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

Wed May 1 10:52:56 EDT 2013

Hi Patricia,

It is not the same as the last proposal, because the same target, spanning 
the same acceptance is used for either the difference of counts or the 
ratio.

In the last proposal, the acceptance was different for parallel vs perp, and 
the target length could also change between the two configurations. Now the 
acceptance and length stay the same, because it's the same cup, and the 
field is constant.

But even now, we don't have a true asymmetry. We are doing two sequential 
measurements, not a simultaneous one. So for both the ratio and the 
difference of counts, the charge and the detector efficiency are not the the 
same for pol vs unpol. All other factors indeed are normalizations.

In summary, taking the difference gets us to b1 directly, at the price of 
the errors in Accept. and pf. The ratio takes us to Azz, at the price of the 
error in f, and to b1 at the additional price of the error in F1. Since Pzz 
is expected to dominate the errors, and is common to difference or ratio, 
take your pick.

Cheers,

Oscar

On Wed, 1 May 2013 10:25:15 -0400
  Patricia SOLVIGNON <solvigno at jlab.org> wrote:
> Hi Oscar.
> 
> I think we are still running in the same problem as at the last time we 
>propose the sigma_para - sigma_perp method. It is the difference of two 
>huge numbers to extract a very small number. The method of using two cups 
>work well for getting g1 and control its systematics because the 
>unpolarized cross section never comes into play. Just looking at equation 
>(2) of your note tells me that we are back to the same issue as the last 
>proposal. From the statistics point-of-view, it is true that the 
>unpolarized cross section using the method you propose will cancel but it 
>will stay in the systematics.
> I convince myself a while ago that there is no other way to get b1 than by 
>the asymmetry method because it is the only way to truly cancel the 
>unpolarized cross section contribution in the statistics and in the 
>systematics as well. Of course the asymmetry method suffers from the 
>statistics but that can be overcome with beam time request and/or going to 
>large acceptance spectrometer. If I remember well, Dustin came up with the 
>same conclusion.
> 
> Bests,
> Patricia
> 
> -- 
> Patricia SOLVIGNON
> Staff Scientist
> Jefferson Lab
> 
> Current address : 
> Jefferson Lab
> Suite 6, MS. 12H4                               Room C121 (Cebaf Center)
> 12000 Jefferson Avenue                      Office:   (757)-269-6933
> Newport News, VA 23606
> 
> On Apr 30, 2013, at 5:59 PM, O. A. Rondon <or at virginia.edu> wrote:
> 
>> 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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>>> 
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