[PPT] - Simultaneous Global Analysis of Polarized and Unpolarized PDFs and PowerPoint Presentation

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Simultaneous Global Analysis of Polarized and Unpolarized PDFs and Fragmentation Functions Nobuo Sato

Old Dominion University CTEQ Workshop Parton Distributions as a Bridge from Low to High Energies Jefferson Lab, 2018

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Motivations

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Mapping the parton strucure of the nucleon

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Challenges: + Quantitative limits of x, Q2, z, ... where factorization theorems are applicable + Universality of non perturbative objects → predictive power + QCD analysis framework that extracts simultaneously all non-perturbative objects (including TMDs) + Framework with the same theory assumptions

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Mapping the parton strucure of the nucleon

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Need for a reliable Bayesian likelihood analysis: + Retire maximum likelihood methods that can lead to biased results (CT, CJ, MMHT, DSSV, ...) + Embrace likelihood analysis via MC methods (JAM, NNPDF) + Faithful representation of uncertainties consistent with Bayes’ theorem

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Bayesian likelihood analysis

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Inclusion of modern data analysis techniques + Bayesian theorm P(f|data) = L(data, f)π(f) + Estimation of expectation values and variances:

data resampling
partition and cross validation
iterative Monte Carlo (IMC)
nested sampling

sampler priors fit fit fit posteriors

riginal data

pseudo data training data fit parameters from minimization steps validation data validation posterior as initial guess prior

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History

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JAM15: ∆PDFs

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NS, Melnitchouk, Kuhn, Ethier, Accardi (PRD)

10−2 0.1 0.2 0.3 0.4 0.5

JAM15 no JLab

0.1 0.3 0.5 0.7

x∆u+

10−2 −0.15 −0.10 −0.05

x∆d+

0.1 0.3 0.5 0.7 10−2 −0.04 −0.02 0.00 0.02 0.04 0.1 0.3 0.5 0.7

x∆s+

10−2 −0.1 0.0 0.1 0.2 0.1 0.3 0.5 0.7

x x∆g

10−2 −0.05 0.00 0.05 0.10 0.15 0.1 0.3 0.5 0.7

xDu

10−2 −0.10 −0.05 0.00 0.05 0.10 0.15

xDd

0.1 0.3 0.5 0.7 10−2 −0.010 −0.005 0.000 0.005 0.010

xHp

0.1 0.3 0.5 0.7 10−2 −0.04 −0.02 0.00 0.02 0.04 0.06

xHn

0.1 0.3 0.5 0.7

x

Inclusion of all JLab 6 GeV data → 0.1 < x < 0.7 Non vanishing twist 3 quark distributions Residual twist 4 contributions consistent with zero

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JAM15: d2 matrix element

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NS, Melnitchouk, Kuhn, Ethier, Accardi (PRD)

1 2 3 4 5

Q2 (GeV2)

−0.005 0.000 0.005 0.010 0.015 0.020

d2

(a)

JAM15 p JAM15 n lattice

1 2 3 4 5

Q2 (GeV2)

(b)

E155x RSS E01–012 E06–014 JAM15

Existing measurements of d2 are in the resonance region → quark-hadron duality d2(Q2) ≡

1

dxx2 2gτ3

1 (x, Q2) + 3gτ3 2 (x, Q2)

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JAM15: ∆PDFs

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NS, Melnitchouk, Kuhn, Ethier, Accardi (PRD)

10−3 10−2 0.1 0.2 0.3 0.4 0.5

JAM15 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

SU2, SU3 constraints imposed What determines the sign of ∆s+?

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JAM16: FFs

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NS, Ethier, Melnitchouk, Hirai, Kumano, Accardi (PRD)

0.2 0.4 0.6 0.8 0.2 0.6 1.0 1.4

zD(z)

π+

K+

u+

0.2 0.4 0.6 0.8 0.2 0.6 1.0 1.4

π+

K+

d+

0.2 0.4 0.6 0.8 0.2 0.6 1.0 1.4

π+

K+

s+

0.2 0.4 0.6 0.8 z 0.2 0.6 1.0 1.4

zD(z)

π+

K+

c+

0.2 0.4 0.6 0.8 z 0.2 0.6 1.0 1.4

π+

K+

b+

0.2 0.4 0.6 0.8 z 0.2 0.6 1.0 1.4

π+

K+

g

π and K Belle, BaBar up to LEP energies JAM and DSS DK

s+

consistent

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JAM17: ∆PDF +FF

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Ethier, NS, Melnitchouk (PRL)

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4

x∆u+

JAM17 JAM15

0.2 0.4 0.6 0.8 1 −0.15 −0.10 −0.05

x∆d+

0.4 0.8 10−3 10−2 10−1 −0.04 −0.02 0.02 0.04 x(∆¯

u + ∆ ¯ d)

DSSV09

0.4 0.8 10−3 10−2 10−1 −0.04 −0.02 0.02 0.04

x(∆¯ u − ∆ ¯ d)

0.4 0.8 x 10−3 10−2 10−1 −0.04 −0.02 0.02 0.04 x∆s+

JAM17 + SU(3)

0.4 0.8 x 10−3 10−2 10−1 −0.1 −0.05 0.05 0.1 x∆s−

No SU(3) constraints Sea polarization consistent with zero Precision of ∆SIDIS is not sufficient to determine sea polarization

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JAM17: ∆PDF +FF

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Ethier, NS, Melnitchouk (PRL)

1.1 1.2 1.3 Normalized yield

gA

SU(2) 0.5 1

a8

SU(3) 0.2 0.3 0.4 0.5 Normalized yield

∆Σ

−0.2 0.2

∆¯ u ∆ ¯ d

−

Flat priors that gives flat a8 in

rder to have an unbias

extraction of a8 Data prefers smaller values for a8 → 25% larger total spin carried by quarks. a3 which is in a good agreement with values from β decays within 2%.

bs.

JAM15 JAM17 gA 1.269(3) 1.24(4) g8 0.586(31) 0.46(21) ∆Σ 0.28(4) 0.36(9) ∆¯ u − ∆ ¯ d 0.05(8)

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Present

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JAM18: Universal analysis (preliminary)

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Goals + Extract PDFs, ∆PDFs and FFs simultaneously

DIS, SIDIS(π, K), DY
∆DIS, ∆SIDIS(π, K)
e+e−(π, K)

+ Consistent extraction of s and ∆s 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 Andres, Ethier, Melnitchouk, NS, Rogers

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JAM18: PDFs (preliminary)

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10−3 10−2 10−1

x

0.0 0.2 0.4 0.6

xf(x)

SIDIS

g/10 u− d− 10−3 10−2 10−1

x

0.0 0.2 0.4

SIDIS

¯ d ¯ u 10−3 10−2 10−1

x

0.0 0.1 0.2 0.3

SIDIS

Q2 = 10 GeV2 s ¯ s

¯ d − ¯ u constrained mainly by DY SIDIS is in agreement with DY’s ¯ d − ¯ u s − ¯ s = 0

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JAM18: PDFs (preliminary)

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10−3 10−2 10−1

x

0.0 0.2 0.4 0.6

xf(x)

SIDIS

g u− d− 10−3 10−2 10−1

x

0.0 0.2 0.4

SIDIS

¯ d ¯ u 10−3 10−2 10−1

x

0.0 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

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JAM18: upolarized sea (preliminary)

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10−2 10−1

x

0.8 1.0 1.2 1.4 1.6

¯ d/¯ u

SIDIS

10−2 10−1

x

0.0 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

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JAM18: ∆PDFs (preliminary)

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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 better known than ∆¯ s It means, most of the uncertainty

n ∆s+ is from ∆¯

s

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JAM18: IMC runs (preliminary)

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10−2 10−1

x

0.0 0.5 1.0 1.5 2.0 2.5

xf(x)

10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.5 1.0 1.5 2.0 2.5

xf(x)

10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.5 1.0 1.5 2.0 2.5

xf(x)

10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.5 1.0 1.5 2.0 2.5

xf(x)

g uv dv

10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5

¯ d ¯ u

10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5

s ¯ s

← flat priors ← DIS no HERA ← DIS with HERA ← DIS with HERA + DY

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... and beyond

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SIDIS+Lattice analysis of nucleon tensor charge

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Lin, Melnitchouk, Prokudin, NS, Shows (PRL)

x

8
4

4

HERMES p

z

4
2

2 4 0.2 0.4 0.6

4
2

2

π+ π− x

8
4

4

Asin(φh+φs)

UT

(%)

COMPASS p

z

2

2 0.2 0.4 0.6

2

2 0.1 0.2

x

6
4
2

2

COMPASS d

0.2 0.4 0.6

z

2
2

0.2 0.4 0.6 Ph⊥

4
2

2

π+ π−

0.2 0.4 0.6

x

–3 –2 –1 1

hu

1

hd

1 0.2 0.4 0.6

z

–0.4 –0.2 0.2 0.4

zH⊥(1)

1(fav)

zH⊥(1)

1(unf)

0.2 0.4

δu

–1.2 –0.8 –0.4

δd

SIDIS SIDIS+lattice (a) 0.5 1

gT

2 4 6

normalized yield (b)

SIDIS+lattice SIDIS

Extraction of transversity and Collins FFs from SIDIS AUT +Lattice gT In the absence of Lattice, SIDIS has no significant constraints on gT

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First global Monte Carlo analysis of pion PDFs

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Barry, NS, Melnitchouk, Ji (PRL)

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First global Monte Carlo analysis of pion PDFs

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Barry, NS, Melnitchouk, Ji (PRL)

How to probe pion structure

+ π + A → l¯ l + X (Drell-Yan) + π + A → γ + X (prompt photons) + e + p → e′ + n + X (SIDIS) → small xπ gluon PDF

p n π

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First global Monte Carlo analysis of pion PDFs

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p n π

dσ dxdQ2dy ∼ fp→π+n (y) ×

q

1 x/y

dξ ξ C(ξ) q

x/y

ξ , Q2

p

n π π

χEFT pQCD

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First global Monte Carlo analysis of pion PDFs

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0.001 0.01 0.1 10 100

Q2

E615 NA10 H1 ZEUS

0.3 0.5 0.7 xπ 0.2 0.4 0.6 xF 100 101 102 d2σ/d√τdxF (×3i)

i = 0 i = 7

E615 0.2 0.4 0.6 xF 10−1 100

d2σ/d√τdxF

NA10

252 GeV 194 GeV

10−3 10−2 10−1 xπ 10−2 10−1 100 101

F LN(3)

2 (×3i) i = 0 i = 6 xL = 0.91 xL = 0.82

H1 10−3 10−2 10−1

xπ

10−2 10−1 100

r

(×3i)

i = 0 i = 5 xL = 0.94 xL = 0.85

ZEUS

Our new analysis extends previous pion PDF analysis down to x ∼ 0.001 The OPE+pQCD can describe the HERA data simultaneously with the DY data

F LN(3)

2

(x, Q2, y) = 2fp→π+n(y)F π

2 (xπ, Q2)

r(x, Q2, y) = d3σLN/dxdQ2dy

d2σinc/dxdQ2 ∆y

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First global Monte Carlo analysis of pion PDFs

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0.001 0.01 0.1 1

xπ

0.1 0.2 0.3 0.4 0.5 0.6

xπf(xπ)

DY DY+LN DY DY+LN DY DY+LN valence sea glue/10 model dep.

Significant reduction of the uncertainties Non-overlapping uncertainties → tensions among the data Accuracy will be improved with future TDIS (JLab12/EIC)

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First global Monte Carlo analysis of pion PDFs

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101 102 103

Q2 (GeV2)

0.2 0.4 0.6

xπ

sea glue valence

GRS SMRS

0.1 0.2 0.3 0.4 0.5 0.6 xπ 0.1 0.2 0.3 0.4

normalized yield

sea

DY DY+LN

glue

DY DY+LN

valence

DY DY+LN

Constraints from HERA significantly increase xg

π.

The role of the glue is more important than suggested by DY alone In contrast, the strength of the sea is reduced Due to momentum sum rule

xvalence

π

decreases

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First global Monte Carlo analysis of pion PDFs

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0.1 0.2 0.3 0.4 0.5

x

−0.01 0.01 0.02 0.03 0.04

x( ¯ d − ¯ u)

SeaQuest

s exp t exp t mon Regge P-V

E866 E866

We performed an additional analysis

f LN+DY+E866

→ good description of E866 data except for large x

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Summary and outlook

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2015 2016 2017 2018 2019 2020 webfitter RHIC data TMDs EIC

10−3 10−2 0.1 0.2 0.3 0.4 0.5 JAM15 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

1 2 3 4 5 Q2 (GeV2) −0.005 0.000 0.005 0.010 0.015 0.020

d2

(a)

JAM15 p JAM15 n lattice 1 2 3 4 5

Q2 (GeV2) (b)

E155x RSS E01–012 E06–014 JAM15 0.2 0.4 0.6 0.8 0.2 0.6 1.0 1.4 zD(z)

π+ K+ u+

0.2 0.4 0.6 0.8 0.2 0.6 1.0 1.4

π+ K+ d+

0.2 0.4 0.6 0.8 0.2 0.6 1.0 1.4

π+ K+ s+

0.2 0.4 0.6 0.8 z 0.2 0.6 1.0 1.4 zD(z)

π+ K+ c+

0.2 0.4 0.6 0.8 z 0.2 0.6 1.0 1.4

π+ K+ b+

0.2 0.4 0.6 0.8 z 0.2 0.6 1.0 1.4

π+ K+ g

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4

x∆u+ JAM17 JAM15

0.2 0.4 0.6 0.8 1 −0.15 −0.10 −0.05

x∆d+

0.4 0.8 10−3 10−2 10−1 −0.04 −0.02 0.02 0.04 x(∆¯

u + ∆ ¯ d) DSSV09

0.4 0.8 10−3 10−2 10−1 −0.04 −0.02 0.02 0.04

x(∆¯ u − ∆ ¯ d)

0.4 0.8 x 10−3 10−2 10−1 −0.04 −0.02 0.02 0.04 x∆s+ JAM17 + SU(3) 0.4 0.8 x 10−3 10−2 10−1 −0.1 −0.05 0.05 0.1 x∆s− 0.2 0.4

δu

–1.2 –0.8 –0.4

δd

SIDIS SIDIS+lattice (a) 0.5 1

gT

2 4 6

normalized yield (b)

SIDIS+lattice SIDIS

0.001 0.01 0.1 1

xπ

0.1 0.2 0.3 0.4 0.5 0.6

xπf(xπ)

DY DY+LN DY DY+LN DY DY+LN valence sea glue/10 model dep.

10−2 10−1

x

0.0 0.5 1.0 1.5 2.0 2.5

xf(x)

10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.5 1.0 1.5 2.0 2.5

xf(x)

10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.5 1.0 1.5 2.0 2.5

xf(x)

10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5 10−2 10−1

x

0.0 0.5 1.0 1.5 2.0 2.5

xf(x)

g uv dv

10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5

¯ d ¯ u

10−2 10−1

x

0.0 0.1 0.2 0.3 0.4 0.5

s ¯ s

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Backup

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χEFT setup

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The splitting function (y = k+/p+ = x/xπ) fp→π+n(y) = g2

AM2

(4πfπ)2

dk2

⊥

y(k2

⊥ + y2M2)

(1 − y)2D2

πN

|F|2 UV regulators used in the literature F =

              

[1 − (t−m2

π)2

(t−Λ2)2 ]1/2

Pauli-Villars (Λ2 − m2

π)/(Λ2 − t)

t-dependent monopole exp[(t − m2

π)/Λ2]

t-dependent exponential exp[(M2 − s)/Λ2] s-dependent exponential y−απ(t) exp[(t − m2

π)/Λ2]

Regge exponential,