Spin dependent en cross section at small and medium Q2
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1 Sasso, 004/03/18 Session 3, Talk ID 3.5 Spin dependent en cross section at small and medium Q Contents: Introduction Kinematic DIS Regime (Q>1GeV, W>4GeV) Small Q Limit (Q=0 GeV) GDH sum rule Medium Q Quark-Hadron Duality, Generalized GDH sum rule, Small Q Summary Page 1
2 Sasso, 004/03/18 Session 3, Talk ID 3.5 Electron Scattering: en e', k' e, k Q=-q=-(k-k') = E E ' q=, q N, P=(M, 0) Invariant mass for the nucleon system W = P q = M M Q Page
3 Sasso, 004/03/18 Session 3, Talk ID 3.5 Double Polarized en Scattering From longitudinally polarized electron: Q 0 electron scattering virtual photon absorption Q =0 N 1/ N 3/ real photon absorption Polarized beam & polarized target: 1/ 3/ 1/ 3/ 1/ 3/ Page 3
4 Sasso, 004/03/18 Session 3, Talk ID 3.5 Introduction Neutrino beam, and νn scattering: Information at the small and medium Q became important. Fully polarized beam Spin dependent en scattering: Double polarized scattering experiments in the wide Q range Perturbative QCD based QPM works fine at the large Q. Q=0 measurements up to a few GeV photon as the small Q limit Measurements at the small and medium Q also have been performed. Page 4
5 Sasso, 004/03/18 Session 3, Talk ID 3.5 Kinematics Q = k k ' W =M x=1.0 g ir n e t t ca V o gi n e R e c n e S G na c 4 o ti < s s a l DIS W Re E < M Q x= M 0 x 1 W-M 1 GeV 0 GeV = E E ' Page 5
6 Sasso, 004/03/18 Session 3, Talk ID 3.5 Structure of this talk Deep Inelastic Scattering: Small Q limit x=1.0 Spin dependent Structure Function Q GDH sum rule experiment Medium Q Region: Quark Hadron Duality Generalized GDH 1GeV 0 s e R e c n a on DIS Small Q: Page 6
7 Sasso, 004/03/18 Session 3, Talk ID 3.5 Deep Inelastic Scattering Structure Function e N e' X F i x,q, g i x,q Q q P x=, y= = p P E M Parton Distribution x: momentum fraction of parton y: energy fraction of γ* q x, Q, q x, Q P= M, 0 d dx dq L W F 1 x = q e q q x W>4GeV Q>1GeV Page 7
8 Sasso, 004/03/18 Session 3, Talk ID 3.5 Structure Functions of Nucleon Phys. Rev. D 66, (00) Naïve Quark Parton Model: F 1 x = q e q q x q x g 1 x = q e q q x q x q±(x): x: number density of quark with helicity ± inside nucleon momentum fraction x carried by quark 1 R x, Q F x, Q = x F 1 x, Q 1 Q dependence: DGLAP QCD evolution equation Page 8
9 Sasso, 004/03/18 Session 3, Talk ID 3.5 Double Spin Asymmetry: A1 HERMES: Phys.Lett.B44(1998)484 E155: Phys.Lett.B493(000)19 E143: Phys.Rev.D58(1998)11003 EMC: Nucl.Phys.B38(1989)1 SMC: Phys.Rev.D58(1998)11001 Double Spin Asymmetry of virtual photon absorption cross section 1/ 3/ g 1 A 1= ~ 1/ 3/ F 1 Very weak Q dependence of A1: has been observed in the DIS regime. 1 < Q < 100 GeV Page 9
10 Sasso, 004/03/18 Session 3, Talk ID 3.5 Small Q limit: real photon absorption Q x=1.0 s e R 0 GeV e c n a on io g Re n 0 x 1 DIS Page 10
11 Sasso, 004/03/18 Session 3, Talk ID 3.5 Real photon absorption cross section from PDG W = P q Page 11
12 Sasso, 004/03/18 Session 3, Talk ID 3.5 Spin Dependent Cross Section: GDH sum rule Gerasimov-Drell-Hearn -Hosoda-Yamamoto (GDH) sum rule: I N = 0 d [ 3/ 1/ ] = N M κn: anomalous magnetic moment Ip = 04 μb, In = -33 μb Experiments: Mainz-MAMI Bonn-ELSA Measured Processes: Eγ= 0. to 0.8 GeV Eγ= 0.68 to.9 GeV Circularly Polarized γ Solid state Polarized p/d target X N N N n 0 N... Page 1
![I GDH =04 [ b] P 33(13) Eγ=00 D13(150) F15(1680) ~ I GDH = F35(1905) 0 1800 (MeV)](/docs-images/93/114462882/images/13-3.jpg "Regge approach gives -~-13μb above 1.8GeV Page 13")
13 Sasso, 004/03/18 Session 3, Talk ID 3.5 Cross section: σ3/ σ1/ Phys. Rev. Lett. 87, 0003 (001) Δσ=σ3/-σ 1/: Phys. Rev. Lett. 91, (003) Obtained running GDH Integral: d =8[ b] th. I GDH =04 [ b] P 33(13) Eγ=00 D13(150) F15(1680) ~ I GDH = F35(1905) (MeV) Regge approach gives -~-13μb above 1.8GeV Page 13
14 Sasso, 004/03/18 Session 3, Talk ID 3.5 Spin Dependent Cross Section: σ1/, σ3/ D13(150) F15(1680) F35(1905) Phys. Rev. Lett. 91, (003) Unpol. σ γp cross section Page 14
15 Sasso, 004/03/18 Session 3, Talk ID 3.5 Medium Q HERMES experiment: Polarized electron beam from HERA: Ee=7.6GeV Polarized gas targets (H/D/3 He) Double spin asymmetry in the resonance region Quark-Hadron duality in the spin sector Structure function in the resonance region Generalized GDH sum rule Page 15
16 Sasso, 004/03/18 Session 3, Talk ID 3.5 Quark Hadron Duality in A1 Phys. Rev. Lett. 90, / 3/ A1= 1/ 3/ A1 in Resonance Region (HERMES) Electron: 7.6 GeV Target: Pol. Hydrogen Q: 1. ~ 1 GeV W: 1.0 ~ 4.0 GeV A1 in DIS (Q > 1GeV, W > 4GeV): HERMES Phys.Lett.B44(98)484 SMC Phys.Rev.D58(1998)11001 E143 Phys.Rev.D58(1998)11003 E155 Phys.Lett.B493(000)19 Page 16
17 Sasso, 004/03/18 Session 3, Talk ID 3.5 Generalized GDH sum rule Q Q x= =1.0 M Generalized GDH Integral: W-M Q 1 GeV 0 GeV I GDH Q = DIS x0 0 x min x 0 GDH Integral M = Q W M 1/,Q 3/, Q 8 x g 1 x, Q g x, Q d x 16 d = 1 0 M K x Q 0 * sign is opposite to the formula shown before.. IGDHp(0) = - 04 μb Page 17
18 Sasso, 004/03/18 Session 3, Talk ID 3.5 Generalized GDH sum HERMES Eur. Phys. J. C 6, 57 Full W region DIS: W>4GeV Resonance: W<4GeV Soffer - Teryaev Aznauryan Electron: Target: Q: W: 7.6 GeV Pol. Hydrogen / Pol. Deuterium 1. ~ 1 GeV 1.0 ~ 45 GeV 1/ = 3/ Page 18
19 Sasso, 004/03/18 Session 3, Talk ID 3.5 Smaller Q: Q 0 Q x=1.0 1 GeV x 0 GeV 3 x min NH3, 15ND3: CLAS@JLab He: DIS ν0 Generalized GDH sum rule: 15 R e c n a n o s Re n o i g e x0 E94010@JLab Phys. Rev. Let. 91(003)00, Phys. Rev. C 67(003)05504 Phys. Rev. Let. 89(00)4301 Page 19
20 Sasso, 004/03/18 Session 3, Talk ID 3.5 Double Spin Asymmetry in Resonance Region 1/T 3/T A1 x,q = T A1 A Proton Target A x,q = LT T Electron:.6 and 4.3 GeV Target: Pol. 15NH3 / Pol. 15ND3 Q: 0.15 ~ 1.64 GeV W: 1.0 ~.6 GeV Phys. Rev. Lett. 91, 00 Phys. Rev. C 67, Deuteron Target ηa Page 0
21 Sasso, 004/03/18 Session 3, Talk ID 3.5 Comparison with the real photon results 1 GeV x0 x=1.0 Q e c n a n o s ion e R eg R DIS x min 0 GeV Proton Target W= Phys. Rev. Lett. 91, 00.1 (GeV) Page 1
22 Sasso, 004/03/18 Session 3, Talk ID 3.5 Generalized GDH sum rule in the small Q region Phys. Rev. Lett. 91, 00 Low x contribution: with g1 parameterization Γp1: crosses 0 around Q=0.3 GeV Page
23 Sasso, 004/03/18 Session 3, Talk ID 3.5 Summary Spin dependent Structure function, g1 in the DIS regime Q > 1GeV, W > 4 GeV Very weak dependence of the double spin asymmetry, A1. pqcd based Parton Model describes data well. GDH integral as a small Q limit Cross section difference, Δσ, from 0. to 1.8 GeV was measured. Obtained running IGDHp(1.8GeV)=8 μb. (IGDHp=04μb) Page 3
24 Sasso, 004/03/18 Session 3, Talk ID 3.5 Summary Quark-Hadron duality in the HERMES kinematic region the duality was observed. Generalized GDH sum rule DESY and JLab have been performed. (down to Q = 0. GeV) IGDHp changes sign around Q = 0.3 GeV where is a transition from the partonic and resonance picture of nucleon structure. Page 4
25 Sasso, 004/03/18 Session 3, Talk ID 3.5 References PDG: Phys. Rev. D 66 (00) Structure functions: EMC: HERMES: E143: SMC: E155: Nucl. Phys. B38(1989)1 Phys. Lett.B44(1998)484 Phys. Rev. D58(1998)11003 Phys. Rev. D58(1998)11001 Phys. Lett. B493(000)19 Generalized GDH sum rule: HERMES: CLAS: Eur. Phys. J. C 6(00)57 Phys. Rev. C 67(003)05504 Phys. Rev. Lett. 91(003)00 Quark-Hadron Duality: HERMES: Phys. Rev. Lett. 90(003)0900 GDH sum rule: Mainz: Bonn: Phys. Rev. Lett. 87(001)0003 Phys. Rev. Lett. 91(003)19001 for the plots and data presente Page 5
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