Re: LA11364
    Production of mesons and baryons at high rapidity and high $p_T$
    in proton-proton collisions at $\sqrt{s}$ = 200 GeV
    by I. Arsene, I.G. Bearden, D. Beavis, S. Bekele, C. Besliu, et al.

Dear Dr. Christopher Wesselborg,

We thank both referees for their comments and suggestions. We have studied them carefully and applied appropriate actions to the letter. We give a detailed reply to each comment or suggestion from each referee:

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Report of Referee A -- LA11364/Arsene
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 1)  On a sentence extending from page 3 to page 4 of the manuscript,
 and again on page 7, the authors present an opinion on the
 reason for the failure of NLO QCD with the parton distributions
 and fragmentation functions they tested.  Quoting from the latter
 instance,  ". . . because it [NLO QCD] does not include the effects
 of baryon transport . . . "

 Recommendation: this sentence could be acceptable if the word
 "perhaps" were inserted before "because".  There is apparently
 no room in this format for the discussion of options other than
 baryon transport, even if they could be ruled out.   In fact,
 it's not completely clear what they mean by "baryon transport"
 in this context.  It should be defined.  A similar modification
 of the earlier statement on transport is also in order.

OUR REPLY:
We have changed the text in three places to add a definition of baryon number transport and to leave some room for other options to explain the failure of NLO calculation of proton and anti-proton spectra.

The first mention to "baryon transport" in the text appears in:
Page 3 Paragraph 2 where we state:
"The difference between $p / \pi^{+}$ and $\bar{p} / \pi^{-} $ at y=3.3 is remarkable and caused by an unexpectedly large proton yield at these rapidities. Such large yield may be
related to the mechanism that transfers baryon number from beam to intermediate rapidities. 
What remains as an open question is the mechanism that gives these protons such high $p_{T}$. "

This sentence will be changed to provide a definition of "baryon number transport" and clarify the comparison between the $p / \pi^{+}$ and $\bar{p} / \pi^{-} $. The new sentence reads:
"The difference between $p / \pi^{+}$ and $\bar{p} / \pi^{-} $ at at both rapidities is remarkable and caused by an unexpectedly large proton yield at these rapidities. Such large yield may be
related to the mechanism that transfers a conserved quantity; the baryon number from beam to intermediate rapidities i.e. baryon number transport. What remains as an open question is how  a mechanism that is thought to be mainly restricted to the longitudinal component of the momentum, gives these protons such high $p_{T}$. "

We mention "baryon transport" again in the summary (page 4 first paragraph) 
Where we state:
 "NLO pQCD calculations reproduce reasonably well the produced particle (pions and kaons) distributions but p and pbar cannot simultaneously be described well by any of available fragmentation functions." 

To us, the most obvious missing mechanism in the collinear factorization of the cross sections used in NLO calculations is  one that determines how the initial baryon number carried by both beam protons is distributed in rapidity space. Our understanding of this phenomena so far, is that this transfer is considered non-perturbative and happens mainly along the longitudinal momentum.  We agree with your suggestion that we should only list a possible reason for the failure of NLO calculations to describe the spectra of protons and pbars. 
The  sentence that follows in the same  paragraph will then read:

"These results show a limitation of the factorized description of p+p cross sections, perhaps because it does not include the effects of baryon number transport that, as the data suggests, may extend to high pt"

 
 2)  The claim of complete dominance by "gluon baryon pair production
 ..." in the caption for Fig. 3 then needs elaboration.    Is this
 the case for all fragmentation sets, and is it a matter of a factor
 of 10 or 5, or what?  Also, given the failure of one of the modern
 fragmentation functions by a factor of 10, one wonders how strong
 are the physics conclusions that can be reached on the basis of
 the baryon contributions from any of these sets.

 Recommendation:  we need a much clearer presentation of how the
 fragmentation functions were used, and why, in the main text.

OUR REPLY:

The caption of Fig. 3 states:
The $p$ and  ${\bar p}$ are compared with the calculation using the AKK set divided by 2 
(dashed red line in on-line version). The division by 2 conveys the dominance of gluon baryon pair production at high rapidity. "

This only applies to the calculations using the AKK set of fragmentation functions. This new set of FF is different to KKP or K mainly in their increased contribution from gluons fragmenting into p and pbars. As we state in page 3 paragraph 4, this contribution can reach values as high as 80% for pt<5GeV/c. We also emphasize in the text that  gluons would fragment into equal numbers of protons or pbars. We make use of  this last fact to claim that AKK/2 should reproduce equally well the proton and pbar spectra. 

We did not perform the calculations, they were done by Werner Vogelsang as is indicated in the text as soon as we describe the comparison between the  calculations and our measurements. We focused on the use of the AKK set to describe protons and pbars because the RHIC STAR collaboration reported recently a good description of protons and pbars at mid-rapidity (Phys.Lett. B637 (2006) 161-169) The agreement between the measured p+pbar and the calculation with the AKK set is good at y=2.95 but it cannot be reconciled  with the small pbar/p ratio measured at y~3. In contrast, the NLO calculations that use the AKK set produce large pbar/p ratios both at mid-rapidity and at y~3

 3) CTEQ6 parton distributions should be referenced.
Done we now include the following reference for the CTEQ6 PDFs: 
J. Pumplin et al. JHEP 0207 (2002) 012  [arXiv:hep-ph/0201195].

 4) Some indication is needed of the motivation for and origin of
 the "modifications" to fragmentation functions described in the
 middle of page 6.  Is a reference in order, or is this the first
 time these modifications were ever done?  Why have the authors
 chosen these specific multiplication factors of 1+z and 1-z?

As we said in our reply to your previous question, W. Vogelsang performed the calculation with standard fragmentation functions KKP and K, the modifications he applied to the KKP set are done for the first time but they are an extension of accepted procedures that have been used for awhile by the NLO community. That is the main reason for us to include an as brief as possible description of the modifications. We have added a reference to give the reader some background on NLO calculations and the use of additional 1-z) terms.
 
The use of linear suppression factors (1-z) is an accepted practice to emphasize the unfavored nature of fragmentation into a positive pions from a quark that is not a pi+ valence quark. The following quote from 
E. Reya, Phys.Rept.69:195,1981 (page 302) may clarify our previous statement:

"Further constraints come from experiment [252]. Semi-inclusive neutrino reactions (eqs. (10.3) and
(10.4)) tell us that the favored “valence” distributions such as D^{pi+}_u, behave as  (c — z) for z —> 1
with c >=  1 (but close to 1). Similarly, data [252] on the neutrino(anti-neutrino) induced production ratio pi+/pi- (pi-/pi+) dictate the z-dependence of the ratio of favored (“valence”) to unfavored (“sea”) fragmentation
functions [253] to be D^{pi+}_u/D^{pi-}_u ~  (c — z)^-1 with c >~ 1 (but close to 1); for simplicity we assume this latter ratio to hold also for kaons."

Vogelsang's modifications to the KKP consisted in multiplying  the function D^{pi0}_q by the same  linearly suppressing term (1-z) whenever the parton q is unfavored (not a valence quark) and to recover the relation 
D^{pi0}_q = 1/2(D^{pi+}_q + D^{pi-}_q) he   multiplies D^{pi0}_q by (1+z)  to obtained the fragmentation functions of favored quarks. The following quote from the same author may clarify the definition of favored and unfavored quarks:

"As an intuitive example let us first discuss a model of how to construct fragmentation functions for
pions and kaons, but neglecting baryons [251]. Isospin and charge-conjugation invariance reduces the
number of independent D^{pi}_q fragmentation (or quark decay) functions to three [249]; these can be
further reduced to two by assuming [250] that D^{pi+}_s is approximately equal to D^{pi+}_d  both of which are
unfavored (“sea”) with respect to D^{pi+}_u (the favored “valence” decay function) since the parent quark u
can directly form a  pi+ by combining with a d-bar (produced from a bremsstrahlung gluon which converts
into a dd-bar), whereas to make a  pi+ from either d or s requires the creation (via gluon bremsstrahlung) of
at least two new flavor pairs u u-bar and d d-bar. Thus we have (remember that pi+= (u d-bar) and pi- = (u-bar d)) ....."

To our knowledge, this is the first time charge separated fragmentation functions have been obtained from functions fragmenting into neutral pions, but we will modify the text to add the reference mentioned above:

Page 3 paragraph 3 will be changed to read:

"Modifications were necessary  to obtain functions producing the separate charges for both $\pi $ and $K$. 
These modifications are based in functional forms supported by measurement \cite{ E. Reya, Phys.Rept.69:195,1981) and involve the following operations: ..... "

 5)  In Fig. 1, the caption states that errors are statistical.
 I didn't see a presentation of systematic errors in the figures,
 even though they are clearly of interest. Could they be different
 for protons and antiprotons? Presumably not, but it might be nice
 to have this said explicitly. Also the meaning of the shaded
 regions in Fig. 2 needs some explanation.

You are right to point out that we omitted the description of the systematic errors in Fig. 2. We are modifying the Fig. 2 caption.

The systematic errors are not shown in Fig. 1 because they are almost unnoticeable in semi-log scale. Table I in the text lists the estimates for several sources of systematic errors. In particular we estimate that our particle identification introduces some systematic error that is different for each particle species.
The shaded rectangles seen in Fig. 2 show the estimated systematic errors for the different ratios.  Our studies show that a naive cancellation of all of our systematic error does not occur. The figure caption has been modified and now reads:

"Particle ratios versus $p_T$ at y=2.95 and 3.3. Top) $\pi^-/\pi^+$, Middle) ${\bar p}/p$  and Bottom) $p/\pi^+$ (red circles) and ${\bar p}/\pi^-$ (blue squares). The shaded rectangles indicate an overall systematic error (17%) estimated for these ratios. The dashed line shows an upper limit for the
$(p+\bar{p})/(\pi^{+} + \pi^{-})$ ratio from $e^+ e^-$ collisions."

We have also realized that Table I only lists the pion systematic error related to particle identification. We will add two more columns, one for kaons and the other for both protons and anti-protons. Our estimates do not show a difference in particle identification related systematic errors between p and pbar. 

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Report of Referee B -- LA11364/Arsene
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1. Page 4, paragraph 3, line 4: It is stated that the minimum bias
trigger cross section is "estimated". On what basis is this done?

We have changed the sentence to add some details. We have also corrected the text to mention the actual correction used in the spectra generation. 

The estimate was done with events generated by PYTHIA and the GEANT simulation of the BRAHMS setup.
The text was changed to add clarity: 

Page 2 second paragraph changed to read:
"This trigger required that at least one hit is detected in both sides of the array.
We used events generated with PYTHIA \cite{Pythia} and a GEANT simulation of the BRAHMS setup to estimate that this trigger  can access to $70 \pm 5\%$  of the total inelastic proton-proton cross section of 41 mb." 

Table I has a list of the different contributions to the systematic error in our measurements, We realized that the error on the overall normalization is too low (1.5%) and should be changed to 7%. The overall normalization factor is wrongly quoted in the text as being equal to 15+-1% it will be changed to 13+- 7% (this change does not affect the figures as they have the correct normalization). 

2. Page 5, paragraph 1, line 2: The track reconstruction efficiencies
were extracted from the data. How is this done? I understand that
there is not much space for detailed technical explanations in a PRL,
but it would be nice to at least get an idea of the procedure.

The corresponding sentence (page 2 paragraph 4) will be more explicit:

“Tracking and matching efficiencies for each of the 5 tracking stations in the spectrometer were calculated by constructing full tracks with only 4 stations and evaluating the efficiency of the 5 th station. These efficiencies are of the order of 80-90% and are included in the extraction of the cross sections.”

   

3. Page 5, paragraph 3, line 3: The pi-/pi+ ratio at y=2,95 (fig. 2,
upper left) is not "falling steadily". There is a  feature from
roughly pt = 1.5 to 3.5 GeV, which is beyond statistical errors. This
is not seen at y=3.3. Can you comment on that?

We have changed the sentence to add the rapidity correspondance of each panel and changed the expression "falling steadily" into "falling trend" . 

The feature visible in the pi-/pi+ ratio at y=2.95 may be related to the pi+ spectrum, it is most likely related to our ability to match magnetic field settings. We have not been able to pinpoint the exact nature of this mismatch and have allocated a 10% contribution to the overall systematic error of 17% shown with grey boxes in the figures. The ratio at y=3.3 is constructed from the same magnetic field settings but at different region of our spectrometer acceptance.  
When we look at this ratio at both rapidities we see a consistently falling trend. The text has been changed:

Page 3 second paragraph:

"The upper panels of Fig. \ref{fig:ratio} show the $\pi^{-} / \pi^{+}$ ratio at y=2.95 and 3.3 respectively. Both ratios display a falling trend as a function of $p_{T}$. "

4. Figure 2 (lower left panel): There is a patten in the p/pi+
ratio at y = 2.95 which is not present at y=3.3 (lower right
panel). Interestingly, it is again in the pt range 1.5 - 2.5. There
is no mentioning in the text about this structure. Can it be
attributed to the pi+ spectrum, entering in the denominator in
both ratios?

Yes, it could be that the feature seen at y=2.95 in the pt range of 1.5-2.5  in the p/pi+ ratio can be attributed to the pi+ spectrum, but that statement would exclude possible effects in the proton distribution, we would rather see the measured ratio as is, within the quoted systematic errors. 

5. Figure 3: Data are compared to NLO pQCD for y=2.95. Are the
findings at y=3.3 similar?

Yes they are. All RHIC collaborations make the tabulated data available once their papers are accepted  for publication. We intend to continue that trend and offer as well, the NLO calculations corresponding to each spectra.