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1 / 20
Combined analysis of polarized and unpolarizedPDFs and fragmentation functions
Nobuo SatoUniversity of ConnecticutSpin18, (Spin physics in Nuclear Reactions and Nuclei)Ferrara, 2018
2 / 20
Motivations
Motivations
3 / 20
SIDIS data from JLab 12 brings new challenges
+ Quantitative limits of x,Q2, z, ... where factorizationtheorems are applicable
+ Universality of non perturbative objects→ predictive power
+ QCD analysis framework that extracts simultaneouslyall non-perturbative objects (including TMDs)
+ Framework with the same theory assumptions
Motivations
4 / 20
Inclusion of modern data analysis techniques
+ Bayesian likelihood analysis
P(f |data) = L(data, f)π(f)
+ Estimation of expectation values and variances:
o maximum likelihood + Hessian (+tolerance)o maximum likelihood + Lagrange multiplierso nested samplingo data resamplingo partition and cross validationo iterative Monte Carlo (IMC)
5 / 20
History
JAM15: ∆PDFs (NS, Melnitchouk, Kuhn, Ethier, Accardi)
6 / 20
10−3 10−2
0.1
0.2
0.3
0.4
0.5JAM15
JAM13
DSSV09
NNPDF14
BB10
AAC09
LSS10
0.1 0.3 0.5 0.7
x∆u+
10−3 10−2
−0.14
−0.10
−0.06
−0.02
x∆d+
0.1 0.3 0.5 0.7 x
10−3 10−2
−0.04
−0.02
0.00
0.02
0.1 0.3 0.5 0.7
x∆s+
10−3 10−2
−0.1
0.0
0.1
0.2
0.1 0.3 0.5 0.7 x
x∆g
+ Inclusion of all the JLab 6GeV data
+ Determination of twist 3 g2
+ SU2, SU3 constraints imposed:
+ DSSV and JAM ∆s+ isinconsistent
JAM16: FFs (NS, Ethier, Melnitchouk, Hirai, Kumano, Accardi)
7 / 20
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
zD(z
)
u+
π+
K+
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
d+
π+
K+
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
s+ JAM
HKNS
DSS
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
zD(z
)
c+
π+
K+
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
b+
π+
K+
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
g
π+
K+
+ π and K Belle, BaBar up to LEP energies+ JAM and DSS DK
s+ consistent
JAM17: ∆PDF +FF (Ethier, NS, Melnitchouk)
8 / 20
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4 x∆u+
JAM17
JAM15
0 0.2 0.4 0.6 0.8 1
−0.15
−0.10
−0.05
0 x∆d+
0.4 0.810−3 10−2 10−1
−0.04
−0.02
0
0.02
0.04 x(∆u + ∆d)
DSSV09
0.4 0.810−3 10−2 10−1
−0.04
−0.02
0
0.02
0.04
x(∆u−∆d)
0.4 0.8x
10−3 10−2 10−1
−0.04
−0.02
0
0.02
0.04 x∆s+
JAM17 + SU(3)0.4 0.8
x10−3 10−2 10−1
−0.1
−0.05
0
0.05
0.1 x∆s−
+ No SU(3) constraints
+ Sea polarizationconsistent with zero
+ Precision of ∆SIDIS isnot sufficient todetermine seapolarization
9 / 20
Present
JAM18: Universal analysis (preliminary)
10 / 20
Data sets
+ DIS, SIDIS(π,K), DY+ ∆DIS, ∆SIDIS(π,K)+ e+e−(π,K)
Theory setup
+ Observables computed at NLO in pQCD+ DIS structure functions only at leading twist (W 2 > 10 GeV2)
Likelihood analysis (first steps)+ Use maximum likelihood to find a candidate solution+ Use resampling to check for stability and estimate uncertainties+ 80 shape parameters and 91 data normalization parameters:
171 dimensional space+ Sampling to be extended with IMC/Nested Sampling
Andres, Ethier, Melnitchouk, NS, Rogers
JAM18: PDFs (preliminary)
11 / 20
10−3 10−2 10−1 x0.0
0.2
0.4
0.6
xf
(x)
SIDIS
g/10
u−
d−
10−3 10−2 10−1 x0.0
0.2
0.4
SIDIS
d
u
10−3 10−2 10−1 x0.0
0.1
0.2
0.3
SIDIS
Q2 = 10 GeV2
s
s d− u constrained mainly by DY
SIDIS is in agreement with DY’sd− u
s− s 6= 0
JAM18: PDFs (preliminary)
12 / 20
10−3 10−2 10−1 x0.0
0.2
0.4
0.6
xf
(x)
SIDIS
g
u−
d−
10−3 10−2 10−1 x0.0
0.2
0.4
SIDIS
d
u
10−3 10−2 10−1 x0.0
0.1
0.2
0.3
SIDIS
s
s Comparison with other groups+ dashed: MMHT14+ dashed-dotted: CT14+ dotted: CJ15+ dot-dot-dash: ABMP16
Big differences for s, s distributions
JAM18: upolarized sea (preliminary)
13 / 20
10−2 10−1 x0.8
1.0
1.2
1.4
1.6
d/u
SIDIS
10−2 10−1 x0.0
0.2
0.4
0.6
0.8
1.0
(s+s)/(u
+d
)
SIDIS
JAM18
CT14
MMHT14
CJ15
ABMP16
10−2 10−1 x
−0.02
0.00
0.02
x(s−s)
SIDIS
For CJ and CT, s = s
MMHT uses neutrino DIS
SIDIS favors a strange suppression
and a larger s, s asymmetry
JAM18: ∆PDFs (preliminary)
14 / 20
10−3 10−2 10−1 x−0.2
0.0
0.2
0.4
0.6
x∆f
(x)
∆SIDIS
∆g
∆u+
∆d+
10−3 10−2 10−1 x−0.002
−0.001
0.000
0.001
0.002
∆SIDIS
∆d
∆u
10−3 10−2 10−1 x−0.002
−0.001
0.000
0.001
0.002
∆SIDIS
∆s
∆s Recall no SU2,SU3 imposed
∆s,∆u,∆d are much betterknown than ∆s
It means, most of the uncertaintyon ∆s+ is from ∆s
JAM18: polarized sea (preliminary)
15 / 20
∆f/f → 1 only realized for u
Polarized sea asymmetry isconsistent with zero
JAM18: helicity PDFs (preliminary)
16 / 20
0.2 0.4 x0.0
0.2
0.4
0.6
0.8
1.0
f↓ /f↑
u0.2 0.4 x
0
1
2
3
4
d0.2 0.4 x
0.8
0.9
1.0
1.1
1.2
s
0.2 0.4 x0.8
0.9
1.0
1.1
1.2
u0.2 0.4 x
0.8
0.9
1.0
1.1
1.2
d0.2 0.4 x
0.8
0.9
1.0
1.1
1.2
s
Helicity distributions seems to be the same for the sea
JAM18: moments (preliminary)
17 / 20
obs. JAM15 JAM17 JAM18 JAM18 [truncated]gA 1.269(3) 1.24(4) 1.163(5) 1.107(5)g8 0.59(3) 0.4(2) 0.5(4) 0.39(2)
∆Σ 0.28(4) 0.36(9) 0.3(2) 0.386(7)∆u−∆d 0 0.05(8) 0.0002(6) −0.0001(5)
∆g 1(15) – 0.22(1) 0.172(9)
Large uncertainties on the full ∆Σ stem from
JAM18 [truncated] means integration over ∆DIS and ∆SIDISkinematics ∆s
JAM18: ∆g (preliminary)
18 / 20
JAM18
∫ 10.05 dx∆g(x) = 0.145(5)
∫ 0.050.001 dx∆g(x) = 0.229(9)
Not so bad for a prediction?
DSSV14
JAM18: FFs (preliminary)
19 / 20
0.2 0.4 0.6 0.8 z0.0
0.2
0.4
0.6
0.8
1.0
zD(z
)
π+
SIDIS
0.2 0.4 0.6 0.8 z0.0
0.1
0.2
0.3
0.4
SIDIS
K+ g
u
d
s
c
d
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
zD(z
)
u+
π+
K+
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
d+
π+
K+
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
s+ JAM
HKNS
DSS
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
zD(z
)
c+
π+
K+
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
b+
π+
K+
0.2 0.4 0.6 0.8 z
0.2
0.6
1.0
1.4
g
π+
K+
JAM16
gluon FFs are significantlyaffected by SIDIS
This feature is key for pTdifferential SIDIS → see mytalk “3D Structure of theNucleon: TMDs”
Summary and outlook
20 / 20
First universal analysis of PDFs, ∆PDF and FFs
+ New insights on nucleon sea distributions (s, s asymmetry)
+ π and K gluon FFs are required by SIDIS to peak at larger z→ relevant for TMD physics
+ The universal analysis will to be extend to TMD analysis
Next steps
+ Perform additional checks using IMC and Nested Sampling
+ Make predictions to high energy observables and check the genuinepredictive power of the universal analysis
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