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

[O. A. Rondon]

Hi Ellie,

The additional asymmetry is eq. (28) of Arenhoevel, A_T^{ed}. It
involves P_b*P_zz, not P_z, see eq. (23). In his notation

A_V^d    = doesn't appear in Jaffe or HERMES
A_T^d    = A_zz,
A_V^{ed} = A_1, (see below about A2)
A_T^{ed} = doesn't appear in Jaffe or HERMES

I've also added A2, since we are measuring A_parallel = D*(A1 +
\eta*A2), where \eta = \epsilon*sqrt(Q^2)/(E - E'*\epsilon). \epsilon is
the usual longitudinal virtual photon polarization.

A1 and A2 are exactly what Arenhoevel has in eq. (27), in terms of F'_T
and F'_{LT}. We know
A1 = (sigma_T^(1/2) - sigma_T^(3/2))/sigma_T and
A2 = sigma_{LT}/sigma_T.

F'_{LT} is not the same as the F_{LT} of eq. (25).

Note that HERMES eq. (1) uses \simeq because, although they measured
A_para like we propose, they neglected A2. The \eta factor must be
favorable at 27 GeV.

Also, the fact that A1 and A2 are just other names for F'_T, F'_{LT}
shows that it's perfectly all right to measure A_zz with longitudinal
field, although I don't know which of the F's in eq. (26) could be
interpreted as the A_zz = 2/3 b1/F1.

Npol
= sigma'_U*[1 + (D*(A1 + \eta*A2)*P_z + A_T^{ed}*P_zz)*P_b + A_v^d*P_z +
A_zz*P_zz]

and
Nu   = sigma_U*(1 + APV*P_b),

Note that in Arenhoevel, there is no APV, or any beam-only asymmetry.

Cheers,

Oscar