[b1_ana] Fwd: Uncertainties in measuring b1/Azz

[O. A. Rondon]

Hi,

I think that the form of Azz in eq. (20) of the draft, or eq. (4) in the
section we shared with Steve, obscures the method. He is still thinking
of a difference, which indeed is the numerator.

I think that if we use the form that I've been advocating, which the
same that is given in the appendix with the derivation of the dilution
factor, it should be clearer that it is a ratio - 1, not a difference.

In any case, in addition to addressing Steve's comments, at least we
should write the equation for Azz as

Azz = 2/(f*Pzz)*(Np/Nu - 1),

just as it's given in Werner's and Heinz's proposal (without the
dilution factor, which they missed like we were before I found it).

That proposal got an A-, (in spite of the missing f) because even though
it has even more sources of systematic errors than ours, it was very
clear. We should be able to clarify everything, too.

For example, we are taking Q_pol/Q_unpol = 1. We need to keep them and
propagate their errors. The same applies to the detector efficiencies.

And we do need to specify f, maybe a plot f(x), at least a number
(~0.26). Pzz is, of course, given, but it wasn't in what we gave Steve.

Cheers,

Oscar

Patricia SOLVIGNON wrote:
> 
> Begin forwarded message:
> 
>> *From: *"Stephen A. Wood" <saw at jlab.org <mailto:saw at jlab.org>>
>> *Subject: **Uncertainties in measuring b1/Azz*
>> *Date: *May 3, 2013 4:40:27 PM EDT
>> *To: *Patricia Solvignon-Slifer <solvigno at jlab.org <mailto:solvigno at jlab.org>>
>>
>> Patricia:
>>
>> Thank you for showing me the document describing estimates of errors in 
>> measuring b1.
>>
>> The formula for estimating statistical errors (or rather time needed to 
>> achieve a given statistical precision) looks correct to me.
>>
>> In the discussion of systematic errors, the uncertainties discussed appear to 
>> mostly relate to the scale of b1 or Azz.  While important, these scale 
>> systematics are not the dominant systematics.  The main systematic will be 
>> unknown differences in the calibrations, efficiencies, luminosities etc 
>> between the two polarization states.
>>
>> This is similar to experiments with polarized beam, particularly parity 
>> experiments, where one worries that about unknown differences in rate between 
>> the two helicities that are not due to the physics of interest.  These 
>> differences could be due to fluctuations in target density, fluctuations in 
>> beam current measurement calibration etc.  In such experiments, these 
>> systematics are mitigated by reversing the beam polarization quickly so that 
>> efficiencies, target densities etc don't have time to drift.
>>
>> With a rate of switching polarization states of hours or days, there will be 
>> drifts in things, drifts that get magnified because this measurement is a 
>> subtraction of large numbers.  I don't know what the target (f * Pzz * 
>> delta-Azz) is, but it is 10^-something where something is certainly >= 4.  If, 
>> for example, the detector efficiency were to drift by 1% between the two 
>> polarization states, and this drift was unknown, it would be a complete killer.
>>
>> I think the main systematic drift effects will be
>>
>> 1.  Drifts in beam current measurement calibration
>> 2.  Drifts in detector efficiency
>> 3.  Drifts in luminosity
>>
>> I am sure there are others.
>>
>> There can be many subtle effects in any of these.  BCM efficiency could depend 
>> on ambient temperature which will have daily variations as well as several 
>> hour variations due to AC cycling.  The BCM calibration at different currents 
>> could be different, making
>>
>> Detector efficiency can drift for a variety of reasons, for example including 
>> fluctuations in gas quality, HV drift or drifts in spectrometer magnetic field.
>>
>> There can be difficult to know changes in luminosity.  As I understand it, the 
>> target is a set of discrete beads.  So, when the beam moves, the thickness of 
>> the target seen by the beam changes.  Or if the amount of helium seen by the 
>> beam changes, the rate changes.
>>
>> It may be that all of these systematics can be addressed, but it may not be 
>> possible to make a completely convincing case by the the of the PAC.  But I 
>> think it is important to acknowledge all the systematics you can think of and 
>> acknowledge the difficulty of beating them down. (Otherwise PAC members or the 
>> technical review will point them out.) There are things that can be pointed to 
>> such as the big effort that went into modernizing BCMs for g2p and Qweak. 
>>  Some of that effort may be useful in this case.  It would be good to sketch 
>> out a plan for studying the systematic effects.  There will be plenty of time 
>> to do parasitic systematic effects studies during the experimental program 
>> that will precede an eventual b1 run.
>>
>> It would be helpful if you could remind me of the expected numerical values of 
>> f and Pzz, and the desired deltaAzz.
>>
>> Steve
> 
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