== Physics Comments ==
(1) Fitting a single exponential to the untagged decay time distribution is a good approximation to determine the effective lifetime, but is not an exact method. The result only becomes exact when performing an unbinned NLL fit between 0 and infinity in the absence of any acceptance function. In all other cases there is a small bias of the order of 0.1%, which depends on the value of y_s, A_DeltaGamma (or cos[phi_s] in your case) and most importantly the acceptance. The exact size of this bias can only be estimated using toys. See for example arxiv 1204.1735, or section 10.12 of LHCb-ANA-2012-049.
Since you quote a precision up to the per-mille level as well as discuss systematic uncertainties as small as 0.001, also this bias needs to be addressed.

(2) Could you motivate your choice to use the B- normalisation as the default setup? Why is the Bd->D-Ds+ mode not used as the default normalisation mode? Then you would have a 6 particle final state in both the signal and normalisation, compared to a 6 versus 5 particle one now. In particular, we know that the upper lifetime acceptance depends mainly on the IPz of all of the final state particles (see the B lifetime analysis). So having an additional particle could have an effect on the upper lifetime acceptance.

(3) You write (Line 75) that you have loose PID requirements which are >95% efficient. That is difficult to understand. Looking at the ANA note we see that the efficiency ratio of Bd over Bs is about 0.7, while the only difference between the two modes is the PID efficiency of a single kaon versus pion. Why is this ratio not closer to 1? A similar question can be asked about Fig 1. This ratio is about 1.7, which can be partially explained by the additional kaon in the Bs->DsDs mode, but not fully (the efficiency to reconstruct an additional particle is about 70-80%). Could you explain this effect?

(4) The cross-feed from Bd->D-Ds+ is allowed to vary freely in the fit and the associated uncertainty should therefore already be accounted for in the statistical uncertainty on tau_eff returned by the fitter. The result is also compatible with expectations from calibration. Why is it therefore still necessary to add an extra systematic uncertainty to this? If you think that the yield returned by the fit cannot be trusted, then you should have fixed it in the nominal fit too.

(5) Can you demonstrate (at least in the ANA note) that the efficiency ratio between Bs->D-Ds+ and Bd->D-Ds+ is indeed exactly/mathematically equal to 1? The difference in mass between Bd and Bs leads to a difference in the momentum spectra of the final state particles, which can have many small effects (geometrical acceptance, trigger, reconstruction, ...) on the efficiency ratio. We would therefore like to see the equivalent of Fig. 1 for Bs->D-Ds+ added to the ANA note. In case you can't argue that the ratio is precisely 1, this binned efficiency ratios should be properly taken into account (like you do for Bs->DsDs) and thus affect both the statistical and systematic uncertainty. Even if the results are compatible with 1, as they currently are for Bs->DsDs (Fig. 14 in the ANA note); there is in principle no difference between both measurements.

(6) Can you motivate the choice of binning? How does your result depend on the chosen binning?

(7) How would the result change if you change the positions of the bin centres assuming tau=1.38 ps?


== Textual Comments ==
General:  By writing Bsbar instead of Bs whenever you write out the decay places you in a difficult situation. There are many examples in the text which become very confusing or even inconsistent (e.g. sometimes you write Bsbar meson and sometimes Bs meson). For instance when you talk about the Bsbar lifetime. People might compare such a number with the Bs lifetime and extract CPV from that number. Writing Bs instead of Bsbar will remove most of this confusion and will be more coherent with other LHCb papers.

Abstract: If Gamma_L is just 1/tau_eff then there is really no need to put this number in the abstract. Please consider removing that line.
>From the theoretical point of view, the main motivation to measure the Bs->DsDs lifetime is to use tau_eff as an alternative way to extract phi_s (as given in the introduction and the motivation for PRL). You are therefore specifically interested in the difference between 1/tau_eff and Gamma_L. Quoting Gamma_L would confuse the message you want to bring across.
If you want to give a results for Gamma_L (not in the abstract) then write explicitly under which assumptions for phi_s this is.
Line 2: Add a space between "(CKM)" and "mechanism".
Line 8-9: Inconsistent notation: You write B_s^0 mixing, but B_s meson.
Equation 2: Replace the equality with an approximation sign.
Line 15: You miss the closing bracket.
Line 15: You could add Ref 3 here as well, as it also give the expansion in powers of y_s.
Equation 3: The numerator has twice the same decay descriptor.
Line 31: Write "Bs meson" instead of "\bar{B}_s^0 meson".
Line 69-73: The notation of the reconstructed decay modes with and without parentheses is not consistent.
Line 138: Abbreviate "Figure 3" to "Fig. 3" to be consistent with other references.
Line 150: The fact that the results from the two normalisations come out exactly within 0.003 ps seems a pure coincidence, given that the uncertainty is much larger. Please add the uncertainty to the number.
Line 164: How can you fix the cross feed from Bd->D-Ds+ using (prompt?) D*->D0pi calibration data? Please add some explanation in the text.
Line 169-171: This bias only affects the conversion between tau_eff and Gamma_L and is hence out of place here. It should be placed after Line 173. Please clarify the text.
Line 170: What do you assume for phi_s here? My calculations give 0.0007 +/- 0.0001 (SM), or 0.0024 +/- 0.0063 (Bs->JpsiKK) or 0.0000 +/- 0.0007 (Bs->JpsiKK + Bs->Jpsipipi).
Line 206: There is a word missing after Bs->DsDs. Suggestion: "The resulting effective lifetime of the Bs->DsDs mode is".

PRL justification: (Just a warning) It seems like PRL no longer asks for such a justification.


== Other Requests ==
(1) Figures:
- Can you add horizontal error bars to Fig. 3, to make the binning explicitly visible?
- Can you make Figs. 2 and 4 in the same style (at least: make legend in Fig. 4 non-bold)?
- Can you add the label "LHCb simulation" to Fig. 1 and "LHCb" to Fig. 3?

(2) The numbers quoted in the paper do not always match those in the latest version of your ANA note. We assume some parts of the analysis have been improved in between both write-ups, but could you still update the numbers in the ANA note? Specifically:
- The PID efficiencies in Line 86-87 versus ANA Table 1
- The BDT efficiencies in Line 102 versus ANA Line 279
- The difference between both normalisation modes in Line 150 versus ANA Line 515