Spin Structure Functions of the Deuteron from CLAS/EGB Data Nevzat Guler (for the CLAS Collaboration) Old Dominion University OULINE Formalism Experimental setup Data analysis Results and Conclusion
Motivation S + N q + G + L q L q G q q u + d + s + u + d + Contributions from different quark helicities s Simple quark model with relativistic corrections predicts Σ~60% Experimental results for the total quark spin contribution stays around 30% ± 0% CLAS EGB : Measure double spin asymmetry. Very interesting kinematic range that begins from resonance region and extends into DIS region: from hadronic to quark-gluon degrees of freedom. Calculate spin dependent structure functions. Determine Q evolution of the structure functions and compare to the predictions by OPE and ChP. wo ends of the kinematic region are constrained by two very important sum-rules: GDH at low Q and Bjorken sum rule at high Q.
Double polarized inclusive electron scattering Long. Polarized Electron e P e e θ e Long. Polarized Nucleon P t ψ ν Q W x Kinematics E - 4EE' M Q M E' ν + Sin M ν θ Q Cross section can be expressed in terms of virtual photon asymmetries A and A. d de' d Ω [ ( )] Γ ν + ε + P P ε cosψ + ε ( ε ) sinψ A A L e t A ( ν,q ) d de' d de' dω dω ( ) ( ) d de' Ω ( ) + ( ) d de' d d Ω Difference in the cross sections for two cases is expressed as double spin asymmetry.
Virtual Photon Asymmetries / ( ν ) 3 / ( ν ) In the scaling region at large Q (kinematic region where you begin to see individual quarks as point particles), quarks may be considered almost free (by the asymptotic freedom..), so the transversly polarized virtual photon interacts with the individual quarks, which are also polarized the same or opposite to the proton s spin. he / or the 3/ are the spins of the possible final states A / / + 3 / 3 / A / + L 3 /
EXPERIMEN: (θ,e ) (θ,e ) measurable A + BRIDGE: d de' d Ω [ ( )] Γ ν + ε + P P ε cosψ + ε ( ε ) sinψ A L e t A A +η A A D D E ε / E ε Q ; η ; + ε R E E ' ε R L HEORY: 3 / ( ν ) A / / + 3 / 3 / A / + L 3 / / ( ν )
Spin Structure Function g ( x,q ) g ( x,q ) ν Q F ( x,q ) A ( x,q ) + A ( x,q ) q ν N N First moment of g Γ ( Q ) g ( x,q ) dx at Q at Q I Γ GDH Closely related to the spin carried by quarks. M 8 Q 0 Slope of Γ is constrained by the GDH sum rule απ ν M I th GDH / 3 / ( ( ν ) ( ν )) Q 8M κ 0 dν ν 4 κ Γ ChP GDH sum rule operator product expansion quark models Lattice QCD? DIS pqcd Q (GeV ) Dramatic change of sign of Γ from DIS-regime to the value at the real photon point. At low Q, g (x,q ) is dominated by resonance excitations.
Q evolution of the GDH integral Both Bjorken and GDH sum rules are fundamental sum rules Small Q GDH sum rule Experiments at Mainz, Bonn Chiral perturbation theory? Intermediate Q Extended GDH sum rule I M / 3 / dν GDH ( Q ) ( ( ν,q ) ( ν,q )) 8π α ν ν th Several different models Experiments at JLAB(CLAS/Hall A/Hall C) A good test of at what distance scale pqcd corrections and higher twist expansions will break down and physics of confinement dominate. Γ Large Q Bjorken Sum rule Experiments at CERN,SLAC,DESY Higher order QCD expansion Γ 6 p n S Q ( Q ) Γ ( Q ) g A - +... g α ( Q π ) 6 A DIS pqcd operator product expansion ChP quark models Lattice QCD? GDH sum rule Q (GeV ) EGB has good precision data with wide Q coverage to aswer some of these questions.
Detector CEBAF Large Acceptance Spectrometer Large kinematic coverage Detection of charged and neutral particles Multi particle final states Polarized NH3 & ND3
Event in CLAS Electrons are detected as a coincidence in the Electromagnetic Calorimeter and the Cerenkov Counter Electron momentum is reconstructed from trajectory in Drift chambers 0.5 to esla Magnetic field. orodial magnetic field can be configured for inbending or outbending operations (reference to electron) Dynamically polarized NH 3 and ND 3 NH 3 polarization: 50-60%. ND 3 polarization: 0-30%. K LHe cooling bath C, 5 N and 4 He targets to measure the dilution factor
Kinematics Different Configurations for Input Beam Energy (MeV), Magnetic Field (+ or torus current): 606+ 606-73- 86+ 56+ 56-438+ 438-565- 575+ 575-5743- 5 Different argets: NH3, ND3, C, N5 and Empty 3 billion events.6 and 5.7 GeV data has been analyzed before and results are published. Currently analyzing the full data with addition of.5 and 4. GeV data. 0.05 < Q < 4.5 GeV in 39 bins W < 3.0 GeV in 0 MeV 300 bins
Asymmetry Analysis After identifying the electrons, the raw asymmetry is calculated In an asymmetry analysis acceptance and detector efficiency of the cross sections cancel out N / Q + N + + A raw N + / Q + N / / Q Q Α cor raw Α raw R R R r r A N +/- he event rates for different helicities +/- Q +/- Integrated beam charge for each helicity P b Beam Polarization P t arget Polarization DF Dilution factor R r Contamination R A Ratio of Asymmetries A A DF cor raw P P * b t Double spin asymmetry
A +ηa for the Deuteron PRELIMINARY
A Deuteron PRELIMINARY A3/ transition is dominant (3)P33 N(50-35)D3/S3 A/ transition is dominant
A Deuteron PRELIMINARY W(GeV) A
A Proton PRELIMINARY W(GeV) A
g Deuteron PRELIMINARY
g Deuteron PRELIMINARY W(GeV) g
g Proton PRELIMINARY W(GeV) g
A Proton, creating parametrization of data for better models
Γ Deuteron, Data and Data+DIS results
Γ Deuteron, Comparison to previous analysis smaller errors
Γ Deuteron, Comparison to world data
Γ Deuteron, Comparison to world data
Γ Deuteron, Comparison to world data
Γ Proton, Comparison to world data
Γ Proton, Comparison to world data
Γ Proton, Comparison to world data
Γ 3 and Γ 5 Deuteron
Γ 3 and Γ 5 Proton
Conclusion Inclusive measurements on the proton and the deuteron have been analyzed for full statistics. High precision measurement of the proton and deuteron spin structure functions in the resonance region. Proton and deuteron structure function g is deeply affected by the resonance contribution. Moments of g calculated, show strong variation with Q. Results support some phenomenological calculations, but do not well support chp calculations. By using the proton and the deuteron data, spin structure functions of the neutron will extracted soon.