x or From pQCD and different models : (1 x ) 2 (1 x ) 1 - - PowerPoint PPT Presentation

Pion Valence Quark Distribution

(1 − x)β

Large- fall-off

x β ∼ 1 β ∼ 2

Experiment at JLab and COMPASS to explore large- behavior From pQCD and different models : (1 − x)2

(1 − x)1

• r

x

Large- region: small config constrained by confinement dynamics

x

β ∼ 1.6

Raza Sabbir Sufian

Lattice QCD Calculations

µ2 ∼ 16 GeV2

PRELIMINARY In preparation

Quasi PDFs (Ji, 2013) Pseudo-PDFs (Radyushkin, 2017) Lattice Cross Sections (Ma & Qiu, 2014, 2017)

Lattice Cross Sections

Collaboration: Edwards, Egerer, Karpie, Orginos, Ma, Qiu, Richards, RSS

Collaboration: Karpie, Orginos, Radyushkin, Richards, Zafeiropoulos, RSS arXiv:1909.08517

Phys.Rev. D99 (2019) no.7, 074507

Pion PDF from Light-Front Holographic QCD

HLFHS Collaboration: Brodsky, de Teramond, Deur, Dosch, Liu, RSS

10−4 10−3 10−2 10−1 100

x

0.0 0.2 0.4 0.6

xq(x)

µ2 = 10 GeV2

uv dv

NNPDF3.0 MMHT2014 CT14 LFHQCD (NNLO)

0.0 0.2 0.4 0.6 0.8 1.0

x

0.0 0.1 0.2 0.3 0.4 0.5

xq(x)

µ2 = 27 GeV2 LFHQCD (NLO) LFHQCD (NNLO) WRH2005 ASV2010 Conway et al.

H(⇣) = ✓ −@2

ζ + 4L2 − 1

4⇣2 + U(⇣) ◆ (⇣) = M 2(⇣) (

◆ ✓ ⇣ ⌘ u u

• x2P

x1P b⊥

Modify conformal AdS space by a dilation profile

eφ(z) = eκ2z2

~ ⇣ = p x(1 − x) ~ b⊥i, ⇣ = |~ ⇣ |

ζ ⇐ ⇒ z

de Teramond, Brodsky PRL 2009 GeV (emergent mass scale ! Same for mesons and baryons)

κ ≈ 0.52

A semiclassical approximation to QCD Relativistic, frame-independent Color confining, massless pion mq → 0 Symmetry between observed mesons and observed baryons

Regge behavior at low x, pQCD counting rule at large x

2.0 2.2 2.4 2.6 2.8 3.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 q (Gev) Geff(q)

PRELIMINARY

Phys.Rev.Lett. 120 (2018) no.18, 182001 Phys.Rev. D95 (2017) no.1, 014011 Phys.Rev. D98 (2018) no.11, 114004

arXiv:1909.13818

Mapping of AdS gravity to QCD quantized at fixed light-front time

c2 = 0.875

U(ζ) = κ4ζ2 + 2κ2(J − 1)