Dear Liming, dear Sheldon,

Congratulations with another very interesting paper.
Please find our comments, on behalf of the Nikhef group, below.

Best regards, Maurizio, Kristof, Niels, Wouter & Tjeerd

General:
------------
- there are a few footnotes in the text. Beware that PRL does not accept them. 
  Include the relative comments in the text.


Main comments/questions:
------------------------
L.260/261 [Q: why is the mass veto different for Psi(2S) and 
X(3872) ?]

L.283 [Q: Do you really mean B0->JpsiK3pi, and not Bs0->JpsiK3pi ?
If you really mean B0->JpsiK3pi, then Bs0->JpsiK3pi decays will 
cause a problem, as they show up under the B0 peak.]

L.301 [Q: How is the fit done? Is it background subtracted? 
How are the error bars of the open circles obtained? 
For the Bs0, at large m, a few open circles
are higher than the closed ones; how is that possible?]

L.318 [Q: What resonance structures were assumed when calculating 
these efficiencies?]

L.342: [Q: how is this efficiency calculated?]

Tab.2: [It's pretty curious that most of the systematic errors 
have the same value of 2.0. While a reader in LHCb could guess 
where all these numbers are coming from, an external reader may 
get confused. A brief description on how they are calculated is 
desireable]

L.369,370 [Q: Some of the phases do not have the +- ambiguity, 
and others have. Is this intentional?]

L.343+4 [Q: The asymmetric error +0.007 -0.008 is not consistent 
with the numbers in Tab.2]

L.373 [Q: We missed the logic here.  
In principle, the tetraquark wavefunction could also contain 
[ud][ubardbar] , even if the B0s also decays to f1. The Bs0
could decay to f1 through the other two components?]


Textual comments:
-----------------
L.7 [Not elegant to start sentence with particle name, how about:]
"The decays of B0 and Bs0 mesons into J/psi4pi are investigated ..."

L.10/12 [The 2 phrases within commas becomes difficult to read, how about:]
"The f1(1285) mixing angle between the strange and non-strange components of its 
wave function in the qqbar structure model is determined to be +-(...)."

L.211 "as the JPC equals 0+- eta and eta' exhibit mixing" ->
"as the eta and eta', with JPC=0+-, exhibit mixing"

L.215 other exotic -> other, exotic

L.217 ["B->Jpsif" are not final states.]  
Use of B->Jpsif finals states ->
Use of B decays to Jpsif final states (where B generically refers to B0 or Bs0 mesons)

L.22 One-third -> One third

L.242: "... by use either of ..." -> "... by using either requirements on the
IP or detachment ..."

L.255 ["when parity inverted" is very confusing, and confuses more than that it
clarifies. Please rewrite.]

L.259 [Add decay descriptor "B->" for clarity:]
eliminate candidate Psi(2S)pipi and X(3872)pipi events ->
eliminate B->Psi(2S)pipi and B->X(3872)pipi candidates

L.272 S2/(S+B) -> S/sqrt(S+B)

L.274: [Please explain what you mean with: "This optimization provides a choice
of requiring BDT>0.1" You mean that 0.1 is the optimal cut? Better is:]
"The resulting optimal BDT requirement is BDT~$>~0.1$."

L.280 events -> candidates

L.282 one mode -> the mode

L.283 appear as a four pion -> appear as signal

L.287,289, etc: [add hyphen] four pion mass -> four-pion mass

L.291 [you don't fit the 'number of events', but you fit a distributions, omit "number of"]

Fig.1 [caption:] signal crystal ball -> crystal ball

L.298 [Unclear what is done. Better is:]
"...is then fit in each mass bin by ((1-alpha)sin2theta + alpha(1+cos2theta)/2), where ..."


L.301 [bit sloppy:] 
"We also show on Fig.2 the helicity +-1 yields." ->
"The event yields with helicity +-1 are also shown in Fig.2."

L.304: "There also is a large and wider peak ..." -> Either 'wider'  
requires a point of comparison, or -if you implicitly compare with f1-  
it should be 'larger'.

L.310 paper -> Letter

L.313/4 "We find 22476+-177 Bs candidates"


L.320/1 PDF -> shapes

L.320: [Q: you quote your largest systematic as 5% from the decay model. This
  systematic is the limiting factor in most precise evaluation of the branching
  ratios. Nevertheless this is not described anywhere in the text. How is this
  systematic evaluated? A brief description would help the
  reader and the journal reviewer to accept it.]

L.326: [Q: you use the central value from PDG for the f1(1285) mass. Do you apply
  any momentum calibration to your sample? If not, how do you protect from the
  0.3% mass bias introduced by detector misalignments?]

L.326,337 [Q: The width comes out 1.5sigma too big, whwreas the resolution of 
3 MeV seems quite small. How is the 3 MeV determined?]

L.329: [Q: We'd like some clarification on the background description. Did you
  perform any study that justifies the use of a Gaussian for describing this
  distribution? Does it correctly take into account phase space effects?]

L.329 [Omit 'overall':] "... overall Gaussian shapes ..." 

L.330: "We restrict the fits to region ..." -> 
"We restrict the fits to the region ..."

L.342 [This is unclear: ] 
"using an efficiency of 0.1820+-0.0036%" ->
"using a relative efficiency of (18.20+-0.36)% "

Fig.2 [move plot to top or bottom of page, and remove 'Preliminary']

L351-352: [It is not clear whatis ment with "B0 high mass shape". Suggestion below.]
"For the B0 high mass shape we change from a Gaussian shape to a second order polynomial." 
->
"For the shape of the m(4pi) distribution above the f1(1285) resonance in the 
B0 case, the Gaussian shape is changed to a second order polynomial."

Tab.2 [move plot to top or bottom of page, and 3.7 is not the quadratic sum of 1.5.]

L.357 [omit "call it the"]

L.367 "by others -> "previously"

L.379: [Rephrase removing the 'So we' at the beginning of the sentence. It's too colloquial.]

Tab.3 [align the "10^-4" in the central column]

Tab. 3: [Is this table really needed? You could consider removing it if you
  need to gain some space. Furthermore, I don't think it's appropriate to a PRL
  article having unnecessary table.]

L.390: [We would rephrase this like:] 
"This is the first time f(1285) is observed in ..."

Refs:
Collaboration -> collaboration