Combined α_s measurements from event shapes at LEP

Combinations of α_s(M_Z) from each centre-of-mass energy range

		LEP1 (Q = M_Z)	LEP2 (Q > M_Z)	All
Fit results	α_s(M_Z)	0.1199	0.1202	0.1202
	Stat. error	± 0.0002	± 0.0006	± 0.0003
	Exp. error	± 0.0008	± 0.0010	± 0.0009
	Hadr. error	± 0.0017	± 0.0010	± 0.0013
	Theory (upper)	+ 0.0048	+ 0.0045	+ 0.0047
	Theory (lower)	– 0.0048	– 0.0046	– 0.0047
	Syst. error	± 0.0051	± 0.0048	± 0.0049
	Total error	± 0.0052	± 0.0048	± 0.0050
	χ² / d.o.f.	7.9/ 20	85.0/142	93.0/163
		LEP1 (Q = M_Z)	LEP2 (Q > M_Z)	All
Weights by variable	T	14.2 %	12.2 %	13.2 %
	M_H	27.3 %	16.2 %	23.0 %
	C	12.2 %	13.6 %	13.7 %
	B_T	10.0 %	8.2 %	7.9 %
	B_W	16.7 %	31.7 %	26.0 %
	y₂₃	19.6 %	18.2 %	16.2 %
		LEP1 (Q = M_Z)	LEP2 (Q > M_Z)	All
Weights by CM energy	91.2 GeV	100 %	–	40.5 %
	133.0 GeV	–	8.7 %	5.2 %
	161.0 GeV	–	3.4 %	1.9 %
	172.0 GeV	–	2.1 %	1.2 %
	183.0 GeV	–	16.0 %	9.6 %
	189.0 GeV	–	27.9 %	16.6 %
	200.0 GeV	–	17.6 %	10.2 %
	206.0 GeV	–	24.4 %	14.8 %
		LEP1 (Q = M_Z)	LEP2 (Q > M_Z)	All
Weights by experiment	ALEPH	29.5 %	25.9 %	26.2 %
	DELPHI	22.7 %	20.8 %	22.9 %
	L3	21.6 %	26.0 %	25.2 %
	OPAL	26.2 %	27.4 %	25.8 %
		LEP1 (Q = M_Z)	LEP2 (Q > M_Z)	All
Total negative weight		0.0 %	-1.6 %	-1.4 %

Combinations of α_s (M_Z) from each observable

Fits by observable Colour EPS
Greyscale EPS

		T only	M_H only	C only	B_T only	B_W only	y₂₃ only	All
Fit results	α_s(M_Z)	0.1245	0.1200	0.1213	0.1242	0.1158	0.1181	0.1202
	Stat. error	± 0.0006	± 0.0005	± 0.0006	± 0.0005	± 0.0005	± 0.0008	± 0.0003
	Exp. error	± 0.0011	± 0.0010	± 0.0011	± 0.0012	± 0.0010	± 0.0015	± 0.0009
	Hadr. error	± 0.0017	± 0.0012	± 0.0016	± 0.0016	± 0.0008	± 0.0005	± 0.0013
	Theory (upper)	+ 0.0053	+ 0.0041	+ 0.0054	+ 0.0065	+ 0.0050	+ 0.0025	+ 0.0047
	Theory (lower)	– 0.0052	– 0.0042	– 0.0052	– 0.0060	– 0.0052	– 0.0029	– 0.0047
	Syst. error	± 0.0056	± 0.0044	± 0.0056	± 0.0066	± 0.0053	± 0.0031	± 0.0049
	Total error	± 0.0057	± 0.0045	± 0.0057	± 0.0066	± 0.0053	± 0.0033	± 0.0050
	χ² / d.o.f.	15.3/ 31	12.9/ 31	12.8/ 25	10.2/ 28	10.5/ 28	5.8/ 15	93.0/163
		T only	M_H only	C only	B_T only	B_W only	y₂₃ only	All
Weights by variable	T	100 %	–	–	–	–	–	13.2 %
	M_H	–	100 %	–	–	–	–	23.0 %
	C	–	–	100 %	–	–	–	13.7 %
	B_T	–	–	–	100 %	–	–	7.9 %
	B_W	–	–	–	–	100 %	–	26.0 %
	y₂₃	–	–	–	–	–	100 %	16.2 %
		T only	M_H only	C only	B_T only	B_W only	y₂₃ only	All
Weights by CM energy	91.2 GeV	20.6 %	29.9 %	18.2 %	19.1 %	17.9 %	25.4 %	40.5 %
	133.0 GeV	11.1 %	7.3 %	9.4 %	6.3 %	6.5 %	2.3 %	5.2 %
	161.0 GeV	5.5 %	3.7 %	4.9 %	4.8 %	3.7 %	1.9 %	1.9 %
	172.0 GeV	3.6 %	3.0 %	3.4 %	3.3 %	4.0 %	0.5 %	1.2 %
	183.0 GeV	12.7 %	13.1 %	13.3 %	14.1 %	16.2 %	12.7 %	9.6 %
	189.0 GeV	19.6 %	18.6 %	19.4 %	17.0 %	18.4 %	13.6 %	16.6 %
	200.0 GeV	13.2 %	9.1 %	15.0 %	17.8 %	16.3 %	13.0 %	10.2 %
	206.0 GeV	13.7 %	15.4 %	16.3 %	17.6 %	17.0 %	30.6 %	14.8 %
		T only	M_H only	C only	B_T only	B_W only	y₂₃ only	All
Weights by experiment	ALEPH	24.8 %	23.6 %	29.4 %	25.9 %	25.9 %	45.9 %	26.2 %
	DELPHI	24.1 %	24.4 %	22.9 %	22.0 %	21.3 %	–	22.9 %
	L3	26.6 %	27.0 %	29.3 %	26.5 %	26.9 %	–	25.2 %
	OPAL	24.5 %	25.0 %	18.3 %	25.6 %	26.0 %	54.1 %	25.8 %
		T only	M_H only	C only	B_T only	B_W only	y₂₃ only	All
Total negative weight		0.0 %	0.0 %	0.0 %	0.0 %	0.0 %	0.0 %	-1.4 %

Combinations of α_s (M_Z) from each experiment

Fits by experiment Colour EPS
Greyscale EPS

		ALEPH only	DELPHI only	L3 only	OPAL only	All
Fit results	α_s(M_Z)	0.1201	0.1221	0.1225	0.1182	0.1202
	Stat. error	± 0.0007	± 0.0010	± 0.0007	± 0.0008	± 0.0003
	Exp. error	± 0.0008	± 0.0016	± 0.0014	± 0.0020	± 0.0009
	Hadr. error	± 0.0011	± 0.0016	± 0.0013	± 0.0010	± 0.0013
	Theory (upper)	+ 0.0046	+ 0.0053	+ 0.0050	+ 0.0040	+ 0.0047
	Theory (lower)	– 0.0047	– 0.0052	– 0.0050	– 0.0042	– 0.0047
	Syst. error	± 0.0048	± 0.0057	± 0.0053	± 0.0047	± 0.0049
	Total error	± 0.0049	± 0.0058	± 0.0053	± 0.0047	± 0.0050
	χ² / d.o.f.	27.5/ 47	9.3/ 30	28.8/ 39	20.0/ 44	93.0/163
		ALEPH only	DELPHI only	L3 only	OPAL only	All
Weights by variable	T	8.4 %	20.4 %	10.9 %	11.1 %	13.2 %
	M_H	14.8 %	31.5 %	35.9 %	15.9 %	23.0 %
	C	12.7 %	11.6 %	12.6 %	1.6 %	13.7 %
	B_T	7.4 %	26.4 %	13.1 %	1.9 %	7.9 %
	B_W	34.5 %	10.1 %	27.5 %	31.9 %	26.0 %
	y₂₃	22.1 %	–	–	37.5 %	16.2 %
		ALEPH only	DELPHI only	L3 only	OPAL only	All
Weights by CM energy	91.2 GeV	39.3 %	38.7 %	21.7 %	33.5 %	40.5 %
	133.0 GeV	8.2 %	10.7 %	7.6 %	1.0 %	5.2 %
	161.0 GeV	4.3 %	5.4 %	2.6 %	0.9 %	1.9 %
	172.0 GeV	3.0 %	3.9 %	2.3 %	0.5 %	1.2 %
	183.0 GeV	7.9 %	6.7 %	20.0 %	8.1 %	9.6 %
	189.0 GeV	13.3 %	12.9 %	21.5 %	20.7 %	16.6 %
	200.0 GeV	11.5 %	11.6 %	10.9 %	9.4 %	10.2 %
	206.0 GeV	12.5 %	10.0 %	13.4 %	25.8 %	14.8 %
		ALEPH only	DELPHI only	L3 only	OPAL only	All
Weights by experiment	ALEPH	100 %	–	–	–	26.2 %
	DELPHI	–	100 %	–	–	22.9 %
	L3	–	–	100 %	–	25.2 %
	OPAL	–	–	–	100 %	25.8 %
		ALEPH only	DELPHI only	L3 only	OPAL only	All
Total negative weight		-2.4 %	0.0 %	-0.4 %	-8.3 %	-1.4 %

Running of α_s(Q) with energy scale

Running plot Colour EPS
Greyscale EPS

C.M. energy Q	α_s(Q)	Stat. error	Exp. error	Hadr. error	Theory error
91.2 GeV	0.1199	± 0.0002	± 0.0008	± 0.0017	+ 0.0048 – 0.0048
133.0 GeV	0.1130	± 0.0015	± 0.0012	± 0.0013	+ 0.0045 – 0.0044
161.0 GeV	0.1101	± 0.0024	± 0.0014	± 0.0011	+ 0.0042 – 0.0042
172.0 GeV	0.1048	± 0.0027	± 0.0017	± 0.0009	+ 0.0041 – 0.0041
183.0 GeV	0.1079	± 0.0013	± 0.0008	± 0.0008	+ 0.0038 – 0.0039
189.0 GeV	0.1092	± 0.0008	± 0.0009	± 0.0008	+ 0.0037 – 0.0038
200.0 GeV	0.1079	± 0.0009	± 0.0010	± 0.0007	+ 0.0036 – 0.0037
206.0 GeV	0.1079	± 0.0009	± 0.0008	± 0.0007	+ 0.0034 – 0.0035

Matthew Ford, 15 June 2004

Combined αs measurements from event shapes at LEP

Combinations of αs(MZ) from each centre-of-mass energy range

Combinations of αs (MZ) from each observable

Combinations of αs (MZ) from each experiment

Running of αs(Q) with energy scale

Combined α_s measurements from event shapes at LEP

Combinations of α_s(M_Z) from each centre-of-mass energy range

Combinations of α_s (M_Z) from each observable

Combinations of α_s (M_Z) from each experiment

Running of α_s(Q) with energy scale