[b1_ana] draft proposal v02

[Dustin Keller]

Hi,
As I mentioned these relative errors you seem to be pointing too have
already been considered at least to a small degree.  What I am concerned
with is when steve says:

"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"

This statement (to me) seems to request a demonstration that
the drifts do not lead to a deltaAzz much larger than 1*10^-4.

The key point here is that if J.P. what right about the drifts
1% is seen in about 90 days for 2.)  But its 1.) that may still
need some explanation.

dustin



On Sat, 4 May 2013, Oscar Rondon-Aramayo wrote:

> Hi,
>
> Actually, since Q and epsilon are only factors of Np, Nu, they aren't scales
> of Azz. Steve is right. We still have a difference: Np/Nu - 1, with Np/Nu ~
> 1.
>
> So, we need to keep track of Q and e even in the statistical error. The only
> way of doing this right is to propagate the errors for both Q's and e's in
> detail.
>
> Oscar
>
>
> On Fri, 03 May 2013 21:38:37 -0400
>  "Oscar  Rondon-Aramayo" <or at cms.mail.virginia.edu> wrote:
>> Hi,
>>
>> To further remove any confusion about our method and its errors, I suggest
>> that instead of writing eq. (19) in terms of charge normalized, efficiency
>> corrected counts, we display the charges and efficiencies explicitly, and
>> use raw counts. Although we stated the kind of counts we are using in that
>> eq. just above it, it seems Steve missed it.
>>
>> Per eqs. (32) and (33) in the appendix 2.2.3, this means just moving Q's
>> and epsilons to the l.h.sides, since N1 and N are indeed raw counts there,
>> and don't make any approximations, like Q1 ~ Q, etc.
>>
>> Then, the l.h.s. of eq. (34) would be
>>
>> (Q/Q1)*(e/e1)*(N1/N) and
>>
>> eq. (19) becomes
>>
>>  Azz =  2/(f*Pzz)*[(Q/Q1)*(e/e1)*(N1/N) - 1]
>>
>> where it's evident that Q's and e's are normalizations or scale factors,
>> just like f and Pzz, and change the text above the equation to say raw
>> counts, not normalized and corrected ones.
>>
>> I don't see any other way to make it any clearer.
>>
>> And, of course, we need to emphasize somewhere that the statistical error
>> is
>> always based on the RAW counts.
>>
>> Cheers,
>>
>> Oscar
>>
>>
>>
>> On Fri, 3 May 2013 17:43:55 -0400
>>  Karl Slifer <karl.slifer at unh.edu> wrote:
>>> Hi all,
>>>
>>> I got a ton of comments, and I think I've implemented them all.  I think
>>> the most substantial pertain to the following: (equation numbers refer to
>>> the attached draft)
>>>
>>> Eq 17 and 19: Azz expressed as ratio - 1 as suggested by Oscar
>>>
>>> Eq 22 : Total time expressed in terms of R_T as noted by Patricia and
>>> concurred by Ellie and Oscar.
>>>
>>> Page 23 Charge determination systematic : modified to reflect Oscar and
>>> JP's suggestions
>>>
>>> There were a lot more, so please double check that your suggestions have
>>> been satisfactorily included.
>>>
>>> The overhead and target sections are still in progress.  Anyone have time
>>> to help with that?
>>>
>>> thanks,
>>>
>>> Karl
>>>
>>>
>>> ---
>>> Karl J. Slifer
>>> Assistant Professor
>>> University of New Hampshire
>>> Telephone : 603-722-0695
>>
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