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 |
Quasi-free A_para |
Plot for all energies at 11, 12, 13 and 14 degrees |
Plot for all angles at 5755, 5355, 4955, 4555 , 4155 and 3755 GeV |
|
Quasi-free A_perp |
Plot for all energies at 11, 12, 13 and 14 degrees |
Plot for all angles at 5755, 5355, 4955, 4555 , 4155 and 3755 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.
Comparison of Born and radiated
cross section for QE , inelastic and total Plot of f_rc |
Plot of cross sections Plot of frc |
Model cross section
15 MeV
bin file ( W,xn_qe_born,xn_qe_rad,xn_inel_born,xn_inel_rad,xn_tot_born,xn_tot_rad) |
Comparison of Born,
external rad only and full radiated QE and inel model for Apara and Aperp Plot of A_rc |
Apara Plot Aperp Plot A_rc Plot |
Model
Apara 15 MeV file Model
Aperp 15 MeV file (W,apara_mod_qe_born,apara_mod_qe_extrad,apara_mod_qe_allrad ,apara_mod_inel_born,apara_mod_inel_extrad,apara_mod_inel_allrad) |
Comparison of measured, QE
subtracted and full radiated (Born) data for Apara and Aperp |
Apara Plot Aperp Plot |
Data 15 MeV
bin file ( W,apar_data_measured,error,aper_data_measured,error ,apar_data_qe_subtracted,error,aper_data_qe_subtracted,error ,apar_data_born,error,aper_data_born,error) |
Comparison of measured, QE
subtracted and full radiated (Born) data for A1 and A2 |
A1 Plot A2 Plot |
Data 15 MeV bin file ( W,a1_data_measured,error,a2_data_measured,error, a1_data_qe_subtracted,error,a2_data_qe_subtracted, error,a1_data_born,error,a2_data_born,error) |
Comparison of measured, QE
subtracted and full radiated (Born) data for g1 and g2 |
g1 W Plot g1 X plot g2 W Plot g2 X plot |
Data 15 MeV bin file (W,Xbj,g1_data_measured,error,g2_data_measured,error, g1_data_qe_subtracted,error,g2_data_qe_subtracted ,error,g1_data_born,error,g2_data_born,error) |
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.
A1
fit parameters |
|||
Resonance |
Center |
Width |
Amplitude |
Delta |
1.270 +/- 0.016 |
0.198 |
-0.325 +/- 0.122 |
R3 |
1.545 |
0.264 |
0.267 +/- 0.064 |
R4 |
1.734 |
0.098 |
0.0987 +/- 0.076 |
DIS |
Alpha |
b1 |
b2 |
b3 |
b4 |
0.00 |
0.101 +/- 0.125 |
0.140 +/- 0.282 |
0.00 |
0.00 |
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.
Fit form for A1 A1 error matrix | Fit form for A2 A2 error matrix | Parameter file |
Data file |
"DIS2" |
Constant |
file |
file |
"DIS2" + error |
Constant | file | file |
"DIS2" - error | Constant | file | file |
"DIS2" | Constant+ error | file | file |
"DIS2" + error | Constant+ error | file | file |
"DIS2" - error | Constant+ error | file | file |
"DIS2" | Constant - error | file | file |
"DIS2" + error | Constant - error | file | file |
"DIS2" - error | Constant - error | file | file |
"DIS2" | "DIS2" |
file | file |
"DIS2" + error | "DIS2" | file | file |
"DIS2" - error | "DIS2" | file | file |
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.
Hall B Option |
A1 model description |
A2 model Description |
1 |
APARMS.DAT in resonance region
and DIS |
APARMS.DAT in resonance
region, g2WW in DIS |
2 |
A1_REF.DAT in resonance
region,APARMS.DAT
in DIS |
APARMS.DAT in resonance region, g2WW in DIS |
3 |
APARMS.DAT in resonance region and DIS | A2_REF.DAT in resonance region, g2WW in DIS |
4 |
A1_REF.DAT in resonance region,APARMS.DAT in DIS | A2_REF.DAT in resonance region, g2WW in DIS |
5 |
APARMS.DAT in resonance region and DIS | A2 = 0 |
6 |
A1_RES.DAT in resonance region,APARMS.DAT in DIS | A2_RES.DAT in resonance region, g2WW in DIS |
7 |
APARMS.DAT in resonance region and DIS | APARMS.DAT in resonance
region, g2WW in DIS plus extra twist term |
8 |
APARMS.DAT in resonance region and DIS | model based on DMT in resonance region, g2WW in DIS |
9 |
APARMS.DAT in resonance region and DIS | SOFFER LIMIT FOR A2 in DIS and in resonance region |
10 |
APARMS.DAT in resonance region and DIS | SOFFER LIMIT divided by W FOR A2 in DIS and in resonance region |