CLAS Collaboration at Jefferson Lab Deuteron Spin Structure function g 1 at low Q 2 from EG4 Experiment Krishna P. Adhikari, Sebastian E. Kuhn Old Dominion University Division of Nuclear Physics, APS 2012

Inelastic Inclusive Lepton Scattering & structure functions The kinematics of a DIS process can be completely described in terms of any two of these Lorentz invariant variables Probe resolution Energy transfer Elasticity Invariant mass of X Cross-section: In the case of a target polarization along the beam: Structure functions characterize the deviation from point-like behavior of the target and thus give information on its internal structure and dynamics Where, and, +/- for antiparallel/parallel beam-target polarizations EG4 measurement:

Importance of low Q 2 measurement The spin structure function g 1 (x,Q 2 ) and its moments provide crucial information on the internal structure of the target. At low momentum transfer (Q 2 ), one can study the transition from partonic (quark-gluon) to hadronic (nucleonic) descriptions of Strong interaction by testing & constraining effective theories based on QCD such as Chiral Perturbation Theory (Chiral-PT). As Q 2 goes near zero, the first moment of g 1 is constrained by the GDH sum rule & its Chiral-PT extensions. Thus one can test the validity of these rules on deuteron. In combination with available proton information, deuteron data can be used to extract corresponding neutron information. 11

Plot Courtesy of N. Guler & S.E. Kuhn (EG1b)

EG4Experimental Setup CEBAF  Electron beam: High duty cycle, longitudinally polarized (85- 87%), from CEBAF (Beam Energies – (3.0, 2.3, 2.0, 1.3, 1.0) GeV  Targets: Longitudinally polarized solid 15 NH 3 (P~85%) & 15 ND 3 (P~35%) - Dynamic Nuclear Polarization technique - microwave radiation to induce hyperfine transitions to the desired polarization state (in 1K liquid helium bath & 5T field)  CLAS detector: Large acceptance, Multi-layered (DC,CC,SC,EC), 6 independently instrumented sectors (only 6 th used in this experiment); Momentum Resolution < 1%  Runtime Polarimetry: Moeller (beam) & NMR (target) 6S

Kinematic coverage of EG4 (2006) EG1b Kinematic Coverage (for comparison) Lowest Eb: 1.6 GeV Kinematics similar to the Hall A measurements on the neutron using (polarized 3He) NH 3 runs (EG4) W Q2Q2 ND 3 runs (EG4) Eb=1.3GeV Eb=2.0 GeV W Q2Q <Q 2 <0.5 Resonance region well covered

Particle selection Cuts X. Zheng

Simulation of Deuteron Data Will compare data with simulation to extract g 1 (x,Q 2 ) & the errors. Cross-sections for simulation produced with “RCSLACPOL” program  Generates polarized & unpolarized (both Born & radiated) cross sections  Based on the standard approach by Shumeiko & Kuchto (NP B219, 412 (1983)) as well as Mo & Tsai (RMP 41, 205 (1969)), including external radiation in the target.  Updated with the most recent models on polarized and un-polarized structure functions (F 1, F 2, A 1 & A 2 ) and an implementation of the folding algorithm developed by W. Melnitchouk & Y. Kahn (PRC 79 (3), ) for structure functions of deuteron.  Extensively tested & used – at SLAC (E142, E143, E154, E155 & E155x) & Jlab (EG1a/b). The models fitted to & tested with data from EG1b as well as world data on both A 1 & A 2 over a wide range of Q2 and W, including the resonance region and the DIS region. GEANT3 based simulation for detector response. Analyze simulated data exactly like experimental data & compare.

Very-preliminary result (Data & Simulation) Quasi-elastic peak ∆-resonance Higer resonances This is only one of the two ND3 data sets i.e. from 2GeV data. The other data set taken with 1.3 GeV beam energy will extend the coverage further down in Q 2.

Expected precision/results Expected precision for deuteron Expected precision for proton Plots courtesy – A. Deur, JLab

Summary Measurement of spin structure function g 1 (x,Q 2 ) & its moments at low Q 2 will shed light on the internal nucleon structure & the transition from partonic to hadronic descriptions of strong interaction. Polarized electron scattering data on polarized Ammonia with kinematics covering resonance region down to very low Q 2 has been collected by EG4 experiment in JLab Hall-B. Process to extract g 1 (x,Q 2 ) comparing data to corresponding simulation has begun. Final results expected in 2013.

Expected result for Proton & Bjorken Sum Expected Bjorken Sum Expected precision for neutron

New Cerenkov Counter in the 6 th sector (INFN Genoa) Cerenkov photons Reflected photons photons in the PMT plane PMT Incoming electrons Same gas (n= ) and DAQ as before 15 modules each with 2 spherical mirrors (R=140 cm)  =±12°  =2° 2 PMTs Only one reflection  =2°  =±12° Simulated response of the new CC Very high and uniform electron detection efficiency (~99.9%), a high pion rejection ratio (of the order of ).

Method to Extract g 1 The basic idea - study the dependence of the simulated count difference (∆n) on the model input for g 1 directly through the full blown simulation, and then use tables of Born and radiated cross section differences for various model inputs as estimates of systematic uncertainties.  Repeat simulation by slightly increasing (e.g., by 0.1) the model input for both proton & neutron asymmetries A 1 (keep other model ingredients constant), which amounts to a small change in g 1 :  Simulated ∆n changes correspondingly & the proportionality factor C(W,Q 2 ) is evaluated: Statistical error is propagated to g 1 in similar fashion.