General
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* [A general theoretical motivation is lacking. The intro of [2]
can be an example?]

Abstract
--------
* [it is unclear that the 3rd unc effectively is the production asymmetry.
How about:]
'and the third is the uncertainty on the B+- production asymmetry,
driven by the knoweldge of ACP(B+->J/psiK).'

1 Intro
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L.15 [a 'publication' cannot measure, how about:]
'but did not include a measurement of its asymmetry [3].'

3 Signal
--------
L.108,112 [Is the fraction of part.reco background relevant? 
It strongly depends on the size of the mass window? What is the mass window?]

L.115,125 [An exponential does not have a slope, but an exponent?]

Fig.2: [Please add the charge of the final state particles to the labels!]

Tab.1 [The last row suggests this is the result of the fit to the full sample.
Instead it is the simple sum of the rows above. I suggest to remove the 3rd row.]
4 ACP
-----
L.130 'physical' -> 'final'
L.131 'have an even number or zero kaons' -> 'have two or zero kaons'

Eq.(3) [The left-hand side is not A^raw_CP! Please remove subscript 'CP'. ]

L.150 'where the statistical uncertainties' -> 'where the uncertainties'

Tab.2 [The '0.016' and '0.020' in the last row 'Total' seem to be reversed!?]

5 Syst
------
Fig.3 [What is the horizontal band in the right figure around mKpi^2 = 10 GeV2 ?]

6 Phase space
-------------
Fig.5 [caption: you mention twice m2<15 GeV2; one of them must be wrong.
I suggest you also indicate this cut inside the figure.]

Fig.6+8 [Add the legend for the empty/full triangles in the figure.]

L.221 [Please motivate why you select m_high>15, as you do for m_low<0.4.
Maybe you can also indicate that region in Fig.3 left.]

Refs
----
[6] Physics Letters -> Phys. Lett.