Notes on Deuteron Radiative Corrections

1. Determine the radiation lengths of ND3 target plus materials for Perp and Parallel running. Determined from the single arm Monte Carlo.

Field	ta (%)	tb (%)
Parallel ( PF = 55.3)	2.7	2.8
Perp (PF = 61.0)	3.2	2.8

2.  Obtained from Arenhovel the deuteron quasi-free cross sections, Apara and Aperp. Gave Arenhovel a grid of Ebeam,Epr and theta_e points for calculation. Arenhovel used the Lomon parametrization of proton and neutron Ge and Gm.  Arenhovel produced asymmetries for 25 combinations of Ebeam ( 5.755, 5.355, 4.955, 4.555, 4.155 and 3.755 GeV) and electron scattering angle ( 11, 12, 13, 14, and 15 degrees) for W between 0.605 and 2.0 GeV.

         1.  Comparison of the cross section at theta_e =13 degrees as a function of W between Arenhovel and the y-scaling model show that his model underpredicts the cross section by 50% which is large. Peter Bosted suggests that this could be a problem with the integration in getting the inclusive cross section.  Will contact Arenhovel about this. Could effect the Aperp and Apara.
         2. Comparison of  Apara and Aperp the asymmetries ( no correction for 15N background) between Arenhovel and the data show better agreement than the cross section.
                i. Also shown in the plot are calculation assuming a simple PWIA where Ad =0.93*(sig_ep*Aep+sig_en*A_en)/(sig_ep+sig_en).  The factor of 0.93 is to account for the D-state in the deuteron wavefunction.
                ii.  Apara is almost independent of proton and neutron Ge/Gm, but Aperp is sensitive to proton Ge/Gm ( not too sensitive to neutron Ge/Gm). Aperp = -0.136 using proton Ge/Gm from pol transfer experiment while Aperp = -0.125 when using proton Ge/Gm = 1 (dipole).

2a.  For the deuteron inelastic cross sections and quasi-elastic cross sections use quasi-elastic code and inelastic code from fits by Peter Bosted to data. An example code which calls these routines and a script to compile the code. One also needs code which has a subroutine for the EMC effect.

3.   Radiative corrections (Updated June 3rd, 2007 to reflect the latest Te analysis done by Oscar. This shifted the deuteron bottom parallel target polarizations by a factor of 0.9643 and the deuteron bottom perp target polarizations by 1.0026.  Previously, updated March 10 2007 to reflect new 15N correction factors for inelastic region, for quasi-elastic no correction is done. Plot of Apara comparing results with old and new TE. ). Large  data 15 MeV file and data 30 MeV file with kinematics and the asymmetries. The new nitrogen correction factors make a small change in the asymmetries as shown in comparison for Apara and Aperp show.

4. Fits of the A1 inelastic ( after subtracting the quasi-free background).
       a. Using the complete 17 parameter function that was used for proton A1 and A2 does not make sense since with 45 MeV binning there are only 19 data points.
      b. Try a fit in which the starting parameters  are a fit to the proton A1 and allow Delta center and amplitude to change, R2 amplitude set to zero and amplitude of R3 and R4 to change and the b1 and b2 parameters for the DIS to change with b3=b4=alpha=0. DIS contribution is x^alpha*(b1+ b2*x + b3*x^2+ b4*x^3). A plot  shows the fit and the contributions of the different resonances and DIS. The final fit parameters ( the second column a fit to A2).  The  error matrix  for the fit with the square root of the diagonal matrix elements being the error on  Delta amplitude, R3 amplitude, R4 amplitude,  Delta width and DIS b1 and b2 parameters. The program is an example which gets the A1 and error on A1 for a given W and Q2 ( compile using this script) .
       c. For A2  just take a weighted average of the data which gives A2 = 0.083 +/- 0.017. A plot shows the fit to A2 using the same form as the A1 fit. A plot compares data A2 born ( after QE and radiative corrections) using a constant value of A2 for radiative corrections or a fit to A2. The value of A2 is not sensitive to the choice.

      c. A plot comparing the radiative corrected A1 data from the fit and the radiative corrected data after going through the radiative corrections code the second time shows almost no difference.

5. Systematic study:  For the proton systematics, we used a variety of Hall B models to investigate the systematics of the radiative corrections. For the deuteron, the Hall B models did not match the A1 data.  Decide to fit measured A1 with parameters of the Breit-Wgner resonance fixed to the V6c proton A1 except allowing the  Delta center and amplitude to change, R2 amplitude set to zero and amplitude of R3 and R4 to change and have different DIS parametrizations. The basic form of the DIS parametrization is x^alpha*(b1+ b2*x + b3*x^2+ b4*x^3).  A plot  of A1 shows fit and the error band for the "DIS2" fit compared to data and  results of fits using different DIS parametrizations.  For the systematic study, did the radiative corrections with the  A1 fit +/- error band in different combinations of A2 = constant +/- error.  In addition, did comparisons with A2 fit using the "DIS2" form.

6. Comparisons to MAID. Plot of A1 and A2 compared to data.

7. Comparisons to EG1B. A plot comparing RSS deuteron data to five Q2 points in the  EG1B data.  A plot comparing RSS deuteron data to the  EG1B data averaging together Q2 = 0.7-1.0 and Q2 = 1.2-1.4 data and EG1A data averaged over Q2 = 0.65-1.3 .  Plot comparing the three Hall B A1 options in the radiative correction code to the RSS data. Plot comparing the seven Hall B A2 options in the radiative correction code to the RSS data.  Below is a table of the 10 options which are different combinations of A1 and A2 models.  Plot comparing difference in A1(radiated)-A1(Born) for each of the Hall B options compared to difference using the fit to RSS data. Plot comparing difference in A2(radiated)-A2(Born) for each of the Hall B options compared to difference using the fit to RSS data.