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

Wed May 1 10:40:31 EDT 2013

Hi Karl,

We met with Dustin  last evening and after going in detail over the formulas 
for the ratio Npol/Nun, we found that the unpolarized sigma_N, sigma_D and 
sigma_He (see my last email) can be collected in one group, which cancels 
with the denominator (all unpolarized), leaving a term 
sigma_D*Azz*Pzz/denominator, which I realized can be written as f*Azz*Pzz, f 
= dilution factor.

With the dilution factor, the formulas in Dustin's third row of equalities 
in his Observables2 report, which are valid only for pure D (the HERMES 
case), can also be used for ND3 targets.

In summary, we can take the ratio of the pol to unpol counts, which takes us 
to Azz, at the price of the dilution factor and its error, plus the need to 
use some form of F1 to get b1 from Azz, or the difference, which takes us 
directly to b1.

In both cases the systematic errors, other than the charge and detector 
efficiency are normalizations, and since the error on Pzz is expected to 
dominate, it really is a matter of taste, once we have the numbers on hand. 
We'll surely try both.

For the statistical errors, f enters in the Azz time estimate, but Q*A*l*pf 
enter in the difference (Pzz is in both). I need to do some numbers yet 
(everyone should try) to compare the two approaches.

Finally, today we have the SANE meeting at 3:30, so I can join b1 from 1:00 
to 3:30.

Cheers,

Oscar

On Wed, 1 May 2013 09:18:48 -0400
  Karl Slifer <karl.slifer at unh.edu> wrote:
> Hi all,
> 
> The methodology is the central question and I think we have to resolve any
> lingering doubts today.  I highly encourage that everyone really read
> Oscar's note (Eq 19 and 20) and his last email before we discuss today.
> 
> I would really not like to delay till tomorrow if possible since time is 
>so
> tight. I hope we can get a majority to participate at 3pm.  Please let me
> know if you can't.
> 
> -Karl
> 
> 
> 
> ---
> Karl J. Slifer
> Assistant Professor
> University of New Hampshire
> Telephone : 603-722-0695
> 
> 
> On Tue, 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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