[b1_ana] b1 phone meeting April 29 (note time)

[O. A. Rondon]

Hi Dustin,

Dustin Keller wrote:
> You can only benefit from the systematic reduction if you us Azz as
> discussed yesterday.  But at this point I am not partial.
>
> dustin
>

In the experiment, we only have counts. What we need to show to the PAC
is how we go from the counts Npol and Nu, to Azz or b1. A measured
quantity needs to be on one side and physics on the other. Lets say we
start with your ratio Npol/Nu - 1 = Pzz*Azz, which only requires Pzz >0.

We need to prove that the lhs reproduces the rhs. We have, in general,
N = Q*e*A*l*sigma. But since N are counts from everything in the target,
it is not a simple matter of canceling quantities that stay the same
when the polarization changes:

Npol = Qpol*epol*Apol*lpol*sigma_pol
     = Qpol*epol*Apol*lpol*[(sigma_N+3*sigma_Dpol)*pf + sigma_He*(1-pf)]

Nu   = Qu*eu*Au*lu*[(sigma_N+3*sigma_D)*pf + sigma_He*(1-pf)]

sigma_N and sigma_He are the same, always unpol. And
sigma_Dpol = sigma_D(1+Pzz*Azz).

Then, since Apol = Au = A, and lpol = lu = l,

Npol/Nu =
(Qpol/Qu)*(epol/eu)*[(sigma_N+3sigma_D(1+ Azz*Pzz))*pf+..)]/[(sigma_N+..

where I just put ..., because I don't see how it can be simplified to
just leave Azz*Pzz + 1, to equal the rhs.

On the other hand, if instead of taking the ratio Npol/Nu first, we take
the difference first, it's indeed possible to isolate the required
Pzz*b1 on on side, like I do in my draft, eq. (19) or (20). And in
fact, we don't even need to bother with Azz, because we get b1 without
having to multiply Azz by F1, introducing one more systematic error.

So, in summary, once one substitutes all the ingredients for your sigmas
we get, or ought to get, eq.(19) or (20) back.

In both of those equations, the systematics for Pzz, A, and l(pf) are
normalization factors, just like we want them to be, for control of
systematics, but the charge and the detector efficiency are not common
factors, they depend on the period when the data are taken, either pol.
or unpol.

My point is that for the proposal, we must spell this all out, to give
explicit sources of errors, and to calculate times or statistical errors
correctly. For example, the statistical error must be sqrt(Npol + N_U) ~
sqrt(2N), because it is just the error of a difference, etc.

We need to have a consensus on how the method is going to be described
in the proposal, which needs to be done in the most precise way to avoid
any confusion due to ambiguities.

Cheers,

Oscar


> On Tue, 30 Apr 2013, O. A. Rondon wrote:
> 
>> Hi,
>>
>> Since I couldn't stay until the end of the meeting, and I don't think
>> there will be minutes of it, I would like to share some ideas for the
>> proposal draft.
>>
>> Basically, what we need is an equation with the measured quantity on one
>> side and b1 or Azz on the other. Based on what I think the consensus
>> was, to measure polarized minus unpolarized counts on a single cup with
>> the target field aligned along the beam, I've updated the draft of my
>> method, see subsection 0.2, which discusses this. Eq. (19) or eq. (20)
>> meet the conditions stated above. This is the approach I would subscribe
>> to, unless there is another version that is shown to also represent the
>> procedure, which should be circulated as soon as possible. The draft
>> is here
>> http://twist.phys.virginia.edu/~or/b1/b1_method-v2.pdf
>>
>> Cheers,
>>
>> Oscar
>>
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>