Phi angle in CM frame for different runs: Difference between revisions

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|}<br>
|}<br>


== Correlation plots with<math>cos\theta_{pion}^{CM} , W</math> , and <math>  Q^2</math> ==


The angle is (0, 360).<br>
;
{| border="1"  |cellpadding="20" cellspacing="0
|-
| <math>cos\theta_{pion}^{CM}</math> vs <math>\phi_{diff}^{CM}</math>  ||  <math>W</math> vs <math>\phi_{diff}^{CM}</math>|| <math>Q^2</math> vs <math>\phi_{diff}^{CM}</math>
|-
|[[Image:pion_cos_theta_in_cm_frame_vs_phi_angle_difference_in_cm_frame_with_cuts.gif|300px]] || [[Image:missing_mass_vs_phi_angle_cm_frame.gif|300px]] || [[Image:Q_sqrd_vs_phi_angle_cm_frame.gif|300px]]
|}<br>
Same table as above but with the cut  1.0 < W < 1.5
{| border="1"  |cellpadding="20" cellspacing="0
|-
| <math>cos\theta_{pion}^{CM}</math> vs <math>\phi_{diff}^{CM}</math>  ||  <math>W</math> vs <math>\phi_{diff}^{CM}</math>|| <math>Q^2</math> vs <math>\phi_{diff}^{CM}</math>
|-
|[[Image:pion_cos_theta_in_cm_frame_vs_phi_angle_difference_in_cm_frame_Wlt1.5.gif |300px]] || [[Image:missing_mass_vs_phi_angle_cm_frame_Wlt1.5.gif|300px]] || [[Image:Q_sqrd_vs_phi_angle_cm_frame_Wlt1.5.gif|300px]]
|}<br>
Same table as above but with the cuts 1.0 < W < 1.25 GeV , 20 MeV bins in W and 15 degree bins in <math>\phi</math>
{| border="1"  |cellpadding="20" cellspacing="0
|-
| <math>cos\theta_{pion}^{CM}</math> vs <math>\phi_{diff}^{CM}</math>  ||  <math>W</math> vs <math>\phi_{diff}^{CM}</math>|| <math>Q^2</math> vs <math>\phi_{diff}^{CM}</math>
|-
|[[Image:pion_cos_theta_in_cm_frame_vs_phi_angle_difference_in_cm_frame_Wlt1.3.gif|300px]] || [[Image:missing_mass_vs_phi_angle_cm_frame_Wlt1.3.gif|300px]] || [[Image:Q_sqrd_vs_phi_angle_cm_frame_Wlt1.3.gif|300px]]
|}<br>
Same table as above but with the cuts 1.0 < W < 1.5 GeV and -0.2 < <math>cos\theta_{pion}^{CM}</math> < 0
{| border="1"  |cellpadding="20" cellspacing="0
|-
| <math>cos\theta_{pion}^{CM}</math> vs <math>\phi_{diff}^{CM}</math>  ||  <math>W</math> vs <math>\phi_{diff}^{CM}</math>|| <math>Q^2</math> vs <math>\phi_{diff}^{CM}</math>
|-
|[[Image:pion_cos_theta_in_cm_frame_vs_phi_angle_difference_in_cm_frame_Wlt1.5_ct-0.1.gif|300px]] || [[Image:missing_mass_vs_phi_angle_cm_frame_Wlt1.5_ct-0.1.gif|300px]] || [[Image:Q_sqrd_vs_phi_angle_cm_frame_Wlt1.5_ct-0.1.gif|300px]]
|}<br>
Insert the same table as above but with the cuts 1.15 < W < 1.25 GeV and -0.1 < <math>cos\theta_{pion}^{CM}</math> < 0, 20 MeV bins in W and 15 degree bins in <math>\phi</math>
{| border="1"  |cellpadding="20" cellspacing="0
|-
| <math>cos\theta_{pion}^{CM}</math> vs <math>\phi_{diff}^{CM}</math>  ||  <math>W</math> vs <math>\phi_{diff}^{CM}</math>|| <math>Q^2</math> vs <math>\phi_{diff}^{CM}</math>
|-
|[[Image:pion_cos_theta_in_cm_frame_vs_phi_angle_difference_in_cm_frame_Wlt1.2_ct-0.1.gif|300px]] || [[Image:missing_mass_vs_phi_angle_cm_frame_Wlt1.2_ct-0.1.gif|300px]] || [[Image:Q_sqrd_vs_phi_angle_cm_frame_Wlt1.2_ct-0.1.gif|300px]]
|}<br>
Insert the same table as above but with the cuts  W < 1.25 GeV and -0.1 < <math>cos\theta_{pion}^{CM}</math> < 0, 20 MeV bins in W and 15 degree bins in <math>\phi</math>
{| border="1"  |cellpadding="20" cellspacing="0
|-
| <math>cos\theta_{pion}^{CM}</math> vs <math>\phi_{diff}^{CM}</math>  ||  <math>W</math> vs <math>\phi_{diff}^{CM}</math>|| <math>Q^2</math> vs <math>\phi_{diff}^{CM}</math>
|-
|[[Image:pion_cos_theta_in_cm_frame_vs_phi_angle_difference_in_cm_frame_Wlt1.25_ct-0.1.gif|300px]] || [[Image:missing_mass_vs_phi_angle_cm_frame_Wlt1.25_ct-0.1.gif|300px]] || [[Image:Q_sqrd_vs_phi_angle_cm_frame_Wlt1.25_ct-0.1.gif|300px]]
|}<br>




Line 145: Line 88:
  Then insert phi -vs- theta
  Then insert phi -vs- theta


[[Image:cos_theta_of_pion_in_cm_vs_phi_angle_difference_in_cm_frame_EC_cuts_0-9_M_x_1-1_1-1_W_1-5_1735_files.gif|400px]]<br>
{| border="1"  |cellpadding="20" cellspacing="0
|-
| NH3 target || N15 and C12 target
|-
|[[Image:cos_theta_of_pion_in_cm_vs_phi_angle_difference_in_cm_frame_EC_cuts_0-9_M_x_1-1_1-1_W_1-5_1735_files.gif|400px]]||[[Image:cos_theta_of_pion_in_cm_vs_phi_angle_difference_in_cm_frame_EC_cuts_0-9_M_x_1-1_1-1_W_1-5_186_files_N15C12.gif|400px]]
|}<br>
 


{| border="1"  |cellpadding="20" cellspacing="0  
{| border="1"  |cellpadding="20" cellspacing="0  
Line 168: Line 117:
[[Image:1111.gif|400px]]<br>
[[Image:1111.gif|400px]]<br>


  1.4 < Q^2 < 1.8  1.13< W <1.17
Cuts: EC_inner>0.06, EC_tot/p>0.2, nphe>2.5, <math>0.9<M_x<1.1</math>, <math>1.1<W<1.5</math> and <math>0.6<cos\theta_{pion}^{CM}<0.8</math>.<br>
[http://clasweb.jlab.org/cgi-bin/clasdb/msm.cgi?eid=14&mid=16&data=on]
[[Image:phi_angle_cm_frame_vs_rate_two_results_compared_cos_theta_0-6_0-8.jpg|500px]]<br>


cos(theta_pi) phi(pi+) dsigma/dOmega Data errors Systematic errors


dimensionless degree mcbn/sterad mcbn/sterad mcbn/sterad
Cuts: EC_inner>0.06, EC_tot/p>0.2, nphe>2.5, <math>0.9<M_x<1.1</math>, <math>1.44<W<1.46</math> and <math>0.6<cos\theta_{pion}^{CM}<0.8</math>.<br>
[http://clasweb.jlab.org/cgi-bin/clasdb/msm.cgi?eid=14&mid=16&data=on]
[[Image:phi_angle_cm_frame_vs_rate_two_results_compared_cos_theta_0-6_0-8_W_1-45.jpg|500px]]<br>


0.3 7.5 0.23121 0.03482 0.0881
==cos_theta_pion_CM_Frame_vs_Phi_angle_in_CM_Frame for different W(missing mass) cuts==


0.3 22.5 0.26869 0.06138 0.10488


0.3 127.5 0.8338 0.0946 0.00803


0.3 142.5 0.75189 0.07331 0.01173
{| border="1"  |cellpadding="20" cellspacing="0  
|-
| 1.14<W<1.16 || 1.16<W<1.18 || 1.18<W<1.2 || 1.2<W<1.22 || 1.22<W<1.24
|-
| [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-15.gif|200px]] || [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-17.gif|200px]] || [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-19.gif|200px]] || [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-21.gif|200px]] ||
[[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-23.gif|200px]]
|}<br>


0.3 157.5 0.51962 0.06065 0.01193


0.3 172.5 0.51907 0.05707 0.00719
{| border="1"  |cellpadding="20" cellspacing="0  
|-
| 1.24<W<1.26 || 1.26<W<1.28 || 1.28<W<1.3 || 1.3<W<1.32 || 1.32<W<1.34
|-
| [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-25.gif|200px]] || [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-27.gif|200px]] || [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-29.gif|200px]] || [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-31.gif|200px]] ||
[[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-33.gif|200px]]
|}<br>


0.3 187.5 0.52325 0.0595 0.01046


0.3 202.5 0.62424 0.06558 0.03508
{| border="1"  |cellpadding="20" cellspacing="0  
|-
| 1.34<W<1.36 || 1.36<W<1.38 || 1.38<W<1.4 || 1.4<W<1.42 || 1.42<W<1.44
|-
| [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-35.gif|200px]] || [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-37.gif|200px]] || [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-39.gif|200px]] || [[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-41.gif|200px]] ||
[[Image:cos_theta_of_pion_CM_Frame_vs_phi_angle_in_CM_Frame_W_1-43.gif|200px]]
|}<br>


0.3 217.5 0.7166 0.07414 0.01469
==Phi_angle_in_CM_Frame for 1.44<W<1.46==


0.3 232.5 0.88201 0.08297 0.00386


0.3 247.5 0.93528 0.10613 0.02175
{| border="1"  |cellpadding="20" cellspacing="0
|-
| <math>0.8<cos\theta_{pion}^{CM}<1</math> || <math>0.6<cos\theta_{pion}^{CM}<0.8</math> || <math>0.4<cos\theta_{pion}^{CM}<0.6</math> || <math>0.2<cos\theta_{pion}^{CM}<0.4</math> || <math>0<cos\theta_{pion}^{CM}<0.2</math>
|-
| [[Image:phi_angle_in_CM_Frame_cos_theta_0-8_1_W_1-45.gif|200px]] || [[Image:phi_angle_in_CM_Frame_cos_theta_0-6_0-8_W_1-45.gif|200px]] || [[Image:phi_angle_in_CM_Frame_cos_theta_0-4_0-6_W_1-45.gif|200px]] || [[Image:phi_angle_in_CM_Frame_cos_theta_0-2_0-4_W_1-45.gif|200px]] ||
[[Image:phi_angle_in_CM_Frame_cos_theta_0_0-2_W_1-45.gif|200px]]
|}<br>


0.3 337.5 0.25797 0.05635 0.13169


0.3 352.5 0.14197 0.02875 0.0614
{| border="1"  |cellpadding="20" cellspacing="0
|-
| <math>-0.8>cos\theta_{pion}^{CM}>-1</math> || <math>-0.6>cos\theta_{pion}^{CM}>-0.8</math> || <math>-0.4>cos\theta_{pion}^{CM}>-0.6</math> || <math>-0.2>cos\theta_{pion}^{CM}>-0.4</math> || <math>0>cos\theta_{pion}^{CM}>-0.2</math>
|-
| [[Image:phi_angle_in_CM_Frame_cos_theta_-0-8_-1_W_1-45.gif|200px]] || [[Image:phi_angle_in_CM_Frame_cos_theta_-0-6_-0-8_W_1-45.gif|200px]] || [[Image:phi_angle_in_CM_Frame_cos_theta_-0-4_-0-6_W_1-45.gif|200px]] || [[Image:phi_angle_in_CM_Frame_cos_theta_-0-2_-0-4_W_1-45.gif|200px]] ||
[[Image:phi_angle_in_CM_Frame_cos_theta_0_-0-2_W_1-45.gif|200px]]
|}<br>


0.5 7.5 0.179 0.02725 0.00658
==Phi_angle_CM_Frame_vs_Relative_Rate for Missing Mass equal to 1.45 GeV==


0.5 22.5 0.30852 0.04432 0.03407
{| border="1"  |cellpadding="20" cellspacing="0
|-
| <math>0.8<cos\theta_{pion}^{CM}<1</math> || <math>0.6<cos\theta_{pion}^{CM}<0.8</math> || <math>0.4<cos\theta_{pion}^{CM}<0.6</math> || <math>0.2<cos\theta_{pion}^{CM}<0.4</math> || <math>0<cos\theta_{pion}^{CM}<0.2</math>
|-
| [[Image:phi_angle_in_CM_Frame_vs_Relative_Rate_cos_theta_0-8_1_W_1-45.jpg|200px]] || [[Image:phi_angle_in_CM_Frame_vs_Relative_Rate_cos_theta_0-6_0-8_W_1-45.jpg|200px]] || [[Image:phi_angle_in_CM_Frame_vs_Relative_Rate_cos_theta_0-4_0-6_W_1-45.jpg|200px]] || [[Image:phi_angle_in_CM_Frame_vs_Relative_Rate_cos_theta_0-2_0-4_W_1-45.jpg|200px]] ||
[[Image:phi_angle_in_CM_Frame_vs_Relative_Rate_cos_theta_0_0-2_W_1-45.jpg|200px]]
|}<br>


0.5 37.5 0.5206 0.07215 0.01749


0.5 97.5 1.12986 0.08825 0.01938
{| border="1"  |cellpadding="20" cellspacing="0
|-
| <math>-0.6>cos\theta_{pion}^{CM}>-0.8</math> || <math>-0.4>cos\theta_{pion}^{CM}>-0.6</math> || <math>-0.2>cos\theta_{pion}^{CM}>-0.4</math> || <math>0>cos\theta_{pion}^{CM}>-0.2</math>
|-
|[[Image:phi_angle_in_CM_Frame_vs_Relative_Rate_cos_theta_-0-6_-0-8_W_1-45.jpg|200px]] || [[Image:phi_angle_in_CM_Frame_vs_Relative_Rate_cos_theta_-0-4_-0-6_W_1-45.jpg|200px]] || [[Image:phi_angle_in_CM_Frame_vs_Relative_Rate_cos_theta_-0-2_-0-4_W_1-45.jpg|200px]] ||
[[Image:phi_angle_in_CM_Frame_vs_Relative_Rate_cos_theta_0_-0-2_W_1-45.jpg|200px]]
|}<br>


0.5 112.5 1.09252 0.10256 0.06597
==Pion_theta_angle_in_Lab_Frame_vs_phi_angle_in_CM_Frame==


0.5 127.5 0.9763 0.08506 0.01533
{| border="1"  |cellpadding="20" cellspacing="0  
|-
| electron sector  || pion_theta_angle_vs_phi_angle_in_CM_Frame_before_cuts || pion_theta_angle_vs_phi_angle_in_CM_Frame_after_cuts(EC_inner>0.06, EC_tot/p>0.2, nphe>2.5, <math>0.9<M_x<1.1</math>, <math>1.1<W<1.5</math> ) 
|-
| 1 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_before_cuts_sector_1.gif|300px]] || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_sector_1.gif|300px]]
|-
| 2 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_before_cuts_sector_2.gif|300px]] || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_sector_2.gif|300px]]
|-
| 3 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_before_cuts_sector_3.gif|300px]] || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_sector_3.gif|300px]]
|-
| 4 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_before_cuts_sector_4.gif|300px]] || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_sector_4.gif|300px]]
|-
| 5 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_before_cuts_sector_5.gif|300px]] || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_sector_5.gif|300px]]
|-
| 6 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_before_cuts_sector_6.gif|300px]] || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_sector_6.gif|300px]]
|-
|}<br>


0.5 142.5 0.79077 0.07363 0.00473
0.5 157.5 0.59172 0.06821 0.00877
0.5 172.5 0.58077 0.06074 0.00335
0.5 187.5 0.50715 0.06304 0.00339
0.5 202.5 0.70732 0.07237 0.00357
0.5 217.5 0.88784 0.06989 0.00937
0.5 232.5 0.94631 0.08343 0.01849
0.5 247.5 1.00856 0.10138 0.0134
0.5 262.5 1.10049 0.10723 0.02199
0.5 292.5 1.03853 0.12326 0.02233
0.5 307.5 0.79737 0.09255 0.02999
0.5 322.5 0.47804 0.05456 0.06938
0.5 337.5 0.22268 0.0358 0.01679
0.5 352.5 0.1918 0.02612 0.00524
0.7 7.5 0.30337 0.0306 0.00398
0.7 22.5 0.30258 0.03349 0.00667
0.7 37.5 0.46911 0.04764 0.01997
0.7 52.5 0.57902 0.063 0.00552
0.7 67.5 0.97887 0.08763 0.00523
0.7 82.5 1.03443 0.08417 0.03062
0.7 97.5 1.17882 0.09053 0.00646
0.7 112.5 0.77904 0.07607 0.00368
0.7 127.5 0.82434 0.07262 0.00653
0.7 142.5 0.59427 0.06226 0.03665
0.7 157.5 0.74611 0.06865 0.02487
0.7 172.5 0.66586 0.07026 0.0199
0.7 187.5 0.69131 0.066 0.02584
0.7 202.5 0.68681 0.06741 0.04256
0.7 217.5 0.86021 0.07673 0.00771
0.7 232.5 0.71823 0.06485 0.00523
0.7 247.5 1.01875 0.07804 0.01166
0.7 262.5 0.96511 0.08223 0.01259
0.7 277.5 0.88611 0.07973 0.00523
0.7 292.5 0.78151 0.0745 0.02159
0.7 307.5 0.567 0.05758 0.0221
0.7 322.5 0.54127 0.0554 0.01185
0.7 337.5 0.29805 0.03881 0.00821
0.7 352.5 0.31606 0.03496 0.02255
0.9 7.5 0.46812 0.04844 0.00794
0.9 22.5 0.43017 0.04467 0.0078
0.9 37.5 0.52086 0.05095 0.00808
0.9 52.5 0.46469 0.04821 0.00821
0.9 67.5 0.72754 0.06163 0.00574
0.9 82.5 0.74611 0.0728 0.00751
0.9 97.5 0.83247 0.06562 0.01103
0.9 112.5 0.66814 0.06182 0.00379
0.9 127.5 0.86453 0.06943 0.00463
0.9 142.5 0.62351 0.06141 0.00539
0.9 157.5 0.67536 0.06566 0.01181
0.9 172.5 0.7917 0.07021 0.00883
0.9 187.5 0.67283 0.06538 0.00671
0.9 202.5 0.69394 0.06482 0.01046
0.9 217.5 0.93148 0.07572 0.01137
0.9 232.5 0.85828 0.07093 0.011
0.9 247.5 0.92765 0.07794 0.00996
0.9 262.5 0.82349 0.07194 0.00628
0.9 277.5 0.78016 0.06459 0.01851
0.9 292.5 0.70836 0.06817 0.01541
0.9 307.5 0.60915 0.05905 0.01231
0.9 322.5 0.49794 0.04657 0.00566
0.9 337.5 0.4766 0.05517 0.00839
0.9 352.5 0.74038 0.0689 0.01111


{| border="1"  |cellpadding="20" cellspacing="0
|-
| pion sector  || pion_theta_angle_vs_phi_angle_in_CM_Frame_after_cuts(EC_inner>0.06, EC_tot/p>0.2, nphe>2.5, <math>0.9<M_x<1.1</math>, <math>1.1<W<1.5</math> ) 
|-
| 1 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_pion_sector_1.gif|300px]]
|-
| 2 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_pion_sector_2.gif|300px]]
|-
| 3 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_pion_sector_3.gif|300px]]
|-
| 4 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_pion_sector_4.gif|300px]]
|-
| 5 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_pion_sector_5.gif|300px]]
|-
| 6 || [[Image:pion_theta_angle_vs_phi_angle_in_cm_frame_after_cuts_pion_sector_6.gif|300px]]
|-
|}<br>


[[http://iac.isu.edu/mediawiki/index.php/Analysis Back to Analysis]]
[[http://iac.isu.edu/mediawiki/index.php/Analysis Back to Analysis]]

Latest revision as of 14:21, 13 August 2008

EC_total, [math]\displaystyle{ cos\theta_{pion}^{CM} }[/math] vs [math]\displaystyle{ \phi_{diff}^{CM} }[/math], missing mass, [math]\displaystyle{ \theta_{e} }[/math] vs [math]\displaystyle{ \phi_{e} }[/math]

Electron Momentum vs EC_total


Missing Mass

[math]\displaystyle{ \theta_{e}^{LAB} }[/math] vs [math]\displaystyle{ \phi_{e}^{LAB} }[/math]



[1]

Phi lab [math]\displaystyle{ \varphi^{LAB} }[/math]

The angle is (0, 360).


electron sector [math]\displaystyle{ \varphi_{e}^{LAB} }[/math] [math]\displaystyle{ \varphi_{pion}^{LAB} }[/math] [math]\displaystyle{ \varphi_{e}^{LAB} - \varphi_{pion}^{LAB} }[/math] after correction
1
2
3
4
5
6


Phi CM [math]\displaystyle{ \varphi^{CM} }[/math]

The phi angle after rotation and transformation to the CM frame

electron sector [math]\displaystyle{ \varphi_{e}^{CM} }[/math] [math]\displaystyle{ \varphi_{pion}^{CM} }[/math]
1
2
3
4
5
6





[2]





Phi_angle_in_CM_Frame for different [math]\displaystyle{ cos\theta_{pion}^{CM} }[/math] cuts

Used 1735 files. The following cuts are applied: [math]\displaystyle{ 0.9<M_x<1.1 }[/math], [math]\displaystyle{ 1.1<W<1.5 }[/math] and EC cuts.

Insert plot of M_x and W to show cuts



Then insert phi -vs- theta
NH3 target N15 and C12 target



[math]\displaystyle{ 0.8<cos\theta_{pion}^{CM}<1 }[/math] [math]\displaystyle{ 0.6<cos\theta_{pion}^{CM}<0.8 }[/math] [math]\displaystyle{ 0.4<cos\theta_{pion}^{CM}<0.6 }[/math] [math]\displaystyle{ 0.2<cos\theta_{pion}^{CM}<0.4 }[/math] [math]\displaystyle{ 0<cos\theta_{pion}^{CM}<0.2 }[/math]



[math]\displaystyle{ -0.8>cos\theta_{pion}^{CM}>-1 }[/math] [math]\displaystyle{ -0.6>cos\theta_{pion}^{CM}>-0.8 }[/math] [math]\displaystyle{ -0.4>cos\theta_{pion}^{CM}>-0.6 }[/math] [math]\displaystyle{ -0.2>cos\theta_{pion}^{CM}>-0.4 }[/math] [math]\displaystyle{ 0>cos\theta_{pion}^{CM}>-0.2 }[/math]




Cuts: EC_inner>0.06, EC_tot/p>0.2, nphe>2.5, [math]\displaystyle{ 0.9<M_x<1.1 }[/math], [math]\displaystyle{ 1.1<W<1.5 }[/math] and [math]\displaystyle{ 0.6<cos\theta_{pion}^{CM}<0.8 }[/math].
[3]


Cuts: EC_inner>0.06, EC_tot/p>0.2, nphe>2.5, [math]\displaystyle{ 0.9<M_x<1.1 }[/math], [math]\displaystyle{ 1.44<W<1.46 }[/math] and [math]\displaystyle{ 0.6<cos\theta_{pion}^{CM}<0.8 }[/math].
[4]

cos_theta_pion_CM_Frame_vs_Phi_angle_in_CM_Frame for different W(missing mass) cuts

1.14<W<1.16 1.16<W<1.18 1.18<W<1.2 1.2<W<1.22 1.22<W<1.24



1.24<W<1.26 1.26<W<1.28 1.28<W<1.3 1.3<W<1.32 1.32<W<1.34



1.34<W<1.36 1.36<W<1.38 1.38<W<1.4 1.4<W<1.42 1.42<W<1.44


Phi_angle_in_CM_Frame for 1.44<W<1.46

[math]\displaystyle{ 0.8<cos\theta_{pion}^{CM}<1 }[/math] [math]\displaystyle{ 0.6<cos\theta_{pion}^{CM}<0.8 }[/math] [math]\displaystyle{ 0.4<cos\theta_{pion}^{CM}<0.6 }[/math] [math]\displaystyle{ 0.2<cos\theta_{pion}^{CM}<0.4 }[/math] [math]\displaystyle{ 0<cos\theta_{pion}^{CM}<0.2 }[/math]



[math]\displaystyle{ -0.8>cos\theta_{pion}^{CM}>-1 }[/math] [math]\displaystyle{ -0.6>cos\theta_{pion}^{CM}>-0.8 }[/math] [math]\displaystyle{ -0.4>cos\theta_{pion}^{CM}>-0.6 }[/math] [math]\displaystyle{ -0.2>cos\theta_{pion}^{CM}>-0.4 }[/math] [math]\displaystyle{ 0>cos\theta_{pion}^{CM}>-0.2 }[/math]


Phi_angle_CM_Frame_vs_Relative_Rate for Missing Mass equal to 1.45 GeV

[math]\displaystyle{ 0.8<cos\theta_{pion}^{CM}<1 }[/math] [math]\displaystyle{ 0.6<cos\theta_{pion}^{CM}<0.8 }[/math] [math]\displaystyle{ 0.4<cos\theta_{pion}^{CM}<0.6 }[/math] [math]\displaystyle{ 0.2<cos\theta_{pion}^{CM}<0.4 }[/math] [math]\displaystyle{ 0<cos\theta_{pion}^{CM}<0.2 }[/math]



[math]\displaystyle{ -0.6>cos\theta_{pion}^{CM}>-0.8 }[/math] [math]\displaystyle{ -0.4>cos\theta_{pion}^{CM}>-0.6 }[/math] [math]\displaystyle{ -0.2>cos\theta_{pion}^{CM}>-0.4 }[/math] [math]\displaystyle{ 0>cos\theta_{pion}^{CM}>-0.2 }[/math]


Pion_theta_angle_in_Lab_Frame_vs_phi_angle_in_CM_Frame

electron sector pion_theta_angle_vs_phi_angle_in_CM_Frame_before_cuts pion_theta_angle_vs_phi_angle_in_CM_Frame_after_cuts(EC_inner>0.06, EC_tot/p>0.2, nphe>2.5, [math]\displaystyle{ 0.9<M_x<1.1 }[/math], [math]\displaystyle{ 1.1<W<1.5 }[/math] )
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pion sector pion_theta_angle_vs_phi_angle_in_CM_Frame_after_cuts(EC_inner>0.06, EC_tot/p>0.2, nphe>2.5, [math]\displaystyle{ 0.9<M_x<1.1 }[/math], [math]\displaystyle{ 1.1<W<1.5 }[/math] )
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