[b1_ana] draft V3

[Oscar Rondon-Aramayo]

Hi Karl,

Here is the deal:

1. Take eq. (19) of the proposal and multiply it times N*f*Pzz/2,
N*f*Pzz/2*Azz  = N1 - N

keeping in mind that N are charge normalized counts, this is exactly eq.(19) 
of
the difference method. To see that, just replace Azz = (-2/3)*b1/F1d.

The only thing we did in going from the differences to the proposal
was to trade K*x*A*l for f*N*F1. In both cases it's a difference, N1 -
N.

2. Since the difference method's eq.(20) is an explicit expression showing
us how to deal with the charge and detector drifts, I propose that we use
the numeric estimate of what the combined drifts need to be to attain a
given absolute error on b1, based on eq. (20).

For example, we know that the HERMES point is b1(x=.45) = .4E-2. To have an
error of 0.001 on b1, the drifts of Q and e would need to be < 0.4%/20 h
measurement cycle.

In general, per eq. (14) of the difference method, the absolute systematic
effect of Q and e will be

(dQ/Q + de/e) < 3.3E-3/(8.5*dsigma_D/sigma_D)

If we use a conservative dsigma_D/sigma_D = 0.03, the drifts would need to
be  < 1.3% for a 3.3E-3 absolute error. For a 1E-3 error, the drifts need to
be < 0.4% as I say above.

Obviously, this is a model dependent estimate. To make it model independent,
(dQ/Q + de/e) < ~ desired absolute systematics/(8.5*dsigma_D/sigma_D)

Say we want 1E-3 everywhere, and we are confident dsigma_D/sigma_D <= 3% at 
the relevant kinematics
(dQ/Q + de/e) < .004.

This error on b1 can be converted to an error on Azz multiplying times 3/2 
F1d(x).

I'm not opposed to other formulations of the error propagation. They must 
agree numerically with the above estimates, given the same assumptions, 
since there is only one method.

Cheers,

Oscar


   




On Sat, 4 May 2013 18:47:45 -0400
  Karl Slifer <karl.slifer at unh.edu> wrote:
> Hi All,
> 
> I've posted the updated draft at
> 
> https://dl.dropboxusercontent.com/u/59933793/tensor_b1_v03.pdf
> 
> There is some lagtime for implementation, but I think this reflects pretty
> well where our discussion was about 24 hours ago.  However, we still need:
> 
> -updated rates/kin plots from Ellie or Patricia and values for the table
> 
> -some consensus on how to address Steve's comments.
> 
> It seems we have three options with time running short.
> 
> 1) List all possible factors that drift with time and atleast sketch a plan
> to deal with them.
> 
> 2) go back to difference of counts.
> 
> 3) Cancel submission and work on this for next PAC.
> 
> I lean to the first, Oscar leans to the second.  I'd very much like to find
> some consensus on this.  Am I the only one still nerding it up in front of
> my computer on this beautiful spring day?
> 
> -Karl
> 
> PS : If anyone makes suggestions for changes I would very much appreciate
> that they be in a form that I can put into the document quickly.
> 
> ---
> Karl J. Slifer
> Assistant Professor
> University of New Hampshire
> Telephone : 603-722-0695