[b1_ana] Fwd: PR12-13-011

[O. A. Rondon]

We know that we don't want P_b to avoid issues like HERMES, from A_para
= D*(A_1 + eta*A_2).

If we have to share the source with other Halls that need P_b, because
b1 cannot be scheduled along with another P_b = 0 experiments, since
A_para matters only during the P_zz.ne.0 half cycles, we would need to
propagate the errors of P_b*P_z*A_para vs P_zz*A_zz.

Since A_1/A_zz ~ 100, we have
sigma_pol = sigma_u*(1 + f*P_b*P_z*D*A_1 + f*P_zz*A_zz)
          = sigma_u*[1 + f*A_zz(P_b*P_z*D*100 + P_zz)]

The error on A_zz from D*P_b*P_z should be smaller than that from P_zz,
but even for twice as large a P_zz error as the proposal's, (so the
scale error would be ~20% relative to A_zz)

100*D*sqrt((P_b*dP_z)^2 + (P_z*dP_b)^2) <~ 2 dP_zz

or, with D ~ 0.3

sqrt((P_b*dP_z)^2 + (P_z*dP_b)^2) <~ 7E-2 dP_zz = 2.2E-3,

for dP_zz/P_zz ~ 16%, P_zz ~ 20%.

The error is dominated by the irreducible term P_z*dP_b ~ 5E-3, since
P_z = 0.45 >> P_b ~ small and, for any P_b, dP_b < 0.01 is very hard to
achieve.

My A_1/A_zz may be too pessimistic, but even a 25:1 ratio would be at
the margin of measuring a very small residual P_b to 0.01 absolute,
while doubling our normalization error.

So we should ask for true unpolarized beam, unless someone knows that
the required precision is achievable. Can't the laser light be just
unpolarized?

Cheers,

Oscar

Karl Slifer wrote:
> ---------- Forwarded message ----------
> From: *Jay Benesch*
> Date: Friday, May 10, 2013
> Subject: PR12-13-011
> To: slifer at jlab.org
> 
> 
> Karl,
> 
> Stupid question about the deuteron tensor structure function proposal that
> I don't understand well enough to answer myself - and I have to comment on
> this at the TAC meeting Tuesday afternoon.  I've just begun to read it.  I
> haven't dug up my copy of PR12-11-110.  (Do I need to or does this stand
> alone?)
> 
> When you request unpolarized beam, do you really mean unpolarized beam, or
> can you take whatever polarization results from full longitudinal
> polarization in another hall?  I think the source group would have to
> change laser and wafer to get unpolarized beam.
> 
> I trust you'll accept more questions as they arise during my reading over
> the weekend.
> 
> Jay
> 
> TAC Technical Advisory Committee
> 
> 
> 
> 
> 
> 
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