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

JAM PDFs, structure functions at large x Nobuo Sato University of Connecticut Quark Hadron Duality Workshop James Madison University, 2018 1 / 20

Motivations 2 / 20

Motivations JLab 12 brings new challenges + Quantitative limits of x, Q 2 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 observables 3 / 20

Motivations 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 k 2 1 � � θ ( x (1 − x ) M 2 − k 2 T f ( x, k T ) = πM 2 Φ x + T ) xM 2 + If intrinsic transverse momentum is bounded → sets constraints on TMDs (ask J. Collins) 4 / 20

PDFs at high x 5 / 20

High- x analysis setup Data sets + DIS: SLAC ( p, d ) , NMC ( p, d/p ) , BCDMS ( p, d ) + DY: E866 ( p, d ) Q 2 Q 2 E866( p, d ) 100 200 10 SLAC( p, d ) 100 NMC( p, d/p ) BCDMS( p, d ) W 2 = 4GeV 2 W 2 = 10GeV 2 1 0 . 8 x F x 0 . 2 0 . 4 0 . 6 0 . 8 0 . 2 0 . 4 0 . 6 DIS DY 6 / 20

High- x analysis setup Theory setup + Observables computed at NLO in pQCD + DIS structure functions only at leading twist ( W 2 > 10 GeV 2 ) + No nuclear corrections for d data Target Mass Corrections (see T. Rogers talk) + Massless target approximation (MTA) + x → x N + Aivazis-Olness-Tung (AOT) + Georgi-Politzer (GP) 7 / 20

High- x analysis setup Two likelihood analyzes + HWF ≡ High W fit : W 2 > 10GeV 2 + LWF ≡ Low W fit : W 2 > 4GeV 2 Q 2 100 10 SLAC( p, d ) NMC( p, d/p ) BCDMS( p, d ) W 2 = 4GeV 2 W 2 = 10GeV 2 1 x 0 . 2 0 . 4 0 . 6 0 . 8 8 / 20

Results: Data vs. theory SLAC ( p, d ) χ 2 / N pts = 7710 / 998 χ 2 / N pts = 1595 / 998 χ 2 / N pts = 2302 / 998 χ 2 / N pts = 2348 / 998 data / theory (HWF) 1 . 4 1 . 4 1 . 4 1 . 4 1 . 2 1 . 2 1 . 2 1 . 2 1 . 0 1 . 0 1 . 0 1 . 0 0 . 8 0 . 8 0 . 8 0 . 8 x N MTA AOT GP 0 . 6 0 . 6 0 . 6 0 . 6 0 . 8 x 0 . 8 x 0 . 8 x 0 . 8 x 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 χ 2 / N pts = 1375 / 998 χ 2 / N pts = 831 / 998 χ 2 / N pts = 973 / 998 χ 2 / N pts = 942 / 998 1 . 4 1 . 4 1 . 4 1 . 4 data / theory (LWF) 1 . 2 1 . 2 1 . 2 1 . 2 1 . 0 1 . 0 1 . 0 1 . 0 0 . 8 0 . 8 0 . 8 0 . 8 x N MTA AOT GP 0 . 6 0 . 6 0 . 6 0 . 6 0 . 8 x 0 . 8 x 0 . 8 x 0 . 8 x 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 Predictions of HWF fail even with any TMC The LWF give a good description for any TMC 9 / 20

Results: Data vs. theory SLAC ( p, d ) χ 2 / N pts = 7710 / 998 χ 2 / N pts = 1595 / 998 χ 2 / N pts = 2302 / 998 χ 2 / N pts = 2348 / 998 20 20 20 20 Q 2 (HWF) 8 8 8 8 4 4 4 4 x N MTA AOT GP 2 2 2 2 0 . 8 x 0 . 8 x 0 . 8 x 0 . 8 x 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 χ 2 / N pts = 1375 / 998 χ 2 / N pts = 831 / 998 χ 2 / N pts = 973 / 998 χ 2 / N pts = 942 / 998 20 20 20 20 Q 2 (LWF) 8 8 8 8 4 4 4 4 x N MTA AOT GP 2 2 2 2 0 . 8 x 0 . 8 x 0 . 8 x 0 . 8 x 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 Sizes of the blobs are proportional to χ 2 TMC improves the description at large x and Q 2 ∼ 8 GeV 2 10 / 20

Results: F 2 Q 2 = 1 . 69 GeV 2 Q 2 = 10 . 00 GeV 2 AOT and GP x N gives similar 1 . 4 1 . 4 (HWF) AOT results GP 1 . 2 1 . 2 F 2 / F MTA 2 1 . 0 1 . 0 x N differs from AOT and MTA 0 . 8 0 . 8 x x 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 1 . 4 1 . 4 (LWF) 1 . 2 1 . 2 F 2 / F MTA 2 1 . 0 1 . 0 0 . 8 0 . 8 x x 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 11 / 20

Results: u v PDF Q 2 = 1 . 69 GeV 2 Q 2 = 10 . 00 GeV 2 TMC with HWF (HWF) 1 . 4 x N 1 . 4 AOT are basically 1 . 2 1 . 2 GP compatible 1 . 0 1 . 0 u v /u MTA v 0 . 8 0 . 8 Inclusion of 0 . 6 0 . 6 high- x data do x x 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 change PDFs 1 . 4 1 . 4 (LWF) 1 . 2 1 . 2 1 . 0 1 . 0 u v /u MTA v 0 . 8 0 . 8 0 . 6 0 . 6 x x 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 12 / 20

Results: d v PDF Q 2 = 1 . 69 GeV 2 Q 2 = 10 . 00 GeV 2 The change in (HWF) 1 . 4 x N 1 . 4 AOT d v relative to u v 1 . 2 1 . 2 GP indicates onset 1 . 0 1 . 0 d v /d MTA of nuclear effects v 0 . 8 0 . 8 0 . 6 0 . 6 x x 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 1 . 4 1 . 4 (LWF) 1 . 2 1 . 2 1 . 0 1 . 0 d v /d MTA v 0 . 8 0 . 8 0 . 6 0 . 6 x x 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 13 / 20

Discussion 14 / 20

Discussion What do we leaned? + TMCs( x N , 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 p T spectrum in SIDIS 15 / 20

SIDIS p ⊥ h � � p + y h = 1 2 ln h p − h Current fragmentation Collinear factorization Current fragmentation Soft region Target region TMD factorization ???? Fracture functions y h Different regions are sensitive to distinct physical mechanisms 16 / 20

Theory framework for current fragmentation small transverse W large transverse FO momentum momentum p ⊥ p ⊥ h h Current fragmentation Current fragmentation Collinear factorization Collinear factorization Current fragmentation Soft region Target region Current fragmentation Soft region Target region TMD factorization ???? Fracture functions TMD factorization ???? Fracture functions y h y h outgoing detected detected quark hadron hadron outgoing ⊗ quark ⊗ incoming quark incoming quark 17 / 20

Theory framework for current fragmentation small transverse W large transverse FO momentum momentum p ⊥ p ⊥ h h Current fragmentation Current fragmentation Collinear factorization Collinear factorization matching region Current fragmentation Soft region Target region Current fragmentation Soft region Target region TMD factorization ???? Fracture functions TMD factorization ???? Fracture functions y h ASY y h outgoing detected detected quark hadron hadron outgoing ⊗ quark ⊗ incoming quark incoming quark 18 / 20

The large p T SIDIS The p T cross section @ LO � 1 dσ dξ � e 2 ξ − xf q ( ξ, µ ) d q ( ζ ( ξ ) , µ ) H ( ξ ) ∼ q 2 q dxdQ 2 dzdp T xz T 1 − z + x q Q 2 Comments : + ξ min is q T 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 19 / 20

Summary and outlook 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 20 / 20