[d2n-analysis-talk] BPM uncertainty <-> BigBite momentum uncertainty (FWD)

[Diana Parno]

FYI, here's Seamus's ballpark estimate of the effect of BPM uncertainty on 
the BigBite momentum reconstruction.

Diana

---------- Forwarded message ----------
Date: Tue, 09 Feb 2010 19:10:11 -0500
From: Seamus Riordan <riordan at jlab.org>
To: Diana Parno <dparno at cmu.edu>
Subject: Re: BigBite query

Hey Diana,

The calibrations probably don't contribute too much.  What will probably change 
Q^2 the most is the uncertainty in the vertical position, which will affect the 
momentum reconstruction.  You can estimate how much the momentum will change 
(and propagate it to Q^2) through the expression:

p = C/(theta_2 - theta_1)

where theta_1 is the electron out of plane angle before it enters the magnet 
and theta_2 is the out of plane angle after it leaves the magnet.  The 
difference is the deflection angle.  The constant is related to the total field 
integral and electron charge, which you should be able to determine empirically 
from the data.  (I remember for BigBite at the maximum current is something 
like C~0.3 GeV*rad).

The uncertainty in theta_1, dth_1, from the raster is something like D_y/D_BB, 
D_y is the RMS of the raster width, D_BB is the distance of the middle of 
BigBite from the target.  (BigBite is about 60 cm deep when half way up if I 
remember, so add 30cm from the distance to the magnet face)

dp = C*dth_1/(theta_2 - theta_1)^2

So, plugging some reasonable values like dth_1 = 2*mm/1.5m ~ 1 mrad. 
C/(theta_2 - theta_1)^2 = p^2/C ~ 3 GeV/rad for p = 1 GeV and C = 0.3 GeV*rad

dp is then something like 3 MeV, which is smaller than the nominal momentum 
resolution of 10 MeV.  You can propagate the uncertainty to Q^2 = 
2EE'(1-cos(th_e)) (or whatever the proper expression is) for what your 
kinematics are.

***  I'm just working that out off the top of my head and you should check my 
reasoning and numbers, which are GEn biased ***  Let me know if you have any 
questions.

Best regards,
Seamus

Diana Parno wrote:
> Hi Seamus,
> 
> I'm stuttering toward the BPM calibration for d2n, and we've run into the 
> interesting problem that the HARP positions don't seem to be completely 
> accurate. Do you have a ballpark sense for how uncertainty in BPM/raster 
> calibrations might propagate to uncertainty in Q^2 values for BigBite?
> 
> Diana


-- 
Dr. Seamus P. Riordan			riordan at jlab.org
University of Virginia			Office: (757) 269-6037
Post-doctoral Research Associate	Pager:  (757) 584-0051

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