Spin-dependent PDFs at large x

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1 Physics Opportunities at an Electron-Ion Collider (POETIC V) Yale University September 22, 24 Spin-dependent PDFs at large Wally Melnitchouk

2 Outline Why is nucleon (spin) structure at large interesting? Parton distributions at large new JAM global analysis of polarized PDFs 2 finite-q effects & nuclear corrections Role of orbital angular momentum behavior of q/q ratios Future prospects (JLab 2 GeV, EIC) 2

3 Large- PDFs Most direct connection between quark distributions and models of nucleon structure is via valence quarks most cleanly revealed at >.4.6 structure of hadron or structure of probe? p g f (,Q) u u d.4.2 sea valence uv dv! u d! s g/5 p u u d 3

4 Large- PDFs Ratios of quark distributions particularly sensitive to quark-gluon dynamics in nucleon SU(6) spin-flavor symmetry d/u /2 u/u 2/3 A p 5/9 d/d /3 A n Symmetry broken by e.g. color-spin interaction scalar diquark dominance (M >M N ); only u quarks couple to scalar diquarks d/u u/u d/d /3 A p A n Feynman, γ-hadron Interactions (972) Close, PLB 43, 422 (973); Close, Thomas, PLB 22, 227 (988) 4

5 Perturbative QCD In QCD, eceptional configurations of proton wave function generated from typical wave function (for which i /3 ) by echange of 2 hard gluons, with mass k 2 k /( 2 ) Farrar, Jackson, PRL 35, 46 (975) Since k 2 is large, coupling at q-g verte is small use lowest-order perturbation theory! Assume wave function vanishes sufficiently fast as and unperturbed wave function dominated by 3-quark Fock component with SU(2) SU(3) symmetry k 2 5

6 Perturbative QCD If spectator diquark spins are anti-aligned (helicity of struck quark = helicity of proton) can echange transverse or longitudinal gluon If spectator diquark spins are aligned (helicity of struck quark = helicity of proton) can echange only longitudinal gluon Coupling of (large- k 2 ) longitudinal gluon to (small- p 2 ) quark is suppressed by (p 2 /k 2 ) /2 ( ) /2 w.r.t. transverse q ( ) 2 q ( ) 5 6

7 Perturbative QCD Phenomenological consequences of S z = qq dominance assuming unperturbed SU(6) wave function, d/u /5 dominance of helicity-/2 photoproduction cross section σ /2 σ 3/2 for all quark flavors q, q/q and therefore all polarization asymmetries A for pion, epect F π 2 ( ) 2 7

8 Large- region suffers from - dearth of precision data 2 - finite-q corrections (higher twists,...) - nuclear corrections (D, 3He data) - systematic treatment 2 of Q and W cuts n A JLab at GeV JLab E99-7 ( 3 He) SLAC E42 ( 3 He) SLAC E43 ( 2 H) SLAC E54 ( 3 He) HERMES ( 3 He) SMC ( 2 H) Q pqcd-based model Valence quark models Bjorken 8

9 Large- region suffers from - dearth of precision data 2 - finite-q corrections (higher twists,...) - nuclear corrections (D, 3He data) - systematic treatment 2 of Q and W cuts PDFs poorly determined for >.5 (!u +!u)/(u + u ) (!d +!d)/(d + d) This work HERMES.5.5 [4] RCQM(!q v /q v )[6] LSS2 [2] Statistical [23] LSS(BBS) [] " /3 -/3 9

10 Jefferson Lab Angular Momentum (JAM) global analysis * * Nobuo Sato, (Pedro Jimenez-Delgado), Alberto Accardi, Jake Ethier, WM Harut Avakian, Brad Sawatzky,...

11 JAM global analysis Motivation - maimally utilize high-precision, high-statistics spin data at lower energies ~ 5 eperiments completed at JLab, with data straddling resonance & DIS regions eplore systematics of lowering kinematic cuts down to Q 2 > GeV 2, W 2 > 3.5 GeV 2 (cf. CTEQ-JLab or ABM unpolarized PDFs analyses) constrain (poorly-determined) PDFs at large 2 control of nuclear and finite-q corrections perform fit to unpolarized PDFs under similar set of conditions (JR4 PDFs; no assumptions about R)

12 JAM global analysis Complete collection of world s inclusive polarized DIS data (interactive database at Fit eperimental asymmetries (longitudinal & transverse) rather than derived structure functions A = σ σ σ + σ = D(A + ηa 2 ) A = σ σ σ + σ = d(a 2 ξa ) A = (g γ 2 g 2 ) F, A 2 = γ (g + g 2 ) F 2

13 JAM global analysis Comparison of global spin PDF efforts ept theory π (LO) 3

14 Comparison of global spin PDF efforts reference = leading twist fit with no new corrections JAM global analysis Δu + Δu Δd Δd q + q + q reference AAC9 DSSV9 BB LSS Q 2 = GeV Δs Δg

15 Nuclear effects Incoherent scattering from nucleons in nucleus A ( ) epand in powers of p 2 /M 2 and binding energy Weak Binding Approimation (WBA) g A i (, Q 2 )= N dy y f N ij (y, γ) g N j (/y, Q 2 ) i, j =, 2 where γ = q /q = +4M 2 2 /Q 2 and N light-cone momentum fraction y = p q P q = p + γp z M Spin-dependent smearing functions f N ij (y, γ) = d 3 p (2π) 3 DN ij (ε, p, γ) δ y ε + γp z M 5

16 Nuclear effects Effective polarization approimation (EPA) f N ii (y, γ) σ z N δ(y ) assumes nuclear corrections independent of and Q 2 3 e.g. for He g 3 He σ z p g p + σ z n g n f N i=j (y, γ) contributions where (neglecting smearing) g 3 He = g 3 He (N) + g 3 He ( ) g 3 He ( ) = Pn +2P p + (g p 4gn ) constrained to fit Bjorken sum rule for A=3 ( g A ( 3 H) ) Bissey et al., PRC 65, 6437 (22) Ethier, WM, PRC 88, 5 (23) 6

17 Nuclear effects.2.8 (a) free n 3 He (EPA) no g d A (,Q 2 ) He (EPA + ) 3 He ( = smear) 3 He (full smear)..2 constraint.9.8 Δq + (smear) / Δq + (ref) (EPA) u Ethier, WM, PRC 88, 5 (23) significant effect (esp. on d-quark) from nuclear smearing cf. EPA neutron asymmetry at 3 in He nucleus obfuscated by smearing 7

18 QCD analysis Basic DIS observables: polarization asymmetries A =(g γ 2 g 2 ) 2 ( + γ 2 )F 2 F L, 2 A 2 = γ(g + g 2 ) ( + γ 2 )F 2 F L 2 Q evolution performed using Mellin moments f (n) (Q 2 )= d n f(, Q 2 ) Structure function (moments) at leading twist g (n),τ=2 = 2 q e 2 q ( C (n) qq g (n) 2,τ=2 = n n g(n),τ=2 q (n) + C (n) g g (n) ) τ (at NLO) 8

19 QCD analysis Parametrization at scale Q 2 = µ 2 (= GeV 2 ) q + () =N a ( b) b ( + A + B) constraints from hadronic weak decays u +() d +() =.269(3), u +() + d +() 2 s +() =.586(3) Antiquark PDFs do not contribute directly to DIS; shape fied by assuming lim q =2lim q + Gluon PDF weakly constrained by DIS; fit only N g & B g 3 LT parameters 9

20 Statistical analysis QCD analysis least-squares estimated with complete treatment of systematic uncertainties (~ correlation matri) error estimated with the Hessian approach vicinity of the minimum (tolerance) characterized by χ 2 = χ 2 χ 2 min T 2 = (other groups use different criteria) 2

21 Higher twist corrections QCD analysis twist-3 part of g g (τ=3) = γ 2 g (τ=3) 2 2 dy y g(τ=3) 2 Bluemlein, Tkabladze NPB 553, 427 (999) spines approimation for twist-4 part g (τ=4) = h() Q 2 twist-3 part of g 2 g (τ=3) 2 = t log +( )+ 2 ( )2 + 4 additional HT parameters - total of 27 parameters inspired by LCWF model 4 t i ( ) i i= Braun et al., PRD 83, 9423 (2) 2

22 QCD analysis Target mass corrections (twist-2) g corrections in moment space g (n) = n M 2 j= Q 2 j (n + j)! j!(n )!(n +2j) 2 g(n+2j) () = g (n) () + M 2 n 2 (n + ) M 4 Q 2 (n + 2) 2 g(n+2) () + O Q 4 Wandzura-Wilczek relation also holds for target mass corrected g 2 Bluemlein, Tkabladze NPB 553, 427 (999) Brown et al., PRC 553, 427 (23) 22

23 JAM distributions Target mass corrections (twist-2).2. Δq + (TMC) / Δq + (no TMC) u (a) relevant for distributions at.5 d 23

24 JAM distributions Higher twist corrections (b) d.2 u.8.6 Δq + (LT+HT) / Δq + (LT) large enhancement of d in presence of HTs significant improvement in χ 2 :.7.98 (3 σ) 24

25 Higher twist corrections JAM distributions A A LT+HT LT p 3 He ( 5) d A Q 2 = 5 GeV 2 A 2 p d 3 He A polarization asymmetries similar for LT & LT+HT fits large enhancement of A 2 asymmetries at large 25

26 JAM distributions τ = 2 g τ = 3 proton neutron τ = 2 g 2.2 τ = τ = Q 2 = GeV important contributions to proton and contributions to neutron τ =3 g, g 2 τ =4 g (determined simultaneously!) 26

27 JAM distributions Δu Δd + ref. + smear + TMC + HT Δu + /u + Δd + /d + Q 2 = GeV significantly larger d at.3 greatest effect on polarized PDFs from HT corrections 27

28 JAM distributions.. (a) Δu + / Δu + (JAM) (b) Δd + / Δd + (JAM).9.8 Q 2 2, W (LT+HT).9 Q 2, W 2 3 (LT+HT) Q 2, W 2 4 (LT+HT) Q 2, W (LT only) PDFs relatively stable w.r.t. cuts in Q and W 2 2 (5% of all data points in Q < 2 GeV region) significant reduction in d with strong W cut (to avoid HT corrections) - cf. NNPDF analysis 28

29 Orbital angular momentum Current data cannot discriminate between different behaviors Impose JAM+ fit pqcd constraint on PDFs by hand.8.6 JAM JAM+ SLAC E43 HERMES A p..6.2 A 3He SLAC E42 HERMES JLab E

30 Orbital angular momentum Earlier analysis suggested need for additional nonzero OAM (L = ) component in nucleon wave function z L z = L z = 3 leading (-) behavior from L z = component L = gives additional log 2 z (-) enhancement of q q ( ) 5 log 2 ( ) Avakian, Brodsky, Deur, Yuan PRL 99, 82 (27) 3

31 Orbital angular momentum Earlier analysis suggested need for additional nonzero OAM (L = ) component in nucleon wave function z q/q u SLAC HERMES Hall-A CLAS d LSS98 with log 2(-) term 3

32 Orbital angular momentum Earlier analysis suggested need for additional nonzero OAM (L = ) component in nucleon wave function z q/q u SLAC HERMES Hall-A CLAS d LSS98 with log 2(-) term LO etraction L z= term needed to delay d turnover until larger Avakian, Brodsky, Deur, Yuan PRL 99, 82 (27) 32

33 Orbital angular momentum Global JAM & JAM+ fits can accommodate data without need for additional L = terms z Δu + JAM SIMP OAM JAM+ OAM Δu + /u +. Q 2 = GeV Δd Δd + /d OAM and OAM+ fits use Jimenez-Delgado et al., arxiv: (24) f = N α ( ) β + N α ( ) 5 log 2 ( ) can also accommodate data, with similar overall χ 2 33

34 Orbital angular momentum Global JAM & JAM+ fits can accommodate data without need for additional L = terms z OAM and OAM+ fits use f = N α ( ) β + N α ( ) 5 log 2 ( ) can also accommodate data, with similar overall χ 2 34

35 Future plans A number of JLab 6 GeV eperiments still being analyzed EGb (CLAS); SANE (Hall C) recently completed (not yet included in fits) - d2n (Hall A); EG-DVCS (CLAS) Several upcoming JLab 2 GeV eperiments will measure A (p, d, 3 He) up to ~.8 A n Hall C 35

36 Future plans.25.5 relative error JAM +2 GeV Δu Δd + Q 2 = GeV will significantly reduce PDF uncertainties at large (~ 7% for ~.6-.8) 36

37 Future possibilities electroweak structure functions neutral current e.g. unpolarized lepton + longitudinally polarized hadron gives (spin-dependent) parity-violating asymmetry A PV = σpv (S L ) σ PV ( S L ) σ PV (S L )+σ PV ( S L ) = G F Q 2 4 ga e f(y) gγz 2πα F γz + g e V g γz 5 F γz g γz = q e q g q V ( q + q) g γz 5 = q e q g q A ( q q) analog of F 3 unique window on spin-flavor decomposition 37

38 electroweak structure functions charged current Future possibilities. g W = u + ū + c + s (σ(p R ) - σ(p L )) / (σ(p R ) + σ(p L )).5. W - W + g W 5 = u + ū c + s flavor decomposition of polarized nucleon sea s s, c c, Accardi et al., arxiv:

39 tagged structure functions -.2 Longitudinal spin asymmetry in conditional DIS e + D e + p + X Q 2 = 3-2 GeV 2 Free neutron Future possibilities 2-3 GeV GeV 2 Spin asymmetry A Kinem. limit = R = s en = GeV 2 Integrated luminosity 2 7 nb M N 2 t from recoil momentum [GeV 2 ] Pawel Nadel-Turonski 39

40 Tensor polarized D structure function gives unique opportunity to study non-nucleonic effects in nuclei no free-nucleon analog in parton model b = 2 e 2 q (δ T q + δ T q) q d b = 8 Future possibilities δ T q = q () q(+) d 8δ T ū +2δ T d + δt s for tensor-unpolarized sea (cf. Gottfried sum rule) + q ( ) 2 Close, Kumano PRD 42, 2377 (99) in convolution model, b vanishes for nucleons in S-state; small nonzero D-state contribution 4

41 Future possibilities b d.5..5 HERMES PRL 95, 242 (25) HERMES data suggest polarization of tensor sea! b d d b =(.35 ±. ±.8) 2 Q 2 /GeV theoretical situation unclear: (anti)shadowing, pion echange, 6q configs, final-state interactions,...? JLab2 eperiment E2-3- will cover.5 < <.5 - EIC would settle question of CK sum rule 4

42 Outlook Nucleon (spin) structure cleanly revealed through large- PDFs focus of new JAM global QCD analysis requires control of theoretical corrections at large (nuclear, higher twists) Future JAM analysis will study polarization of sea quarks and gluons semi-inclusive DIS for flavor separation (in progress) polarized pp cross sections (inclusive jet & pion production) for g (M. Stratmann s jet code) maimally utilize JLab 6 GeV, 2 GeV, RHIC-spin, EIC,... data over all available kinematics 42