New JAM global analysis of spin-dependent PDFs

Transcription

1 QCD Evolution Jefferson Lab, May 26, 2015 New JAM global analysis of spin-dependent PDFs Wally Melnitchouk Jefferson Lab Angular Momentum (JAM) Collaboration Nobuo Sato, Jacob Ethier, Alberto Accardi (Pedro Jimenez-Delgado) 1

2 JAM global analysis Motivation - maimally utilize high-precision, high-statistics spin data at lower (& higher) energies ~ 15 eperiments completed at JLab, with data straddling resonance & DIS regions eplore systematics of lowering kinematic cuts down to Q 2 > 1 GeV 2, W 2 > 3.5 GeV 2 (cf. CJ, JR, ABM unpolarized PDFs analyses) 2 control of nuclear and finite-q corrections perform fit to unpolarized PDFs under similar set of conditions (no assumptions about R) constrain (poorly-determined) PDFs at large etract higher twist (twist-3) distributions 2

3 JAM global analysis Complete collection of world s inclusive polarized DIS data (interactive database at EMC(npts = 10) 10 2 SMC(npts = 28) 10 2 SLAC(npts = 853) Q Q Q HERMES(npts = 103) 10 2 (2015) 10 2 JLab(npts = 1798) Q Q COMPASS (npts = 81) Q soon to be etended to SIDIS & polarized pp data 3

4 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 1 + ηa 2 ) A = σ σ σ + σ = d(a 2 ξa 1 ) where A 1 =(g 1 γ 2 2 g 2 ) (1 + γ 2 )F 2 F L 2 A 2 = γ(g 1 + g 2 ) (1 + γ 2 )F 2 F L remove assumptions about R = σ L /σ T ratio 4

5 JAM global analysis Complete collection of world s inclusive polarized DIS data (interactive database at Significant contribution of JLab data to global database # pts RUN0 no JLab 800 proton 700 deuteron600 helium # pts RUN1 with JLab

6 JAM global analysis Complete collection of world s inclusive polarized DIS data (interactive database at Significant contribution of JLab data to global database # pts no RUN0 JLab 250 with RUN1 JLab 200 # pts no RUN0 JLab with RUN1 JLab Q especially at high (0.1 < < 0.6) and low Q (1 < Q < 3 GeV ) 6

7 Issues at large - dearth of precision data 2 - at fied Q, large means low W 2 - finite-q corrections (higher twists,...) - nuclear corrections 3 (D, He data) PDFs poorly determined for > 0.5 Large- PDFs (!u +!u)/(u + u ) (!d +!d)/(d + d) 1 This work HERMES [41] RCQM(!q v /q v )[6] LSS2001 [21] Statistical [23] LSS(BBS) [11] " Zhang et al., JLab E /3 1-1/3 7

8 SU(6) spin-flavor symmetry Large- PDFs d/u 1/2 u/u 2/3 A p 1 5/9 d/d 1/3 A n 1 0 Symmetry broken by e.g. color-spin interaction scalar diquark dominance (M >M N ); d/u 0 u/u 1 d/d 1/3 Perturbative one-gluon echange dominance of helicity-1/2 configurations A p 1 1 A n 1 1 d/u 1/5 q/q 1 A 1 1 8

9 JAM QCD analysis Parametrization at scale Q 2 = µ 2 0 (= 1 GeV 2 ) q + () =N α (1 b) β (1 + γ) q + q + q constraints from hadronic weak decays u +(1) d +(1) =1.269(3), u +(1) + d +(1) 2 s +(1) =0.586(31) 2 Q evolution performed in moment space f (n) (Q 2 )= 1 0 d n 1 f(, Q 2 ) Structure function (moments) at leading twist g (n) 1,τ2 = 1 2 q e 2 q ( C (n) qq g (n) 2,τ2 = n 1 n g(n) 1,τ2 q (n) + C (n) g g (n) ) Wandzura-Wilczek relation τ (at NLO) 9

10 Inclusive DIS data constrain JAM QCD analysis u + & d + distributions mostly insensitive to polarized strangeness and glue for inclusive-only analysis, fi shape of s +, g using results from DSSV; normalization free total of 10 shape parameters for leading twist PDFs Assume can be described as sum of and higher twist terms g 1,g 2 τ =2 g 1 = g τ2(tmc) 1 + g τ3(tmc) 1 + g1 τ4 g 2 = g τ2(tmc) 2 + g τ3(tmc) 2 10

11 Target mass corrections (twist-2) use standard OPE derivation, e.g. in closed form g1 TMC () = 1)( + ξ) ξρ 3 g(0) 1 (ξ)+(ρ2 ξρ 4 1 ξ dξ ξ g(0) 1 (ξ ) (ρ2 1)(3 ρ 2 ) 2ρ 5 1 ξ dξ ξ 1 ξ dξ g(0) ξ 1 (ξ ) ξ =2/(1 + ρ) ρ 2 =1+4M 2 2 /Q 2 lim M/Q 0 gtmc 1 or series epansion g TMC 1 () = j=0 1 j! M 2 Q 2 j ( ) j+1 j+1 ( ) j+1 (2j G()) G() = 1 dy y 1 y dy y g(0) 1 (y ) 11

12 Target mass corrections (twist-2) g1() 0.06 p no TMC n no TMC p GP full n GP full pj=1 nj=1 pj=2 nj=2 pj=3 nj=3 Q2 = 1.0GeV

13 Target mass corrections (twist-2) g1() 0.06 p no TMC n no TMC p GP full n GP full pj=1 nj=1 pj=2 nj=2 pj=3 nj=3 Q2 = 2.0GeV

14 Target mass corrections (twist-2) g1() 0.06 p no TMC n no TMC p GP full n GP full pj=1 nj=1 pj=2 nj=2 pj=3 nj=3 Q2 = 3.0GeV

15 Target mass corrections (twist-2) g1() 0.06 p no TMC n no TMC p GP full n GP full pj=1 nj=1 pj=2 nj=2 pj=3 nj=3 Q2 = 4.0GeV

16 Target mass corrections (twist-2) g1() 0.06 p no TMC n no TMC p GP full n GP full pj=1 nj=1 pj=2 nj=2 pj=3 nj=3 Q2 = 5.0GeV

17 Target mass corrections (twist-2) g1() 0.06 p no TMC n no TMC p GP full n GP full pj=1 nj=1 pj=2 nj=2 pj=3 nj=3 Q2 = 6.0GeV

18 Target mass corrections (twist-2) g1() 0.06 p no TMC n no TMC p GP full n GP full pj=1 nj=1 pj=2 nj=2 pj=3 nj=3 Q2 = 7.0GeV

19 Target mass corrections (twist-2) g1() 0.06 p no TMC n no TMC p GP full n GP full pj=1 nj=1 pj=2 nj=2 pj=3 nj=3 Q2 = 8.0GeV

20 Target mass corrections (twist-2) g1() 0.06 p no TMC n no TMC p GP full n GP full pj=1 nj=1 pj=2 nj=2 pj=3 nj=3 Q2 = 9.0GeV

21 Target mass corrections (twist-2) g1() 0.06 p no TMC n no TMC p GP full n GP full pj=1 nj=1 pj=2 nj=2 pj=3 nj=3 Q2 = 10.0GeV

22 Target mass corrections (twist-2) Δq + (TMC) / Δq + (no TMC) u (a) JAM d Jimenez-Delgado et al., PRD 89, (2014) differences between TMC and no-tmc results immaterial whether use full or series approimation 22

23 Higher twist corrections twist-3 part of g 1 g τ3 1 =(ρ 2 1) related to twist-3 part of g τ dy y gτ3 2 g 2 Bluemlein, Tkabladze NPB 553, 427 (1999) JAM13 twist-3 part of g 2 inspired by LCWF model g τ3 2 = t 0 log +(1 )+ 1 2 (1 )2 + 2 NOT Q SUPPRESSED! 4 t i (1 ) i 1 i=1 Braun et al., PRD 83, (2011) splines approimation for twist-4 part JAM13 g τ4 1 = h() Q 2 23

24 Higher twist corrections twist-3 part of g 1 g τ3 1 =(ρ 2 1) related to twist-3 part of g τ dy y gτ3 2 g 2 Bluemlein, Tkabladze NPB 553, 427 (1999) twist-3 part of g 2 parametrized via twist-3 PDFs JAM15 D τ3 () =N a (1 ) b (1 + c) - at parton level similar functional form also for twist-4 part JAM15 g τ4 1 = N a (1 ) b (1 + γ ) 1 Q 2 - at hadron level 24

25 Higher twist corrections (b) JAM13 d 1.2 u Δq + (LT+HT) / Δq + (LT) Jimenez-Delgado et al., PRD 89, (2014) large enhancement of found in JAM13 analysis d in presence of HTs 25

26 Nuclear corrections nuclear binding and Fermi motion described by (spin-dependent) smearing functions g A i () = dy y f N ij (y) g N j (/y) f 11 n (y, ) f n 11(y) (a) ρ = 1 ρ = 1.5 ρ = y f p 11 (y, ) (y) (a) ρ = 1 ρ = 1.5 ρ = y effective polarization approimation (EPA) f N (y) σ z N δ(y 1) 26

27 Nuclear corrections (a) free n 3 He (EPA) no g JAM13 d A 1 (,Q 2 ) He (EPA + ) 3 He ( =1 smear) 3 He (full smear) constraint Δq + (smear) / Δq + (ref) (EPA) u Ethier, WM, PRC 88, 5 (2013) significant effect (esp. on d-quark) from nuclear smearing cf. effective polarization approimation (EPA) neutron asymmetry at 3 in He nucleus 1 obfuscated by smearing 27

28 JAM13 distributions Δu Δd + ref. + smear + TMC + HT Δu + /u + Δd + /d JAM13 Q 2 = 1 GeV 2 Jimenez-Delgado et al., PRD 89, (2014) significantly larger d at 0.3 greatest effect on polarized PDFs from HT corrections 28

29 New JAM15 analysis Including all data, total χ 2 = 3420 for 2887 points, or χ 2 dof =1.18 SLAC E155 Atpep JLabHallA E Apa3He SLAC E143 Apep JLabHallA E Ape3He HERMES data1 A2p SLAC E155 Aped SMC data1 A1d SLAC E155 Apap JLabHallA E Ape3He JLabHallB eg1 dvcs 1 Apad JLabHallB eg1b ApaDp SMC data2 A1p JLabHallB eg1 dvcs 2 Apap SLAC E155 Apep SLAC E155 Apad SLAC E143 Apad JLabHallB eg1 dvcs 1 Apap JLabHallB eg1b ApaDd SLAC E154 Ape3He SLAC E143 Aped COMPASS data 1 A1d SLAC E155 Atped HERMES data1 Apad SLAC E143 Apap JLabHallA E Apa3He SLAC E142 A13He COMPASS data 1 A1p COMPASS data 2 A1p SLAC E154 Apa3He SLAC E142 A23He JLabHallA E Ape3He SLAC E80130 Apap SMC data2 A1d SMC data1 A1p EMC A1p HERMES data1 A1n HERMES data1 Apap JLabHallA E Apa3He Npts(T > D) Npts(T < D) χ 2 DOF 29

30 New JAM15 analysis Error analysis uses Hessian method to propagate parameter uncertainties χ 2 for parameters p χ 2 (p) = i (data i thy i (p)) 2 σ 2 uncor,i + σ2 cor,i Hessian matri H ij = 1 2 χ 2 (p) p i p j p=best deviations of parameters from their best values parametrized by scale factors {t i } in eigenbasis of covariance matri C = H 1 {ê i } p = i t i ê i 30

31 probability distribution assumed to factorize in {ê i } P( p) i New JAM15 analysis P i (t i ) i ep 1 2 χ2 (t i ) P(t0) t + t t 0 P(t12) t 12 normal dist 68% 95% not all distributions are Gaussian! errors on observable O defined in terms of edges of confidence regions t ± i δo 2 + i ma 2 O(t + i ) O(0), O(t i ) O(0), 0 δo 2 i ma O (0) O(t + i ), O(0) O(t i ),

32 New JAM15 analysis Correlations between fit parameters τ 3,4 τ 2 RUN0 T4n h4 T4n h3 T4n h2 T4n h1 T3n t3 T3n t2 T3n t1 T3n t0 T4p h4 T4p h3 T4p h2 T4p h1 T3p t3 T3p t2 T3p t1 T3p t0 gn sp N dp d dp b dp a dp N up d up b up a up N up N up a up b up d dp N dp a dp b dp d sp N gn T3p t0 T3p t1 T3p t2 T3p t3 T4p h1 T4p h2 T4p h3 T4p h4 T3n t0 T3n t1 T3n t2 T3n t3 T4n h1 T4n h2 T4n h3 T4n h4 no JLab data twist 2 twist 3 & 4 32

33 New JAM15 analysis Correlations between fit parameters τ 3,4 τ 2 RUN0 T4n h4 T4n h3 T4n h2 T4n h1 T3n t3 T3n t2 T3n t1 T3n t0 T4p h4 T4p h3 T4p h2 T4p h1 T3p t3 T3p t2 T3p t1 T3p t0 gn sp N dp d dp b dp a dp N up d up b up a up N up N up a up b up d dp N dp a dp b dp d sp N gn T3p t0 T3p t1 T3p t2 T3p t3 T4p h1 T4p h2 T4p h3 T4p h4 T3n t0 T3n t1 T3n t2 T3n t3 T4n h1 T4n h2 T4n h3 T4n h4 no JLab data twist 2 twist 3 & 4 33

34 New JAM15 analysis Correlations between fit parameters T4n h4 1.0 T4n h4 1.0 τ 3,4 τ 2 RUN0 T4n h3 T4n h2 T4n h1 T3n t3 T3n t2 T3n t1 T3n t0 T4p h4 T4p h3 T4p h2 T4p h1 T3p t3 T3p t2 T3p t1 T3p t0 gn sp N dp d dp b dp a dp N up d up b up a up N no JLab data RUN1 T4n h3 0.8 T4n h2 T4n h1 T3n t3 0.6 T3n t2 T3n t1 T3n t0 0.4 T4p h4 T4p h3 0.2 T4p h2 T4p h1 T3p t3 0.0 T3p t2 T3p t1 0.2 T3p t0 gn sp N 0.4 dp d dp b dp a 0.6 dp N up d 0.8 up b up a up N up N up a up b up d dp N dp a dp b dp d sp N gn T3p t0 T3p t1 T3p t2 T3p t3 T4p h1 T4p h2 T4p h3 T4p h4 T3n t0 T3n t1 T3n t2 T3n t3 T4n h1 T4n h2 T4n h3 T4n h4 with JLab data up N up a up b up d dp N dp a dp b dp d sp N gn T3p t0 T3p t1 T3p t2 T3p t3 T4p h1 T4p h2 T4p h3 T4p h4 T3n t0 T3n t1 T3n t2 T3n t3 T4n h1 T4n h2 T4n h3 T4n h4 twist 2 twist 3 & 4 less correlation between LT and HT parameters with inclusion of JLab data 34

35 New JAM15 analysis u + & d + distributions Q 2 =1.0GeV 2 JAM15 q=u + DSSV q=d + DSSV q=u + q=d Q 2 =1.0GeV 2 q=u + q=d q 0.1 q no JLab with JLab JAM15 PDFs consistent with DSSV, within errors reduced uncertainties with inclusion of JLab data 35

36 New JAM15 analysis u + & d + distributions ratio to central u + Q 2 =1.0GeV 2 no JLab ratio to central u + Q 2 =1.0GeV 2 with JLab ratio to central d + Q 2 =1.0GeV 2 ratio to central d + Q 2 =1.0GeV 2 JAM error reduction most dramatic for d + at large 36

37 New JAM15 analysis Total LT + TMC T3 T g1 g proton neutron Q 2 =1.0GeV no JLab 37

38 New JAM15 analysis Total LT + TMC T3 T g1 g proton neutron Q 2 =1.0GeV with JLab error reduction also on HT contributions no reliable constraint on neutron HT (set to zero) 38

39 Outlook Ongoing JAM15 analysis studying impact of JLab 6 GeV inclusive DIS data at low W, high Future analysis to study polarization of sea quarks & gluons semi-inclusive DIS for flavor separation polarized pp cross sections (inclusive jet & π for g maimally utilize data over all available kinematics (JLab 6 GeV, 12 GeV, RHIC-spin, EIC...) production) Longer term goal - etend analysis to transverse spin (transversity) and momentum (TMDs) 39