June 18, 2010 Spin Physics Physics From Spin Observables Narbe Kalantarians University of Virginia Potential Spin Physics From a Transversely Polarized Solid Target at 12GeV Workshop on Polarized Target Experiments for 12GeV

Spin Physics Goals Measure spin structure function g 2 (x,Q 2 ) and spin asymmetries A 1,2 (x,Q 2 ) for proton with as broad an x coverage as possible, at constant Q 2. Learn all we can about proton SSFs from a double polarization inclusive measurement - Twist 3 effects from moments of g 1 & g 2 : Matrix element - Comparisons with Lattice QCD, QCD sum rules, bag models, chiral quarks. - Study x dependence (test nucleon models) and Q 2 dependence (evolution). - Method: - Measure inclusive asymmetries for 2 polarized target configurations relative to polarized beam: parallel and near-perpendicular - Detect electrons with novel large solid angle detector(s) like BETA/(Super)BigBite.

Polarized DIS Longitudinal Target Polarization  n = 0 Transverse Target Polarization  n =  Beam helicity

Obtaining Quantities Of Interest Measured double-spin asymmetries f dilution factor P B Average Beam Polarization P T Average Target Polarization Calculate physics asymmetries using measured ones Obtain SSFs from A 1 & A 2 and unpolarized structure-function F 1 (x)

Spin-Structure Functions g 1 (x,Q 2 ) is defined with a dependence on quark helicity q +/- (x,Q 2 ) g 2 (x,Q 2 ) is more complex. Contains part dependent on g 1 (g 2 WW ) and another on higher order terms - h T chiral-odd transversity term (twist-2),  involves quark-gluon correlations (twist-3). - m (current) quark mass.

Spin-Structure Sum Rules - Burkhardt-Cottingham (not from OPE) d N measure twist-3 contributions (m << M, h T not very large) OPE: moments of g 1 & g 2 related to twist-2 (a N ) and twist-3 (d N ) matrix elements - Efremov-Leader-Teryaev (Combined with neutron data from JLab Halls A,C)* *PR

Physics Asymmetries: A p 1 Constrain extrapolations of A p 1 x->1. A par & A perp needed to get model-free A 1 & A 2. measurement of A 2 will contribute to improving world’s A 1 data. pQCD SU(6)

Spin Structure Functions: g 1, g 2 x dependence at constant Q 2. Focusing on region most sensitive to x 2 g 1 & x 2 g 2

Matrix Element: d p 2 Expected errors for d 2 from SANE (  d 2 ): -  d 2 (Q 2 = 3GeV 2 ) = 7x10 -4 for 0.3 < x <  d 2 (3.5 < Q 2 < 6.5GeV 2 ) = 2x10 -4 for 0.4 < x < 1.0

Kinematic Coverage Complementary to SANE 2(3) Beam Energies (0.1uA): (4.4GeV), 6.6GeV, 8.8GeV. Extensive x coverage at constant Q 2 with detector set at scattering angles at 20,40 0. SANE W=2

Kinematic Coverage 2(3) Beam Energies (0.1uA): (4.4GeV), 6.6GeV, 8.8GeV. Extensive x coverage at constant Q 2 with detector set at scattering angle at 20,40 0. E’ >1.3GeV, W>1.075GeV. In the process of looking at asymmetries.

Dramatic discrepancy between Rosenbluth and recoil polarization technique. Multi-photon exchange considered the best candidate for the explanation Spin Observables provide an independent measurement. Using Spin Observables: Form-Factor Ratio Bigger part lifts up small part (spin observables).

Measuring the Form-Factor Ratio The elastic asymmetry, The beam-target asymmetry, Here, A P = + Nc A m f P B P T A p = - br SinΘ*Cos  * - aCosΘ* r 2 + c r = G E P /G M P a, b, c = kinematic factors Θ*,  * = pol. and azi. Angles between q and S A m = Measured Asymmetry P B,P T = Beam & Target Pol. f = Dilution Factor Nc = A Correction Term From these kinematics, r2 << c P T + = ~70.0%, P B = ~80.0%,

Estimated Rates and Errors E beam Q 2 mom E’  e  p Q 2 I(uA)  (cm^2/sr)  p  e Rate(/hr) time(days) Counts E E E Q 2 asym Asym err  Ge/Gm  Ge/GM err

Estimated Rates and Errors Q 2 asym Asym err  Ge/Gm  Ge/GM err

UVa Target Superconducting magnet from Oxford Instruments. Produces 5T field at 79A. Polarizes via Dynamic Nuclear Polarization (DNP) with frequency 28GHz/T at 5T => 140GHz. Polarization measured by NMR. Proton Larmor frequency 42.6MHz/T in 5T field => 213MHz Frozen solid NH(D) 3 target. Luminosity ~10 35 cm -1 s -1. Recently repaired at Oxford!

Work To Do: Determine best detector(s) to use, and at which setting(s). Get expected results for SSFs and higher twist quantities. Determine amount of beam-time needed. …

Summary From a 0th order look, using UVa target considering:  Spin Physics Can measure double polarization inclusive scattering to obtain g 1, A 1, 2 and d 2 at broad kinematic coverage. Would take data with beam energies of (4.4) 6.6 & 8.8 GeV with polarized beam and target in parallel and near-perpendicular fields. Increase coverage by using large acceptance detector(s) e.g. BETA or (Super)BigBite.  Using Spin Observables Measure ratio of nucleon form-factors  G M /G E. Higher Q 2 coverage, providing independent measurement. Use large acceptance detector(s), similar to spin-structure case. H. Baghdasaryan, M. Jones, O. Rondon, D. Day

Support Slides

Additional Motivation Complementary to RSS (E ). Measure A 1 & A 2 at higher Q 2 & W. Reduce error in extrapolations and moments of A meas.

BigCal Tracker Cerenkov Lucite Hodoscope Big Electron Telescope Array – BETA 3 planes of Bicron Scintillator provide early particle tracking. N 2 Cerenkov gas Provides particle ID 8 mirrors and 8 PMTs 28 bars of 6cm wide Lucite Bars oriented horizontally for Y tracking PMTs on either side of bar provides X resolution Lead glass calorimeter 1744 blocks aprox. 4cm x 4cm (Protvino), 3.8cm x 3.8cm (RCS) energy and position measurement Forward Tracker (Norfolk State) Cerenkov (Temple) Lucite Hodoscope (NCA&T) BigCal (IHEP,Protvino,W&M,Lanzhou)

Dynamic Nuclear Polarization Refrigerator K Magnetic Field 2-6T Microwaves GHz NMR Polarization Protons: % Deuterons: 20-50% Employs paramagnetic radicals, which provide electron-proton hyperfine splitting in a high magnetic field at moderate-low temperature Microwaves drive “forbidden transitions” to propagate polarization.

A Q-meter is connected in series to the NMR coil with inductance L C and resistance r C, which is imbedded in the target sampling. The impedance Z C of this circuit is written where  is the filling factor of the coil. Measurement of Polarization

The desired transitions and are forbidden. Using the fact that the dipole-dipole interaction exists: 2 distant magnetic moments => dipole-dipole interaction << Zeeman splitting This results in a mixing of nuclear states, allowing for the desired interactions, though with a much less probability than those allowed (10 -4 ). Forbidden Transitions H I Z S Z -1/2 1/2 1/2 1/2 -1/2 1/2 -1/2  PR  R  PR forbidden E

Q-meter Piece of equipment used in testing of rf circuits. Measures Q “Quality-factor” of a circuit, or how much how much energy is dissipated per cycle in a non-ideal reactive circuit. For inductors

Target Performance J. Maxwell ~71%

Degree of Polarization P. Dilution factor f, ratio of free polarizable nucleons to the total amount of nucleons in the sample and is dependant on kinematics. Here P and f correct for the fact that the target is not 100% polarized and contains other materials. The (raw) asymmetry is then expressed as The amount of beam-time needed t to obtain a statistical error  A has the dependency Where  is the density of the material. Important Criteria

Monte Carlo Use for training ANN. Obtain understanding of reconstruction. Provide understanding of efficiencies for df. Using F1F209 model from P. Bosted, E. Christy, and V. Mamyan. recgen E’ 80  180   recgen 