00 GeV.
4-jet fraction at c.m. energy 172.00 GeV.
4-jet fraction at c.m. energy 183.00 GeV.
4-jet fraction at c.m. energy 189.00 GeV.
4-jet fraction at c.m. energy 200.00 GeV.
4-jet fraction at c.m. energy 206.00 GeV.
5-jet fraction at c.m. energy 91.20 GeV.
5-jet fraction at c.m. energy 133.00 GeV.
5-jet fraction at c.m. energy 161.00 GeV.
5-jet fraction at c.m. energy 172.00 GeV.
5-jet fraction at c.m. energy 183.00 GeV.
5-jet fraction at c.m. energy 189.00 GeV.
5-jet fraction at c.m. energy 200.00 GeV.
5-jet fraction at c.m. energy 206.00 GeV.
>=6-jet fraction at c.m. energy 91.20 GeV.
>=6-jet fraction at c.m. energy 133.00 GeV.
>=6-jet fraction at c.m. energy 161.00 GeV.
>=6-jet fraction at c.m. energy 172.00 GeV.
>=6-jet fraction at c.m. energy 183.00 GeV.
>=6-jet fraction at c.m. energy 189.00 GeV.
>=6-jet fraction at c.m. energy 200.00 GeV.
>=6-jet fraction at c.m. energy 206.00 GeV.
An updated analysis using about 1.5 million events recorded at $\sqrt{s} = M_Z$ with the DELPHI detector in 1994 is presented. Eighteen infrared and collinear safe event shape observables are measured as a function of the polar angle of the thrust axis. The data are compared to theoretical calculations in ${\cal O} (\alpha_s^2)$ including the event orientation. A combined fit of $\alpha_s$ and of the renormalization scale $x_{\mu}$ in $\cal O(\alpha_s^2$) yields an excellent description of the high statistics data. The weighted average from 18 observables including quark mass effects and correlations is $\alpha_s(M_Z^2) = 0.1174 \pm 0.0026$. The final result, derived from the jet cone energy fraction, the observable with the smallest theoretical and experimental uncertainty, is $\alpha_s(M_Z^2) = 0.1180 \pm 0.0006 (exp.) \pm 0.0013 (hadr.) \pm 0.0008 (scale) \pm 0.0007 (mass)$. Further studies include an $\alpha_s$ determination using theoretical predictions in the next-to-leading log approximation (NLLA), matched NLLA and $\cal O(\alpha_s^2$) predictions as well as theoretically motivated optimized scale setting methods. The influence of higher order contributions was also investigated by using the method of Pad\'{e} approximants. Average $\alpha_s$ values derived from the different approaches are in good agreement.
The weighted value of ALPHA-S from all the measured observables using experimentally optimized renormalization scale values and corrected for the b-mass toleading order.
The value of ALPHA-S derived from the JCEF and corrected for heavy quark mass effects. The quoted errors are respectively due to experimental error, hadronization, renormalization scale and heavy quark mass correction uncertainties.
Energy Energy Correlation EEC.
Asymmetry of the Energy Energy Correlation AEEC.
Jet Cone Energy Fraction.
1 - Thrust (1-T).
Oblateness O.
C-Parameter C.
Heavy Jet Mass.
Sum of the Jet Masses.
Difference of the Jet Masses.
Wide Jet Broadening BMAX.
Total Jet Broadening BSUM.
Differential 2-Jet Rate E0 Scheme D2(E0).
Differential 2-Jet Rate P0 Scheme D2(P0).
Differential 2-Jet Rate P Scheme D2(P).
Differential 2-Jet Rate Jade Alogrithm D2(Jad).
Differential 2-Jet Rate Durham Alogrithm D2(Dur).
Differential 2-Jet Rate Geneva Alogrithm D2(Gen).
Differential 2-Jet Rate Cambridge Alogrithm D2(Cam).
Energy Energy Correlation EEC.
Energy Energy Correlation EEC.
Energy Energy Correlation EEC.
Energy Energy Correlation EEC.
Asymmetry of the Energy Energy Correlation AEEC.
Asymmetry of the Energy Energy Correlation AEEC.
Asymmetry of the Energy Energy Correlation AEEC.
Asymmetry of the Energy Energy Correlation AEEC.
Jet Cone Energy Fraction.
Jet Cone Energy Fraction.
Jet Cone Energy Fraction.
Jet Cone Energy Fraction.
1 - Thrust (1-T).
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