RSS Analysis

RSS homepage.

Weekly Minutes

Technotes/reports for RSS

Proton Radiative Corrections Tables

Spin Structure Moments

03/13/08

1. Papers
   
   1. Updated draft of moments prl. (File rssm_031308.pdf)

08/14/07

1. Papers
   
   1. Update of proton RC section (pdf,src) for long paper.
   2. First draft of moments prl. (File rssm.pdf)

07/31/07

1. Papers
   
   1. Implemented Oscar's comments on the moments technote.
   2. First draft of proton RC section (pdf,src) proton RC section for long paper

05/15/07

1. Moments
   
   1. Added LSS05 PDF.
   2. Evaluated Matsuda and Uematsu integrals
   3. Posted full table of results.

04/30/07

1. Moments
   
   1. In my note I found Gam2p^DIS = 0.0236+-0.0054, using average +- standard deviation of Scenarios I and III. (For Scenario III I exluded the NLO-2 version of PDFs).
   2. Oscar made two suggestions:
      1. Average of Scenario I and all four Scenario III PDFS, +- sqrt(variance)/(N-1) : (plot)
      2. Same as above but with PDF's normalized to the ratio Int_0^x0 g1(regge)/Int_0^x0 g1(pdf) : (plot)

04/23/07

1. Higher Moments
   
   1. Higher moments of g1 compared to PDFs and models.

04/10/07

1. Moments
   
   1. Comparison of Loman vs Mergell versions of elastic contribution to moments Table plot.
   2. Chiral soliton models compared to data.
   3. Gammaa_2p
   4. DIS07 talk slides.
   5. moments note draft.

03/26/07

1. Fitting Routine
   
   1. Modified version of Fitting Routine

03/19/07

1. DIS fit parameters in A1,A2
   
   1. I took a closer look at the A1A2 DIS fit, by fitting our data with 5 separate functional forms. Each form assumed four BW resonances (3parameters each) as in the normal fit. For the DIS I evaluated:
      • 0 terms : DIS= 0 (no DIS )
      • 1 term : DIS= b0
      • 2 terms : DIS= b0 + b1 x
      • 3 terms : DIS= b0 + b1 x + b2x^2
      • 4 terms : DIS= b0 + b1 x + b2x^2 +b3x^3
      • 5 terms : DIS= (b0 + b1 x + b2x^2 +b3x^3) x^alpha. (what we normally use)
   2. spreadsheet
   3. A1
   4. A2
   5. Conclusions:
      • Almost all the fits give good reduced chi2, and most of the simpler fits give a better reduced chi2 than what we are using. For what it's worth, our background is best described by a constant.
      • The A1 resonance parameters are suprisingly stable no matter what background is chosen: The peak centers vary by <=1%, The peak widths vary by <=25% The peak heights vary by <=10%, excpet for the Delta which varies by <=20%.
      • The resonance parameters show very little dependence (~1%) on the initial fit guesses. The DIS parameters on the other hand can show several hundreds of percents variation.
      • Given these results, I don't give too much significance to any of the DIS parameters we have found.
      • That being said, the radiative corrections have very little dependence on the DIS fit form. (As Oscar showed, we're basically assuming A1 is independent of Q2) The only effect any of this has on the RC's occurs near threshold where we have huge error bars.

03/05/07

1. DIS contribution to Gam1
   
   1. Oscar points out that Bianchi and Thomas have a Phys. Lett. B article in addition to their Nucl. Phys B. Proceedings. The DIS fit is slightly different in the two papers. (Plot)
   2. The effect on RSS DIS integral is only 1.9%:
      • Nucl. Phys B (Proc. Suppl.) 82 (2000) 256. Gamma_1^{DIS}(1.279) = 0.0681 +- 0.0099
      • Phys. Lett. B 450 (1999) 439. Gamma_1^{DIS}(1.279) = 0.0694 +- 0.0100
   3. I'm using the Nucl. Phys B. fit parameters.
2. Elastic contribution to Gam2
   
   1. Assuming 5% error on Mergell et al form factors. (Plot)
3. DIS contribution to Gam2
   
   1. Including Gam2 in summary note
   2. G2WW
4. MAID Model Integration limits
   
   1. Modified MAID model integration limit to match RSS data coverage.
   2. Gam1
   3. Gam2

02/26/07

1. Moments
   
   1. Working to finalize moments.
   2. New page with summary of results: Spin Structure Moments
2. Gamma_1 DIS contribution
   
   1. Oscar's Regge fit : 0.0683 +- 0.0069 (proton)
   2. Bianchi and Thomas: 0.0681 +- 0.0099 (proton)
   3. Bianchi and Thomas: -0.0288 +- 0.0098 (neutron)
   4. Oscar's Regge fit : -0.1562 +- 0.4426 (neutron)
   5. Data used in BT fit : plot. (From Nucl. Phys. Proc. Suppl. 82, 256(2000).)
3. Propagation of RSS Fit errors
   
   1. Small Monte Carlo which randomizes the delta peak height uniformly over 1 sigma.
   2. This code could be generalized for all the parameters and to use gaussian instead of uniform distribution.

01/22/07

1. Evolution to constant Q2
   
   1. Following Peter's suggestion : assume g1/F1 is independent of Q2.
   2. Then g1(Q2=1.3) = g1(Q2)/F1(Q2) * F1(Q2=1.3)
   3. Here's the result for deuteron.
   4. Plot of g1/F1
   5. Note : I am using an old version of deuteron F1D. It's pretty close to the F1D in Mark's tables, but I still need to update it.
   6. Here's the result for Neutron.
   7. Plot of Neutron Gamma_1 evolved to Q2=1.279

01/16/07

1. Quark Polarizations
   
   1. Update : Using "per-nucleon" values for deuteron structrure functions leads to more reasonable results: new plot.
   2. Cleaner plot for presentation.
2. Preliminary Neutron Moments
   
   1. Forming moments from Shige's table of neutron g1,g2.
   2. gam1
   3. gam2
   4. d2
3. Alternative method
   
   1. S. Scopetta, et al nucl-th/9709015 : This paper claims I_D = (1-3/2w_d)(I_n+I_p)/2 good to 3% in resonance region for Q2 = 1 GeV2, and that similar relation holds for g1d. But when I try to use this relation for our g1p,g1d, I don't get reasonable results.
4. Misc.
   
   1. Nice proton/deuteron data webpage.

12/18/06

1. Quark Polarizations
   
   1. Forming Delta u/u and Delta d/d following eq. 2-3 of nucl-ex/0605028.
   2. I use g1d and F1d from Mark's radiatively corrected files, and g1p, F1p from proton files
   3. I start with 15 MeV binned data : g1p,g1d vs W
   4. For reference here's comparison to Compass g1d and Compass A1d
   5. Text file of Compass data.
   6. Preliminary results for all data points satisfying W>1770 MeV.
   7. Preliminary results for weighted average of all points satisfying W>1770 MeV.
   8. Note : there is newer hermes data from PRD 71, 012003 (2005) which I haven't included yet.

09/18/06

1. Preliminary Moments
   
   1. Preliminary results on RSS Moments

09/11/06

1. PDFs and TMCs
   
   1. Working to implement pdfs and target mass corrections (TMCs) into my code to evaluate DIS contribution to the moments.
   2. Double checked TMC code against Sidorov and Stamenov Mod.Phys.Lett.A21:1991,2006 to make sure I was using it correctly.
   3. Here's the comparison to figure 2 in above publication: Fig 2a Fig 2b Fig 2c
   4. PB: Peter's code based on Blumlein and Tkabladze (exact). PS: Patricia's code based on Sidorov and Stamenov (approximation).
   5. The discontinuities in PB curve arise from the integration method and can be reduced with finer binning. Also, since the plots represent (g1^TMC - g1)/g1 the size of the discontinuity is insignificant.
   6. Absolute value of TMC at 1 GeV
2. Moments
   
   1. g1(1.279)
   2. Gamma_1

08/28/06

1. Moments
   
   1. As check of codes, reproduced E142 and E143 Gamma_1.
   2. E142
   3. E143
   4. Conclusion: for Gamma_1 = Sum (g1*dx) :
      • E142 uses
        • dx = xhi -xlo (all bins)
      • E143 uses
        • dx_1 = (X_2 - X_1 )
        • dx_i = (X_i+1 - X_i-1)/2.
        • dx_n = (X_n - X_n-1)
   5. plot

06/29/06

1. Pass VI
   
   1. Pass VI Results
   2. resonance contributions to the fit.
2. 
   
3. Model dependence
   
   1. For A1, I include 3 models : OR ,Hall B fit, and Fit to world excluding Hall B.
   2. For A2, I include 5 models : OR, Hall B fit, DMT, A2=0, AO.
   3. Here are some plots showing effect on standard deviation for A1,A2, Apar and Aperp
      1. A1
      2. A2
      3. Apara
      4. Aperp
   4. And here's a plot which gives an idea of how A1,A2 errors propogate into Apar, Aperp

06/22/06

1. Model Dependence
   
   1. Previously, I was looking at the variation in Apar, Aperp across the available models. I don't think this was appropriate, since all the models I use begin with A1, A2. Apar and Aper are then formed from A1,A2.
   2. So now, looked at the available A1,A2 models, evaluating the chi2/N compared to our born A1,A2.
      1. Available fits to A1 with [Chi2/N]
      2. Available fits to A2 with [Chi2/N]
      3. Standard deviation for A1
      4. Standard deviation for A2

05/24/06

1. Pass VI
   
   1. Comparison with P.Bosted/K. Griffeon EG1 Radiative corrections for kinematic close to RSS(E0=5.7 GeV, Q2=1.2). I'm using a "best guess" for EG1 radiation lengths.  Also, it seems I am not using same input models. Nevertheless, get pretty good agreement:
      
   • Unpolarized Cross Section
   • Parallel Asymmetry
   • Parallel Asymmetry with RC factors.
   2. Completed a full pass on RSS data using exact kinematics, nitrogen correction, etc.
   • Fit parameters converge in three iterations.
   • Had some problems with stat. error propogation (division by zero) so left Stat error unchanged by radiative corrections for now.
   • Apara and Aperp 
     
   • A1 and A2
   3. Checks:
   • Polrad compared to radcor
   • Apara from different models : Systematic effect on RC
   • Aperp from different models : Systematic effect on RC

03/16/06

1. Elastic tail subtraction
   1. New version of elastic tail subtraction note
2. External RCs
1. As suspected, traced error back to my external radiation procedure.
   1. I was feeding the code a table of cross sections at lower Es,Ep, and allowing it to interpolate to the kinematics needed for RCs.
   2. The interpolation was done with respect to y=nu/E, which is not a good choice for our kinematics.
   3. When I replace the interpolation with a direct call to Eric's model, I get very good agreement with Peter's code.
   4. Cross checked MoTsai, Miller and Stein versions of peaking approximation. All give very similar results.
   5. Two issues remain:
      1. Need clarification on application of ionization loss: Is it applied in replay engine? It's easy to make this correction to my RCs, but it was my understanding that it is performed already by engine.
      2. Significant difference between peaking approximation and exact result at large W (3rd resonance and above). Need to code in this correction.

03/09/06

1. Error in Pass V
1. Procedure:
   1. Form Deltasigma from measured Asymmetry and radiated christy model of unpolarized XS
   2. Perform RC
   3. Divide by Born xs to obtain final Born asymmetry.
2. I was using central kinematics in step one, but statistically weighted average in step 3. Comparison
2. New Pass
   1. Ran a debugging pass, turning off all second order corrections (statistics weighted kinematics and nitrogen asymmetry correction.)
   2. Effect on parallel asymmetry: (with error bars) (without)
   3. Some concern raised by Oscar as to size of radiative corrections at W=1350,1500. Effect most noticible using the OR model
   4. This could possibly arise from two issues: Q2-dependence of oscr model, or enhanced peaks in oscr model (which match our data).
   5. To test, I tweaked the resonacne peak heights in the OR model to more closely resemble MAID and HALLB, while leaving the Q2-dependence unchanged: ( plot )
   6. Here's the ( result ). I conclude that the major difference between models, as far as RCs are concerned, is the size of the higher resonance peaks. The Q2-dependence is not too important.
   7. Recall: The other models don't reproduce our data too well.
3. Current conclusions
   1. Iteration process seems correct. The resulting Born spectra reproduces our measured data well after I radiate it. ( plot ).
   2. This implies that if there is a problem, it lies in the model input, or the radiative process.
   3. With regard to the model, Q2-dependence not such a big factor, and OR reproduces our data pretty well.
   4. With regard to the radiative process: internal RC seem small ( plot ) so if there is a problem, it is most likely in the external part.
   5. Two possibilities
      • Everything is fine, we just have external corrections to asymm that are much bigger than internal (seems unlikely)
      • Or, Error in my external corrections. Double checking external RC's against Peter's code.

03/01/06

1. Inelastic Radiative Correction Systematics:
1. The following plots show an estimate of the inelastic RC systematic, obtained by comparing the born asymmetry which results from using three different input models (Oscar's, MAID, and Hall B).  "Sigma" signifies the standard deviation of the three models, while "Delta" is |Oscar-HallB|.  Delta is probably more relevent than sigma for W>1400 MeV, where MAID is not doing so well.  The lower panel shows the relative size of these two quantities. The relative statistical uncertainty is shown as the filled band for comparison. The dashed lines indicate the average.
   
1. Apar plot
   
2. Aper plot
   
2. The relative error is pretty meaninless in regions where the asymmetry is small or cross zero. So this plot compares the absolute value of the RC systematics to the absolute value of the statistical error. For the most part, the systematic estimate is smaller than the statistical error.
2. 
   
3. Elastic Tail Subtraction Systematics:
4. Some clue what is happening with first W bin:
   1. Apar before application of the DF.
   2. Apar after application of the DF.
   3. The parallel Dilution Factor.

02/23/06

1. Pass V RC
1. Results
2. Difference from last week's Beta results
1. I performed last week's results using the incorrect nitrogen asymmetry correction. Now I am using Mark's latest files : bot para bot perp top para top perp
2. Also, I realized that my radiative corrections were not converging due to an unlucky choice of initial parameters in the fit. So the radiative corrections were getting a little bit bigger on each iteration.
3. The following plots shows the difference between using last week's fit parameters and the correct ones:
   • g1 and g2
   • A1 and A2
   • Apar and Aperp
3. Systematics
1. The Nitrogen asymmetry correction has very little effect on the Q2-dependence of the fit. This plot shows the Q2-varation of the fit for A1 and A2 for 4005 < E0 < 5755 MeV ( the energies I need for the radiative corrections). nc0 : not corrected for nitrogen asymmetry. nc1 : corrected for nitrogen asymmetry.
2. For comparison, heres the same plot from the MAID and Hall B models
3. Model dependence: Here are some plots showing the variation in the final Born asymmetry that results from choosing different models for A1 and A2. The three models are MAID, Hall B, and Oscar's fit. Only Oscar's fit reproduces our data well, so this comparison gives a "worst-case" scenario of our RC model dependence. Note also that these plots already have the elastic tail subtracted, so they address only the inelastic RC.
   1. Apar
   2. Apar (without error bars for clarity)
   3. Aperp
   4. Aperp (without error bars for clarity)

02/16/06

1. Pass V RC
1. Beta results. SHOULD NOT BE USED.
2. The fit parameters here are not converged, and the Nitrogen asymmetry correction is not the latest. THEY SHOULD NOT BE USED.

12/15/05

1. Pass IV RC
1. Completed with out of plane correction and using statistically weighted kinematics (plots).
2. Very small change compared to previous result (plots).
3. Plots showing size of radiative corrections (without error bars) and (with erorr bars).
4. Complete tables are available from the radiative correction summary page.
2. 
   
3. A1, A2 fit
   1. Latest fit :

      A1 Peak Center (MeV)	A1 Width(MeV)	A2 Peak Center(MeV)	A2 Width (MeV)
      1210.0	155.3	1226.9	155.5
      1350.1	68.4	1334.7	92.8
      1547.9	281.9	1495.9	172.1
      1739.9	138.9	1669.0	163.5
      ChiSq/n	1.33	ChiSq/n	1.62

   2. All fit parameters, formatted for insertion in code: (here)
   3. Table of model generated physics quantities (here)
   4. Results of fit to stt, slt instead of A1,A2 (here)
4. 
   
5. Proceedings
1. Proceeding for Spin Praha: (here)
6. 
   
7. SLAC Data
1. All the tables of SLAC data I used for my plots (here)
8. 
   
9. Peter's Model
   1. Comparison to Hall A Nitrogen and He3 cross sections (here).
10. 
    
    

11/24/05

1. 
   
2. RC pass IV
   1. I'm using Oscar's fit code directly now for the RC.
   2. Procedure:
      1. Obtain initial fit parameters from our elastic tail subtracted data.
      2. Radiate the resulting Q2-dependent fit.
      3. Compare to our measured data to obtain RC factors.
      4. Apply RC factors to measured data to obtain Born asymmetries.
      5. Obtain new fit parameters from Born asymmetries.
      6. GOTO Step 2.
   3. The iterations converge pretty quickly: A1 A2
   4. Pass IV Tables Plots
3. 
   
4. Nitrogen corrections
   1. I repeated the whole RC process with and without the nitrogen asymmetry corrections. (In the following plots "nc" signifies nitrogen corrections have been applied. "nonc" signifies they have not.)
   2. Here's a look at the effect on the purely additive radiative correction factors.
   3. And here's the effect on the asymmetries: Apar Aper A1 A2
   4. There is only a significant difference for the first two data points. Since these two data points have huge statistical and systematic error I think it makes little difference whether I apply the correction or not (contrary to what I said at the last meeting.)
   5. The only possible issue I see, is effect on integrals. Looks like only a three percent effect on GDH SR, negligible for Gam1, Gam2. Will look a little deeper at this.
5. 
   
6. Resonance Fit results
   1. Oscar's fitting code spits out the resonance center and peak width.
   2. This pass of RCs gives similar results to what Oscar found before, but the delta is a little better behaved.
   3. The nitrogen asymmetry correction has little effect on the physics here also.
      • I get the following results when no Nitrogen Correction is applied:

        A1 Peak Center (MeV)	A1 Width(MeV)	A2 Peak Center(MeV)	A2 Width (MeV)
        1213.7	198.6	1226.2	154.2
        1347.6	64.1	1335.0	93.3
        1550.7	282.3	1497.2	174.2
        1739.2	118.4	1668.0	169.3
        ChiSq/n	1.28	ChiSq/n	1.55

      • And the following results with Nitrogen Correction:

        A1 Peak Center (MeV)	A1 Width(MeV)	A2 Peak Center(MeV)	A2 Width (MeV)
        1210.0	164.4	1226.2	155.1
        1347.9	66.0	1334.8	93.2
        1549.3	279.5	1497.1	172.7
        1738.4	120.3	1668.0	168.2
        ChiSq/n	1.37	ChiSq/n	1.65

        
        
7. RC Overview
1. For reference, here's an overview of the RC passes to date:
   1. PASS I : Used simple spline fit to our data combined with lower energy "data" from MAID model. Liang xs model used.
   2. PASS II : Had serious bug. Results not released.
   3. PASS III: Used model (MAID or Hall B) spectra only. No input from our data. The model was radiated and the resulting RC factor applied directly to our measured data. Problem: large model dependence since neither model reproduces our data that well.
   4. PASS IV : Q2-dependent fit to our data is radiated and resulting RC factor applied to our measured data.
8. 
   
9. Statistical Error Propogation
1. Went back and transformed all my equations into functions of Apar & Aperp, the actual measured quantities of RSS in order to simplify the error propagation.
2. The change in central values for g1,g2,A1,A2,etc. was negligible. There was a slight (but visible) change in propagated statistical error.
3. Ultimately, this has no effect on anything but my plots.
10. 
    
11. To Do/In Progress
1. Oscar requests a RC pass using the actual out of plane angle. Working on it.
2. RC systematics.
12. Update: Comparison to EG1b
1. plot
2. zoomed in plot

11/17/05

1. RC
1. Looking at effect of nc on threshold region.
2. Trying to master Oscar's fit code.
3. Iterate on the data starting from elastic tail subtracted A1, A2 to minimize model dependence.

11/10/05

1. RC
1. Some plots displaying size of radiative corrections. 
   
2. Trying to use Frank's statistically weighted W bins, instead of bin center.  Some issues to resolve before I implement.
2. To do/In progress. High Priority
1. Evaluating RC systematics :
   1. Difference between data and model.
   2. Difference between data and model.
   3. Difference between data and model.
   4. Alternatively : Some fixed fraction of correction.
2. Collisional loss correction.
3. To do/In progress. Low Priority
1. Statistical error propagation.
2. Updating integral plots: Gamma_1 ( Resonance, Full ).
3. EG1A Wmax from Fatemi thesis.
4. Integral systematics.

11/3/05

1. RC
   1. Eric's new df has small effect on asymmetry before RC.
   2. Standard plots
   3. Sent initial results to Oscar to start the iteration over...
   4. UPDATE : Some plots displaying size of radiative corrections.
2. Integrals
   1. Some plots of integrated quantities using 3rd iteration from 6/14/05 set.
   2. See same difference between different definitions of d2 that was pointed out by Oscar a while back.
   3. Using Bianchi and Thomas paramaterization of DIS contribution to integrals.

10/13/05

1. RC
   1. Iterating on Oscar's Q2-dependent fit.
   2. Second iteration
   3. Third iteration

10/06/05

1. Hall B Model
   1. Found manual to Sebastien's Hall B model. Very helpful.
   2. So the model A1 is a combination of DIS, AO, and a fit to all world data prior to the CLAS data.
2. Pass II
   1. PASS II results are incorrect and should not be used. There was a serious bug in my code.
3. Pass III
   1. No iterative procedure. Just radiating input model to find RC factor at RSS kinematic.
   2. Radiative Corrections using Hall B model
   3. Radiative Corrections using MAID model
   4. Model Dependence of RC.
   5. Comparison of final results to models (Hall B input)
   6. Comparison of final results to models (MAID input)
   7. Comparison to PASS I and PASSII.
4. Comparison to EG1B
   1. Size of Eg1b RC to APAR.
   2. Comparison of RSS and Eg1b
   3. Comparisonof RSS and Eg1b (zoomed).
   4. Purely additive correction to APAR.
   5. Contributions to the Radiative corr ections to APAR.
5. Tail subtraction
   1. The elastic tail subtraction is very sensitive to the unpolarized model used: ( plot ) ( plot )
   2. Get the most "reasonable" result for APAR when using Christy's 2004 fit or by shifting the 6/14/05 fit by 15 MeV (=1/2 our binsize).
   3. For now I am sticking with standard 6/14/05 fit.
6. New Christy Model
   1. There is a new model version: 07/22/05
   2. It's not officially released yet.

09/29/05

1. Model dependence of RC
   1. To get around previously noted problems, I tried simply radiating input model to get RC factor at RSS kinematic.
      (no iterative procedure, and not including our data as input).
   2. But get very different RC factor depending on input model.
   3. In retrospect, this is not too surprising since the radiative corrections contains a term directly proportional to the input born model.
      1. Contributions to RC
   4. However, the relative size of the radiative correction is almost model independent.
   5. But will need to handle zero crossings properly.
2. Scaling of Models
   1. To get better model, I tried to determine the scaling factor with incident energy for the Hall B and MAID models, so we could simply apply this scale factor to our data.
   2. Linear scaling (MAID)
   3. Linear scaling (HallB)
   4. Conclusion: Applying a linear scaling factor that is independent of W is not sufficient. The scaling factor is not linear and even more it depends on W.. For this reason, scaling by mott won't be good enough either.

09/22/05

1. Pass II
   1. Working to understand issues with Pass II inelastic radiative corrections.
   2. Large rc factor around W=1400 MeV may be due to problem with my input model.
   3. Working Oscar's fit into code as possible input model.

09/16/05

1. Pass II
   1. Pass II complete
   2. Plots showing effect of radiative corrections.
   3. Comparison to models.
      
   4. A1 comparison to pass I.
   5. Effect of radiative corrections on asymmetry

09/09/05

09/02/05

08/16/05

07/25/05

07/15/05

07/08/05

06/02/05

06/01/05

05/27/05

05/19/05

05/13/05

05/05/05

04/28/05

04/13/05

03/31/05

03/24/05

03/17/05

03/09/05

03/03/05

02/24/05

02/17/05

02/10/05

02/03/05

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