or! What We ve Learned from Polarized Electron Scattering, Karl J. Slifer University of New Hampshire
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1 or! What We ve Learned from Polarized Electron Scattering, Karl J. Slifer University of New Hampshire
2 or! What We ve Learned from Polarized Electron Scattering, I ve! (in the last few months)! Karl J. Slifer University of New Hampshire
3 This Talk Burkhardt Cottingham Sum Rule! What does the JLab data tell us?! Is it enough to make a definitive statement?! Higher Twist Measurements at Jlab! Target Mass Corrections! impact on the clean extraction of Higher Twist! +New Spin Structure Data Highlights! time permitting!
4 Inclusive Electron Scattering *! W When we add spin degrees! of freedom to the target! and beam, 2 Addiitonal SF! needed.! Inclusive Polarized! Cross Section! all four SF needed for a complete description of nucleon structure
5 Parton Model Interpretation of the! Structure Functions! Impulse Approximation in DIS! no time for interaction between partons! electron! xp! Nucleon! distributions of quark momentum and spin in the nucleon.! runs over all quark flavors!???!
6 Burkhardt-Cottingham Sum Rule H.Burkhardt and W.N. Cottingham! Annals Phys. 56 (1970) 453.! Relies on the virtual Compton scattering amplitude S 2 falling to zero! faster than 1/º as º 1! Discussion of possible causes of violations! R.L. Jaffe Comm. Nucl. Part. Phys. 19, 239 (1990)! If it holds for one Q 2 it holds for all!
7 BC Sum Rule P! Measured x Existing World Data on Γ 2! for Proton Neutron and 3 He! N! BLACK : E (Hall A, 3 He)! BROWN : E155. (SLAC NH3, 6 LiD)! 3 He! Note:! SLAC Measured = 0.02 < x < 0.8! JLAB Measured Resonance Region!
8 BC Sum Rule Measured x BRAND NEW DATA! P! Very Preliminary! RED : RSS. (Hall C, NH 3,ND 3 )! K. Slifer, O. Rondon et al. in preparation! BLUE: E (Hall A, 3 He)! N! courtesy of P. Solvignon! very prelim! GREEN: E (Hall A, 3 He)! courtesy of V. Sulkosky! 3 He! Thanks also to the spokesmen of these experiments!! RSS: Mark Jones, Oscar Rondon! E01-012: N. Liyanage, J.P.Chen, Seonho Choi! SaGDH: J.P. Chen, A. Deur, F. Garabaldi!
9 BC Sum Rule Measured x P! Good agreement with MAID model! of resonance region for JLab data! N! very prelim! 3 He!
10 BC Sum Rule P! Measured x Neutron results around Q 2 =1.3 GeV 2! from 2 very different experiments:! RSS in Hall C: Neutron from ND 3 & NH 3! E in Hall A : Neutron from 3 He! N! very prelim! Excellent agreement! 3 He!
11 BC Sum Rule Measured x P! N! Good overlap at low Q 2 of the! old and new neutron data! very prelim! E94010 : Hall A 3 He old! E Hall A 3 He new! 3 He!
12 BC Sum Rule P! Measured x Difference between N and 3 He Sum rules! 3 He! N! N! very prelim! Elas! QE! 3 He P n Neutron +2P p Proton! Δ 3 He! π threshold! Note: 3 He requires use of nuclear elastic!
13 BC Sum Rule BC = RES+DIS+ELASTIC! RES : Here refers to measured x-range! DIS : refers to unmeasured low x part! of the integral. Not strictly Deep! Inelastic Scattering due to low Q 2! Assume Leading Twist Behaviour! Elastic: From well know FFs (<5%)!
14 BC Sum Rule 0<X<1 :Total Integral! P! BC = RES+DIS+ELASTIC! N! 3 He! very prelim! RES : Here refers to measured x-range! DIS : refers to unmeasured low x part! of the integral. Not strictly Deep! Inelastic Scattering due to low Q 2! Assume Leading Twist Behaviour! Elastic: From well know FFs (<5%)!
15 BC Sum Rule 0<x<1 P! BC satisfied w/in errors for JLab Proton! 2.8σ violation seen in SLAC data! N! very prelim! BC satisfied w/in errors for Neutron! (But just barely in vicinity of Q 2 =1!)! 3 He! BC satisfied w/in errors for 3 He!
16 BC Sum Rule P! Wasteland! Proton g2p still relatively unknown! for such a fundamental quantity.! Need more high quality data like RSS! N! Upcoming Experiments! Sane: setting up now! 2.3 < Q 2 < 6 GeV2! 3 He! g2p in Hall A, 2011! < Q 2 < 0.4 GeV 2!
17 BC Sum Rule P! Measured x 0<x<1 What can BC tell us about Low-X?! Alternatively, if we assume BC holds! we can learn something about the! unmeasured part of Integral! N! very prelim! BC = 0 => Res + Elas + DIS! Unmeasured Low-x part! 3 He! DIS = -(RES+ELAS)!
18 BC Sum Rule P! Measured x 0<x<1 What can BC tell us about Low-X?! N! very prelim! Unmeasured Low-X! DIS = -(RES+ELAS)! 3 He!
19 BC Sum Rule Measured x 0<x<1 Neutron BC Sum! Standard Deviations from Zero! Q 2! Tot σ! Stat σ! very prelim! Just on the edge of being interesting! Statistical precision allows! unambiguous test, but limited! by large systematics.! Highly desirable to revisit E94010! systematics. RC and DIS could! perhaps be improved with newer! data.!
20 Higher Moment Cornwall Norton Moment! 1 ε 0 I(Q 2 ) = 2 x 2 (2g + 3g )dx 1 2 I(Q 2 ) the twist-3 matrix element but very interesting all the same.! More on this later...!
21 I(Q 2 ) PROTON! Existing World Data on Ι(Q 2 )! BLACK : E94010! M. Amarian, et al. PRL. 92 (2004) BROWN : E155! P.Anthony, et al. PLB. 553 (2003) 18 RED : RSS.! Wesselman, Slifer, Tajima et al. PRL 98(2007) Magenta: E99-117! NEUTRON! X. Zheng et al. PRC 70(2004) What s happening! at large Q 2?!
22 I(Q 2 ) BRAND NEW DATA! MAID Model! Very Preliminary! RED : RSS. (Hall C, NH 3,ND 3 )! K. Slifer, O. Rondon et al. in preparation BLUE: E (Hall A, 3 He)! NEUTRON! very prelim! courtesy of P. Solvignon! GREEN: E (Hall A, 3 He)! courtesy of V. Sulkosky! stat only! Thanks also to the spokesmen of these experiments!! RSS: Mark Jones, Oscar Rondon! E01-012: N. Liyanage, J.P.Chen, Seonho Choi! SaGDH: J.P. Chen, A. Deur, F. Garabaldi!
23 I(Q 2 ) QCDF Group! I(Q 2 )->0 for Q 2 =0 and Q 2 =infinity! largest around Q 2 =1! Not too useful to the OPE in this! region, but excellent gauge of! QCD complexity! very prelim! (i.e. where s the most difficult! place to make any meaningful! QCD calculation?)! stat only!
24 I(Q 2 ) QCDF Group! Osipenko et al. PRD. 71 (2005) Shaded Region: Estimate of I(Q 2 )! very prelim! Large uncertainty due to lack of! knowledge of g2p! stat only!
25 I(Q 2 ) E g2p! projected! SANE! Upcoming 6 GeV Experiments! Sane: Fall 2008! 2.3 < Q 2 < 6 GeV2! g2p in Hall A, 2011! < Q 2 < 0.4 GeV 2! d2n in Hall A, 2009! Q 2 = 3 GeV 2!
26 Operator Product Expansion Expansion of SF moments in powers of 1/Q 2 ( twist )! example:! 1 Γ 1 (Q 2 ) = g 1 (x,q 2 )dx = 0 µ 2 (Q 2 ) Q τ 2 τ = 2,4,... ( f 2 ) µ 4 = 1 9 M 2 a d leading twist! twist-3! twist-4! Lowest order (twist-2) maps to the succesful parts of the parton model.! Higher twists arise from non-perturbative multiparton interactions!
27 Cornwall-Norton Moments 1 ε 0 I(Q 2 ) = 2 x 2 (2g + 3g )dx 1 2 = d 2 (Q 2 ) + ϑ M 2 Q 2 Typical method of extracting! twist-3 matrix element! But completely ignores TMC! Very significant below Q 2 5! Y.B. Dong PRC 77(2008) ! Y.B.Dong PLB 653,(2007)18!
28 Nachtmann Moments:! Nachtmann Moments 1 M 3 2 (Q 2 ) = dx ξ 4 x x 2 0 ξ g x 2 ξ d = M 2 Q x 2 2 g 2 Matsuda & Uematsu, N.Phys. B53(1998)301! Piccione & Ridolfi N. Phys. B513(1998)301! Generalization of CN moments to protect from the TMC! M 2 Q 0 M x 2 (2g 1 + 3g 2 )dx Reduces to familiar form! Not a new idea, but difficult to implement unless g 2 measured simultaneously with g 1!
29 Quantifying Size of TMC R(Q 2 ) = 2M 3 2 (Q 2 ) I(Q 2 ) R->1 in case of vanishing nucleon mass! R always less than 1 => I(Q 2 ) overestimates twist-3! Target Mass Corrections must be applied in order to obtain clean dynamical Twist-3!
30 Generalization of Γ 1 M 1 1 (Q 2 ) = 1 0 dx x ξ 2 x ξ 1 9 M Q 2 xξ g 1 M Q 2 4 x 2 3 g 2 Matsuda & Uematsu, N.Phys. B53(1998)301! M 2 Q 0 M 1 Piccione & Ridolfi N. Phys. B513(1998)301! 2 1 Γ 1 Osipenko et al. PRD 71, (2005)! Global analysis of g1p data. Allows to! cleanly extract leading twist term.! Proton! TMC not as large as for I(Q 2 )!
31 Summary Burkhardt Cottingham Sum Rule! Good coverage for Neutron. Proton g2p is still relatively unknown.! Data seems to validate BC, but at the 2.5σ level around Q 2 =1! Important to update the systematics of the old experiments! Assuming BC holds, we can use JLab data to say something about low-x.! Target Mass Effects! TMC are significant at JLab kinematics! Nachtmann moments protect the SSF from TMC! Must use Nachtmann Moments in order to cleanly extract Higher twists! JLab 6 GeV Program! Still lots of Good Physics to be completed before the upgrade.!
32
33 References BLACK : E (Hall A, 3 He)! M. Amarian, et al. PRL. 92 (2004) K. Slifer, et al. PRL. 101:022303,2008 RED : RSS. (Hall C, NH 3,ND 3 )! Wesselman, Slifer, Tajima et al. PRL 98(2007) Slifer, Rondon et al. in preparation BROWN : E155. (SLAC NH3, 6 LiD)! P.Anthony, et al. PLB. 553 (2003) 18 Magenta E99-117(Hall A, 3 He)! X. Zheng et al. PRC 70(2004) BLUE: E (Hall A, 3 He)! P. Solvignon et al. arxiv: (PRL accepted) P. Solvignon et al. in preparation SHADED : Theory! Osipenko et al. PRD. 71 (2005)
34 BC Sum Rule Unmeasured Contributions! ELASTIC: X=1! Low-X Estimate! Assume g 2 =g 2 WW at low x.! Supported by RSS data! 15% variation seen depending on! choice of g 1 used.! g 1 el (x,q 2 ) = δ(x 1)G M (Q 2 ) G E (Q 2 ) + τg M (Q 2 ) 2(1+ τ) g 2 el (x,q 2 ) = δ(x 1)τG M (Q 2 ) G E (Q 2 ) G M (Q 2 ) 2(1+ τ) (Form Factor uncertainties less than 5%)!
35 Summary Hydrogen Hyperfine Structure! Extended GDH SUM! Resonance Structure! Measure of! QCD complexity! Spin Polarizability! Systematic uncertainty! In Measurements of! Ideal place to test ÂPT calcs!
36 JLab Kinematic Coverage Overview of available kinematic! range at JLab! Uniquely positioned to provide! data in transition region of QCD!
37 Target Mass Corrections Purely kinematic effects from finite value of 4M 2 x 2 /Q 2 g 1 (x,q 2 ) = g 1 (x,q 2,M = 0) + M Q g (1)TMC 2 1 (x,q 2 ) + h(x,q2 ) Q 2 + ϑ (1/Q 4 ) From PQCD Purely kinematical Higher twist 1 0 x 2 g 1 (x,q 2 )dx = 1 a 2 + ϑ M 2 2 Q x 2 g 2 (x,q 2 )dx = 1 3 d 2 ( a 2 ) + ϑ M 2 Q 2
38 I(Q 2 ) Chiral Soliton WGR! Chiral Soliton Wakamatsu! PQCD Evolution! QCDSF Group! Q 2 evolution predicted well by PQCD! and Chiral Soliton models.! very prelim! WGR: PRD55 (1997) 6910! Wakamatsu: PLB 487(2000)118! PQCD: Nucl. Phys. B201 (1982) 141! QCDSF: PRD63, (2001)! stat only!
39 g 2 Structure Function Wandzura-Wilczek relation! PLB 72 (1977) 195! Leading twist determined entirely by g 1! g 2 doesn t exist in Parton Model.! Good quantity to study higher twist! Higher twist!
40 Inclusive Electron Scattering *! W Inclusive Cross Section! deviation from point-like behavior! characterized by the Structure Functions!
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