Elong-13-04-29

Rates Update

→ For the plots below, I assume the following:

Target Material	ND3
Target Length	3 cm
fdil	6/20
pf	0.65
Pzz	20%
E0	11 GeV
xBjorken	0.1, 0.3, 0.5, 0.75, 1.0
Q2	Variable
θq	Calculated
θe'	Calculated
E'	Calculated
W	Calculated

→ θ_e' and E' limits were added for each spectrometer

→ Error bars shown are statistical only

→ F1 and F2 are calculated using the Bosted fits, which lets us extend into a higher <x> range

→ It is valid for 0<W<3.2 GeV and 0.2<Q²<5 GeV²

→ The error bars are calculated from:

File:2013-04-29-dAzz.png

Maximizing Rate (Minimizing dA_zz)

If we set the spectrometer such that we aim to increase the rate as high as we can, it will get us the lowest (statistically) achievable A_zz.

The settings above give us the highest rates we can achieve, and thus the lowest error bars on A_zz. Each of the <x> values is set over the course of 1 PAC-week, allowing us to take any four of the above points.

<x>	dAzz with SHMS	dAzz with HMS	db1 with SHMS	db1 with HMS
0.1	0.00619	0.0316	0.0200	0.0770
0.3	0.00564	0.0203	0.00691	0.0244
0.5	0.0192	0.0204	0.00819	0.00853
0.75	0.00765	0.0593	0.00187	0.00444
1.0	0.0136	0.699	0.00421	0.00279

The db1 Problem

→ Since db₁ is calculated from , it is dependent upon F₁
→ For each of the <x> values that I've been looking at, the following show what the Bosted code produces as a function of Structure Function vs. Q^2
→ For the plots below, the structure functions are calculated within the allowable Q ² and W² ranges of the Bosted fits
→ The two vertical lines indicate the Q ² values where dA_zz has been minimized

Structure Function vs. Q ² for <x>=0.1

Structure Function vs. Q ² for <x>=0.3

Structure Function vs. Q ² for <x>=0.5

Structure Function vs. Q ² for <x>=0.75

Structure Function vs. Q ² for <x>=1.0

Minimizing db₁

If we set the spectrometer at the lowest allowed values of F1 (from above), it will get us the lowest (statistically) achievable db₁.

The settings above give us the lowest statistical error bars we can achieve on db₁. Each of the <x> values is set over the course of 1 PAC-week, allowing us to take any four of the above points.

<x>	dAzz with SHMS	dAzz with HMS	db1 with SHMS	db1 with HMS
0.1	0.00656	0.0316	0.0211	0.0770
0.3	0.0140	0.0203	0.0171	0.0244
0.5	0.0183	0.0204	0.00779	0.00853
0.75	0.00765	0.0593	0.00187	0.00444
1.0	0.0596	0.699	0.00103	0.00279

--E. Long 17:20, 26 April 2013 (UTC)