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

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 1 / 32

Motivations 2 / 32

Mapping the parton strucure of the nucleon Challenges: + Quantitative limits of x, Q 2 , 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 3 / 32

Mapping the parton strucure of the nucleon 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 4 / 32

Bayesian likelihood analysis fit Inclusion of modern data analysis techniques sampler priors fit posteriors fit + Bayesian theorm P ( f | data) = L (data , f ) π ( f ) original data pseudo prior data + Estimation of expectation values and variances: training validation data data as initial o data resampling fit guess o partition and cross validation parameters from o iterative Monte Carlo (IMC) validation minimization steps o nested sampling posterior 5 / 32

History 6 / 32

JAM15: ∆ PDFs NS, Melnitchouk, Kuhn, Ethier, Accardi (PRD) 0 . 5 0 . 15 JAM15 x ∆ u + xD u Inclusion of all JLab 6 GeV 0 . 4 0 . 10 no JLab 0 . 3 0 . 05 data → 0 . 1 < x < 0 . 7 0 . 2 0 . 00 0 . 1 − 0 . 05 10 − 2 0 . 1 0 . 3 0 . 5 0 . 7 10 − 2 0 . 1 0 . 3 0 . 5 0 . 7 0 . 15 xD d − 0 . 05 0 . 10 Non vanishing twist 3 quark 0 . 05 − 0 . 10 distributions 0 . 00 x ∆ d + − 0 . 05 − 0 . 15 − 0 . 10 10 − 2 10 − 2 0 . 1 0 . 3 0 . 5 0 . 7 0 . 1 0 . 3 0 . 5 0 . 7 0 . 04 0 . 010 0 . 02 0 . 005 Residual twist 4 0 . 00 0 . 000 − 0 . 005 contributions consistent with − 0 . 02 x ∆ s + xH p − 0 . 010 − 0 . 04 zero 10 − 2 10 − 2 0 . 1 0 . 3 0 . 5 0 . 7 0 . 06 0 . 1 0 . 3 0 . 5 0 . 7 0 . 2 xH n x ∆ g 0 . 04 0 . 02 0 . 1 0 . 00 0 . 0 − 0 . 02 − 0 . 1 − 0 . 04 10 − 2 10 − 2 0 . 1 0 . 3 0 . 5 0 . 7 x 0 . 1 0 . 3 0 . 5 0 . 7 x 7 / 32

JAM15: d 2 matrix element NS, Melnitchouk, Kuhn, Ethier, Accardi (PRD) 0 . 020 JAM15 p E155x ( a ) ( b ) 0 . 015 Existing measurements of d 2 JAM15 n RSS lattice E01 – 012 are in the resonance region 0 . 010 d 2 E06 – 014 → quark-hadron duality JAM15 0 . 005 0 . 000 − 0 . 005 1 2 3 4 5 1 2 3 4 5 Q 2 (GeV 2 ) Q 2 (GeV 2 ) � 1 dxx 2 � � d 2 ( Q 2 ) ≡ 2 g τ 3 1 ( x, Q 2 ) + 3 g τ 3 2 ( x, Q 2 ) 0 8 / 32

JAM15: ∆ PDFs NS, Melnitchouk, Kuhn, Ethier, Accardi (PRD) 0 . 5 JAM15 0 . 02 x ∆ u + 0 . 4 JAM13 DSSV09 0 . 00 0 . 3 SU2, SU3 constraints imposed NNPDF14 BB10 0 . 2 − 0 . 02 AAC09 x ∆ s + LSS10 0 . 1 − 0 . 04 What determines the sign of ∆ s + ? 10 − 3 10 − 2 10 − 3 10 − 2 0 . 1 0 . 3 0 . 5 0 . 7 0 . 1 0 . 3 0 . 5 0 . 7 − 0 . 02 0 . 2 − 0 . 06 0 . 1 − 0 . 10 0 . 0 x ∆ d + x ∆ g − 0 . 14 − 0 . 1 10 − 3 10 − 2 10 − 3 10 − 2 0 . 1 0 . 3 0 . 5 0 . 7 0 . 1 0 . 3 0 . 5 0 . 7 x x 9 / 32

JAM16: FFs NS, Ethier, Melnitchouk, Hirai, Kumano, Accardi (PRD) 1 . 4 1 . 4 1 . 4 u + d + s + π and K Belle, BaBar up 1 . 0 π + 1 . 0 π + 1 . 0 zD ( z ) to LEP energies π + 0 . 6 0 . 6 0 . 6 K + K + K + 0 . 2 0 . 2 0 . 2 JAM and DSS D K s + 0 . 2 0 . 4 0 . 6 0 . 8 0 . 2 0 . 4 0 . 6 0 . 8 0 . 2 0 . 4 0 . 6 0 . 8 consistent 1 . 4 1 . 4 1 . 4 c + b + g 1 . 0 π + 1 . 0 π + 1 . 0 π + zD ( z ) 0 . 6 0 . 6 0 . 6 K + K + 0 . 2 0 . 2 0 . 2 K + 0 . 8 z 0 . 8 z 0 . 8 z 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 10 / 32

JAM17: ∆ PDF +FF Ethier, NS, Melnitchouk (PRL) x ∆ u + x ∆ d + 0 0 . 4 No SU(3) constraints 0 . 3 − 0 . 05 0 . 2 − 0 . 10 JAM17 0 . 1 JAM15 Sea polarization consistent with zero − 0 . 15 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 0 0 . 2 0 . 4 0 . 6 0 . 8 1 0 . 04 x (∆¯ u + ∆ ¯ 0 . 04 d ) 0 . 02 0 . 02 Precision of ∆ SIDIS is not sufficient to 0 0 determine sea polarization − 0 . 02 − 0 . 02 − 0 . 04 − 0 . 04 u − ∆ ¯ DSSV09 x (∆¯ d ) 10 − 3 10 − 2 10 − 1 10 − 3 10 − 2 10 − 1 0 . 4 0 . 8 0 . 4 0 . 8 0 . 04 x ∆ s + 0 . 1 x ∆ s − 0 . 02 0 . 05 0 0 − 0 . 02 − 0 . 05 − 0 . 04 − 0 . 1 JAM17 + SU(3) 0 . 8 x 0 . 8 x 10 − 3 10 − 2 10 − 1 10 − 3 10 − 2 10 − 1 0 . 4 0 . 4 11 / 32

JAM17: ∆ PDF +FF Ethier, NS, Melnitchouk (PRL) g A a 8 Normalized yield SU(2) SU(3) Flat priors that gives flat a 8 in order to have an unbias 1 . 1 1 . 2 1 . 3 0 0 . 5 1 extraction of a 8 Normalized yield ∆Σ u ∆ ¯ ∆¯ − d Data prefers smaller values for a 8 → 25% larger total spin 0 . 2 0 . 3 0 . 4 0 . 5 − 0 . 2 0 0 . 2 carried by quarks. obs. JAM15 JAM17 a 3 which is in a good agreement with values from β g A 1 . 269(3) 1 . 24(4) decays within 2% . g 8 0 . 586(31) 0 . 46(21) ∆Σ 0 . 28(4) 0 . 36(9) u − ∆ ¯ ∆¯ d 0 0.05(8) 12 / 32

Present 13 / 32

JAM18: Universal analysis (preliminary) Andres, Ethier, Melnitchouk, NS, Rogers Goals + Extract PDFs, ∆ PDFs and FFs simultaneously o DIS, SIDIS ( π, K ) , DY o ∆ DIS, ∆ SIDIS ( π, K ) o 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 14 / 32

JAM18: PDFs (preliminary) ¯ d ¯ u 0 . 6 0 . 4 xf ( x ) 0 . 4 g/ 10 0 . 2 0 . 2 u − d − SIDIS SIDIS 0 . 0 0 . 0 10 − 3 10 − 2 10 − 1 x 10 − 3 10 − 2 10 − 1 x 0 . 3 s ¯ s ¯ d − ¯ u constrained mainly by DY 0 . 2 SIDIS is in agreement with DY’s ¯ d − ¯ u s − ¯ s � = 0 0 . 1 Q 2 = 10 GeV 2 SIDIS 0 . 0 10 − 3 10 − 2 10 − 1 x 15 / 32

JAM18: PDFs (preliminary) ¯ d u ¯ 0 . 6 0 . 4 xf ( x ) 0 . 4 g 0 . 2 0 . 2 u − d − SIDIS SIDIS 0 . 0 0 . 0 10 − 3 10 − 2 10 − 1 x 10 − 3 10 − 2 10 − 1 x 0 . 3 s s ¯ Comparison with other groups 0 . 2 + dashed: MMHT14 + dashed-dotted: CT14 0 . 1 + dotted: CJ15 + dot-dot-dash: ABMP16 SIDIS 0 . 0 Big differences for s, ¯ s distributions 10 − 3 10 − 2 10 − 1 x 16 / 32

JAM18: upolarized sea (preliminary) 1 . 0 JAM18 1 . 6 d ) u + ¯ CT14 0 . 8 MMHT14 1 . 4 CJ15 s ) / (¯ 0 . 6 u d/ ¯ ABMP16 ¯ 1 . 2 0 . 4 ( s + ¯ 1 . 0 0 . 2 SIDIS SIDIS 0 . 8 0 . 0 10 − 2 10 − 1 x 10 − 2 10 − 1 x 0 . 02 For CJ and CT, s = ¯ s s ) x ( s − ¯ MMHT uses neutrino DIS 0 . 00 SIDIS favors a strange suppression and a larger s , ¯ s asymmetry − 0 . 02 SIDIS 10 − 2 10 − 1 x 17 / 32

JAM18: ∆ PDFs (preliminary) 0 . 6 0 . 002 ∆ ¯ ∆ g d ∆ u + ∆¯ u 0 . 4 0 . 001 x ∆ f ( x ) ∆ d + 0 . 2 0 . 000 0 . 0 − 0 . 001 ∆SIDIS ∆SIDIS − 0 . 2 − 0 . 002 10 − 3 10 − 2 10 − 1 x 10 − 3 10 − 2 10 − 1 x 0 . 002 ∆ s ∆¯ s Recall no SU2,SU3 imposed 0 . 001 u, ∆ ¯ ∆ s, ∆¯ d are much better 0 . 000 known than ∆¯ s − 0 . 001 It means, most of the uncertainty on ∆ s + is from ∆¯ s ∆SIDIS − 0 . 002 10 − 3 10 − 2 10 − 1 x 18 / 32

JAM18: IMC runs (preliminary) 2 . 5 0 . 5 0 . 5 2 . 0 0 . 4 0 . 4 xf ( x ) 1 . 5 0 . 3 0 . 3 ← flat priors 1 . 0 0 . 2 0 . 2 0 . 5 0 . 1 0 . 1 0 . 0 0 . 0 0 . 0 10 − 2 10 − 1 x 10 − 2 10 − 1 x 10 − 2 10 − 1 x 2 . 5 0 . 5 0 . 5 2 . 0 0 . 4 0 . 4 xf ( x ) 1 . 5 0 . 3 0 . 3 ← DIS no HERA 1 . 0 0 . 2 0 . 2 0 . 5 0 . 1 0 . 1 0 . 0 0 . 0 0 . 0 10 − 2 10 − 1 x 10 − 2 10 − 1 x 10 − 2 10 − 1 x 2 . 5 0 . 5 0 . 5 2 . 0 0 . 4 0 . 4 xf ( x ) 1 . 5 0 . 3 0 . 3 ← DIS with HERA 1 . 0 0 . 2 0 . 2 0 . 5 0 . 1 0 . 1 0 . 0 0 . 0 0 . 0 10 − 2 10 − 1 x 10 − 2 10 − 1 x 10 − 2 10 − 1 x 2 . 5 0 . 5 0 . 5 2 . 0 g 0 . 4 0 . 4 xf ( x ) ¯ 1 . 5 0 . 3 0 . 3 d s ¯ s u v 1 . 0 0 . 2 0 . 2 ← DIS with HERA + DY d v 0 . 5 0 . 1 u ¯ 0 . 1 0 . 0 0 . 0 0 . 0 10 − 2 10 − 1 x 10 − 2 10 − 1 x 10 − 2 10 − 1 x 19 / 32

... and beyond 20 / 32

SIDIS+Lattice analysis of nucleon tensor charge Lin, Melnitchouk, Prokudin, NS, Shows (PRL) 4 h u zH ⊥ (1) 4 π + 0 . 4 2 1 1 1(fav) 0 2 0 0 . 2 0 0 - 4 - 2 - 2 π − 0 – 1 HERMES p - 4 h d zH ⊥ (1) - 8 - 4 – 0 . 2 (%) – 2 1 x z 2 0 . 2 0 . 4 0 . 6 1(unf) 2 4 – 0 . 4 A sin( φ h + φ s ) – 3 0 - 0 - 0 x z 0 0 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 δd SIDIS normalized yield (a) SIDIS+lattice (b) - 4 6 UT - 2 SIDIS - 2 - 8 COMPASS p – 0 . 4 2 0 . 2 0 . 4 0 . 6 2 x - 2 z 4 0 0 – 0 . 8 0 2 - 2 SIDIS+lattice - 2 π + - 4 π − – 1 . 2 0 - 2 - 4 COMPASS d 0 0 . 2 0 . 4 0 0 . 5 1 g T δu - 6 0 0 . 1 0 . 2 0 . 2 0 . 4 0 . 6 0 . 2 0 . 4 0 . 6 P h ⊥ x z Extraction of transversity and Collins FFs from SIDIS A UT +Lattice g T In the absence of Lattice, SIDIS has no significant constraints on g T 21 / 32

First global Monte Carlo analysis of pion PDFs Barry, NS, Melnitchouk, Ji (PRL) 22 / 32

First global Monte Carlo analysis of pion PDFs 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 x π gluon PDF π p n 23 / 32