>> Dear Reviewer,
Thank you for the comments that you have provided. I have replied
inline and uploaded a new version of the pdf.

thanks for submitting this very relevant and carefully prepared
contribution "Online measurement of LHC beam parameters with the ATLAS
High Level Trigger". I recommend to accept this paper, however, with
some minor revisions.

In the beginning of paragraph 4.3, you describe the true beamspot
width as 20mum with a resolution of 10mum. Now, comparing this to
Fig. 2b, the resolution shows a range of 15-140mum and the beamspot
width is about 30mum.

This should be clarified or corrected before acceptance of the paper.

>> Indeed, the text may be seen as mis-leading since the true width is
   not fixed, changing from run to run due to different beta*
   parameters, and over the course of a run due to emittance, and the
   vertex resolution is a strong function of the track
   multiplicity. Since the use of qualifiers such as "roughly" and
   "approximately" do not strongly enough convey that the numbers in
   this paragraph are meant only to give a sense of the difference
   between the x,y and z magnitudes, I propose the following updated
   text:

   The true beamspot width in 2011 was roughly 15 to 45 \mum\ in $x$
   and $y$, and 25 to 75~mm in $z$. The $z$ vertex resolution is
   on the order of 100~\mum, so the resolution is not a significant
   consideration in the measurement. This is not the case in $x$ and
   $y$ where the resolution is on the order of 10~\mum.

The method to determine the true beamspot resolution assumes gaussian
shapes, whereas the distributions have quite significant non-gaussian
contributions. What is the precision of this method?

It would be nice to clarify this point, but is not essential for
acceptance.

>> I assume the statement about non-gaussian contributions comes from
   the tails in Fig. 1? Those figures display the x, y, and z position
   of all vertices with >= 6 tracks. When plotted in bins of track
   multiplicities, the non-gaussian tails are significantly reduced,
   especially at high multiplicites (>~ 12 tracks, though this number
   depends on which track quality cuts are used) where there is very
   little background. This is true of both the vertex position
   distribution from which the un-corrected widths are extracted, and
   the split-vertex distributions from which the resolutions are
   extracted.  In addition, the gaussian fits are only performed
   within +- 1.8 RMS of the mean. In this region, the distribution is
   highly gaussian at all track multiplicites, as described later in
   the paper.

   I have modified the caption of Fig 1 to make the track requirement
   obvious:

   The $x$~\subref{fig:pos:x}, $y$~\subref{fig:pos:y}, and
   $z$~\subref{fig:pos:z} distribution of primary vertices
   reconstructed online with $\ge 4$ tracks in the High Level Trigger
   in 1 minute of data-taking.
   

In contrast of the generally well and carefully written paper, the
last paragraph of section 4.3 (starting with "The method makes waste
of good vertices with large numbers of tracks..") is very difficult to
read. Also, the logic of the paragraph seems inverted as the method is
unusable for vertices with a *small* number of tracks.

This paragraph needs some rewriting for acceptance.

>> The offending paragraph has been re-written and split up as follows:

    Unfortunately, the split-vertices probe the resolution for
    vertices with half as many tracks as the primary vertex.  For a
    sample of reconstructed vertices with up to $n_{Max}$ tracks per
    vertex, in the best case all those above $n_{Max}/2$ will
    effectively be thrown out as we do not have an estimate of their
    resolution. Figure~\ref{fig:res} demonstrates this. It shows the
    width of the primary vertex width, the resolution measurement, and
    the resolution-corrected beamspot width as a function of track
    multiplicity for the $x$-axis. The primary vertex width
    distribution extends up to 75 tracks per reconstructed vertex,
    whereas the resolution and corrected width only extend up to 36.

    Finally, the systematic uncertainties and background effects at
    low track multiplicities can cause large deviations in the
    resolution-corrected width measurement. As the size of these
    effects diminish, the corrected width distribution flattens,
    typically as it approaches the size of the resolution
    measurement. At higher track multiplicities, the statistical
    variations in the resolution measurement become more significant.