Dear Dr. Dusling,


We would like to thank the referees for their helpful remarks and hope
we can address all their questions satisfactorily here and in the
revisions made to the paper.

In revising the paper we discovered an error in plotting the
phenomonological predictions on Figure 2.  This has been corrected on
the new version.

We have also rewritten the section describing the MIE method as
suggested by Referee C.

The table of results has been expanded to include the results using
the four combinations of radiative correction prescriptions: Mo-Tsai
or Maximon-Tjon, and order alpha^3 or exponentiated.

To address the request to show the results from the other recent
experiments for comparison we have added a new figure.  The problem
with comparing the different experiments arises from that fact that
the results are all at different values for (epsilon, Q^2).  To plot
this properly would require a three dimensional figure with the
results as points with error bars above the two dimension plane of
epsilon and Q^2.  Theoretical predictions would appear as surfaces in
such a plot. To approximate this effect we have chosen to plot the
difference between the results and the theoretical prediction of
P.G. Blunden (N+Delta) evaluated at the epsilon and Q^2 appropriate
for each data point.  We plot this difference as a function of
epsilon.  Data points at similar epsilon might have different Q^2
values but the difference to the theoretical curve is correct and
allows a comparison of the measurements relative to Blunden's
calculations.  In this figure it is clearly seen that the data from
the three experiments are all consistent with each other relative to
the calculations.  Furthermore then are systematically below the
calculations by approximately 2% which is roughly constant with
epsilon implying that the calculations have the correct epsilon
dependence.   

To answer the other questions from the referees we quote their remarks
and answer each below in the following text.

> ----------------------------------------------------------------------
> Report of Referee A -- LY14962/Henderson
> ----------------------------------------------------------------------
>
> The manuscript describes a measurement of the hard two photon exchange
> in proton lepton-scattering, which is presumed to be a contributor to
> the discrepancies observed between Rosenbluth and polarization type
> measurements. The field of lepton-nucleon scattering is currently a
> highly relevant field in modern-day nuclear physics due to the recent
> measurements of the proton charge radius in muonic hydrogen, which
> exhibit a strong disagreement between electron and muon results. While
> the measurements described to not directly address this issue, they
> are certainly relevant and serve to motivate theoretical efforts
> related to the nucleon structure.
>
> The manuscript gives a concise and accessible description of the
> OLYMPUS experiments and the measurement, but unfortunately does not
> give a clear conclusion as to whether two photon effects are driving
> the mentioned difference, but rather, motivates further research on
> this issue. I find the manuscript worthy of publication in PRL since
> it addresses important issues, even without reaching a firm
> conclusion. I do however have a few comments which should be addressed
> before publication:
>
> 1. The authors claim that their results are consistent with the VEPP
> and JLab results. However, both these experiments, whose results have
> been published in PRL claim to support the resolution of the form
> factors discrepancy with two photon effects. This claim seems to be at
> odds with the claim made by the current manuscript, who mention that
> their resort to not serve to resolve the discrepancy. Since the
> uncertainties in all three experiments are of similar size, I would
> expect the claim to either be different or for the authors to state
> more clearly why they claim different than the other two experiments.


The new figure 3 shows that all experimental data are in agreement
with respect to Blunden's calculation.  But it is also systematically
lower than the calculation implying that the calculations that address
the discrepancy at higher Q^2 are inconsistent with the data at these
lower values.  In figure 2 the fit to the form factor data by Bernauer
is in good agreement with the OLYMPUS results and if we produced a
similar difference plot using this calculation it would have better
agreement with all the recent experiments.  This suggests that the
model for TPE in Bernauer's fit agrees with the recent measurements as
well as addressing the discrepancy in the form factor data. 


>
> 2. Related to my previous comment. Since the results from the other
> two experiment have already been published, they should be presented
> on the same figure used to present the new results (Fig. 2 in the
> current manuscript) so that the reader may better gauge the
> consistency on the results. Other, less precise, world data, could
> also be included, but it's inclusion is likely of no benefit to the
> reader.


The new figure 3 hopefully addresses these concerns.


>
> ----------------------------------------------------------------------
> Report of Referee B -- LY14962/Henderson
> ----------------------------------------------------------------------
>
> This manuscript reports on a measurement of the positron-to-electron elastic
> scattering off the proton, relating to the probability for hard two-photonexchange
> (TPE). The present results are measurements at the highest
> momentum transfer yet, and follow one year behind the first measurements
> from other laboratories. Since the dependence of the effect on the momentum
> transfer is key to understanding the possible implications of TPE to the
> longstanding puzzle of the elastic form factor ratio, the present results are
> important and should be considered for publication in PRL. The introductory
> paragraph of the paper is written at a level that is accessible to a broader
> audience of non-experts, and correctly gives the motivation for these
> experiments.
> The paper as a whole is well written, and this referee could not identify major
> issues with the data. Hence, the paper could be published as it is. However, I
> would like the authors to consider the remarks listed below.
>
> - the authors combine the results of four independent event selection routines.
> The paper states how the combined statistical uncertainty was determined, but
> not how the actual result was computed. Was an unweighted average used? I
> trust the authors did the correct thing, but adding just one word could satisfy the
> curious reader.


The results for R_2g from the four independent analyses were simply
averaged.  Since the statistical and systematic uncertainties for each
were very similar we deemed this sufficient and unbiased.  We used the
spread in the results at each bin as an additional systematic
uncertainty.


>
> - a little further in the same paragraph, it is stated that the results for the
> background rates in electron and positron samples were found to be "similar" in
> all analyses. What is the meaning of "similar"? Same shape? Same rate?
> Consistent within statistical uncertainty? Please clarify.


The backgrounds in all analyses were similar in magnitude for each Q^2
bin.  At low Q^2 the background was negligible and gradually increased
to around 20% of the signal at the highest Q^2.  This was roughly the
same for all analysis and was also the same for both electron and
positron data sets.


>
> - the largest source of systematic uncertainty is, as could be expected, due to the
> luminosity measurement. It is therefore unfortunate that the authors choose to
> give only one number for this uncertainty, resulting from one out of four
> independent methods. It is stated that these all yield consistent results, but could
> not a line or two be spared to actually show these results?


The slow control, 12 degree, and MIE luminosity determinations gave 
values that were better than their individual uncertinties which
were on the order of 3%, 0.5%, and 0.3% respectively.  The SYMB result
was systematically lower than the others by around 4%.  For brevity we
avoided explaining the details of each method and their absolute and
relative uncertinties.  We intend to publish a longer paper where we
can go into such details.


>
> - the results are compared in Fig.2 to predictions from the literature. It is not
> easy to make a comparison to the results of the other experiments [12,13],
> because each experiment seems to pick its own choice of theoretical predictions.
> This is not helped by the statement in the text "TPE calculations.... predict a
> larger effect at the energies directly measured so far". Does this statement refer
> to any of the predictions shown in fig.2? If so, which one? If not, a reference, or
> show the prediction? This is not entirely trivial, given that the different
> conclusions of the present paper (no significant conclusion on the effect of TPE
> possible) and of [12, 13] (support for the effect of TPE) do not really help in
> resolving this puzzle. This referee does, however, support the cautious
> interpretation of the data/theory comparison given in the present manuscript.


Hopefully the new figure 3 addresses some of these issues.


>
> ----------------------------------------------------------------------
> Report of Referee C -- LY14962/Henderson
> ----------------------------------------------------------------------
>
> This paper presents important results and should be published in PRL.
>
> Olympus is the third of a series of recent high-precision experiments
> focusing on two-photon exchange (TPE) contribution to lepton-proton
> scattering, via the measurement of the ratio of (e^+p) to (e^-p)
> elastic cross sections.
>
> The paper is well written. The ratio R_2gamma and its role in
> understanding the discrepancy between polarized and unpolarized proton
> form factor measurements are clearly explained, as well as the
> practical procedure to extract R_2gamma from the experiment.
>
> A very complete set of results is presented over a large range of
> epsilon (or Q2, being here correlated to epsilon by the fixed beam
> energy). The obtained values of |R_2gamma-1| hardly exceed 1%,
> suggesting that TPE is not enough to fully explain the discrepancy in
> proton form factor measurements, at least for [Q2 < 2 GeV2] which is
> the presently explored range for R_2gamma. This naturally calls for
> future high-precision (e^+p)/(e^-p) experiments at higher Q2, where
> large values of R_2gamma would be necessary to explain the form factor
> discrepancy.
>
> I have three main remarks, listed below, and a few minor comments.
>
> 1) The whole experiment is about radiative corrections (RCs) and how
> they are handled. As said in the text, higher-order RCs (i.e. beyond
> order alpha^3) are becoming significant, in view of the sub-percent
> precision reached experimentally. The authors could say more clearly
> to what extent higher-order RCs become (or will become in the future)
> a limitation for interpreting the TPE effect.


We have modified the text slightly to stress the need for more
theoretical understanding of higher order effects.  However, this
depends on many factors, e.g. how much of the radiative tail is
included in the measurement. It's certainly of crucial interest for
initial state radiation measurements. However, the PRL format does not
allow us to explore these things in detail, and we must defer to a
longer review in the future.


>
> Exponentiation is only an approximate method to estimate the
> higher-order RCs. I see the difference between exponentiated and
> non-exponentiated results (difference |(a)-(b)| in table II) more like
> a theoretical uncertainty attached to the order alpha^3 calculation,
> that should be taken into account when comparing data with theoretical
> curves (fig.2). Figure 1 is also suggestive of how the experimental
> determination of R_2gamma is RC-scheme dependent. High-precision
> experiments like this one really call for improvements in the
> calculation of RCs (higher orders in alpha, but also reducing the
> approximations made at order alpha^3) and this could be said in the
> paper.


We added a sentence to that effect and modified the plot to show the
Mo-Tsai with exponentiated prescription,


>
> 2) I have several comments on one sentence about the multi-interaction
> events: "This method compared the relative rates for lepton-lepton
> coincidences in the SYMB with the rates for simultaneously detecting
> an additional ~ 2 GeV lepton from lepton-proton elastic scattering
> [17,30]."
>
> - The word "relative" is ambiguously placed: what is relative to what?
> is it:
>
> "the rates for lepton-lepton coincidences in the SYMB" relative to
>
> "the rates for simultaneously detecting an additional ..."
>
> or something else? (it could be relative rates compared to other
> relative rates).
>
> - The word "simultaneous" is ambiguous. you probably mean an
> additional lepton in accidental coincidence with the true
> lepton-lepton coinc.?
>
> - This additional lepton: you should add in which detector (the
> SYMB?).


The MIE section has been rewritten and hopefully this is more clear
now.


>
> - Why is this MIE method finally chosen? is it because it gives the
> smallest uncertainty (the 0.36% of next sentence)? it's not clearly
> said. if yes, can one get a clue as to why it gives the smallest
> uncertainty?

We rewrote that paragraph to make it more clear.
Since MIE essentially is a ratio of two measured rates, many systematical
errors drop out or are strongly surpressed, i.e. the theoretical description
of the Moeller/Bhabha cross section, acceptance effects etc.


>
> 3) In the conclusion paragraph, some sentences could be made clearer
> by adding the words marked below between brackets:
>
> "TPE calculations that bring the form factor ratio measurements into
> agreement at large Q2 predict a larger effect [in R_2gamma] at the
> energies directly measured so far".
>
> "Therefore, it is not evident, nor ruled out, that TPE is driving the
> difference [in form factor ratio measurements] at large Q2".
>


The paragraph was rewritten, but we adapted the suggestions.


>
> A few minor comments:
>
> - The background in the elastic samples: is its origin
> known/understood?


Not really.  Some part will be due to pion production not completely
eliminated in the event selection.  Other is noise from beam halo
and/or Moller/Bhabha events stricking the target chamber and showering
into the detector.


>
> - The background subtraction procedure: on what is it based?


The analysis have different approaches. For example, some look at the
coplanarity, which has a clear peak at 180 degrees, and a
triangle-shaped background from random track pairings waas fit to the
wings and subtracted. In each Q^2 bin, the background is determined
via a fit of the background model, and then subtracted from the peak
integral.


>
> - The similarity of background rates for e+ and e- modes: is it
> expected?

More or less, yes. There are two effects at play hear: Positrons had a
slightly cleaner beam, which should produce less noise, but higher
luminosity, which produces more. However, the observed beam behaviours
were quite close, and so are the background rates.


>
> - The (possible) systematic error coming from having run mostly with
> only one toroid polarity: is it addressed somewhere?


Yes, that's essentially the geometry and tracking efficiency. If the opposite-polarity
runs would have had very similar beam conditions, these effects would cancel.


>
> - Table 2: column 1 ("bins") is not very useful.


We dropped this column and added the results with the Maximon-Tjon RC convention.


>
> - Fig. 2, curve labeled "Blunden N": shouldn't it be referenced as [4]
> (instead of ref.[31] in the text, which should apply only to the curve
> "Blunden N+Delta")?.
>


We were in contact with Peter Blunden and follow his advice here.  He
has a paper in preparation that should be completed shortly.
Otherwise he was kind enough to send us his code so we could calculate
at the epsilon and Q^2 values for each data point used in figure 3.


> - Ref. [27]: what is the document type (MIT internal report?)


The reference should be Axel's thesis but a paper is also planned and
should be available in a few months.

If there are any further questions we will be happy to discuss them
further.  Thank you again for your careful review and comments.