JAM PDFs, structure functions at large x Nobuo Sato University of - - PowerPoint PPT Presentation

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JAM PDFs, structure functions at large x Nobuo Sato

University of Connecticut Quark Hadron Duality Workshop James Madison University, 2018

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Motivations

Motivations

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JLab 12 brings new challenges + Quantitative limits of x, Q2 where factorization theorems are applicable + What is the relevant variable that shows scaling? + What properties of partonic dof can we infer? e.g intrinsic transverse momentum + Universality of nonperturbative objects → predictive power + QCD analysis framework that extend to semi-inclusive

• bservables

Motivations

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Understanding target mass corrections

(see T. Rogers talk)

+ There are a variety TMC + In particular Georgi-Politzer (GP) has assumptions on partonic dof + Ellis, Furmanski, Petronzio noted that GP implies f(x, kT) = 1 πM 2 Φ

• x +

k2

T

xM 2

• θ(x(1 − x)M 2 − k2

T)

+ If intrinsic transverse momentum is bounded → sets constraints on TMDs (ask J. Collins)

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PDFs at high x

High-x analysis setup

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Data sets + DIS: SLAC(p, d), NMC(p, d/p), BCDMS(p, d) + DY: E866(p, d)

0.2 0.4 0.6 0.8

x

1 10 100

Q2

SLAC(p, d) NMC(p, d/p) BCDMS(p, d) W 2 = 4GeV2 W 2 = 10GeV2

0.2 0.4 0.6 0.8 xF 100 200

Q2

E866(p, d)

DIS DY

High-x analysis setup

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Theory setup + Observables computed at NLO in pQCD + DIS structure functions only at leading twist (W 2 > 10 GeV2) + No nuclear corrections for d data Target Mass Corrections (see T. Rogers talk) + Massless target approximation (MTA) + x → xN + Aivazis-Olness-Tung (AOT) + Georgi-Politzer (GP)

High-x analysis setup

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Two likelihood analyzes

+ HWF ≡ High W fit : W 2 > 10GeV2 + LWF ≡ Low W fit : W 2 > 4GeV2

0.2 0.4 0.6 0.8

x

1 10 100

Q2

SLAC(p, d) NMC(p, d/p) BCDMS(p, d) W 2 = 4GeV2 W 2 = 10GeV2

Results: Data vs. theory

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0.2 0.4 0.6 0.8 x 0.6 0.8 1.0 1.2 1.4

data/theory (HWF) MTA χ2/Npts = 7710/998

0.2 0.4 0.6 0.8 x 0.6 0.8 1.0 1.2 1.4

xN χ2/Npts = 1595/998

0.2 0.4 0.6 0.8 x 0.6 0.8 1.0 1.2 1.4

AOT χ2/Npts = 2302/998

0.2 0.4 0.6 0.8 x 0.6 0.8 1.0 1.2 1.4

GP χ2/Npts = 2348/998

0.2 0.4 0.6 0.8 x 0.6 0.8 1.0 1.2 1.4

data/theory (LWF) MTA χ2/Npts = 1375/998

0.2 0.4 0.6 0.8 x 0.6 0.8 1.0 1.2 1.4

xN χ2/Npts = 831/998

0.2 0.4 0.6 0.8 x 0.6 0.8 1.0 1.2 1.4

AOT χ2/Npts = 973/998

0.2 0.4 0.6 0.8 x 0.6 0.8 1.0 1.2 1.4

GP χ2/Npts = 942/998

SLAC (p, d) Predictions of HWF fail even with any TMC The LWF give a good description for any TMC

Results: Data vs. theory

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0.2 0.4 0.6 0.8 x 2 4 8 20

Q2 (HWF) MTA χ2/Npts = 7710/998

0.2 0.4 0.6 0.8 x 2 4 8 20

xN χ2/Npts = 1595/998

0.2 0.4 0.6 0.8 x 2 4 8 20

AOT χ2/Npts = 2302/998

0.2 0.4 0.6 0.8 x 2 4 8 20

GP χ2/Npts = 2348/998

0.2 0.4 0.6 0.8 x 2 4 8 20

Q2 (LWF) MTA χ2/Npts = 1375/998

0.2 0.4 0.6 0.8 x 2 4 8 20

xN χ2/Npts = 831/998

0.2 0.4 0.6 0.8 x 2 4 8 20

AOT χ2/Npts = 973/998

0.2 0.4 0.6 0.8 x 2 4 8 20

GP χ2/Npts = 942/998

SLAC (p, d) Sizes of the blobs are proportional to χ2 TMC improves the description at large x and Q2 ∼ 8 GeV2

Results: F2

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0.2 0.4 0.6

x

0.8 1.0 1.2 1.4 F2/FMTA

2

(HWF) Q2 = 1.69 GeV2 xN AOT GP 0.2 0.4 0.6

x

0.8 1.0 1.2 1.4 Q2 = 10.00 GeV2 0.2 0.4 0.6

x

0.8 1.0 1.2 1.4 F2/FMTA

2

(LWF) 0.2 0.4 0.6

x

0.8 1.0 1.2 1.4

AOT and GP gives similar results xN differs from AOT and MTA

Results: uv PDF

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0.2 0.4 0.6

x

0.6 0.8 1.0 1.2 1.4

uv/uMTA

v

(HWF)

Q2 = 1.69 GeV2 xN AOT GP 0.2 0.4 0.6

x

0.6 0.8 1.0 1.2 1.4 Q2 = 10.00 GeV2 0.2 0.4 0.6

x

0.6 0.8 1.0 1.2 1.4

uv/uMTA

v

(LWF)

0.2 0.4 0.6

x

0.6 0.8 1.0 1.2 1.4

TMC with HWF are basically compatible Inclusion of high-x data do change PDFs

Results: dv PDF

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0.2 0.4 0.6

x

0.6 0.8 1.0 1.2 1.4

dv/dMTA

v

(HWF)

Q2 = 1.69 GeV2 xN AOT GP 0.2 0.4 0.6

x

0.6 0.8 1.0 1.2 1.4 Q2 = 10.00 GeV2 0.2 0.4 0.6

x

0.6 0.8 1.0 1.2 1.4

dv/dMTA

v

(LWF)

0.2 0.4 0.6

x

0.6 0.8 1.0 1.2 1.4

The change in dv relative to uv indicates onset

• f nuclear effects

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Discussion

Discussion

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What do we leaned?

+ TMCs(xN, AOT, GP) improves the data/theory agreement at large-x + TMCs(AOT, GP) at LWF give same PDFs/F2 + Are the PDFs at high-x universal? or just curve fitting? → need to validate high-x PDFs in other observables

High-x sensitive observables

+ Lattice QCD: quasi-PDFs, pseudo-PDFs + Collider data: W lepton asymmetry, ... + Large pT spectrum in SIDIS

SIDIS

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p⊥

h

yh

Current fragmentation TMD factorization Current fragmentation Collinear factorization Soft region ???? Target region Fracture functions

yh = 1

2 ln

• p+

h

p−

h

• Different regions are sensitive to

distinct physical mechanisms

Theory framework for current fragmentation

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small transverse momentum

W

p⊥

h

yh

Current fragmentation TMD factorization Current fragmentation Collinear factorization Soft region ???? Target region Fracture functions ⊗

incoming quark

• utgoing

quark detected hadron

large transverse momentum

FO

p⊥

h

yh

Current fragmentation TMD factorization Current fragmentation Collinear factorization Soft region ???? Target region Fracture functions ⊗

incoming quark

• utgoing

quark detected hadron

Theory framework for current fragmentation

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small transverse momentum

W

p⊥

h

yh

Current fragmentation TMD factorization Current fragmentation Collinear factorization Soft region ???? Target region Fracture functions ⊗

incoming quark

• utgoing

quark detected hadron

large transverse momentum

FO

p⊥

h

yh

Current fragmentation TMD factorization Current fragmentation Collinear factorization Soft region ???? Target region Fracture functions ⊗

incoming quark

• utgoing

quark detected hadron

matching region

ASY

The large pT SIDIS

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The pT cross section @ LO dσ dxdQ2dzdpT ∼

• q

e2

q

1

q2 T Q2 xz 1−z +x

dξ ξ − xfq(ξ, µ) dq(ζ(ξ), µ) H(ξ) Comments:

+ ξmin is qT dependent → SIDIS can constrain high-x + It offers flavor separation by looking at π and K + gluon initiated subprocess enters at LO → constraints on high-x gluons

Summary and outlook

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Challenges at high-x

+ Establish a TMC theory consistent with factorization + What can we learn from data and TMCs? + High-x PDF validation → predictive power