Dear All,
We have collected the comments we received from everybody and have listed them below. Please check that your comments are included and that you are happy with the chosen wording.
Best regards,
Roel & Tjeerd
General comments:
- It seems that the time-dependent equations in Eq. (4) are not relevant. - We think that it would be much more informative to present the integrals of Eq. (5) including non-zero phi_s and the production asymmetry, but excluding detector dependent effects. Those should be easy to derive. Then it seems important to indicate early that the time integrated equations are only valid if you ignore the experimental acceptances and that ignoring those actually leads to non-negligible systematic uncertainties.
Did you in the analysis correct these equations for the decay time acceptance? We think that it would be very informative to show how equation 5 changes if you introduce a lower cut off in the lifetime. In your analysis, it seems that this lower cut off is about 1ps, very large compared to the lifetimes. Could you explain how the described optimization procedure resulted in such a large cut?
- Performing the time integration before folding in lifetime biasing effects, like cuts and the lifetime acceptance, is not correct. The lifetime component corresponding to A_0 and A_|| is tau_l, while for A_perp this is tau_h. Since a time acceptance has a different effect on these two components, it should be folded in before the integration over time is performed. This holds for both the lifetime bias introduced by the tight FD chi^2 cut and the detector time acceptance.
Comments in detail:
Abstract: Why do we quote three amplitudes squared if the sum is equal to unity? Like in the quoted B factory papers we can limit ourself to the first two.
Lines 2-3: - FCNC is not used further and the abbreviation is superfluous. - A suggestion to replace "Studies ... tests" by "Triple product asymmetry studies in this decay mode provide a powerful test".
Line 12: - Remove typing error 'of' in "V-A of structure". Consider "vector minus axial vector (V$-$A) structure", as we mention also vectors and pseudo scalars.
Line 14: - Replace "roughly equal longitudinal and transverse components" by Longitudinal fractions of $f_L = |A_0|^2 \approx 0.5$ ".
Line 17-19: - Replace 'predictions' by 'calculations' and "give ... 70%" by "allow for $f_L$ in the range of 0.4-0.7 [2,3]".
Fig. 1, caption: - Replace "helicity frame" by "center-of-mass frame" and 'mode' to "decay mode".
Lines 22-31: - I suppose that a reference here in stead of Eq.~(4) will be sufficient; we only consider the time integrated results.
Lines 32-34: - Replace "If as in this Letter ... integrate to" by "In an ideal situation where we can integrate over the full time range with CP violating phase $\phi_s=0$ and an equal number of B0s and Bbar0s mesons are produced, the time integrals of the functions $K_i(t)$ are:" (Avoid "in this Letter". This is not the analysis that is integrated.) - It would be much more informative to present the integrals including non-zero phi_s and the production asymmetry, but excluding detector dependent effects. Those should be easy to derive.
Lines 40-47: - The '$\pm$' sign in the definition of $V$ is not correct, because $\Phi$ is already negative or positive by definition in Eq.(6). - A rearrangement of the text arround Eq. (6) and the equation itself is suggested in the following changes: - Replace "due either to ... is violated" by "due either to final state interactions or to T violation, which with conservation of CPT also implies CP violation." - Move sentence "This approach ... is required" to line 47. - Replace "There are two ... triple products" by "There are two observables, triple products of unit vectors," and then start the equation directly with on the left sides in addition: "V =" and "U =". - Replace "These are proportional ..." by "From Fig. 1 it can be deduced that $V$ is positive if $cos\theta_1 \cos\theta_2 \gt 0$ and zero or negative otherwise. The T-odd variables $V$ and $U$ are proportional ..."
It could help to draw $n_{V1}$, $n_{V2}$ and $p_{V1}$ vectors in Fig. 1 on the outer sides of the two decay planes.
Lines 55-56: - If sample size the number should be larger than 801. If signal yiels they should have estimated uncertainties. - Avoid "In this Letter".
Line 70: Remove "consisting of ... GEM)". (It is not clear if 'consisting' applies also to 'Hadron' and if 'distinguishes' applies to only 'Muon'.)
Line 72: Add '(L0)' after 'triggering'. (L0 is used later without definition.)
Line 76: Add "of various selection lines". (Lines are used later without description.)
Line 83: We don't quite understand why you need to mention "s-plot" here. If you do, you need to mention what was used as separating variable. (In the end, it is just a fancy sideband subtraction. You wouldn't quote that you use sideband subtraction without explicitly mentioning which sideband.)
Note that the optimization using splot explicitly relies on the fact that the signal and background shapes are independent of your cuts. For the background B mass shape that is almost guaranteed not to be the case. (For example, the background B mass slope will depend on pT cuts, and even on vertex chi2 cuts.) We wonder how you took this into account in the optimization.
Line 87: Remove the sentence about the KL distance like in the table. This is just an artefact of our track finding.
Table 1: - Replace "Cut" by "Selection variable". - Are the IP chi2 cut and FD chi2 cut per dof? What is the number of dofs for the FD cut? (if it is 3, that this quantity is different from what most people outside lhcb think that it is.)
Lines 110-112: - Same remark as above about using 's-plot technique': you always should mention the separating variable. - Typing error "Fig. 3". - What function did you use for the two-body phase space component? How did you take the experimental resolution on the KK invariant mass into account?
Line 128: - You say that you use the measurements of Gs and DGs from a different source, including their errors. However, doesn't one expect that the dominating effect is the decay time acceptance?
Fig. 3, caption: - Remove spurious "is applied". - Add the separating variable used for making the s-plot.
Line 142: - We are actually a bit surprised that the effect of ignoring the decay time acceptance is so small. Looking at your analysis note, the lifetime acceptance effectively introduces a cut off of about 1 ps, large compared to tau_l and tau_H. Why don't you see this directly in the amplitudes? Is it because dG/G is small and the sum of the amplitudes is normalized to 1? The analysis note is very brief here: It shows the final numbers but not actually the toy distributions.
Fig. 4: - Are the fit projections corrected for the angular acceptance? This seems impossible to do with just the acceptance weights. If not, then that should be mentioned in the caption.
Table 3: - Replace the '-' with '0.000'. (A dash makes it seem like you didn't compute it.) - We don't understand why you quote separate results and systematic uncertainties for A_par2. You require the sum of the 3 amplitudes to be unity. So, anything that affects two amplitudes, will also affect the 3rd. It seems better to skip A_par2 completely.
For example, given equation 5, it seems hard to understand why A_par2 and A_02 have different sensitivity to the lifetime acceptance: they have roughly the same size, they appear with the same lifetime in your observables, so why do they not have the same sensitivity to the acceptance?
Line 152: - Remove "This has been checked to be valid in simulation studies". Or explain why you would worry about this.
Line 168: Remove sentence "Measurements ... A_0|^2$". The results do not differ so much from ~0.5 with the large spread the other values have.
Lines 169-170: - Replace "in agreement with that" by "almost equal to that". - Replace "also in reasonable agreement" by "in agreement". 'Also' is not correct and 'reasonable' is not subjective.
Line 175: - Replace 'hypothesis of no CP violation" by "hypothesis of CP conservation".