1 fromdeep-inelasticscattering sblumlein/talks/alph1.pdf · 1 αs fromdeep-inelasticscattering j....
TRANSCRIPT
1
αs from Deep-Inelastic Scattering
J. Blumlein, 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. Blumlein αs-Workshop Geneva, Oct. 2015
2
αs(M2Z) in 1992
G. Altarelli: QCD - 20 Years Later NLO World-Average [23 years ago.]
αs(M2Z)
Rτ 0.117+0.010
−0.016
DIS 0.112± 0.007
Υ Decays 0.110± 0.010
Re+e−(s < 62GeV) 0.140± 0.020
pp → W + jets 0.121± 0.024
Γ(Z → hadrons)/Γ(Z → ll) 0.132± 0.012
Jets at LEP 0.122± 0.009
Average 0.118± 0.007
@ NLO: still right, but for very different reasons.
NLO error: now down to ∼ 0.0050− 0.0040 (TH: scale uncertainty)
3
ΛQCD and αs(M2Z)
older values: 2000 <∼date <
∼2007
NLO αs(M2
Z) expt theory Ref.
CTEQ6 0.1165 ±0.0065 [1]MRST03 0.1165 ±0.0020 ±0.0030 [2]A02 0.1171 ±0.0015 ±0.0033 [3]ZEUS 0.1166 ±0.0049 [4]H1 0.1150 ±0.0017 ±0.0050 [5]BCDMS 0.110 ±0.006 [6]GRS 0.112 [10]BBG 0.1148 ±0.0019 [9]BB (pol) 0.113 ±0.004 +0.009
−0.006[7]
NLO at least: scale errors of ±0.0050
NNLO αs(M2
Z) expt theory Ref.
MRST03 0.1153 ±0.0020 ±0.0030 [2]A02 0.1143 ±0.0014 ±0.0009 [3]SY01(ep) 0.1166 ±0.0013 [8]SY01(νN) 0.1153 ±0.0063 [8]GRS 0.111 [10]A06 0.1128 ±0.0015 [11]BBG 0.1134 +0.0019/ − 0.0021 [9]
N3LO αs(M2
Z) expt theory Ref.
BBG 0.1141 +0.0020/ − 0.0022 [9]
NNLO systematic shifts down
N3LO slight upward shift
BBG: Nf = 4: non-singlet data-analysis at O(α4s): Λ = 234± 26MeV
4
Deep Inelatsic Scattering
q
k′
k
P Wµν
Lµν
Q2 := −q2, x :=Q2
2pq
ν :=Pq
M,
dσ
dQ2 dx∼ WµνL
µν
Wµν(q, P, s) =1
4π
∫
d4ξ exp(iqξ)〈P, s[Jemµ (ξ), Jem
ν (0)]P, s〉
=1
2x
(
gµν −qµqνq2
)
FL(x,Q2)
+2x
Q2
(
PµPν +qµPν + qνPµ
2x−
Q2
4x2gµν
)
F2(x,Q2)
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
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
10-3
10-2
10-1 x
xuv(X)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
10-3
10-2
10-1 x
xuv(X)
0
0.1
0.2
0.3
0.4
0.5
10-3
10-2
10-1 x
xdv(X)
0
0.1
0.2
0.3
0.4
0.5
10-3
10-2
10-1 x
xdv(X)
World data:
NS-analysis
W 2 > 12.5 GeV2, Q2 > 4 GeV2
N3LO :
αs(M2Z) = 0.1141+0.0020
−0.0022
J.B., H. Bottcher, A. Guffanti
Nucl.Phys. B774 (2007) 182.
6
Why an O(α4s) analysis can be performed?
assume an ±100% error on the Pade approximant −→ ±2 MeV in ΛQCD
γapprox:3n =
γ(2)n
2
γ(1)n
Baikov & Chetyrkin, April 2006:
γ3;NS2 =
32
9as +
9440
243a2s +
[
3936832
6561−
10240
81ζ3
]
a3s
+
[
1680283336
1777147−
24873952
6561ζ3 +
5120
3ζ4 −
56969
243ζ5
]
a4s
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
10-3
10-2
10-1
1
10
1 10 102
103
104
105
Q2, GeV2
10-3
10-2
10-1
1
10
1 10 102
103
Q2, GeV2
8
Higher Twist Contributions in the Valence Region
J.B. and H. Bottcher, 2012 (BB) [1207.3170 hep-ph]: NS-tails at NNLO :
0.97
0.975
0.98
0.985
0.99
0.995
1
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
F2p(valence)/F2
p(x)
Q2 = 4 GeV2
Q2 = 10 GeV2
0.97
0.975
0.98
0.985
0.99
0.995
1
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x
F2d(valence)/F2
d(x)
Q2 = 100 GeV2
Using ABKM09 we corrected for non NS-tails in F2(x,Q2).
9
Valence Distributions: higher twist
0
2
4
6
8
10
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
PROTON
CHT(x) [GeV2]
4.0 GeV2 < W2 < 12.5 GeV2
NLO
NNLO
N3LO
x-1
0
1
2
3
4
5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
DEUTERON
CHT(x) [GeV2]
4.0 GeV2 < W2 < 12.5 GeV2
NLO
NNLO
N3LO
x• agreement between p and d analysis, J.B., H. Bottcher Phys.Lett. B662 (2008) 336
• LGT determination of interest
10
αs(M2Z)
❊①♣❡r✐�❡♥t ☛s✭▼❩✮
◆▲❖✁✂✄ ◆▲❖ ◆◆▲❖ ◆✸▲❖☎
❇❈❉✆❙ ✵✿✶✶✶✶ ✝ ✵✿✵✵✶✽ ✵✿✶✶✞✽ ✝ ✵✿✵✵✵✼ ✵✿✶✶✷✻ ✝ ✵✿✵✵✵✼ ✵✿✶✶✷✽ ✝ ✵✿✵✵✵✻
◆✆❈ ✵✿✶✶✼
✰ ✟✠✟✡✡
☞ ✟✠✟✡✌ ✵✿✶✶✻✻ ✝ ✵✿✵✵✞✾ ✵✿✶✶✺✞ ✝ ✵✿✵✵✞✾ ✵✿✶✶✺✞ ✝ ✵✿✵✵✞✺
❙▲❆❈ ✵✿✶✶✹✼ ✝ ✵✿✵✵✷✾ ✵✿✶✶✺✽ ✝ ✵✿✵✵✞✞ ✵✿✶✶✺✷ ✝ ✵✿✵✵✷✼
❇❇● ✵✿✶✶✹✽ ✝ ✵✿✵✵✶✾ ✵✿✶✶✞✹ ✝ ✵✿✵✵✷✵ ✵✿✶✶✹✶ ✝ ✵✿✵✵✷✶
❇❇ ✵✿✶✶✹✼ ✝ ✵✿✵✵✷✶ ✵✿✶✶✞✷ ✝ ✵✿✵✵✷✷ ✵✿✶✶✞✼ ✝ ✵✿✵✵✷✷
❚❛❜❡❧❧❡ ✻✍ ✎♦♠✏✑✒✓✔♦✕ ♦❢ ✖❤✗ ✈✑✘✉✗✔ ♦❢ ✙s✚✛❩✜ ♦✢✖✑✓✕✗❞ ✢② ✣✎✤✥✦ ✑✕❞ ✧✥✎ ✑✖ ✧★✩ ✇✓✖❤ ✖❤✗
✒✗✔✉✘✖✔ ♦❢ ✖❤✗ ✪✑✈♦✒ ✕♦✕✲✔✓✕❣✘✗✖ ✫✖✔ ✣✣✬ ✑✕❞ ✣✣ ♦❢ ✖❤✗ ✤■✦ ✪✑✈♦✒ ✕♦✕✲✔✓✕❣✘✗✖ ✇♦✒✘❞ ❞✑✖✑✱ ✑✖ ✧★✩✱
✧✧★✩✱ ✑✕❞ ✧✸★✩☎ ✇✓✖❤ ✖❤✗ ✒✗✔✏♦✕✔✗ ♦❢ ✖❤✗ ✓✕❞✓✈✓❞✉✑✘ ❞✑✖✑ ✔✗✖✔✱ ❝♦♠✢✓✕✗❞ ❢♦✒ ✖❤✗ ✗✯✏✗✒✓♠✗✕✖✔ ✣✎✤✥✦
✧✥✎ ✦★✳✎✴
11
S+NS DIS Analysis (NNLO)µ=2 GeV, nf=4
0
2.5
5
7.5
10
10-5
10-4
10-3
10-2
xG
x0
2.5
5
7.5
10
0
1
2
3
0.05 0.1 0.15 0.2 0.25
xG
x0
1
2
3
0
0.25
0.5
0.75
1
10-5
10-4
10-3
10-2
x(u-+d
-)/2
x0
0.25
0.5
0.75
1
0
0.05
0.1
0.15
0.2
0.05 0.1 0.15 0.2 0.25
x(u-+d
-)/2
x0
0.05
0.1
0.15
0.2
0
0.2
0.4
0.6
0.8
0.2 0.4 0.6 x
xu
xd
0
0.2
0.4
0.6
0.8
-0.02
0
0.02
0.04
0.06
10-4
10-3
10-2
10-1
x(d--u
-)
x
-0.02
0
0.02
0.04
0.06
0
0.5
1
1.5
2
10-5
10-4
10-3
10-2 x
x(s+s-)/2
0
0.5
1
1.5
2
0
0.05
0.1
0.05 0.1 0.15 0.2 0.25 x
x(s+s-)/2
0
0.05
0.1
ABM12: shaded region, JR: full line (green), NN23: dashes (blue), MRST: dash-dotted (red), CT10: dots.
12
Higher Twist Contributions
ABM11:
Fi(x,Q2) = FTMC,τ=2
i (x,Q2) +H4
i (x)
Q2+
H6i (x)
Q4+ ...
-0.15
-0.125
-0.1
-0.075
-0.05
-0.025
0
0.025
0.05
0.075
0 0.5 x
H2p (1/GeV2)
-0.15
-0.125
-0.1
-0.075
-0.05
-0.025
0
0.025
0.05
0.075
0 0.5 x
HTp (1/GeV2)
-0.15
-0.125
-0.1
-0.075
-0.05
-0.025
0
0.025
0.05
0.075
0 0.5 x
H2 ns (1/GeV2)
❋✐�✉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(M2Z)
ABM11
500
1000
1500
2000
0.105 0.11 0.115 0.12 0.125
αs(MZ)
χ2
HERA
600
700
800
900
0.105 0.11 0.115 0.12 0.125
αs(MZ)
χ2
NMC
700
750
800
0.105 0.11 0.115 0.12 0.125
αs(MZ)
χ2
BCDMS
1000
1250
1500
1750
2000
0.105 0.11 0.115 0.12 0.125
αs(MZ)
χ2
SLAC
218
220
222
224
0.105 0.11 0.115 0.12 0.125
αs(MZ)
χ2
DY
NNLO
NLO
❋✐�✉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(M2Z)
❊①♣❡r✐�❡♥t ☛s✭▼❩✮
◆▲❖✁✂✄ ◆▲❖ ◆◆▲❖
❇❈❉☎❙ ✵✿✶✶✶✶ ✝ ✵✿✵✵✶✽ ✵✿✶✶✺✵ ✝ ✵✿✵✵✶✷ ✵✿✶✵✽✹ ✝ ✵✿✵✵✶✸
◆☎❈ ✵✿✶✶✼
✰ ✆✞✆✟✟
✠ ✆✞✆✟✻ ✵✿✶✶✽✷ ✝ ✵✿✵✵✵✼ ✵✿✶✶✺✷ ✝ ✵✿✵✵✵✼
❙▲❆❈ ✵✿✶✶✼✸ ✝ ✵✿✵✵✵✸ ✵✿✶✶✷✽ ✝ ✵✿✵✵✵✸
❍❊❘❆ ❝♦�❜✳ ✵✿✶✶✼✹ ✝ ✵✿✵✵✵✸ ✵✿✶✶✷✡ ✝ ✵✿✵✵✵✷
❉❨ ✵✿✶✵✽ ✝ ✵✿✵✶✵ ✵✿✶✵✶ ✝ ✵✿✵✷✺
❆❇☎✶✶ ✵✿✶✶✽✵ ✝ ✵✿✵✵✶✷ ✵✿✶✶✸✹ ✝ ✵✿✵✵✶✶
❚❛❜❡❧❧❡ ✹☞ ✌✍♠✎✏✑✒✓✍✔ ✍❢ ✕❤✖ ✈✏✗✉✖✓ ✍❢ ✘s✙✚❩✛ ✍✜✕✏✒✔✖❞ ✜② ✢✌✣✤✥ ✏✔❞ ✦✤✌ ✏✕ ✦✧★ ✇✒✕❤ ✕❤✖
✒✔❞✒✈✒❞✉✏✗ ✑✖✓✉✗✕✓ ✍❢ ✕❤✖ ✩✕ ✒✔ ✕❤✖ ✎✑✖✓✖✔✕ ✏✔✏✗②✓✒✓ ✏✕ ✦✧★ ✏✔❞ ✦✦✧★ ❢✍✑ ✕❤✖ ✪✫✬✯ ❞✏✕✏ ✕❤✖ ✦✤✌
❞✏✕✏ ✕❤✖ ✢✌✣✤✥ ❞✏✕✏ ✕❤✖ ✥✧✯✌ ❞✏✕✏ ✏✔❞ ✕❤✖ ✣✱ ❞✏✕✏✲The values of αs(M
2Z) in NLO and NNLO fits are different.
15
ABM fits including Jet Data: D0 run II dijet
ABKM09 (no re-fit)
Y= 0.20data
/NL
O scale unc.
Y= 0.60
Y= 1.00 Y= 1.40
Y= 1.80 Y= 2.20
MJJ (GeV)
Dat
a/T
heo
ry
0.20.40.60.8
11.21.41.61.8
22.2 < 0.4
max|y|
-1DØ, L = 0.7 fb
0.2 0.4 0.6 0.8 1 1.2 1.40.20.40.60.8
11.21.41.61.8
22.2
Data/NLOSystematic Uncertainty
< 1.6max
1.2 < |y|
= 1.96 TeVs
= 0.7coneR
< 0.8max
0.4 < |y|
0.2 0.4 0.6 0.8 1 1.2 1.4
variationF
µ, R
µMSTW2008 Uncertainty
< 2.0max
1.6 < |y|
< 1.2max
0.8 < |y|
)/2T2
+ pT1
= (pF
µ = R
µ
[TeV]JJM0.2 0.4 0.6 0.8 1 1.2 1.4
CTEQ6.6 w/ Uncertainty
< 2.4max
2.0 < |y|
ABM (2011). Note that the cross section is known to NLO only !
16
D0 run II djet data
Y= 0.20data
/NL
O
Y= 0.60
µR/µF=1 µR/µF=0.5
Y= 1.00 Y= 1.40
Y= 1.80 Y= 2.20
ET (GeV)
Y= 0.20data
/NL
O
Y= 0.60
Y= 1.00 Y= 1.40
Y= 1.80 Y= 2.20
ET (GeV)
before the fit after the fit
ABM (2011) χ2 = 104/110
17
αs(M2Z)
µ=3 GeV
0
1
2
3
4
5
6
0.02 0.04 0.06 0.08 0.1
x
xG(x
,µ)
ABM11
ABM11+ATLAS(1jet,PT>150 GEV)
ABM11+ATLAS(1jet,PT>100 GEV)
ABKM09+D0(1jet)
MSTW08
10-4
10-3
10-2
10-1
1
0.2 0.4 0.6
xxG
(x,µ
)
❋✐�✉r❡ ✷✽✿ ●❧✁♦♥ ❞✂st✄✂❜✁t✂♦♥ ♦❜t❛✂♥☎❞ ❜② ✂♥❝❧✁❞✂♥❣ t❤☎ ❆❚▲❆❙ ❥☎t ❞❛t❛ ✂♥t♦ t❤☎ ❆❇▼✶✶ ❛♥❛❧②s✂s✳
18
αs(M2Z): 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(M2Z): 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◗❬♦❭ ♦❢ ❪❫❴ ✈❑❵❣❴❬ ♦❢ ❦sq✇❩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 αNNLOs .
• 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(M2Z) - Higher Twist Correlation
ABM11 NNLO
-1
-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
coef
fici
ent
of c
orre
lati
on w
ith
α s
H2(x)HT(x)
❋✐�✉r❡ ✷✵✿ ❚❤✁ ❝♦✂✂✁❧❛t✄♦♥ ❝♦✁✍❝✄✁♥t ♦❢ ☛s✭▼❩✮ ✇✄t❤ t❤✁ ♥☎❝❧✁♦♥ t✇✄✆t✲✹ ❝♦✁✍❝✄✁♥t✆ ❍✝ ✭✆♦❧✄❞ ❧✄♥✁✮
❛♥❞ ❍✞ ✭❞❛✆❤✁✆✮ ✈✁✂✆☎✆ ① ❛✆ ♦❜t❛✄♥✁❞ ✄♥ ♦☎✂ ◆◆▲❖ ☞t✳
=⇒ Including scales as Q2 < 10GeV2 requires fit of higher twist terms (Singlet Analysis).
23
αs(M2Z): NNLO Comparison ABM, BBG, NNPDF, MSTW
❉❛t❛ ❙❡t ❆❇▼✶✶ ❇❇● ◆◆✷✶ ▼❙❚❲
❇❈❉▼❙ ✵✿✶✵✹✽ ✝ ✵✿✵✵✶✸ ✵✿✶✶✷✻ ✝ ✵✿✵✵✵✼ ✵✿✶✶✺✽ ✝ ✵✿✵✵✶✺ ✵✿✶✶✵✶ ✝ ✵✿✵✵✾✹
◆▼❈ ✵✿✶✶✺✷ ✝ ✵✿✵✵✵✼ ✵✿✶✶✺✸ ✝ ✵✿✵✵✸✾ ✵✿✶✶✺✵ ✝ ✵✿✵✵✷✵ ✵✿✶✷✶✻ ✝ ✵✿✵✵✼✹
❙▲❆❈ ✵✿✶✶✷✽ ✝ ✵✿✵✵✵✸ ✵✿✶✶✺✽ ✝ ✵✿✵✵✸✹ ❃ ✵✿✶✷✹
✭
�✁✂✂✄� ☎ �✁��✆� ✞♣
�✁✂✟✟� ☎ �✁��✆� ✞❞
❍❊❘❆ ✵✿✶✶✷✻ ✝ ✵✿✵✵✵✷
✭
�✁✂✂✠✠ ☎ �✁��✂✠
�✁✂✟✡✂ ☎ �✁��✡�
✵✿✶✷✵✽ ✝ ✵✿✵✵✺✽
❉❨ ✵✿✶✵✶ ✝ ✵✿✵✷✺ ☛ ☛ ✵✿✶✶✸✻ ✝ ✵✿✵✶✵✵
✵✿✶✶✸✹ ✝ ✵✿✵✵✶✶ ✵✿✶✶✸✹ ✝ ✵✿✵✵✷✵ ✵✿✶✶✼✸ ✝ ✵✿✵✵✵✼ ✵✿✶✶✼✶ ✝ ✵✿✵✵✶✹
❚❛❜❧❡ ✾☞ ✌♦♠♣✍r✐s♦♥ ♦❢ ✎❤✞ ♣✉✏✏s ✐♥ ✑✒✓✔❩✮ ♣✞r ❞✍✎✍ s✞✎ ✕✞✎✇✞✞♥ ✎❤✞ ✖✗✘✂✂✱ ✗✗✙✱ ✚✚✟✂✱ ✘✛✜✢
✍♥✍✏②s✞s ✍✎ ✚✚✣❖✳
=⇒ Despite the NNLO values for αs(M2Z) of NNPDF and MSTW are close to each other, the
contribution of the different data sets differ considerably.
24
O(α2
s)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
10 102
Q2 (GeV2)
x=0.00018
ZEUS(RunI)H1(RunII)
Fc,exact
2 (Nf=3)
Fc,BMSN
2
Fc,asymp
2 (Nf=4)
0
0.1
0.2
0.3
0.4
0.5
10 102
Q2 (GeV2)
x=0.003
0
0.025
0.05
0.075
0.1
0.125
0.15
0.175
0.2
10 102
Q2 (GeV2)
x=0.03
❋✐❣✉r❡ ✶✿ ❈♦♠♣❛�✁s♦♥ ♦❢ ✂❝✷ ✁♥ ❞✁☛✄�✄♥t s☎❤✄♠✄s t♦ ❍✆✲ ❛♥❞ ❩❊❯❙✲❞❛t❛✳ ❙♦❧✁❞ ❧✁♥✄s✝ ●▼❱✞◆ s☎❤✄♠✄
✁♥ t❤✄ ❇▼❙◆ ♣�✄s☎�✁♣t✁♦♥✱ ❞❛s❤✲❞♦tt✄❞ ❧✁♥✄s✝ ✸✲✟❛✈♦� s☎❤✄♠✄✱ ❞❛s❤✄❞ ❧✁♥✄s✝ ✹✲✟❛✈♦� s☎❤✄♠✄✳ ❚❤✄ ✈✄�t✁☎❛❧
❞♦tt✄❞ ❧✁♥✄ ❞✄♥♦t✄s t❤✄ ♣♦s✁t✁♦♥ ♦❢ t❤✄ ☎❤❛�♠✲q✠❛�❦ ♠❛ss ✡❝ ❂ ✆☞✹✸ ●✄❱✳
✶
Heavy Flavor Treatment
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.
mMSc 1.24± 0.03
+0.03
−0.03ABDLM, DIS, FFNS, χ2 = 61/52
mMSc 1.279± 0.013 Chetyrkin et al., e+e−
mMSc 1.275± 0.025 PDG
mPolec 1.67± 0.07 PDG
mPolec 1.25 MMHT [1510.02332] GMVFNS; αs = 0.1167;χ2 = 72/52
26
Heavy Flavor Treatment
50 100 150 200Ξ
-1.0
-0.5
0.5
1.0C m assive ,H2L
asym ptotic
g1 casy
g1 b
g1 c
JB, G. Falcioni, A. De Freitas, DESY 15-171
• Exact O(α2s) 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; Gluck, Reya, Stratmann, 1994; ABM2009–
27
Effect on the Gluon density∆[xG(x)]
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
10-2
10-1
x
ABKM09
ABKM09 with FNMC
2
µ=2 GeV
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
10-2
10-1
x
µ=165 GeV
wrong treatment (FNMC2 ): 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(M2Z) so high ?
αs(M2Z) with σNMC with FNMC
2 difference
NLO 0.1179(16) 0.1195(17) +0.0026 ≃ 1σ
NNLO 0.1135(14) 0.1170(15) +0.0035 ≃ 2.3σ
NNLO + FLO(α3s) 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(M2Z) = 0.1191± 0.0016
Use: W 2 > 12.5 GeV2, Q2 > 10 GeV2 and no HT: αs(M2Z) = 0.1134± 0.0008
NNPDF Q2 > 5GeV2.
29
NNLO Analysesαs(M2
Z)
SY 2001 0.1166± 0.0013 Fep2
SY 2001 0.1153± 0.0063 xF νN3
h. Nucl.
A02 2002 0.1143± 0.0020
MRST03 2003 0.1153± 0.0020
BBG 2004(06,12) 0.1134+0.0019
−0.0021valence analysis, NNLO
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
−0.0040∆χ2 > 1 +h. Nucl.
MMHT 2015 0.1172± 0.0013 +h. Nucl.
30
Other Lower αs Values
NNLO αs(M2Z)
Gehrmann et al. 2009 0.1131 + 0.0028− 0.0022 e+e− thrust
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+0.0012
−0.0008lattice 2+1 fl.
CMS 2013 0.1151+0.0028
−0.0027tt
NLO αs(M2Z)
Frederix et al. 2010 0.1156+0.0041
−0.0034e+e− → 5 jets
H1 2009 0.1160+0.0095
−0.0080ep jets
D0 2010 0.1156+0.0041
−0.0034pp → jets
ATLAS 2012 0.1151+0.0093
−0.0087jets
CMS 2013 0.1148± 0.0052 3/2 jet ratio
NNLO ep and pp jet analyses are utterly needed.
31
32
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33
5. Conclusions
• The N3LO DIS analysis yields : αs(M2Z) = 0.1141± 0.0021
• Correct NNLO anlyses require the fit of d2σ/dxdQ2 and the correct description of FL, Fcc2 .
• NNLO αs(M2Z) 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(M2Z) 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(M2Z) 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.