[b1_ana] Axx

[Oscar Rondon-Aramayo]

Hi,

Here are some considerations about Axx. Werner's proposal defines it as a
tensor analyzing power, on p. 4, beginning of sec. 2. Although the
associated ref. [4] is a private communication by Rocco Schiavilla, and I
could not find a specific paper by him, I found what Axx and the other
tensor analyzing powers (Ayy, Axz, etc.) are.

They come from using beams of polarized deuterons scattering on protons and
other nuclear targets, so in a way are the inverse of polarized target
scattering, somewhat like recoil polarimetry and polarized targets are
related.

The counts associated with Axx (proposal eq. (1)) are coincidence ep counts
that can be associated to Axx because the target field (locus of the
quantization axis) is in the scattering plane (the proposal authors  really
mean near the lab horizontal plane, but that's OK, because the out of plane
angle may not be too big). It is Axx because the polarized deuteron beams
have vertical spins, so phi = +/- pi/2 about the beam axis for the
horizontal target field axis.

You can read all about Axx, etc. in the two papers linked below. It's clear
that it cannot be related to Azz. Axx is an azimuthal asymmetry about the
deuteron beam in dp elastic scattering, or about the q vector in (e,e'p).
But an inclusive experiment integrates it over all phi, which is zero.

So there is no connection between this semi-inclusive analyzing power and
Azz. But Werner's experiment does measure Axx, and since they are in
parallel quasielastic kinematics they can relate it to the shape of the
deuteron. The
N_pol and N_unpol are coincidence events, and they definitely are related to
the m=0, +/-1 states, by his eq. (2) and (3). This is not possible with just
single arm electrons.

Also, the deuteron beam is prepared just like the HERMES deuteron target,
with maximal values of Pzz = 1 and -2, which is what we need for DIS b1 or
even the high x b1 of Frankfurt and Strikman.

So, other than measuring Azz with Pzz < 0, we are left with Jaffe's method,
which could be written exactly in terms of the ratio
sigma_pol/sigma_u = 1 - Pzz/3 b1/F1= 1 - Pzz/2 Azz,
although I don't see the point in going to Azz, since we can get b1 directly
as
b1 = 3F1/Pzz (1 -  sigma_pol/sigma_u).
But this is just the method I've  proposed, neglecting the N and He
contributions, which cause much of the problems in the real experiment.

I recommend the first paper for its clarity.

http://www.sciencedirect.com/science?_ob=MiamiImageURL&_cid=271623&_user=709071&_pii=0370269395013989&_check=y&_origin=article&_zone=toolbar&_coverDate=18-Jan-1996&view=c&originContentFamily=serial&wchp=dGLzVlV-zSkzV&md5=1ea1b8629d6281501137478359e0911c&pid=1-s2.0-0370269395013989-main.pdf

http://arxiv.org/pdf/1207.3509v1

Cheers,

Oscar