Latest revision as of 10:58, 19 September 2008

Quality Checks

Run Summary Table

The table below uses a characteristic DST file to try and estimate the sample size for a semi-inclusive analysis of pion electroproduction. The column marked "cuts" below indicates the number of events kept when the standard EC based electron identification cuts, described above, are used: [math]EC_{tot}\gt 0.2*p [/math] and
[math] EC_{inner}\gt 0.08*p[/math]. The next step will be to compare unpolarized pion production rates in order to evaluate the CLAS detectors efficiencies for measuring charged pions with different torus polarities. The question is whether you get the same rates for negatively charged pions in one torus polarity to positively charged pions using the opposite torus polarity.

Beam Energy	Torus Current	Target	Begin Run	End Run	file used	# trig([math]10^6[/math])	events remaining after [math]e^-[/math] cuts(%)	expected # evts([math]10^6[/math])	events remaining after [math]e^-[/math] and [math]\pi^+[/math] cuts(%)	expected # evts([math]10^6[/math])	events remaining after [math]e^-[/math] and [math]\pi^-[/math] cuts(%)	expected # evts([math]10^6[/math])
4239	2250	NH3	28205	28277	/cache/mss/home/nguler/dst/dst28205_05.B00	1108.72	60.8	674.1	8.3	92.02	3.24	35.92
		ND3	28074	28190	/cache/mss/home/nguler/dst/dst28187_05.B00	1117.87	59.6	666.25	7.99	89.32	3.3	36.9
	-2250	NH3	28407	28479	/cache/mss/home/nguler/dst/dst28409_05.B00	1013.57	24.2	245.28	0.12	1.22	0	0
		ND3	28278	28403	/cache/mss/home/nguler/dst/dst28400_05.B00	1556.04	23.9	371.89	0.02	0.31	0.05	0.51
5735	2250	NH3	27074	27195	/cache/mss/home/nguler/dst/dst27095_05.B00	1442.25	57.7	832.18	9.3	134.13	3.8	59.13
		ND3	27116	27170	/cache/mss/home/nguler/dst/dst27141_05.B00	624.55	59.1	369.10	9.53	59.52	3.9	24.36
	-2250	NH3	26911	27015	/cache/mss/home/nguler/dst/dst26988_05.B00	900.93	80.7	727.05	7.14	64.33	9.9	89.19
		ND3	27022	27068	/cache/mss/home/nguler/dst/dst27055_05.B00	711.53	80	569.22	6.97	49.59	10.1	71.86

Rates

Unpolarized Pion electroproduction

Rates from other experiments in our Kinematic range

Center of Mass Frame Transformation

We have proton and electron. In the Lab frame electron is moving along the x-axis with momentum ;[math]\vec{p_e}[/math] and proton is at rest. The 4-vectors are:

Lab Frame: [math]P_e=[/math]([math]E_e[/math],[math]p_e[/math],0,0) and for proton :[math]P_p=[/math]([math]m_p[/math],0,0,0)
CM Frame: :[math]{P_e}^{\prime}=[/math]([math]{E_e}^{\prime}[/math],[math]{p_e}^{\prime}[/math],[math]0[/math],[math]0[/math]) and for proton :[math]{P_p}^{\prime}=[/math]([math]{E_p}^{\prime}[/math],[math]{p_p}^{\prime}[/math],[math]0[/math],[math]0[/math])

Find such that

Using the last two equations we will get the following for x component:

Example of the Missing Mass Calculation for the following reaction

: electron mass is neglibible

: Mass of a proton

Electron

Proton

[math]\pi^-[/math]

Missing Mass

Conservation of the 4-momentum gives us following

Solving it for the final proton state

In our case 4-vectors for particles are

[math](P_p)_\mu = (m_p, 0, 0, 0)[/math]

Plug and chug

] [ + - -

[math]M_x = 0.9905547 GeV[/math]

Example of the Missing Mass Calculation for the following reaction

Used file dst27095_05.B00. Target [math]NH_3[/math], Beam Energy 5.735 GeV and Torus Current +2250. Event_number=3106861

: electron mass is negligible

: Mass of a proton

: Mass of a neutron

Electron

Neutron

[math]\pi^+[/math]

Missing Mass Calculation

Below is the conservation of the 4-momentum

Solving it for the final neutron state

The 4-vectors for the particles in this event

[math](P_p)_\mu = (m_p, 0, 0, 0)[/math]

] [ + - -

[math]M_x = 0.9395344 GeV[/math]

Missing_Mass(experimental data)

The mean value of the missing mass is around 2.056 GeV.

[math]\phi[/math] angle

[math]\phi[/math] angle for electrons and pions ([math]\pi^+[/math]) in lab frame [math]\phi_{e^-}^{LAB}[/math], [math]\phi_{\pi^+}^{LAB}[/math]

Electron fiducial cut at electron momentum range : 2.15 < < 2.53 GeV for sector 1. The histograms on the right show the < distributions at two values of . The highlighted area in the center indicates the selected fiducial range. [1]

[2]

Phi angles

Below is shown histograms before changing angles by sectors for pions and electrons.

ELECTRON SECTOR vs ELECTRON [math]\phi[/math] ANGLE
dst27095_05.B00, B>0, target material NH3, Target Polarization (78.19) and Beam energy 5.7 GeV	dst26988_05.B00, B<0, target material NH3, Target Polarization (-67.82) and Beam energy 5.7 GeV	dst27109_05.B00, B>0, target material NH3, Target Polarization (-69.81) and Beam energy 5.7 GeV

[math]\phi[/math] ANGLE DISTRIBUTION FOR ELECTRONS AND PIONS(in each event we have just two particles eelctron and positive pion), FILE dst27095_05
ELECTRONS	PIONS(prt_id=4)

SECTOR_VS_[math]\phi[/math] FOR ELECTRONS AND PIONS, FILE dst27095_05
ELECTRONS	PIONS(prt_id=4)

Graph [math]\phi_{\pi}^{CM}[/math] for Pions hitting paddle #7.  The y-axis should be pion counting rate in units of pions per nanCoulomb.

[math]\phi[/math] angle in the Center of Mass Frame

The variables below are in Lab Frame:

From from CLAS

Kinematics of single electroproduction

From the above picture we can write down the momentum x,y and z components for pion in terms of angle and total momentum.

where [math]{p_{\pi x}}^{LAB}[/math] and [math]{p_{\pi y}}^{LAB}[/math] are the x and y components of the pion momentum.

[math](P_e)^{\mu}[/math] - Initial electron 4-momentum
[math](P_N)^{\mu}[/math] - Target Nucleon 4-momentum
[math](P_e^{\prime})^{ \mu}[/math] - Scattered electron 4-momentum
[math](P_h)^{\mu}[/math] - Hadron final state 4-momentum
[math](P_m)^{\mu}[/math] - Meson final state 4-momentum

[math]h=n[/math], [math]m=\pi^+[/math] for

In Inclusive

Then The Missing Mass [math]W = (E_x ^2 - p_x ^2)[/math]

In Exclusive

Then Missing Mass [math] M = (E_h ^2 - p_h ^2)[/math]

Conservation of 4-momentum gives

[math]q^\mu[/math] - 4-momentum of the exchanged virtual photon([math]\gamma[/math])

axis rotation

First the coordinate system is rotated around z-axis by [math]\phi_{\gamma}[/math] angle and then around y-axis by [math]\theta_x[/math] angle. Below is presented the transformation matrix.

Phi rate

|[3]Differential cross section vs in the region at fixed for different bins in

phi angle in cm frame for different runs

 start calculating cross -section

Luminosity Calculation for NH3(Ammonia) target

The target materials are located in the target cells. They are made out of polychlorotrifluoroethylene with a thickness of 0.2 mm. The cells itself are in diameter 15 (15.7) mm and in length 10 (12.7) mm, with 0.025 mm aluminum entrance windows and 0.05 mm kapton exit windows. [4]

Media:fill.factor.ps NH3 Filling Factor Evaluation, R. De Vita, July 1999

[5]

Avogadro Number:

For file dst27095_05.B00 beam current is

electrons per second

counts on Faraday cup.[6]

The luminosity of the continuous electron beam was [math]10^{34}[/math] [math]cm^{-2} sec^{-1}[/math] [7] [8]

Cross Section Calculation

Media:cross_sections_1.pdf

where

is the Luminosity.

is the number of interactions.

is the total cross section.

is the differential solid angle.

is the differential cross section.

Pion Rates -vs- Paddle for opposite sign Torus fields

using all events in which the first particle (the one which caused the trigger) is defined as an electrons and passes the

above electron cuts.

sc_paddle vs X_bjorken 5.7 GeV Beam Energy

no cuts	cuts	cuts
Electrons	B > 0	B<0

[math]\pi^-[/math]	B > 0	B<0

[math]\pi^+[/math]	B > 0	B<0

sc_paddle vs X_bjorken with cuts 5.7 GeV Beam Energy(number of events=2)

[math]\pi^-[/math]	[math]\pi^-[/math]
B>0	B<0

[math]\pi^+[/math]	[math]\pi^+[/math]
B>0	B<0

sc_paddle vs Momentum 5.7 GeV Beam Energy

There is a curvature problem.  When B > 0 then I expect the high momentum electrons to hit the lower
paddle numbers   (inbending).   I can see this when I look at the B>0 plot for electrons with cuts.  
When B < 0 then the electrons  are bending outwards which makes me expect the the higher momentum
electrons will high the higher numbered paddles.  I do not see this for B>0 with electron cuts.

no cuts	cuts	cuts
Electons	B > 0	B<0

[math]\pi^-[/math]	B > 0	B<0

[math]\pi^+[/math]	B > 0	B<0

sc_paddle vs Momentum with cuts 5.7 GeV Beam Energy(number of events=2)

[math]\pi^-[/math]	[math]\pi^-[/math]
B>0	B<0

[math]\pi^+[/math]	[math]\pi^+[/math]
B>0	B<0

Used file dst26988_05.B00(Energy=5.7GeV and Torus=-2250)

Paddle 7 Rates and statistics

The number of events per trigger is measured for the respective DST file above and then the Total number events in the data set is estimated from that.

[math]X_{bj}[/math]	[math]\pi^-[/math](B>0)		[math]\pi^+[/math](B<0)
	Total Number Events [math](10^{3})[/math]	Number events per [math]10^6[/math] triggers	Total Number Events [math](10^{3})[/math]	Number events per [math]10^6[/math] trigger
0.1	5.1	71	24.6	547
0.2	6.9	96	13.7	305
0.3	3.7	51	6.2	137
0.4	3.3	45	2.7	60
0.5	0.9	13	0.99	22

Paddle 17 Rates and statistics

[math]X_{bj}[/math]	[math]\pi^-[/math](B<0)		[math]\pi^+[/math](B>0)
	Total Number Events [math](10^{3})[/math]	Number events per [math]10^{6}[/math] trigger	Total Number Events [math](10^{3})[/math]	Number events per [math]10^{6}[/math] trigger
0.1	6.2	137	4.6	64
0.2	3.5	79	4.9	67
0.3	1.7	39	2.6	36
0.4	0.3	7	2.1	29
0.5	0.1	2	0.6	8

Paddle 5 and 8 Rates and statistics for electrons

[math]X_{bj}[/math]	[math]e^-[/math] sc_paddle=5 (B>0)		[math]e^-[/math] sc_paddle=8 (B<0)
	Total Number Events [math](10^{3})[/math]	Number events per [math]10^{6}[/math] trigger [math](10^{3})[/math]	Total Number Events [math](10^{3})[/math]	Number events per [math]10^{6}[/math] trigger [math](10^{4})[/math]
0.1	384.9	5.314	1665.2	3.706
0.2	382.5	5.282	977.8	2.176
0.3	264.9	3.657	567.1	1.262
0.4	159.5	2.202	328.6	0.7313
0.5	99	1.367	218.2	0.4856

Histograms for 5.7 GeV Beam Energy

Electron energy/momentum	Electron Theta ([math]\theta[/math])	Electron Qsqrd	Electron X_bjorken
B>0 and sc_paddle=5

B<0 and sc_paddle=8

Normalized X_bjorken for electrons

B>0 and sc_paddle=5	B<0 and sc_paddle=8

Asymmetries

Systematic Errors

Media:SebastianSysErrIncl.pdf Sebastian's Writeup

[Back to Analysis]

Difference between revisions of "Quality Checks"

Latest revision as of 10:58, 19 September 2008

Contents

Quality Checks

Run Summary Table

Rates

Unpolarized Pion electroproduction

Rates from other experiments in our Kinematic range

Center of Mass Frame Transformation

Example of the Missing Mass Calculation for the following reaction

Example of the Missing Mass Calculation for the following reaction

Missing_Mass(experimental data)

[math]\phi[/math] angle

[math]\phi[/math] angle for electrons and pions ([math]\pi^+[/math]) in lab frame [math]\phi_{e^-}^{LAB}[/math], [math]\phi_{\pi^+}^{LAB}[/math]

Phi angles

[math]\phi[/math] angle in the Center of Mass Frame

axis rotation

Phi rate

Luminosity Calculation for NH3(Ammonia) target

Pion Rates -vs- Paddle for opposite sign Torus fields

sc_paddle vs X_bjorken 5.7 GeV Beam Energy

sc_paddle vs X_bjorken with cuts 5.7 GeV Beam Energy(number of events=2)

sc_paddle vs Momentum 5.7 GeV Beam Energy

sc_paddle vs Momentum with cuts 5.7 GeV Beam Energy(number of events=2)

Paddle 7 Rates and statistics

Paddle 17 Rates and statistics

Paddle 5 and 8 Rates and statistics for electrons

Histograms for 5.7 GeV Beam Energy

Normalized X_bjorken for electrons

Asymmetries

Systematic Errors

Navigation menu

Search

@@ Line 152: / Line 152: @@
 <math>\phi_{diff}^{LAB} = \phi_e^{LAB} - \phi_{\pi^+}^{LAB} = (120 + 35.3) -26.4 = 128.9</math>
-=====<math>{\phi_{\pi}}^{CM}</math> transformation from LAB frame to CM frame=====
-Used file dst27095_05, event_number=3106861<br>
-[[Image:file_dst27095_event_number_3106861_phi_gamma_theta_x_and_phi_pi_angles_in_cm_frame.jpg|400px]]
-:<math>\beta_{cm} = \frac{5.736}{6.674} = 0.859 < 1</math><br>
-:<math>\gamma_{cm} = \frac{1}{\sqrt{1 - \beta_{cm}^2}} = \frac{1}{\sqrt{1 - 0.859^2}} = 1.9559</math><br>
-:<math>E_e = \sqrt{{p_e}^2 + {m_e}^2} = \sqrt{0.8769^2 + 0.117^2 + 2.56842^2} = 2.7165</math><br>
-;Calculation of <math>{{\phi}_{\gamma}}^{CM}</math>
-:<math>{\phi_{\gamma}}^{CM} = tan^{-1}(\frac{{p_{e z}}^{CM}}{{p_{e z}}^{ CM \prime}})</math><br>
-:<math>{p_{e z}}^{CM} = -\gamma_{CM} \beta_{CM}{p_{e z}}^{LAB} + \gamma_{CM} {p_{e z}}^{LAB} = </math><br>
-::<math> = -1.9559 \times 0.8594 \times 5.736 + 1.9559 \times 5.736 = 1.5773 </math><br>
-:<math>{p_{e z}}^{CM \prime} = -\gamma_{CM} \beta_{CM} E_e + \gamma_{CM} {p_{e z}}^{LAB \prime} = </math><br>
-::<math>= -1.9559 \times 0.8594 \times 2.7165 + 1.9559 \times 2.5684 = 0.4574 </math><br>
-:<math>\phi_{\gamma} = tan^{-1}(\frac{1.5773}{0.4574}) = 73.83  </math><br>
-;Calculation of <math>{\theta_x}^{CM}</math>
-:<math>{\theta_x}^{CM} = cos^{-1}(\frac{p_{e z}^{CM \prime} - {p_{e z}}^{CM}}{\sqrt{{p_{e x}^{CM \prime}}^2 + {p_{e y}^{CM \prime}}^2 + ({p_{e z}^{CM \prime} - {p_{e z}}^{CM}})^2}}) = </math><br>
-::<math> = cos^{-1}(\frac{0.4574 - 1.5773}{\sqrt{0.8769^2 + (-0.117)^2 + (0.4574 - 1.5773)^2}}) = 141.69 </math><br>
-;Calculation of <math>{\phi_{\pi}}^{CM}</math>
-:<math>E_{\pi} = \sqrt{{p_{\pi}}^2 + {m_{\pi}}^2} = </math><br>
-::<math> = \sqrt{(-0.6918)^2 + 0.8242^2 + 2.0764^2 + 0.13969^2} = 2.3428 </math><br>
-:<math>{p_{\pi z}}^{CM} = -\gamma_{CM} \beta_{CM} E_{\pi} + \gamma_{CM} {p_{\pi z}}^{LAB} = </math><br>
-::<math>= -1.9559 \times 0.8594 \times 2.3428 + 1.9559 \times 2.0764 = 0.1232 </math><br>
-:<math>{\phi}_{\pi}^{CM} = tan^{-1}(\frac{{p_{\pi y}}^{CM \prime}}{{p_{\pi x}}^{CM \prime}}) = </math><br>
-::<math> = tan^{-1}(\frac{-sin{{\phi}_{\gamma}} \times p_{\pi x}^{CM} + cos{{\phi}_{\gamma}} \times p_{\pi y}^{CM}}{sin{\theta_x}\times(cos{{\phi}_{\gamma}} \times p_{\pi x}^{CM} + sin{{\phi}_{\gamma}} \times p_{\pi y}^{CM}) + cos{\theta_x} \times p_{\pi z}^{CM}}) = </math><br>
-::<math> = tan^{-1}(\frac{-sin(73.83) \times (-0.6918) + cos(73.83) \times 0.8242}{sin(141.69)\times(cos(73.83) \times (-0.6918) + sin(73.83) \times 0.8242) + cos(141.69) \times 0.1232} = 72.92 </math><br>
 =====Missing_Mass(experimental data)=====
@@ Line 214: / Line 163: @@
 ====== <math>\phi</math> angle for electrons and pions (<math>\pi^+</math>) in lab frame <math>\phi_{e^-}^{LAB}</math>, <math>\phi_{\pi^+}^{LAB}</math>======
-Used file is dst27095_05.B00.Target material is <math>NH_3</math>, Torus +2250 and beam energy 5.7 GeV<br>
+{| border="0" style="background:transparent;"
-{|border="2" colspan = "4"
-!For Electrons <math>e^-</math> with cuts (e_p<3, <math>EC_{tot}>0.2p</math>, <math>EC_{inner}>0.08p</math>, nphe>2.5 and sc_paddle=7) ||For Pions(<math>\pi^+</math>) with cuts for sc_paddle=7
 |-
-|| [[Image:the_absolute_phi_angle_for_electrons_in_lab_frame_with_all_cuts_applied_used_file_dst27095.gif|400px]]
+|
-|| [[Image:the_absolute_phi_angle_for_pions_in_lab_frame_with_all_cuts_applied_used_file_dst27095.gif|400px]]
+[[Image:theta_e_vs_phi_e_and_phi_e_distributions_at_two_values_of_theta_e.jpg|400px x 80px|thumb|Electron fiducial cut at electron momentum range : 2.15 < <math>p_e</math> < 2.53 GeV for sector 1. The histograms on the right show the < <math>\phi_e</math> distributions at two values of <math>\theta_e</math>. The highlighted area in the center indicates the selected fiducial range. [http://arxiv.org/abs/0709.1946] ]]
 |}<br>
-{|border="2"
+[http://www.jlab.org/Hall-B/secure/eg1/alex/AnalysisEG1_AS.html]
-|-
-! colspan="3" | For Electrons with cuts (e_p<3, <math>EC_{tot}>0.2p</math>, <math>EC_{inner}>0.08p</math>, nphe>2.5 and sc_paddle=7)
+====== Phi angles ======
-|-
+Below is shown histograms before changing angles by sectors for pions and electrons.<br>
-! SECTOR 1 || SECTOR 2 || SECTOR 3
+[[Image:e_sector_vs_e_phi_angle_without_cuts_before_change_file_dst27095.gif|350px]]
-|-
+[[Image:pion_sector_vs_pion_phi_angle_without_cuts_before_changing_phi_angles_by_sector_file_dst27095.gif|350px]]
-|| [[Image:electron_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_1_file_dst27095.gif|200px]]
-|| [[Image:electron_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_2_file_dst27095.gif|200px]]
+{|border="2" colspan = "4"
-|| [[Image:electron_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_3_file_dst27095.gif|200px]]
+! colspan="3" |ELECTRON SECTOR vs ELECTRON <math>\phi</math> ANGLE
 |-
-! SECTOR 4 || SECTOR 5 || SECTOR 6
+!dst27095_05.B00, B>0, target material NH3, Target Polarization (78.19) and Beam energy 5.7 GeV ||dst26988_05.B00, B<0, target material NH3, Target Polarization (-67.82) and Beam energy 5.7 GeV||dst27109_05.B00, B>0, target material NH3, Target Polarization (-69.81) and Beam energy 5.7 GeV
 |-
-|| [[Image:electron_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_4_file_dst27095.gif|200px]]
+|| [[Image:e_sector_vs_e_phi_angle_positive_torus_after_change_file_dst27095_without_cuts.gif|300px]]
-|| [[Image:electron_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_5_file_dst27095.gif|200px]]
+||  [[Image:e_sector_vs_e_phi_angle_negative_torus_file_dst27095_without_cuts.gif|300px]]
-|| [[Image:electron_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_6_file_dst27095.gif|200px]]
+||
+[[Image:e_sector_vs_e_phi_angle_positive_torus_file_dst27109_without_cuts.gif|300px]]
 |}<br>
-{|border="2"
+{|border="2" colspan = "4"
+! colspan="2" |<math>\phi</math> ANGLE DISTRIBUTION FOR ELECTRONS AND PIONS(in each event we have just two particles eelctron and positive pion), FILE dst27095_05
 |-
-! colspan="3" | For pions(<math>\pi^+</math>) with cuts for sc_paddle=7
+!ELECTRONS||PIONS(prt_id=4)
 |-
-! SECTOR 1 || SECTOR 2 || SECTOR 3
+|| [[Image:electron_phi_angle_without_cuts_in_Lab_Frame_file_dst27095.gif|300px]]
-|-
+|| [[Image:pion_phi_angle_without_cuts_in_Lab_Frame_file_dst27095.gif|300px]]
-|| [[Image:pions_plus_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_1_file_dst27095.gif|200px]]
-|| [[Image:pions_plus_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_2_file_dst27095.gif|200px]]
-|| [[Image:pions_plus_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_3_file_dst27095.gif|200px]]
-|-
-! SECTOR 4 || SECTOR 5 || SECTOR 6
-|-
-|| [[Image:pions_plus_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_4_file_dst27095.gif|200px]]
-|| [[Image:pions_plus_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_5_file_dst27095.gif|200px]]
-|| [[Image:pions_plus_phi_angle_lab_frame_with_cuts_sc_paddle_7_sector_6_file_dst27095.gif|200px]]
 |}<br>
-The plots below show what happens when you require the nphe from electron to be > 2.5 and you only look for pions in scintillator paddle 7.<br>
- Why is there a big  gap for<math> \phi < 100</math> ?
 {|border="2" colspan = "4"
-||[[Image:phi_angle_difference_cuts_on_electrons_and_pions_no_cuts_on_sc_paddle_and_on_nphe_file_dst27095.gif|300px]]
+! colspan="2" |SECTOR_VS_<math>\phi</math> FOR ELECTRONS AND PIONS, FILE dst27095_05
-||[[Image:phi_angle_difference_cuts_on_electrons_pions_and_nphe_no_cuts_on_sc_paddle_file_dst27095.gif|300px]]
-||[[Image:phi_angle_difference_cuts_on_electrons_pions_and_nphe_no_cuts_on_sc_paddle_file_dst27095_1.gif|300px]]
-|}<br>
- Take a look at theta -vs- phi plots for each sector.  Do the dead spots impact difference?
- Didn't see any big effects.
-[[Image:phi_angle_difference_without_cuts_file_dst27095.gif|400px]]<br>
- Lets try looking at sector distributions
-  plot electron sector number -vs-<math> \phi</math> difference
-[[Image:e_sector_vs_phi_angle_difference_without_cuts_file_dst27095.gif|400px]]<br>
-  plot pion sector number -vs- <math>\phi</math> difference
-[[Image:pion_sector_vs_phi_angle_difference_without_cuts_file_dst27095.gif|400px]]<br>
-  plot <math>\phi</math> difference  with the cure (pion sector # - electron sector #) ==1
-[[Image:phi_angle_difference_when_pion_sector_minus_electron_sector_is_1_file_dst27095.gif|400px]]<br>
-{|border="2"
-|-
-! colspan="3" | e_theta_vs_phi_angle_difference with cuts (e_p<3, <math>EC_{tot}>0.2p</math>, <math>EC_{inner}>0.08p</math>), no cuts on sc_paddle and nphe
-|-
-! SECTOR 1 || SECTOR 2 || SECTOR 3
-|-
-|| [[Image:e_theta_vs_phi_angle_difference_no_cuts_on_sc_paddle_and_on_nphe_sector_1_file_dst27095.gif|200px]]
-|| [[Image:e_theta_vs_phi_angle_difference_no_cuts_on_sc_paddle_and_on_nphe_sector_2_file_dst27095.gif|200px]]
-|| [[Image:e_theta_vs_phi_angle_difference_no_cuts_on_sc_paddle_and_on_nphe_sector_3_file_dst27095.gif|200px]]
 |-
-! SECTOR 4 || SECTOR 5 || SECTOR 6
+!ELECTRONS||PIONS(prt_id=4)
 |-
-|| [[Image:e_theta_vs_phi_angle_difference_no_cuts_on_sc_paddle_and_on_nphe_sector_4_file_dst27095.gif|200px]]
+||[[Image:electron_sector_vs_electron_phi_angle_without_cuts_in_Lab_Frame_file_dst27095.gif|300px]]
-|| [[Image:e_theta_vs_phi_angle_difference_no_cuts_on_sc_paddle_and_on_nphe_sector_5_file_dst27095.gif|200px]]
+|| [[Image:pion_sector_vs_pion_phi_angle_without_cuts_in_Lab_Frame_file_dst27095.gif|300px]]
-|| [[Image:e_theta_vs_phi_angle_difference_no_cuts_on_sc_paddle_and_on_nphe_sector_6_file_dst27095.gif|200px]]
 |}<br>
+[[Image:eelectron_sector_vs_phi_angle_difference_of_electron_and_pion_without_cuts_in_Lab_frame_File_dst27095_05.gif]]<br>
-{|border="2"
+[[Image:eelectron_sector_vs_phi_angle_difference_of_electron_and_pion_without_cuts_in_Lab_frame_File_dst27095_05_after_corrections.gif]]<br>
-|-
-! colspan="3" | For Electrons theta_vs_phi with cuts (e_p<3, <math>EC_{tot}>0.2p</math>, <math>EC_{inner}>0.08p</math>), no cuts on sc_paddle and nphe
-|-
-! SECTOR 1 || SECTOR 2 || SECTOR 3
-|-
-|| [[Image:e_theta_vs_phi_angle_no_cuts_on_sc_paddle_and_on_nphe_sector_1_file_dst27095.gif|200px]]
-|| [[Image:e_theta_vs_phi_angle_no_cuts_on_sc_paddle_and_on_nphe_sector_2_file_dst27095.gif|200px]]
-|| [[Image:e_theta_vs_phi_angle_no_cuts_on_sc_paddle_and_on_nphe_sector_3_file_dst27095.gif|200px]]
-|-
-! SECTOR 4 || SECTOR 5 || SECTOR 6
-|-
-|| [[Image:e_theta_vs_phi_angle_no_cuts_on_sc_paddle_and_on_nphe_sector_4_file_dst27095.gif|200px]]
-|| [[Image:e_theta_vs_phi_angle_no_cuts_on_sc_paddle_and_on_nphe_sector_5_file_dst27095.gif|200px]]
-|| [[Image:e_theta_vs_phi_angle_no_cuts_on_sc_paddle_and_on_nphe_sector_6_file_dst27095.gif|200px]]
-|}<br>
-{| border="0" style="background:transparent;"
-|-
-|
-[[Image:theta_e_vs_phi_e_and_phi_e_distributions_at_two_values_of_theta_e.jpg|400px x 80px|thumb|Electron fiducial cut at electron momentum range : 2.15 < <math>p_e</math> < 2.53 GeV for sector 1. The histograms on the right show the < <math>\phi_e</math> distributions at two values of <math>\theta_e</math>. The highlighted area in the center indicates the selected fiducial range. [http://arxiv.org/abs/0709.1946] ]]
-|}<br>
-[http://www.jlab.org/Hall-B/secure/eg1/alex/AnalysisEG1_AS.html]
   Graph <math>\phi_{\pi}^{CM}</math> for Pions hitting paddle #7.  The y-axis should be pion counting rate in units of pions per nanCoulomb.
@@ Line 385: / Line 270: @@
-<math>\phi_{\gamma} = tan^{-1}(\frac{p_{e x}^{\prime}}{p_{e z}^{\prime}})</math><br>
+<math>\phi_{\gamma} = tan^{-1}(\frac{p_{e y}^{\prime}}{p_{e x}^{\prime}})</math><br>
@@ Line 400: / Line 285: @@
 <math>p_{e z}^{LAB} =  Beam Energy </math><br>
+======axis rotation======
 First the coordinate system is rotated around z-axis by <math>\phi_{\gamma}</math> angle and then around y-axis by <math>\theta_x</math> angle. Below is presented the transformation matrix.<br>
@@ Line 409: / Line 295: @@
-<math>{\phi}_{\pi}^{LAB{\prime}} = tan^{-1}(\frac{{p_{\pi y}}^{LAB{\prime}}}{{p_{\pi x}}^{LAB{\prime}}}) = tan^{-1}(\frac{-sin{\phi_{\gamma}} \times p_{\pi x}^{LAB} + cos{\phi_{\gamma}} \times p_{\pi y}^{LAB}}{sin{\theta_x}\times(cos{\phi_{\gamma}} \times p_{\pi x}^{LAB} + sin{\phi_{\gamma}} \times p_{\pi y}^{LAB}) + cos{\theta_x} \times p_{\pi z}^{LAB}})</math><br>
+<math>{\phi}_{\pi}^{LAB{\prime}} = tan^{-1}(\frac{{p_{\pi y}}^{LAB{\prime}}}{{p_{\pi x}}^{LAB{\prime}}}) = tan^{-1}(\frac{-sin{\phi_{\gamma}} \times p_{\pi x}^{LAB} + cos{\phi_{\gamma}} \times p_{\pi y}^{LAB}}{cos {\theta}_x (cos {\phi_{\gamma}}  p_{\pi x}^{LAB} + sin {\phi_{\gamma}}  p_{\pi y}^{LAB}) - sin {\theta}_x  p_{\pi z}^{LAB}})</math><br>
-<math>{\phi}_{\pi}^{CM} = tan^{-1}(\frac{{p_{\pi y}}^{CM}}{{p_{\pi x}}^{CM}}) = tan^{-1}(\frac{-sin{\phi_{\gamma}} \times p_{\pi x}^{CM} + cos{\phi_{\gamma}} \times p_{\pi y}^{CM}}{sin{\theta_x}\times(cos{\phi_{\gamma}} \times p_{\pi x}^{CM} + sin{\phi_{\gamma}} \times p_{\pi y}^{CM}) + cos{\theta_x} \times p_{\pi z}^{CM}})</math><br>
+<math>{\phi}_{\pi}^{CM} = tan^{-1}(\frac{{p_{\pi y}}^{CM}}{{p_{\pi x}}^{CM}}) = tan^{-1}(\frac{-sin{\phi_{\gamma}} \times p_{\pi x}^{CM} + cos{\phi_{\gamma}} \times p_{\pi y}^{CM}}{cos {\theta}_x (cos {\phi_{\gamma}}  p_{\pi x}^{CM} + sin {\phi_{\gamma}}  p_{\pi y}^{CM}) - sin {\theta}_x  p_{\pi z}^{CM}})</math><br>
@@ Line 423: / Line 309: @@
 ====== Phi rate ======
- Why does the <math>\phi</math> angle only go out to 80 degrees?<br>
+{|border="2" colspan = "4"
+||
+||[[Image:pion_phi_angle_in_cm_frame_vs_differential_cross_section.jpg|400px]] |[http://arxiv.org/abs/0709.1946]Differential cross section vs <math>{\phi_{\pi}}^*</math> in the <math>\Delta(1232)</math> region at fixed <math>cos \theta_{\pi}^* = -0.1</math> for different bins in <math>Q^2</math>
+|}<br>
- Add FC histogram(done)<br>
+[[Image:Q_sqrd_without_cuts_dst27095.gif|300px]]<br>
-[[Image:f_cup_file_dst27095.gif|300px]][[Image:f_cup_integral_file_dst27095.gif|300px]]<br>
+[http://iac.isu.edu/mediawiki/index.php/Phi_angle_in_CM_frame_for_different_runs phi angle in cm frame for different runs]<br>
- Add plot from paper(done),
+  start calculating cross -section
+======Luminosity Calculation for NH3(Ammonia) target ======
+The target materials are located in the target cells. They are made out of polychlorotrifluoroethylene with a thickness of 0.2 mm. The cells itself are in diameter 15 (15.7) mm and in length 10 (12.7) mm, with 0.025 mm aluminum entrance windows and 0.05 mm kapton exit windows. [http://books.google.com/books?id=LEqA4cMrkfIC&pg=PA329&lpg=PA329&dq=target+NH3,+CLAS,+luminosity&source=web&ots=yWZHoDjDDI&sig=yW0oVF1zIQgJZ5yqAMElflnhxsY&hl=en#PPA329,M1]
+[[Media:fill.factor.ps]] NH3 Filling Factor Evaluation, R. De Vita, July 1999<br>
+:<math>L = \frac{i_{scattered}}{\sigma} \sim i_{beam} \rho_{target} l_{target}</math>
+:<math>{\rho}_{ammonia} = 0.971 \frac{g}{cm^3}</math>[http://www.jlab.org/Hall-B/secure/eg1/raffaella/talks/fill_fact/img007.htm]<br>
+:Avogadro Number: <math>N_A = 6.02214 \times\ 10^{23} {mol}^{-1} </math><br>
+:For file dst27095_05.B00 beam current is<br>
+:<math>i_{beam} = 6 nAmp </math><br>
+:<math>1 Amp = 6.242x10^{18}</math> electrons per second<br>
+:<math>L = 6 nAmp \times 0.971 \frac{g}{cm^3} \times l_{target} \times cm =</math>
+::<math>= 6 \times 10^{-9} \times 6.242 \times 10^{18} \times 0.971 \times l_{target} \times \frac{ [\# of electrons]}{[second]} \times \frac{g}{cm^3} \times cm =</math>
+::<math>= 3.6366 \times 10^{10} \times l_{target} \times \frac{[ \# of electrons]}{[second]} \times \frac{g}{cm^2} =</math>
+::<math>= 3.6366 \times 10^{10} \times \frac{1 mol}{17} \times l_{target} \times \frac{[ \# of electrons]}{[second]} \times \frac{1}{cm^2} =</math>
+::<math>= 3.6366 \times 10^{10} \times \frac{6.02214 \times 10^{23}}{17} \times l_{target} \times \frac{[ \# of electrons]}{[second]} \times \frac{1}{cm^2} =</math>
+::<math>= 1.288 \times 10^{33} \times l_{target} \times \frac{[ \# of electrons]}{second \times cm^2}</math>
+::<math>= 1.288 \times 10^{33} \times 1 \times \frac{[ \# of electrons]}{second \times cm^2}</math>
+::<math>= 1.288 \times 10^{33}  \frac{[ \# of electrons]}{second \times cm^2}</math>
+::<math>1 nAmp = 309</math> counts on Faraday cup.[http://www.jlab.org/~claseg1/analysis/eg1b/FC.html]<br>
+::<math> L = 1.288 \times 10^{33} \frac{1572}{309 \times 6} \frac{[ \# of electrons]}{second \times cm^2} =</math>
+::<math>= 1.09209 \times 10^{33} \frac{[ \# of electrons]}{second \times cm^2}</math><br>
-{|border="2" colspan = "4"
+::<math>= 1.09209 \times 30 \times 10^{33} \frac{[ \# of electrons]}{cm^2} = 3.3 \times 10^{34} \frac{[ \# of electrons]}{cm^2}</math><br>
-||[[Image:phi_angle_in_CM_Frame_for_pions_using_theta_x_and_phi_gamma_angles_file_dst27095_without_cuts_1.gif|300px]][[Image:phi_angle_in_CM_Frame_for_pions_using_theta_x_and_phi_gamma_angles_file_dst27095_without_cuts_2.gif|300px]]
-||[[Image:pion_phi_angle_in_cm_frame_vs_differential_cross_section.jpg|400px]] [http://arxiv.org/abs/0709.1946]
-|}<br>
-  start calculating cross -section, Find luminosity of NH3 target used
-  The luminosity of the continuous electron beam was <math>10^{34}</math> <math>cm^{-2} sec^{-1}</math> [http://arxiv.org/abs/0709.1946v2] [http://books.google.com/books?id=LEqA4cMrkfIC&pg=PA329&lpg=PA329&dq=target+NH3,+CLAS,+luminosity&source=web&ots=yWZHoDjDDI&sig=yW0oVF1zIQgJZ5yqAMElflnhxsY&hl=en#PPA329,M1]<br>
+The luminosity of the continuous electron beam was <math>10^{34}</math> <math>cm^{-2} sec^{-1}</math> [http://arxiv.org/abs/0709.1946v2] [http://books.google.com/books?id=LEqA4cMrkfIC&pg=PA329&lpg=PA329&dq=target+NH3,+CLAS,+luminosity&source=web&ots=yWZHoDjDDI&sig=yW0oVF1zIQgJZ5yqAMElflnhxsY&hl=en#PPA329,M1]<br>
-  Insert Luminosity calculation for NH3 and ND3 targets
+;Cross Section Calculation
+[[Media:cross_sections_1.pdf]]<br>
 : <math>\frac{d\sigma}{d\Omega} = \frac{1}{L} \frac{d^{2}N}{d\Omega dt}</math><br>
@@ Line 448: / Line 369: @@
 :<math> \frac{d\sigma}{d\Omega}</math> is the differential cross section.
-Conservation of Momentum <math>\Rightarrow</math> :
+[[Image:f_cup_file_dst27095.gif|300px]][[Image:f_cup_integral_file_dst27095.gif|300px]]<br>
-<math>\vec{p}_e = \vec{p}_{e^{\prime}} + \vec{p}_{\gamma}</math>   <math>\Rightarrow</math>  <math>\vec{p}_{e^{\prime}} = \vec{p}_e - \vec{p}_{\gamma}</math> <br>
-<math>{p_{e^{\prime}}}^2 = {p_e}^2 - 2 p_e p_{\gamma}cos {\theta_x} + {p_{\gamma}}^2</math><br>
-<math>cos {\theta_x} = \frac {{p_e}^2 + {p_{\gamma}}^2 - {p_{e^{\prime}}}^2}{2 p_e p_{\gamma}}</math><br>
-Conservation of Energy <math>\Rightarrow</math> :
-<math> E_e = E_{e^{\prime}} + E_{\gamma}</math><br>
-<math>\sqrt {(m_e c^2)^2 + (p_e c)^2} = \sqrt {(m_e c^2)^2 + (p_{e^{\prime}} c)^2} + p_{\gamma} c</math><br>
-<math>p_{\gamma} c = \sqrt {(m_e c^2)^2 + (p_e c)^2} - \sqrt {(m_e c^2)^2 + (p_{e^{\prime}} c)^2}</math><br>
-<math>p_{\gamma} = \sqrt {(m_e)^2 + (p_e)^2} - \sqrt {(m_e)^2 + (p_{e^{\prime}})^2}</math><br>
-The <math>cos {\theta_x}</math> can be written in the following way<br>
-<math>cos {\theta_x} = \frac {{p_e}^2 + ( \sqrt {(m_e)^2 + (p_e)^2} - \sqrt {(m_e)^2 + (p_{e^{\prime}})^2})^2 - {p_{e^{\prime}}}^2}{2 p_e ( \sqrt {(m_e)^2 + (p_e)^2} - \sqrt {(m_e)^2 + (p_{e^{\prime}})^2}) }</math> <br>
 ==== Pion Rates -vs- Paddle for opposite sign Torus fields====

Difference between revisions of "Quality Checks"

Latest revision as of 10:58, 19 September 2008

Quality Checks

Run Summary Table

Rates

Unpolarized Pion electroproduction

Rates from other experiments in our Kinematic range

Center of Mass Frame Transformation

Example of the Missing Mass Calculation for the following reaction [math]e^- p^+ \rightarrow (e^-)^{\prime} \pi^{-} X [/math]

Example of the Missing Mass Calculation for the following reaction [math]\vec{e}p \rightarrow (e^-)^{\prime} n \pi^+[/math]

Missing_Mass(experimental data)

[math]\phi[/math] angle

[math]\phi[/math] angle for electrons and pions ([math]\pi^+[/math]) in lab frame [math]\phi_{e^-}^{LAB}[/math], [math]\phi_{\pi^+}^{LAB}[/math]

Phi angles

[math]\phi[/math] angle in the Center of Mass Frame

axis rotation

Phi rate

Luminosity Calculation for NH3(Ammonia) target

Pion Rates -vs- Paddle for opposite sign Torus fields

sc_paddle vs X_bjorken 5.7 GeV Beam Energy

sc_paddle vs X_bjorken with cuts 5.7 GeV Beam Energy(number of events=2)

sc_paddle vs Momentum 5.7 GeV Beam Energy

sc_paddle vs Momentum with cuts 5.7 GeV Beam Energy(number of events=2)

Paddle 7 Rates and statistics

Paddle 17 Rates and statistics

Paddle 5 and 8 Rates and statistics for electrons

Histograms for 5.7 GeV Beam Energy

Normalized X_bjorken for electrons

Asymmetries

Systematic Errors

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Example of the Missing Mass Calculation for the following reaction

Example of the Missing Mass Calculation for the following reaction