1
αs from Deep-Inelastic Scattering
J. Blümlein, DESY
in collaboration with S. Alekhin and S.O. Moch, U. Hamburg
Introduction
• Valence Non-Singlet Analysis
• Combined NS+S Analyses, Inclusion of Collider Data
• Comparison of Results
• Conclusions
•
J. Blümlein
αs -Workshop
Geneva, Oct. 2015
2
αs (MZ2 ) in 1992
G. Altarelli: QCD - 20 Years Later
NLO World-Average
[23 years ago.]
αs (M2Z )
+0.010
Rτ
0.117
DIS
0.112 ± 0.007
Υ Decays
0.110 ± 0.010
Re+ e− (s < 62 GeV)
0.140 ± 0.020
pp → W + jets
0.121 ± 0.024
Γ(Z → hadrons)/Γ(Z → l¯l)
0.132 ± 0.012
Jets at LEP
0.122 ± 0.009
Average
0.118 ± 0.007
−0.016
@ NLO: still right, but for very different reasons.
NLO error: now down to ∼ 0.0050 − 0.0040 (TH: scale uncertainty)
3
ΛQCD and αs (MZ2 )
older values: 2000
NLO
CTEQ6
MRST03
A02
ZEUS
H1
BCDMS
GRS
BBG
BB (pol)
αs (MZ2 )
0.1165
0.1165
0.1171
0.1166
0.1150
0.110
0.112
0.1148
0.113
< date < 2007
∼
∼
expt
±0.0065
±0.0020
±0.0015
±0.0049
±0.0017
±0.006
±0.0019
±0.004
theory
±0.0030
±0.0033
±0.0050
+0.009
−0.006
NLO at least: scale errors of ±0.0050
Ref.
[1]
[2]
[3]
[4]
[5]
[6]
[10]
[9]
[7]
NNLO
MRST03
A02
SY01(ep)
SY01(νN)
GRS
A06
BBG
N3 LO
BBG
αs (MZ2 )
0.1153
0.1143
0.1166
0.1153
0.111
0.1128
0.1134
αs (MZ2 )
0.1141
expt
±0.0020
±0.0014
±0.0013
±0.0063
±0.0015
+0.0019/ − 0.0021
expt
+0.0020/ − 0.0022
NNLO systematic shifts down
N3 LO slight upward shift
BBG: Nf = 4: non-singlet data-analysis at O(αs4 ): Λ = 234 ± 26MeV
theory
±0.0030
±0.0009
theory
Ref.
[2]
[3]
[8]
[8]
[10]
[11]
[9]
Ref.
[9]
4
Deep Inelatsic Scattering
k′
k
2
2
Q := −q ,
Lµν
q
ν :=
P
Wµν
Wµν (q, P, s) =
=
Q2
x :=
2pq
Pq
,
M
dσ
µν
∼
W
L
µν
dQ2 dx
Z
1
d4 ξ exp(iqξ)hP, s[Jµem (ξ), Jνem (0)]P, si
4π
qµ qν
1
gµν − 2
FL (x, Q2 )
2x
q
qµ Pν + qν Pµ
Q2
2x
− 2 gµν F2 (x, Q2 )
+ 2 Pµ Pν +
Q
2x
4x
Structure Functions: F2,L contain light and heavy quark contributions
=⇒ Further Inclusion of Collider Data: DY (W ± , Z), tt, jets.
5
World Data Analysis: Valence Distributions (NS)
0.8
0.8
0.7
0.7
xuv(X)
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
10
-3
10
-2
10
-1
x
0.5
10
-3
10
-2
10
-1
x
World data:
NS-analysis
W 2 > 12.5 GeV2 , Q2 > 4 GeV2
0.5
xdv(X)
0.4
0.3
0.2
0.2
0.1
0.1
0
0
-3
10
-2
10
-1
x
10
N3 LO :
xdv(X)
0.4
0.3
10
xuv(X)
+0.0020
αs (MZ2 ) = 0.1141−0.0022
J.B., H. Böttcher, A. Guffanti
Nucl.Phys. B774 (2007) 182.
-3
10
-2
10
-1
x
6
Why an O(αs4 ) analysis can be performed?
assume an ±100% error on the Pade approximant −→ ±2 MeV in ΛQCD
γnapprox:3 =
(2) 2
γn
(1)
γn
Baikov & Chetyrkin, April 2006:
γ23;N S
=
9440 2
3936832 10240
32
as +
as +
−
ζ3 a3s
9
243
6561
81
1680283336 24873952
5120
56969
+
−
ζ3 +
ζ4 −
ζ5 a4s
1777147
6561
3
243
The results agree better than 20%.
This behaviour is even confirmed for the moments N = 3, 4 by Baikov et al. 2013. The
moments for N = 2, 4 were confirmed by Velizhanin 2012, 2014.
7
Valence Distributions
10
10
1
1
10
10
10
-1
10
-2
10
-3
1
10
10
2
10
3
10
4
10
2
10
5
-1
-2
-3
1
2
Q , GeV
10
10
2
10
3
Q2, GeV2
8
Higher Twist Contributions in the Valence Region
J.B. and H. Böttcher, 2012 (BB) [1207.3170 hep-ph]:
NS-tails at NNLO :
1
0.995
Fp2(valence)/Fp2(x)
0.99
0.985
2
2
Q = 4 GeV
0.98
2
0.97
0.3
2
Q = 10 GeV
0.975
0.4
0.5
0.6
0.7
0.8
0.9
0.8
0.9
x
1
1
0.995
Fd2(valence)/Fd2(x)
0.99
0.985
2
2
Q = 100 GeV
0.98
0.975
0.97
0.3
0.4
0.5
0.6
Using ABKM09 we corrected for non NS-tails in F2 (x, Q2 ).
0.7
x
1
9
Valence Distributions: higher twist
5
10
DEUTERON
PROTON
4
CHT(x) [GeV ]
2
8
4.0 GeV < W < 12.5 GeV
2
2
CHT(x) [GeV ]
2
4.0 GeV2 < W2 < 12.5 GeV2
2
3
6
NLO
NLO
2
NNLO
NNLO
4
N3LO
N3LO
1
2
0
0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
x
• agreement between p and d analysis,
• LGT determination of interest
1
-1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
J.B., H. Böttcher Phys.Lett. B662 (2008) 336
x
1
10
αs (MZ2 )
❊①♣❡r✐ ❡♥t
☛s✭▼❩ ✮
◆▲❖✁✂✄
◆▲❖
◆◆▲❖
◆✸▲❖☎
❇❈❉✆❙ ✵✿✶✶✶✶ ✝✰ ✵✿✵✵✶✽
✵✿✶✶✞✽ ✝ ✵✿✵✵✵✼ ✵✿✶✶✷✻ ✝ ✵✿✵✵✵✼ ✵✿✶✶✷✽ ✝ ✵✿✵✵✵✻
✟✠✟✡✡
◆✆❈
✵✿✶✶✼ ☞ ✟✠✟✡✌ ✵✿✶✶✻✻ ✝ ✵✿✵✵✞✾ ✵✿✶✶✺✞ ✝ ✵✿✵✵✞✾ ✵✿✶✶✺✞ ✝ ✵✿✵✵✞✺
❙▲❆❈
✵✿✶✶✹✼ ✝ ✵✿✵✵✷✾ ✵✿✶✶✺✽ ✝ ✵✿✵✵✞✞ ✵✿✶✶✺✷ ✝ ✵✿✵✵✷✼
❇❇●
✵✿✶✶✹✽ ✝ ✵✿✵✵✶✾ ✵✿✶✶✞✹ ✝ ✵✿✵✵✷✵ ✵✿✶✶✹✶ ✝ ✵✿✵✵✷✶
❇❇
✵✿✶✶✹✼ ✝ ✵✿✵✵✷✶ ✵✿✶✶✞✷ ✝ ✵✿✵✵✷✷ ✵✿✶✶✞✼ ✝ ✵✿✵✵✷✷
❚❛❜❡❧❧❡ ✻✍ ✎♦♠✏✑✒✓✔♦✕ ♦❢ ✖❤✗ ✈✑✘✉✗✔ ♦❢ ✙s ✚✛❩ ✜ ♦✢✖✑✓✕✗❞ ✢② ✣✎✤✥✦ ✑✕❞ ✧✥✎ ✑✖ ✧★✩ ✇✓✖❤ ✖❤✗
✒✗✔✉✘✖✔ ♦❢ ✖❤✗ ✸✪✑✈♦✒☎ ✕♦✕✲✔✓✕❣✘✗✖ ✫✖✔ ✣✣✬ ✑✕❞ ✣✣ ♦❢ ✖❤✗ ✤■✦ ✪✑✈♦✒ ✕♦✕✲✔✓✕❣✘✗✖ ✇♦✒✘❞ ❞✑✖✑✱ ✑✖ ✧★✩✱
✧✧★✩✱ ✑✕❞ ✧ ★✩ ✇✓✖❤ ✖❤✗ ✒✗✔✏♦✕✔✗ ♦❢ ✖❤✗ ✓✕❞✓✈✓❞✉✑✘ ❞✑✖✑ ✔✗✖✔✱ ❝♦♠✢✓✕✗❞ ❢♦✒ ✖❤✗ ✗✯✏✗✒✓♠✗✕✖✔ ✣✎✤✥✦
✧✥✎ ✦★✳✎✴
11
S+NS DIS Analysis (NNLO)
µ=2 GeV, nf=4
3
xG
10
xG
2
7.5
5
1
2.5
0
10
-5
10
-4
10
-3
-
1
10
-2
0
x
0.05
0.1
0.15
-
-
x(u+d)/2
0.2
0.25
x
0.2
0.25
x
0.2
-
x(u+d)/2
0.15
0.75
0.1
0.5
0.05
0.25
0
0.8
10
-5
10
-4
10
-3
10
-2
0
x
0.05
0.1
0.15
0.06
xu
0.6
- -
x(d-u)
0.04
0.4
0.02
0
xd
0.2
-0.02
0
0.2
0.4
0.6
x
10
-4
10
-3
10
-2
10
-1
x
2
0.1
1.5
-
x(s+s)/2
-
x(s+s)/2
1
0.05
0.5
0
10
-5
10
-4
10
-3
10
-2
0
x
0.05
0.1
0.15
0.2
0.25
x
ABM12: shaded region, JR: full line (green), NN23: dashes (blue), MRST: dash-dotted (red), CT10: dots.
12
Higher Twist Contributions
ABM11:
2
Fi (x, Q ) =
FiT M C,τ =2 (x, Q2 )
Hi4 (x) Hi6 (x)
+
+
+ ...
Q2
Q4
0.075
0.075
0.075
0.05
0.05
0.05
0.025
0.025
0.025
0
0
0
-0.025
-0.025
-0.025
-0.05
-0.05
-0.05
-0.075
-0.075
Hp2
-0.1
2
(1/GeV )
-0.1
-0.125
-0.15
-0.075
HTp
2
(1/GeV )
-0.125
0
0.5
-0.15
x
2
Hns
2 (1/GeV )
-0.1
-0.125
0
0.5
-0.15
x
0
0.5
x
❋✐ ✉r❡ ✶✵✿ ❚❤✁ ❝✁♥t✂❛❧ ✈❛❧✄✁s ✭s♦❧☎❞ ❧☎♥✁✮ ❛♥❞ t❤✁ ✆✛ ❜❛♥❞s ✭s❤❛❞✁❞ ❛✂✁❛✮ ❢♦✂ t❤✁ ❝♦✁✍❝☎✁♥ts ♦❢ t❤✁
t✇☎st✲✹ t✁✂♠s ♦☞♥ t❤✁ ☎♥❝❧✄s☎✈✁ ❉■❙ st✂✄❝t✄✂✁ ❢✄♥❝t☎♦♥s ♦❜t❛☎♥✁❞ ❢✂♦♠ ♦✄✂ ◆◆▲❖ ☞t ✭❧✁❢t ♣❛♥✁❧✝ ✞✷ ♦❢
t❤✁ ♣✂♦t♦♥✱ ❝✁♥t✂❛❧ ♣❛♥✁❧✝ ✞✟ ♦❢ t❤✁ ♣✂♦t♦♥✱ ✂☎❣❤t ♣❛♥✁❧✝ ♥♦♥✲s☎♥❣❧✁t ✞✷ ✮✳ ❚❤✁ ❝✁♥t✂❛❧ ✈❛❧✄✁s ♦❢ t❤✁
t✇☎st✲✹ ❝♦✁✍❝☎✁♥ts ♦❜t❛☎♥✁❞ ❢✂♦♠ ♦✄✂ ◆▲❖ ☞t ❛✂✁ s❤♦✇♥ ❢♦✂ ❝♦♠♣❛✂☎s♦♥ ✭❞❛s❤✁s✮✳
13
αs (MZ2 )
2000
χ2
χ2
ABM11
900
NMC
HERA
1500
800
1000
700
500
0.105
0.11
0.115
0.12
600
0.125
0.105
0.11
0.115
0.12
800
αs(MZ)
χ2
χ2
αs(MZ)
BCDMS
0.125
2000
SLAC
1750
750
1500
1250
700
1000
0.105
0.11
0.115
0.12
0.125
0.105
0.11
0.115
0.12
0.125
αs(MZ)
χ2
αs(MZ)
224
DY
222
NNLO
220
NLO
218
0.105
0.11
0.115
0.12
0.125
αs(MZ)
❋✐ ✉r❡ ✶✾✿ ❚❤✁ ✤✷ ✲♣✂♦☞❧✁ ✈✁✂s✄s t❤✁ ✈❛❧✄✁ ♦❢ ☛☎ ✭▼❩ ✮ ❢♦✂ t❤✁ ❞❛t❛ s✁ts ✄s✁❞✱ ❛❧❧ ❝❛❧❝✄❧❛t✁❞ ✇✆t❤ t❤✁
P❉✝ ❛♥❞ ❍❚ ♣❛✂❛♠✁t✁✂s ☞①✁❞ ❛t t❤✁ ✈❛❧✄✁s ♦❜t❛✆♥✁❞ ❢✂♦♠ t❤✁ ☞ts ✇✆t❤ ☛☎ ✭▼❩ ✮ ✂✁❧✁❛s✁❞ ✭s♦❧✆❞ ❧✆♥✁s✞
◆◆▲❖ ☞t✱ ❞❛s❤✁s✞ ◆▲❖ ♦♥✁✮✳
14
αs (MZ2 )
❊①♣❡r✐ ❡♥t
☛s✭▼❩ ✮
◆▲❖✁✂✄
◆▲❖
◆◆▲❖
❇❈❉☎❙
✵✿✶✶✶✶ ✝✰ ✵✿✵✵✶✽
✵✿✶✶✺✵
✝
✵✿✵✵✶✷
✵✿✶✵✽✹
✝
✵✿✵✵✶✸
◆☎❈
✵✿✶✶✼ ✠ ✆✞✆✟✟
✆✞✆✟✻ ✵✿✶✶✽✷ ✝ ✵✿✵✵✵✼ ✵✿✶✶✺✷ ✝ ✵✿✵✵✵✼
❙▲❆❈
✵✿✶✶✼✸ ✝ ✵✿✵✵✵✸ ✵✿✶✶✷✽ ✝ ✵✿✵✵✵✸
❍❊❘❆ ❝♦ ❜✳
✵✿✶✶✼✹ ✝ ✵✿✵✵✵✸ ✵✿✶✶✷✡ ✝ ✵✿✵✵✵✷
❉❨
✵✿✶✵✽ ✝ ✵✿✵✶✵ ✵✿✶✵✶ ✝ ✵✿✵✷✺
❆❇☎✶✶
✵✿✶✶✽✵ ✝ ✵✿✵✵✶✷ ✵✿✶✶✸✹ ✝ ✵✿✵✵✶✶
❚❛❜❡❧❧❡ ✹☞ ✌✍♠✎✏✑✒✓✍✔ ✍❢ ✕❤✖ ✈✏✗✉✖✓ ✍❢ ✘s✙✚❩ ✛ ✍✜✕✏✒✔✖❞ ✜② ✢✌✣✤✥ ✏✔❞ ✦✤✌ ✏✕ ✦✧★ ✇✒✕❤ ✕❤✖
✒✔❞✒✈✒❞✉✏✗ ✑✖✓✉✗✕✓ ✍❢ ✕❤✖ ✩✕ ✒✔ ✕❤✖ ✎✑✖✓✖✔✕ ✏✔✏✗②✓✒✓ ✏✕ ✦✧★ ✏✔❞ ✦✦✧★ ❢✍✑ ✕❤✖ ✪✫✬✯ ❞✏✕✏ ✕❤✖ ✦✤✌
❞✏✕✏ ✕❤✖ ✢✌✣✤✥ ❞✏✕✏ ✕❤✖ ✥✧✯✌ ❞✏✕✏ ✏✔❞ ✕❤✖ ✣✱ ❞✏✕✏✲
The values of αs (MZ2 ) in NLO and NNLO fits are different.
15
ABM fits including Jet Data: D0 run II dijet
scale unc.
Y= 0.20
Y= 0.60
Y= 1.00
Y= 1.40
Y= 1.80
Y= 2.20
Data/Theory
data/NLO
ABKM09 (no re-fit)
2.2 |y|
< 0.4
max
2
1.8
1.6
1.4
1.2
1
0.8
0.6
-1
0.4 DØ, L = 0.7 fb
0.2
2.2 1.2 < |y|
< 1.6
max
2
1.8
1.6
1.4
1.2
1
0.8
0.6
Data/NLO
0.4
Systematic Uncertainty
0.2
0.4 < |y|max < 0.8
s = 1.96 TeV
Rcone = 0.7
1.6 < |y|max < 2.0
0.8 < |y|max < 1.2
µ = µ = (p + p )/2
R
F
T1
T2
2.0 < |y|max < 2.4
µ , µ variation
R
F
MSTW2008 Uncertainty
CTEQ6.6 w/ Uncertainty
0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1 1.2 1.4
MJJ [TeV]
MJJ (GeV)
ABM (2011). Note that the cross section is known to NLO only !
16
µR/µF=1 µR/µF=0.5
Y= 0.20
Y= 0.60
Y= 1.00
Y= 1.80
data/NLO
data/NLO
D0 run II djet data
Y= 0.20
Y= 0.60
Y= 1.40
Y= 1.00
Y= 1.40
Y= 2.20
Y= 1.80
Y= 2.20
ET (GeV)
before the fit
ABM (2011) χ2 = 104/110
ET (GeV)
after the fit
17
αs (MZ2 )
6
xG(x,µ)
xG(x,µ)
µ=3 GeV
ABM11+ATLAS(1jet,PT>150 GEV)
5
ABM11+ATLAS(1jet,PT>100 GEV)
1
10
4
-1
ABM11
3
10
-2
2
ABKM09+D0(1jet)
1
0
10
-3
MSTW08
0.02
0.04
0.06
0.08
0.1
x
10
-4
0.2
0.4
0.6
x
❋✐ ✉r❡ ✷✽✿ ●❧✁♦♥ ❞✂st✄✂❜✁t✂♦♥ ♦❜t❛✂♥☎❞ ❜② ✂♥❝❧✁❞✂♥❣ t❤☎ ❆❚▲❆❙ ❥☎t ❞❛t❛ ✂♥t♦ t❤☎ ❆❇▼✶✶ ❛♥❛❧②s✂s✳
18
αs (MZ2 ): Inclusion of Tevatron Jets (NLO)
❊①♣❡r✐ ❡♥t
☛s✭▼❩ ✮
◆▲❖✁✂✄
◆▲❖
◆◆▲❖☎
❉✵ ✶ ❥❡t
✵✿✶✶✻✶ ✰✟ ✆✝✆✆✹✞
✆✝✆✆✹✽ ✵✿✶✶✾✵ ✠ ✵✿✵✵✶✶ ✵✿✶✶✡✾ ✠ ✵✿✵✵✶✷
❉✵ ✷ ❥❡t
✵✿✶✶✼✡ ✠ ✵✿✵✵✵✾ ✵✿✶✶✡✺ ✠ ✵✿✵✵✵✾
❈❉❋ ✶ ❥❡t ✭❝♦♥❡✮
✵✿✶✶☞✶ ✠ ✵✿✵✵✵✾ ✵✿✶✶✸✡ ✠ ✵✿✵✵✵✾
❈❉❋ ✶ ❥❡t ✭❦❄✮
✵✿✶✶☞✶ ✠ ✵✿✵✵✶✵ ✵✿✶✶✡✸ ✠ ✵✿✵✵✵✾
❆❇✌✶✶
✵✿✶✶☞✵ ✠ ✵✿✵✵✶✷ ✵✿✶✶✸✡ ✠ ✵✿✵✵✶✶
❚❛❜❡❧❧❡ ✺✍ ✎✏♠✑✒✓✔✕✏✖ ✏❢ ✗❤✘ ✈✒✙✉✘✕ ✏❢ ✚s✛✜❩ ✢ ✏✣✗✒✔✖✘❞ ✣② ✤✥ ✇✔✗❤ ✗❤✘ ✏✖✘✕
✣✒✕✘❞ ✏✖ ✔✖✦✙✉❞✔✖❣
☎
✔✖❞✔✈✔❞✉✒✙ ❞✒✗✒ ✕✘✗✕ ✏❢ ✧✘✈✒✗✓✏✖ ★✘✗ ❞✒✗✒ ✔✖✗✏ ✗❤✘ ✒✖✒✙②✕✔✕ ✒✗ ✩✪✫✳ ✧❤✘ ✩✩✪✫ ✬✗ ✓✘❢✘✓✕ ✗✏ ✗❤✘ ✩✩✪✫
✒✖✒✙②✕✔✕ ✏❢ ✗❤✘ ✤■❙ ✒✖❞ ✤❨ ❞✒✗✒ ✗✏❣✘✗❤✘✓ ✇✔✗❤ ✗❤✘ ✩✪✫ ✒✖❞ ✕✏❢✗ ❣✙✉✏✖ ✓✘✕✉♠♠✒✗✔✏✖ ✦✏✓✓✘✦✗✔✏✖✕ ✛✖✘✯✗✲
✗✏✲✙✘✒❞✔✖❣ ✙✏❣✒✓✔✗❤♠✔✦ ✒✦✦✉✓✒✦②✢ ❢✏✓ ✗❤✘ ✱ ★✘✗ ✔✖✦✙✉✕✔✈✘ ❞✒✗✒✳
S. Alekhin, J.B., S. Moch, Phys.Rev. D86 (2012) 054009
=⇒ value depends on data set
=⇒ value depends on the jet algorithm
=⇒ no large values
19
αs (MZ2 ): NNPDF vs Data Sets
❊①♣❡r✐ ❡♥t
☛s ✭▼❩ ✮
◆▲❖✁✂✄
◆▲❖
◆◆▲❖
❇❈❉☎❙
✵✿✶✶✶✶ ✝ ✵✿✵✵✶✽ ✵✿✶✷✵✹ ✝ ✵✿✵✵✶✺ ✵✿✶✶✺✽ ✝ ✵✿✵✵✶✺
◆☎❈✄
✵✿✶✶✾✷ ✝ ✵✿✵✵✶✽ ✵✿✶✶✺✵ ✝ ✵✿✵✵✷✵
✰
✆✞✆✟✟
◆☎❈✄❞
✵✿✶✶✼ ✠ ✆✞✆✟✻
✵✿✶✶✹✡ ✝ ✵✿✵✶✵✼
❃ ✵✿✶✷✹
❃ ✵✿✶✷✹
❙▲❆❈
❍❊❘❆ ■
✵✿✶✷✷✸ ✝ ✵✿✵✵✶✽ ✵✿✶✶✾✾ ✝ ✵✿✵✵✶✾
☞❊❯❙ ❍✷
✵✿✶✶✼✵ ✝ ✵✿✵✵✷✼ ✵✿✶✷✸✶ ✝ ✵✿✵✵✸✵
☞❊❯❙ ❋✷❈
✵✿✶✶✹✹ ✝ ✵✿✵✵✡✵
◆✉❚❡❱
✵✿✶✷✺✷ ✝ ✵✿✵✵✡✽ ✵✿✶✶✼✼ ✝ ✵✿✵✵✸✾
❊✡✵✺
✵✿✶✶✡✽ ✝ ✵✿✵✶✵✵
❊✽✡✡
✵✿✶✶✸✺ ✝ ✵✿✵✵✷✾
❈❉❋ ❲❛✌②
✵✿✶✶✽✶ ✝ ✵✿✵✵✡✵
❈❉❋ ☞r❛♣
✵✿✶✶✺✵ ✝ ✵✿✵✵✸✹ ✵✿✶✷✵✺ ✝ ✵✿✵✵✽✶
❉✵ ☞r❛♣
✵✿✶✷✷✼ ✝ ✵✿✵✵✡✼
❈❉❋ ❘✷❑❚
✵✿✶✷✷✽ ✝ ✵✿✵✵✷✶ ✵✿✶✷✷✺ ✝ ✵✿✵✵✷✶
✰
✆✞✆✆✍✟
❉✵ ❘✷❈❖◆ ✵✿✶✶✡✶ ✠ ✆✞✆✆✍✎ ✵✿✶✶✹✶ ✝ ✵✿✵✵✸✶ ✵✿✶✶✶✶ ✝ ✵✿✵✵✷✾
◆◆✷✶
✵✿✶✶✾✶ ✝ ✵✿✵✵✵✡ ✵✿✶✶✼✸ ✝ ✵✿✵✵✵✼
❚❛❜❡❧❧❡ ✼✏ ✑♦♠✒✓✔✕✖♦✗ ♦❢ ✘❤✙ ✈✓✚✛✙✖ ♦❢ ✜s ✢✣❩ ✤ ♦✥✘✓✕✗✙✦ ✥✧ ★✑✩✪✫✱ ✬✪✑✱ ✓✗✦ ✩✯ ✓✘ ✬✲✳ ✇✕✘❤
✘❤✙ ✔✙✖✛✚✘✖ ♦❢ ✬✬✴❀ ❢♦✔ ✘❤✙ ❁✘✖ ✘♦ ✩❂✫ ✓✗✦ ♦✘❤✙✔ ❤✓✔✦ ✖❝✓✘✘✙✔✕✗❣ ✦✓✘✓ ✓✘ ✬✲✳ ✓✗✦ ✬✬✲✳ ✓✗✦ ✘❤✙
❝♦✔✔✙✖✒♦✗✦✕✗❣ ✔✙✖✒♦✗✖✙ ♦❢ ✘❤✙ ✦✕❄✙✔✙✗✘ ✦✓✘✓ ✖✙✘✖ ✓✗✓✚✧✖✙✦❅
20
❊①♣❡r✐ ❡♥t
☛s ✭▼❩ ✮
◆▲❖✁✂✄
◆▲❖
❇❈❉☎❙ ✖✆❀ ❋✷
✵✿✶✶✶✶ ✝ ✵✿✵✵✶✽
✞
❇❈❉☎❙ ✖❞❀ ❋✷
✵✿✶✶✸✺
✝
✵✿✵✶✺✺
◆☎❈ ✖✆❀ ❋✷
✵✿✶✶✼ ✰☞ ✟✠✟✡✡
✟✠✟✡✻ ✵✿✶✌✼✺ ✝ ✵✿✵✶✵✺
◆☎❈ ✖❞❀ ❋✷
✵✿✶✌✍✺ ✝ ✵✿✵✶✶✺
◆☎❈ ✖✎❂✖✆
✵✿✶✌✽✵
❊✍✍✺ ✖✆❀ ❋✷
✵✿✶✌✵✸
❊✍✍✺ ✖❞❀ ❋✷
✞
❙▲❆❈ ✏✆❀ ❋✷
✵✿✶✶✽✵ ✝ ✵✿✵✵✍✵
❙▲❆❈ ✏❞❀ ❋✷
✵✿✶✌✼✵ ✝ ✵✿✵✵✾✵
◆☎❈✱❇❈❉☎❙✱❙▲❆❈✱ ❋✑
✵✿✶✌✽✺ ✝ ✵✿✵✶✶✺
❊✽✽✍✴◆✉❙❡❛ ✆✆✱ ❉❨ ✪❝✐t❡❲❡❜❜✒✌✵✵✸❜❥
✞
❊✽✽✍✴◆✉❙❡❛ ✆❞❂✆✆✱ ❉❨
✵✿✶✶✼✸ ✝ ✵✿✶✵✼
◆✉❚❡❱ ✗✓❀ ❋✷
✵✿✶✌✵✼ ✝ ✵✿✵✵✍✼
❈❍❖❘❯❙ ✗✓❀ ❋✷
✵✿✶✌✸✵ ✝ ✵✿✵✶✶✵
◆✉❚❡❱ ✗✓❀ ✔❋✕
✵✿✶✌✼✵ ✝ ✵✿✵✵✾✵
❈❍❖❘❯❙ ✗✓❀ ✔❋✕
✵✿✶✌✶✺ ✝ ✵✿✵✶✵✺
❈❈✘❘
✵✿✶✶✾✵
◆✉❚❡❱ ✗✓ ✦ ✖✖❳
✵✿✶✶✺✵ ✝ ✵✿✵✶✼✵
❍✶ ✏✆ ✾✼✲✵✵✱ ✛✜✙✚
✵✿✶✌✺✵ ✝ ✵✿✵✵✼✵
✢❊❯❙ ✏✆ ✾✺✲✵✵✱ ✛✜✙✚
✵✿✶✌✸✺ ✝ ✵✿✵✵✍✺
❍✶ ✏✆ ✾✾✲✵✵✱ ✛✜✚✚
✵✿✶✌✽✺ ✝ ✵✿✵✌✌✺
✢❊❯❙ ✏✆ ✾✾✲✵✵✱ ✛✜✚✚
✵✿✶✶✌✺ ✝ ✵✿✵✶✾✺
❍✶✴✢❊❯❙ ✏✆❀ ❋✷✣❤✤✥♠
✞
❍✶ ✏✆ ✾✾✲✵✵ ✐♥❝❧✧ ❥❡t★
✵✿✶✶✍✽ ✰☞ ✟✠✟✟✩✫
✵✿✶✶✌✼ ✝ ✵✿✵✵✾✸
✟✠✟✟✕✩
✢❊❯❙ ✏✆ ✾✍✲✵✵ ✐♥❝❧✧ ❥❡t★
✵✿✶✌✵✽ ✰☞ ✟✠✟✟✩✬
✟✠✟✟✩✟ ✵✿✶✶✼✺ ✝ ✵✿✵✵✺✺
❉✵ ■■ ✆✯✆ ✐♥❝❧✧ ❥❡t★
✵✿✶✶✍✶ ✰☞ ✟✠✟✟✩✡
✟✠✟✟✩✬ ✵✿✶✶✽✺ ✝ ✵✿✵✵✺✺
❈❉✘ ■■ ✆✯✆ ✐♥❝❧✧ ❥❡t★
✵✿✶✌✵✺ ✝ ✵✿✵✵✹✺
❉✵ ■■ ✳ ✦ ❁✗ ❛★② ✧
✞
❈❉✘ ■■ ✳ ✦ ❁✗ ❛★② ✧
✞
❉✵ ■■ ❃ r❛♣✧
✵✿✶✶✌✺ ✝ ✵✿✵✶✵✵
❈❉✘ ■■ ❃ r❛♣✧
✵✿✶✶✍✵ ✝ ✵✿✵✵✼✵
☎❙❚❲
✵✿✶✌✵✌ ✰☞ ✟✠✟✟✡✷
✟✠✟✟✡❄
◆◆▲❖
✵✿✶✵✽✺ ✝ ✵✿✵✵✾✺
✵✿✶✶✶✼ ✝ ✵✿✵✵✾✸
✵✿✶✌✶✼ ✝ ✵✿✵✵✼✼
✵✿✶✌✶✺ ✝ ✵✿✵✵✼✵
✵✿✶✶✍✵
✞
✞
✵✿✶✶✹✵ ✝ ✵✿✵✵✍✵
✵✿✶✌✌✵ ✝ ✵✿✵✵✍✵
✵✿✶✌✵✵ ✝ ✵✿✵✵✍✵
✵✿✶✶✸✌ ✝ ✵✿✵✵✽✽
✵✿✶✶✹✵ ✝ ✵✿✵✶✶✵
✵✿✶✶✼✵ ✝ ✵✿✵✵✍✵
✵✿✶✶✺✵ ✝ ✵✿✵✵✾✵
✵✿✶✌✌✺ ✝ ✵✿✵✵✼✺
✵✿✶✶✽✺ ✝ ✵✿✵✵✼✺
✞
✞
✵✿✶✌✵✺ ✝ ✵✿✵✵✺✺
✵✿✶✌✶✵ ✝ ✵✿✵✵✍✵
✵✿✶✌✼✵ ✝ ✵✿✵✌✵✵
✵✿✶✶✍✺ ✝ ✵✿✵✵✾✺
✵✿✶✶✍✺ ✝ ✵✿✵✵✾✺
✵✿✶✶✸✸ ✝ ✵✿✵✵✍✸
✵✿✶✶✍✺ ✝ ✵✿✵✵✌✺
✞
✞
✵✿✶✶✸✍ ✝ ✵✿✵✵✽✹
✵✿✶✶✺✼ ✝ ✵✿✵✵✍✼
✵✿✶✶✼✶ ✝ ✵✿✵✵✶✹
❚❛❜❧❡ ✽✒ ❅♦●❏❑P◗❬♦❭ ♦❢ ❪❫❴ ✈❑❵❣❴❬ ♦❢ ❦s q✇❩ ③ ♦④❪❑◗❭❴⑤ ④⑥ ⑦❅⑧⑨⑩❶ ❷⑨❅❶ ❸❹❺❻❼❽❴❪ ❑❭⑤ ⑧❾ ❑❪ ❷❿➀
➁◗❪❫ ❪❫❴ P❴❬❣❵❪❬ ♦❢ ❪❫❴ ⑨⑩➂➃ ➄❪❬ ❪♦ ⑧➅⑩ ❑❭⑤ ♦❪❫❴P ❫❑P⑤ ❬➆❑❪❪❴P◗❭➇ ⑤❑❪❑ ❑❪ ❷❿➀ ❑❭⑤ ❷❷❿➀ ❑❭⑤ ❪❫❴
➆♦PP❴❬❏♦❭⑤◗❭➇ P❴❬❏♦❭❬❴ ♦❢ ❪❫❴ ⑤◗➈❴P❴❭❪ ⑤❑❪❑ ❬❴❪❬ ❑❭❑❵⑥❬❴⑤❶ ➆❢➉ ➊◗➇❬➉ ➋❑ ❑❭⑤ ➋④ ◗❭ ⑨⑩➂➃❾➌➉ ❹❭❪P◗❴❬ ❭♦❪
➇◗✈❴❭ ➆♦PP❴❬❏♦❭⑤ ❪♦ ❦sq✇❩ ③ ➆❴❭❪P❑❵ ✈❑❵❣❴❬ ④❴❵♦➁ ❾➍➎➎❾ ♦P ❑④♦✈❴ ❾➍➎➏❾➐ ◗❭ ➆❑❬❴ ❭♦ ❴PP♦P❬ ❑P❴ ❑❬❬◗➇❭❴⑤
❪❫❴❬❴ ❑P❴ ❵❑P➇❴P ❪❫❑❭ ❪❫❴ ④♦❣❭⑤❬ ❏P♦✈◗⑤❴⑤ ◗❭ ❢♦P● ♦❢ ❪❫❴ ❏❵♦❪❬ ◗❭ ⑨⑩➂➃❾➌➉
MSTW08 vs Data Sets
21
Nuclear Targets
ABM: none
CTEQ: CCFR, CDHSW
JR: none
MMHT: NUTEV, CHORUS
NNPDF: NUTEV, CHORUS
Jet Fits: NLO only!
ABM: singly selected: D0,CDF,ATLAS
CTEQ: CDF, D0, ATLAS, CMS
JR: CDF,D0
MMHT: H1,ZEUS incl., CDF, D0, ATLAS, CMS
NNPDF: CDF, D0, ATLAS, CMS
• Different nuclear targets!
It is likely that the QCD evolution differs off nuclear targets due to the internal composition
(π’s, confinement size varies, etc.; various sources leading to the EMC effect.)
Impact on FL ? Differing EMC effects for different structure functions (NS, S).
• Mixing NLO and NNLO fits necessarily does not lead to an extraction of αsNNLO .
• As the NLO values are higher than those at NNLO αs increases.
• In the strict sense MSTW, MMHT, CT14, and NNPDF are not pure NNLO analyses, but
contain quite a part of data currently being fitted at NLO only.
22
αs (MZ2 ) - Higher Twist Correlation
coefficient of correlation with αs
ABM11 NNLO
1
H2(x)
HT(x)
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
x
❋✐ ✉r❡ ✷✵✿ ❚❤✁ ❝♦✂✂✁❧❛t✄♦♥ ❝♦✁✍❝✄✁♥t ♦❢ ☛s ✭▼❩ ✮ ✇✄t❤ t❤✁ ♥☎❝❧✁♦♥ t✇✄✆t✲✹ ❝♦✁✍❝✄✁♥t✆ ❍✝ ✭✆♦❧✄❞ ❧✄♥✁✮
❛♥❞ ❍✞ ✭❞❛✆❤✁✆✮ ✈✁✂✆☎✆ ① ❛✆ ♦❜t❛✄♥✁❞ ✄♥ ♦☎✂ ◆◆▲❖ ☞t✳
=⇒ Including scales as Q2 < 10 GeV2 requires fit of higher twist terms (Singlet Analysis).
23
αs (MZ2 ): NNLO Comparison ABM, BBG, NNPDF, MSTW
❉❛t❛ ❙❡t
❇❈❉▼❙
◆▼❈
❆❇▼✶✶
✵✿✶✵✹✽ ✝ ✵✿✵✵✶✸
✵✿✶✶✺✷ ✝ ✵✿✵✵✵✼
❇❇●
✵✿✶✶✷✻ ✝ ✵✿✵✵✵✼
✵✿✶✶✺✸ ✝ ✵✿✵✵✸✾
◆◆✷✶
✵✿✶✶✺✽ ✝ ✵✿✵✵✶✺
✵✿✶✶✺✵ ✝ ✵✿✵✵✷✵
❙▲❆❈
✵✿✶✶✷✽ ✝ ✵✿✵✵✵✸
✵✿✶✶✺✽ ✝ ✵✿✵✵✸✹
❃ ✵✿✶✷✹
❍❊❘❆
✵✿✶✶✷✻ ✝ ✵✿✵✵✵✷
❉❨
✵✿✶✵✶ ✝ ✵✿✵✷✺
✵✿✶✶✸✹ ✝ ✵✿✵✵✶✶
☛
✵✿✶✶✸✹ ✝ ✵✿✵✵✷✵
✭
✁✂✂✠✠ ☎ ✁ ✂✠
✁✂✟✡✂ ☎ ✁ ✡
☛
✵✿✶✶✼✸ ✝ ✵✿✵✵✵✼
▼❙❚❲
✵✿✶✶✵✶ ✝ ✵✿✵✵✾✹
✭ ✵✿✶✷✶✻ ✝ ✵✿✵✵✼✹
✁✂✂✄ ☎ ✁ ✆ ✞♣
✁✂✟✟ ☎ ✁ ✆ ✞❞
✵✿✶✷✵✽ ✝ ✵✿✵✵✺✽
✵✿✶✶✸✻ ✝ ✵✿✵✶✵✵
✵✿✶✶✼✶ ✝ ✵✿✵✵✶✹
❚❛❜❧❡ ✾☞ ✌♦♠♣✍r✐s♦♥ ♦❢ ✎❤✞ ♣✉✏✏s ✐♥ ✑✒ ✓✔❩ ✮ ♣✞r ❞✍✎✍ s✞✎ ✕✞✎✇✞✞♥ ✎❤✞ ✖✗✘✂✂✱ ✗✗✙✱ ✚✚✟✂✱ ✘✛✜✢
✍♥✍✏②s✞s ✍✎ ✚✚✣❖✳
=⇒ Despite the NNLO values for αs (MZ2 ) of NNPDF and MSTW are close to each other, the
contribution of the different data sets differ considerably.
24
Heavy Flavor Treatment
2
1.6
0.5
c,asymp
(Nf=4)
F2
c,exact
(Nf=3)
F2
c,BMSN
F2
1.4
1.2
1
O(αs)
0.2
0.175
0.4
0.15
0.125
0.3
0.1
0.8
0.2
0.075
0.6
0.4
x=0.00018
0.2
10
10
0
2
2
0.05
x=0.003
0.025
ZEUS(RunI)
H1(RunII)
0
0.1
0
10
2
Q (GeV )
x=0.03
10
2
2
10
2
Q (GeV )
10
2
2
2
Q (GeV )
❝
✁♥ ❞✁☛✄ ✄♥t s☎❤✄♠✄s t♦ ❍✆✲ ❛♥❞ ❩❊❯❙✲❞❛t❛✳ ❙♦❧✁❞ ❧✁♥✄s✝ ●▼❱✞◆ s☎❤✄♠✄
✷
✁♥ t❤✄ ❇▼❙◆ ♣ ✄s☎ ✁♣t✁♦♥✱ ❞❛s❤✲❞♦tt✄❞ ❧✁♥✄s✝ ✸✲✟❛✈♦ s☎❤✄♠✄✱ ❞❛s❤✄❞ ❧✁♥✄s✝ ✹✲✟❛✈♦ s☎❤✄♠✄✳ ❚❤✄ ✈✄ t✁☎❛❧
❋✐❣✉r❡ ✶✿ ❈♦♠♣❛ ✁s♦♥ ♦❢ ✂
❞♦tt✄❞ ❧✁♥✄ ❞✄♥♦t✄s t❤✄ ♣♦s✁t✁♦♥ ♦❢ t❤✄ ☎❤❛ ♠✲q✠❛ ❦ ♠❛ss ✡❝ ❂ ✆☞✹✸ ●✄❱✳
Interpolating scheme: BSMN (1996) to be used; many private models in use (RT, etc.)
25
Heavy Flavor Treatment: consistent determination of mc
Alekhin, JB, Daum, Lipka, Moch:Phys.Lett. B720 (2013) 172.
ABDLM, DIS, FFNS, χ2 = 61/52
mMS
c
1.24 ± 0.03
mMS
c
1.279 ± 0.013
Chetyrkin et al., e+ e−
mMS
c
1.275 ± 0.025
PDG
mPole
c
1.67 ± 0.07
PDG
mPole
c
1.25
MMHT [1510.02332] GMVFNS; αs = 0.1167; χ2 = 72/52
+0.03
−0.03
26
Heavy Flavor Treatment
C m assive ,H2L
1.0
g1 c
0.5
g1 b
Ξ
50
-0.5
100
150
200
g1 c asy
asym ptotic
-1.0
JB, G. Falcioni, A. De Freitas, DESY 15-171
• Exact O(αs2 ) calculations show the gradual interpolation for charm and bottom effects in DIS as a
function of ξ = Q2 /m2H bridging form NF → NF + 1. [Note the negative corrections at low scales!]
• The matching at Q2 = m2c for NF → NF + 1 is definitely sub-optimal and may lead to wrong
results.
• Adding as complete as possible HQ effects in the fixed flavor scheme in the lower Q2 range is the
better option. Van Neerven 1993; Glück, Reya, Stratmann, 1994; ABM2009–
27
Effect on the Gluon density
∆[xG(x)]
0.8
0.2
0.6
ABKM09
0.4
ABKM09 with F2
0.15
NMC
0.1
0.2
0.05
0
0
-0.2
-0.05
-0.4
-0.1
µ=2 GeV
-0.6
-0.8 -2
10
10
µ=165 GeV
-0.15
-0.2 -2
10
-1
x
10
-1
x
wrong treatment (F2NMC ): larger gluon at x ≃ 0.1
=⇒ It is important to fit the reduced cross sections, including the correct FL -behavior to NNLO.
=⇒ ABM,JR, NNPDF.
28
Why is MSTW’s αs (MZ2 ) so high ?
αs (MZ2 )
with σNMC
with F2NMC
difference
NLO
0.1179(16)
0.1195(17)
+0.0026 ≃ 1σ
NNLO
0.1135(14)
0.1170(15)
+0.0035 ≃ 2.3σ
NNLO + FL O(αs3 )
0.1122(14)
0.1171(14)
+0.0050 ≃ 3.6σ
S. Alekhin, J.B., S. Moch, Eur.Phys.J. C71 (2011) 1723 [arXiv:1101.5261].
=⇒ also fixed target data shall be analyzed using σ.
=⇒ This applies to NMC in particular.
• Wrong treatment of FL (x, Q2 ) in NMC F2 extraction.
=⇒ also necessary for BCDMS, see BBG (2006).
• MMHT still fits structure functions but includes FL @ NLO.
• There is still a significant difference from FL @ NLO and NNLO at low x.
Use: W 2 > 12.5 GeV2 , Q2 > 2.5 GeV2 and no HT: αs (MZ2 ) = 0.1191 ± 0.0016
Use: W 2 > 12.5 GeV2 , Q2 > 10 GeV2 and no HT: αs (MZ2 ) = 0.1134 ± 0.0008
NNPDF Q2 > 5 GeV2 .
NNLO Analyses
29
2)
αs (MZ
SY
2001
0.1166 ± 0.0013
F2ep
SY
2001
0.1153 ± 0.0063
xF3νN h. Nucl.
A02
2002
0.1143 ± 0.0020
MRST03
2003
0.1153 ± 0.0020
BBG
2004(06,12)
0.1134
+0.0019
valence analysis, NNLO
−0.0021
GRS
2006
0.112
valence analysis, NNLO
A06
2006
0.1128 ± 0.0015
JR
2008
0.1128 ± 0.0010
dynamical approach
JR
2008
0.1162 ± 0.0006
including NLO-jets
ABKM
2009
0.1135 ± 0.0014
HQ: FFNS Nf = 3
ABKM
2009
0.1129 ± 0.0014
HQ: BSMN
MSTW
2009
0.1171 ± 0.0014
Thorne
2013
0.1136
[DIS+DY+HT∗ ]
ABM11J
2010
0.1134 − 0.1149 ± 0.0012
Tevatron jets (NLO) incl.
NN21
2011
0.1174 ± 0.0006 ± 0.0001
+h. Nucl.
ABM12
2013
0.1133 ± 0.0011
ABM12
2013
0.1132 ± 0.0011
(without jets)
CTEQ
2013
0.1140
(without jets)
CTEQ
2015
0.1150
+0.0060
∆χ2 > 1 +h. Nucl.
−0.0040
MMHT
2015
0.1172 ± 0.0013
+h. Nucl.
30
Other Lower αs Values
αs (MZ2 )
NNLO
+ 0.0028
− 0.0022
e+ e− thrust
Gehrmann et al.
2009
0.1131
Abbate et al.
2010
0.1140 ± 0.0015
e+ e− thrust
Hoang et al.
2010
0.1123 ± 0.0015
C-param. dist.
Bazavov et al.
2014
0.1166
CMS
2013
0.1151
+0.0012
−0.0008
+0.0028
−0.0027
lattice 2+1 fl.
tt̄
αs (MZ2 )
NLO
+0.0041
Frederix et al.
2010
0.1156
H1
2009
0.1160
D0
2010
0.1156
ATLAS
2012
0.1151
CMS
2013
0.1148 ± 0.0052
−0.0034
+0.0095
−0.0080
+0.0041
−0.0034
+0.0093
−0.0087
NNLO ep and pp jet analyses are utterly needed.
e+ e− → 5 jets
ep jets
pp → jets
jets
3/2 jet ratio
31
32
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33
5. Conclusions
• The N3 LO DIS analysis yields : αs (MZ2 ) = 0.1141 ± 0.0021
• Correct NNLO anlyses require the fit of d2 σ/dxdQ2 and the correct description of FL , F2cc̄ .
• NNLO αs (MZ2 ) values in the range 0.1122 − 0.1147 ± 0.0014 are obtained.
• The various systematic shifts are understood; presently not possible to resolve δαs < 0.0008.
• The difference to the MSTW08 value can be explained.
• Consistent αs and mc fits are mandatory.
• PDF fits, assuming the value of αs may lead to biases, as they are not reaching χ2min in general.
• NLO analyses yield systematic higher αs (MZ2 ) values than NNLO analyses;
averaging of these values is not possible
• Direct relevance for the Higgs search at Tevatron and LHC and
likewise for the other standard candle processes (W/Z, tt).
• Many more αs (MZ2 ) values at NNLO, and even at NLO, come out lower than the present
World average.
• Next important analysis: inclusion of the LHC jet data in complete NNLO fits.