[Clascomment] OPT-IN: Beam-Target Helicity Asymmetry E in K0Lambda and K0Sigma0 Photoproduction on the Neutron

[David Ireland]

Dear Reinhard et al., 

This is a very nice paper. To have been able to extract any results from the limited statistics in these channels is nothing short of heroic! It is also important to point out how the use of BDTs has helped significantly in the analysis. Whilst this technique has been in use in the high-energy community for some time, I do not believe it has been utilized in low-mass hadron physics.

I have a couple of comments that may need to be addressed before submission:
 
- Page 1, line 49-53: It is actually not possible to extract amplitudes with measurements of the minimum number of observables. This is shown in Nys, et al (Phys Lett B., 759 (2016) 260-265), and is because any measurement will have finite accuracy. The complete experiment is a mathematical construct only. I believe it would be more accurate to state something along the lines of:
"To extract amplitudes up to a common, unknown phase, requires the  measurement with sufficient accuracy of observables from each experimental configuration of the three combinations of beam-target, target-recoil and beam-recoil polarization."
In other words, one does not actually measure observables, rather what is measured are asymmetries depending on beam, target and recoil polarizations.



- Page 2, line 70-71: "The present measurement does not involve final state polarizations". I am afraid that it does! By selecting the pi-minus and the proton to identify the Lambda, this unwittingly biases the events if there is any recoil polarization. The equation describing beam-target intensity:
$1 - \obs{E} P_C^{\gamma} P_L^T $
(my, slightly altered notation of equation 2) is what you have used in this analysis. However, the present measurement is actually a triple polarization measurement, whose intensity is proportional to
$ 1 + \obs{P} P_y^R + \left(\obs{L_x} P_x^R + \obs{L_z} P_z^R \right) P_L^T 
 + \left\{ \obs{C_x}  P_x^R + \obs{C_z} P_z^R - \left( \obs{E} + \obs{H} P_y^R 
 \right) P_L^T \right\} P_C^{\gamma}
$
(Use 
\newcommand{\obs}[1]{\textcolor{red}{\mathbf{#1}}}
to get hopefully colorful equations)
This contains seven "observables", not all of which would drop out in an asymmetry, due to acceptances. This is a hard lesson that we learned in g8, where we noticed that the extracted beam asymmetry was wrong if we did not simultaneously extract four other observables.

The effect is almost negligible for the selection of the Sigma, because the emission of the decay photon is not detected, which means that that the event selection is less biased.

Now in the present case, the small number of events is likely to mask this issue, so I would not necessarily suggest that additional work needs done. If the observable H is small, which could be estimated from the theoretical predictions, there should be no worries.



- Figures 7, 8 and 9: As is mentioned in the text, the accuracy only allows one to state that E is mostly positive or mostly negative for the two energy regions. Note that ALL the theoretical curves are +1 at 0 and 180 degrees. There is a good reason for this: the true value of E *must* be +1 at these values, by virtue of the spin algebra! Fasano, Tabakin and Saghai (PRC 46 (1992) 2430) show that the E observable is in the class of observables where this is true. Because of the course binning, the data look like they violate this rule. It may be prudent to make it clear that the points represent an average over the bin.


Apologies for what may seem like pedantry. None of these issues are show-stoppers, but should be given some thought. I am very happy to discuss them further.

Best wishes,

Dave