Flavor decomposition of collinear PDFs and FFs

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1 EIC User Group Meeting CUA, Washington DC, August 1, 218 Flavor decomposition of collinear PDFs and FFs Wally Melnitchouk JLab Angular Momentum collaboration

2 Outline Unravel flavor (and spin) structure of hadrons by extracting parton distribution functions and fragmentation functions using global QCD analysis with Monte Carlo-based methods Recent highlights: Constraints from Fermilab & JLab data on unpolarized PDFs at high x First extraction of pion PDFs from Drell-Yan and HERA leading neutron production data First combined analysis of polarized DIS + SIDIS + SIA data, with simultaneous extraction of PDFs & fragmentation functions First MC analysis of nucleon s transversity PDFs + lattice QCD

3 Global PDF analysis Universality of PDFs allows data from different processes (DIS, SIDIS, jet production, Drell-Yan ) to be analyzed simultaneously Several dedicated global efforts to extract PDFs using factorization theorems + pqcd at a given order in s CTEQ, MRS/MMHT, HERAPDF, DSSV, use standard maximum likelihood methods ( 2 minimization) NNPDF, JAM use Monte Carlo methods (neural networks, nested sampling) Typically PDF parametrizations are nonlinear functions of PDF parameters, e.g. xf(x, µ) =Nx (1 x) P (x) where P is a polynomial, neural net, multiple local minima present in the 2 function thoroughly scan over sufficiently large parameter space

4 Bayesian approach to global analysis Analysis of data requires estimating expectation values E and variances V of observables O (functions of PDFs) which are functions of parameters Z E[O] = d n a P(~a data) O(~a) Z V [O] = d n a P(~a data) O(~a) E[O] 2 Bayesian master formulas" Using Bayes theorem, probability distribution P given by P(~a data) = 1 Z L(data ~a) (~a) in terms of the likelihood function L

5 Likelihood function Bayesian approach to global analysis L(data ~a) =exp (~a) is a Gaussian form in the data, with 2 function 2 (~a) = X i data i theory i (~a) (data) 2 with priors and evidence (~a) Z Z Z = d n a L(data ~a) (~a) Z tests if e.g. an n-parameter fit is statistically different from (n+1)-parameter fit

6 maximize probability distribution E[O(~a)] = O(~a ) P(~a data)! ~a if O is linear in parameters, and if probability is symmetric in all parameters, V [O(~a)]! Hessian need more robust (Monte Carlo) approach E[O] Bayesian approach to global analysis Standard method for evaluating E, V via maximum likelihood In practice, since in general E[f(~a)] = f(e[~a]), maximum likelihood method often fails 1 N X O(~a k ), V [O] 1 N k X O(~ak ) E[O] 2 k H ij = 1 2 j ~a=~a

7 Monte Carlo methods First group to use MC for global PDF analysis was NNPDF, using neural network to parametrize P (x) in f(x) =Nx (1 x) P (x), are fitted preprocessing coefficients Forte et al. (22) Iterative Monte Carlo (IMC), developed by JAM Collaboration, variant of NNPDF, tailored to non-neutral net parametrizations Markov Chain MC (MCMC) / Hybid MC (HMC) recent proof of principle analysis, ideas from lattice QCD N. Sato et al. (216) Gbedo, Mangin-Brinet (217) Nested sampling (NS) computes integrals in Bayesian master formulas (for E, V, Z) explicitly Skilling (24)

8 Unpolarized Nucleon PDFs

9 Unpolarized PDFs Ubiquity of proton F 2 data (SLAC, BCDMS, NMC, HERA, JLab, ) provides strong constraints on u-quark PDF over large x range xf(x, Q 2 ) Q 2 = 1 GeV 2 CJ15 CJ15 u d d + ū d ū s g/ x Absence of free-neutron data and smaller e q of d quarks limit precision of d-quark PDF, especially at high x nuclear effects in deuterium obscure free-neutron structure extracted from inclusive measurements

10 Valence d/u ratio at high x of particular interest testing ground for nucleon models in x 1 limit d/u! 1/2 SU(6) symmetry d/u! S = qq dominance (color-hyperfine interaction) d/u! 1/5 S z = qq dominance (perturbative gluon exchange) d/u! DSE with qq correlations Unpolarized PDFs d/u CJ15 MMHT14 CT14 JR x considerable uncertainty at high x from deuterium corrections (no free neutrons!) SU(6) DSE helicity scalar qq

11 AW Valence d/u ratio at high x of particular interest significant reduction of PDF errors with new JLab tagged neutron & FNAL W-asymmetry data d +ū! W! ` + CJ15 CDF DØ Unpolarized PDFs d/u CJ15 DIS only + BONuS + ` asym (& Z rap) + W asym x extrapolated ratio at x = 1 d/u!.9 ±.3 does not match any model DSE helicity scalar qq y W upcoming experiments at JLab (MARATHON, BONuS, SoLID) will determine d/u up to x ~.85

12 Light quark sea From perturbative QCD expect symmetric q q sea generated by gluon radiation into pairs q q Ross, Sachrajda (1979) x dependence of ū asymmetry established in FNAL E866 pp/pd Drell-Yan experiment A common explanation for flavor asymmetries in the nucleon ( d ū, s s, ) is meson cloud d Thomas (1984) d _ / u _ NA 51 CTEQ4M E866, PRD 64, 522 (21) x relatively successful phenomenology, but connection with QCD often unclear

13 Light quark sea Rigorous connection with QCD established via chiral EFT N = g A L e 2f N µ 5 µ N 1 (2f ) 2 N µ ( µ ) N + At leading order, gives rainbow, Kroll-Ruderman (for gauge invariance), and tadpole diagrams (a) (b) Matching of quark-level and hadron-level operators with same symmetries (c) (e) (d) O µ 1 µ n q = X h c (n) q/h Oµ 1 µ n h (f) (g) yields convolution representation for PDFs q(x) = X h Z 1 x dy y f h(y) q h v (x/y)

14 (c) Light quark sea More specifically, contributions to quark PDF from (e) different diagrams can be organized as: (d) wave function renormalization (a) rainbow(f) (b) (g) tadpole (c) (d) q(x) =Z 2 q (x)+([f N + f tad ] q )(x) N (a) (b) (e) (a) +([f + f bub ] q (x) + (f KR N (b) q )(x) N (c) (d) (a) (b) (f) (c) (g) (d) (c) rainbow (d) bubble (f) (e) (g) (e) KR (depends on N helicity PDF) (e) Ji, WM, Thomas (215)

15 E866. d ū framework data can be well described within chiral EFT d ū = Light quark sea h f (rbw) i + f (bub) q v x( d ū) SeaQuest E866 s exp t exp t mon Regge P-V x Barry, Sato, WM, C.-R. Ji (218) depends also on pion PDF which can be fit simultaneously!

16 PDFs in the pion Most information on pion PDFs has come from pion-nucleus Drell-Yan data (CERN, Fermilab) A constrains valence PDFs at x (uncertainty from gluon resummation) Q 2 = 16 GeV 2 pion & kaon valence PDFs x u (x) x u K (x) x s K (x) J. S. Conway et al., PRD 39, 92 (1989) x pion sea quark & gluon PDFs at small x mostly unconstrained Hutauruk, Cloet, Thomas (216)

17 PDFs in the pion Recent new (Monte Carlo-based) global analysis used chiral effective field theory to include also leading neutron electroproduction from HERA d 3 LN dx dq 2 dy F LN(3) 2 (x, Q 2,y) 2f /N (y) F 2 (x,q 2 ) y N! N + splitting function (computed from EFT) pion structure function x = x/y x f(x ) DY DY DY+LN DY+LN valence sea glue/1 model dep. DY+LN DY x Barry, Sato, WM, C.-R. Ji (218) first constraints on pion PDFs at low x

18 d 3 /dx dq 2 dy F LP(3) 2 hx i normalized yield.4.6barry, Sato, WM, C.-R. Ji (218).4.2 DY+LN DY hx i glue pion structure valence GRS at intermediate x values (between DY and LN) SMRS sea glue DY+LN DY DY+LN valence sea DY PDFs in the.1 pion DY Q 2 (GeV 2 ) normaliz hx i hx i SMRS GRS DY DY+LN Larger gluon fraction in the pion than without LN constraint Tagged DIS experiment at JLab (a) y =.1 t exp (y cut =.3) t exp (y cut =.2) t mon (y cut =.2) y =.2 HERA JLab x (b) y =.2 HERA x (en! e px) HERA + E866 fit SMRS GRS sea N DY total glue valence sea DY Q 2 (GeV 2 ) will probe extension to hyperon final state could probe kaon structure LN (p beam) and LP (d beam) at EIC!

19 Nucleon Helicity PDFs

20 Proton spin structure Question of how proton spin decomposed into its q & g constituents has engrossed community for > 3 years stimulated advances in theory, experiment & analysis.5 Q2 (GeV2) 1 1 EMC SMC COMPASS HERMES SLAC JLab W 2 = 1 GeV2 W 2 = 4 GeV JAM15 no JLab x u Sato et al (216) x inclusion of JLab data increases # data points by factor ~ 2 s-quark polarization negative from inclusive DIS data (assuming SU(3) symmetry).1.15 x d x s x g x.4

21 Polarization of quark sea? Inclusive DIS data cannot distinguish between q and q _ semi-inclusive DIS sensitive to q & X q e 2 q Σ q(x) D h N*,N * q (z)+ γ N* q M q(x) D h q (z) = Σ q, X γ q X M N N * N but need fragmentation functions! z = E M E Global analysis of DIS + SIDIS data gives different sign for strange quark polarization for different fragmentation functions! s> s< for DSS FFs de Florian et al. (27) for HKNS FFs Hirai et al. (27) need to understand origin of differences in fragmentation!

22 MC analysis of fragmentation functions 1.4 u d s + zd(z) K K K + e + e! hx single-inclusive annihilation (SIA) c b g zd(z) K z K z K z Sato, Ethier, WM, Hirai, Kumano, Accardi (216) favored FFs well constrained; unfavored not as well nontrivial shape of s K fragmentation hard g K fragmentation? (robust feature!)

23 MC analysis of fragmentation functions Fragmentation functions from SIA and (polarized) SIDIS zd h q (z) ū u + + Q 2 = 5 GeV s u + s + K + HKNS DSS z z Ethier, Sato, WM (217) some constraint from SIDIS on unfavored FFs (e.g. s! K + ), but uncertainties still large new result more consistent with DSS at moderate z

24 Simultaneous analysis Simultaneous determination of spin PDFs and FFs, fitting to DIS, SIA and polarized SIDIS (HERMES, COMPASS) data.4 x u JAM17.1 JAM x( ū + d) DSSV x s JAM17 + SU(3) x x d x( ū d) x s x no assumption of SU(3) symmetry s slightly > at high x, consistent with zero s s & ū d consistent with zero Ethier, Sato, WM (217)

25 x s Simultaneous analysis JAM17 + SU(3) x.2 Polarized strangeness in previous, DIS-only analyses was.4 DSSV9.4 negative at x ~.1, induced by SU(3) and parametrization bias DIS+SIDIS, no SU(3) DIS only, with SU(3).5.5 x( ū d) x s.1 Ethier, Sato, WM (217) weak sensitivity to s + from DIS data & evolution SU(3) pulls s + to generate moment ~ -.1 negative peak at x ~.1 induced by fixing b ~ 6-8 less negative s =.3(1) gives larger total helicity =.36(9)

26 Simultaneous analysis Simultaneous analysis of DIS (unpolarized + polarized), SIDIS (unpolarized + polarized), SIA under way minimize uncertainty from unpolarized s & s PDFs xs(x).4.2 Q 2 =2.5 GeV 2 HERMES with D K S (z,q 2 )dz=1.27 Fit CTEQ6L x(u (x)+d (x)) CTEQ6.5S- NNPDF2.3 Andres, Ethier, Sato, WM (218) x indication of S = Z 1 s s asymmetry from neutrino DIS data dx x(s s) =(2. ± 1.4) 1 3 NuTeV (27) from chiral SU(3) loops S =(.4 1.1) 1 3 Salamu, C. Ji, WM, Thomas, Wang (218)

27 Nucleon Transversity PDFs

28 Transversity distributions Extraction of transversity (TMD) g T = R PDF from SIDIS data + isovector moment dx (h u 1 h d 1) from lattice QCD Collins asymmetry A sin( h+ s ) UT / h 1 H? 1 f 1 D 1 h 1 A sin( h+ s) UT (%) HERMES p COMPASS p x x -4 COMPASS d x z z.2.4 z P h? g latt T =1.1(6) 1 h u h d x Lin, WM, Prokudin, Sato, Shows (218) significantly reduced uncertainties with lattice constraint

29 Transversity distributions Extraction of transversity (TMD) g T = R PDF from SIDIS data + isovector moment dx (h u 1 h d 1) from lattice QCD h d 1 d SIDIS.4.8 SIDIS+lattice (a) h u 1 u normalized yield SIDIS+lattice SIDIS.5 1 (b) g T Lin, WM, Prokudin, Sato, Shows (218) distributions do not look very Gaussian! MC analysis gives g T =1. ±.1 maximum likelihood analysis would have given g T.5

30 Outlook New paradigm in global analysis simultaneous determination of collinear distributions using MC sampling of parameter space providing new & more reliable insights into quark/gluon structure of hadrons Short-term: universal QCD analysis of all observables sensitive to collinear (unpolarized & polarized) PDFs and FFs Longer-term: application to global analysis of transverse momentum dependent (TMD) distributions to map out full 3-d image of hadrons