[b1_ana] Follow up on Re: Fwd: Re: A_PV with Deuteron Target

[O. A. Rondon]

Hi Ellie,

I thought some more about your question, and I realized that one thing
that can cause confusion is that sometimes the thinking is in terms of
theory quantities, not of measured ones.

Since we measure the cross sections at different times, we really have

Npol = sigma'_U*(1 + D*A1*P_b*P_z + A_zz*P_zz + A_v^d*P_z)
Nu   = sigma_U*(1 + APV*P_b),

where the measured sigma'_U is not necessarily the same as the one
measured when P_zz = 0.

Since we would like to have Npol/Nu, we could write sigma'_U = sigma_U +
dsigma = sigma_U*(1 + dsigma/sigma_U) to have some cancellations, so

Npol/Nu
= (1 + dsig/sig)*(1 +D*A1*P_b*P_z + A_zz*P_zz + A_V^d*P_z)/(1 + APV*P_b)

For P_b = 0, to first order (i.e. no dsigma*Sum(A_i*P_i) terms,) and for
a nuclear target (not pure deuterium) we have

Npol/Nu = 1 + dsigma/Sigma_U + f(A_zz*P_zz + A_V^d*P_z)

So it's the dsigma piece that Steve Wood has been concerned it could be
as big as the Azz piece, since P_zz and f make the latter even smaller.

As it's written on our proposal, eq. (28), the dsigma/Sigma_U piece has
terms coming from charge calibration and detector efficiency drifts, and
even a combined term, which is second order, so it can be dropped. It
may be a bit confusing because the notation shows deltaQ and
delta\epsilon, although, as the text says dQ is a dimensionless ratio.
It did confuse the theory TAC, anyway.

The whole point is that we are claiming that over 20 hours, dQ/Q and
d\eps/\eps will be of the order of 1E-4 or less, while f*P_zz*Azz =
0.27*0.2*1E-2 = 5.4E-4, so the calibration drift would be a < 20%
effect, maybe.

The question of P_b dependent terms is important at a later stage, in
the interpretation of the measured quantity in terms of pure A_zz.  We
must make sure that those terms, plus the unavoidable A_V^d, are
negligible, by a combination of methods, like the acceptance cuts and
the sum of data for opposite P_z's that I mentioned, although the best
would be to just have exact P_b = 0, since there is another P_b
dependent asymmetry that we are just ignoring, the beam-tensor target
asymmetry A_T^{ed}, Arenhoevel's eq. (28).

Since we are taking data with both HMS and SHMS, which are on opposite
sides of the beam line, it's not possible to align the target field
along q for one without making it much worse for the other than keeping
the field longitudinal. So we'll have to make sure to have a run plan
that includes all the data configurations needed to cancel everything
other than A_zz, which, of course, is just the low x version of Arenhoevel's
A_T^d.

Cheers,

Oscar







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Subject: Re: [b1_ana] Follow up on  Re: Fwd: Re: A_PV with Deuteron Target
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