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

[O. A. Rondon]

Hi,

After thinking a bit about Wally's target-only A_PV asymmetry, I
recalled that actually there is an electromagnetic target-only
asymmetry, per Arenhoevel's Inclusive electrodisintegration paper that
we were discussing when we explored b_1(x~1), see eq. (25).

So, really, the difference pol. - unpol., with P_b.ne.0, is

sig_U*(1 + D*A1*P_b*P_z + A_zz*P_zz + A_v^d*P_z) - sig_U*(1 + APV*P_b),

Since the field is longitudinal, A_v^d may not go away, it depends on
sin(phi_d)*sin(theta_d)/sqrt(2). phi_d and theta_d are the angles of the
field relative to the q vector, so theta_d = theta_q, see fig. 1.

Since the field will be in the horizontal plane, A_V^d would cancel
exactly if the acceptance were symmetric about the plane, but given the
deflection of the scattered electrons by the field, it may not go
entirely away without some acceptance cuts.

The good news is that it is suppressed by the double sine, and since the
angles are small, the contribution is very suppressed: the deflection
for E' = 7.3 GeV is 0.35 deg., which projects to phi_d = 1.6 deg. for
the worst case (HMS at 12.5 deg, E' = 7.3 GeV, theta_q = 22.3 deg.) so
the sine factors are 8E-3, assuming there is NO cancellation between
events with phi_d > 0 and phi_d < 0.

This A_V^d, and any target-only A_PV, can be further canceled by
flipping P_z from one period to the next, and adding the events,
weighted by P_z. So it looks like we'll need to take an equal number of
pol. periods with opposite charge-weighted P_z anyway.

I tried to estimate the magnitude of the kinematic factor rho_{LT} and
the form factor F_{LT}^{1,-1} that enter in eq. (25). For example, from
fig. 14a, I see that at W = Delta(1230), Q^2 = 0.8 GeV^2, the dominant
F_T = 0.038 fm, while fig. 19 shows F_{LT}^{1,-1}(Delta, 0.8 GeV^2) ~
0.9E-4 fm, and it has a decreasing trend with Q^2, which is good for us.

So it looks like the contribution of A_V^d(F_{LT}^{1,-1}) would be about
2E-3 of sigma_U, suppressed by the sine factors ~8E-3, but may be
magnified by rho_{LT}, eq. (5), that seems to be ~ 300, dominated by
1/eta = 1/tan^2(12.5/2) and Q^2 = 3.8, or A_V^d ~ 5E-3, before any
cancellations from adding the data for opposite P_z, and cutting the
acceptance in phi to be symmetric about phi = 0.

I encourage everyone to review these points carefully.

Cheers,

Oscar


O. A. Rondon wrote:
> Hi,
> 
> The classical deuteron PV experiment by Charlie Prescott at SLAC was
> polarized beam on unpolarized deuterons, i.e. Qweak on deuterons.
> 
> To see a PV with unpolarized beam, we would need to make a difference of
> target P_z's. But we aren't making any, and we shouldn't. We can only
> change the P_z sign at the end of every pol. - unpol. cycle. To observe
> any P_z dependent PV asymmetry we would have to subtract
> pol. P_z - pol. (-P_z).
> 
> This would not give us any useful information at the PV level, or even
> at the b1 level. Remember that we are doing pol. - unpol. for b1. In
> fact, if P_b is not exactly zero, in the difference pol. - unpol. there
> are two extra terms:
> 
> sigma_U*(1 + D*A1*P_b*P_z + A_zz*P_zz) - sigma_U*(1 + APV*P_b),
> 
> so Dave must be thinking of the APV*Pb term, which is another reason for
> asking for true unpol. beam. With P_b not zero, this term is always
> there in pol. - unpol., no matter how we change P_z.
> 
> The E155x paper indicates  APV = A_EW ~ 8E-5*Q^2, (for protons or
> deuterons,) so for our proposal, with max. Q^2 <~ 5 GeV^2, A_EW = 4E-4,
> so P_b <~ 20% would be needed to keep it < 1E-4. Again, it would be best
> to measure just
> 
> sigma_U*(1 + A_zz*P_zz) - sigma_U
> 
> At the A_1 level, changing P_z to -P_z might let us see if the A_1 due
> to any residual P_b is not changing from period to period (i.e. if it's
> a real A_1, not a false one, independent of P_z,) but that is not very
> useful: Any P_b related background (A_1 related or not) would need to be
> subtracted from our pol. - unpol. difference. I rather stay with the
> P_z sign that gives the highest P_zz (e.g. +P_z polarizes faster than
> -P_z, or something).
> 
> But someone could come up with additional quantitative estimates that
> may help.
> 
> Cheers,
> 
> Oscar
> 
> Narbe Kalantarians wrote:
>> I'll look further in to this myself. But, so far, it seems that it may
>> not be too worrisome.
>>
>> Narbe
>>
>>
>> -------- Original Message --------
>> Subject:     Re: A_PV with Deuteron Target
>> Date:     Fri, 17 May 2013 11:21:31 -0400 (EDT)
>> From:     Wally Melnitchouk <wmelnitc at jlab.org>
>> To:     Narbe Kalantarians <narbe at jlab.org>
>>
>>
>>
>> Hi Narbe,
>>
>> It's a nice proposal and I hope you get it approved.
>>
>> The paper where (with Tim Hobbs) we discussed PVDIS on polarized
>> nucleons is PRD 77, 114023 (2008), Sec. V.  There we considered
>> only scattering from spin-1/2 targets (in which the deuteron was a
>> proton + neutron), so did not encounter the b1 structure function
>> explicitly.  For unpolarized electrons, taking differences between
>> cross sections with different target polarizations produces a PV
>> asymmetry.
>>
>> Correct me if I'm wrong, but my understanding of b1 is that this is
>> parity-conserving, so it's not clear to me (without writing down the
>> full expressions for the cross sections in terms of the lepton and
>> hadron tensors) how the P-conserving and P-violating contributions
>> mix.  To measure b1 in your experiment, do you need to polarize the
>> electron at all?
>>
>> In any event, the PV contribution is very small and can be calculated
>> in terms of spin-dependent PDFs, so if one is in the DIS region the
>> uncertainty from this would be expected to be small.
>>
>> Unfortunately I leave on a trip to Europe tomorrow so don't have time
>> to look deeper into this, but I'm very curious about this myself.
>> Maybe let me know what you find, and we can discuss further over email,
>> if you like.
>>
>> Cheers
>> Wally
>>
>>
>> On Thu, 16 May 2013, Narbe Kalantarians wrote:
>>
>>> Hi Wally,
>>>
>>> A few of us have proposed a measurement of the deuteron tensor spin
>>> structure function b1 for this upcoming PAC.  This would involve a
>>> (longitudinally) polarized deuteron target and unpolarized (or as low as
>>> possible) beam. I've attached a copy of it, in case you want to see it.
>>> The kinematic range we are considering is
>>> 0.16 < x < 0.49,
>>> 0.8 < Q^2 5.0 GeV^2
>>>
>>> With 11 GeV beam.
>>>
>>> The basic gist of it is to get the tensor asymmetry A_zz and determine
>>> b1 from it.
>>>
>>> We are undergoing the TAC review. The chair of that committee, Dave
>>> Mack, mentioned that there is a PV asymmetry with polarized deuteron
>>> (target).  I recall seeing some calculations you and a student (T.
>>> Hobbes?) did some time a go for this.
>>>
>>> Could you send that write up and let me know if this could be a sizeable
>>> and/or significantly contributing asymmetry to take in to account?
>>>
>>> Thanks,
>>> Narbe
>>>
>>
>>
>>
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