# Responses to PLB Referees

Responses to Reviewers' comments:

We would like to thank the referees for the insightful and constructive comments. We discuss below our detailed replies to your questions and the corresponding explanation of changes to the manuscript. But before we go into the replies to the comments, we want to make the referees aware of changes to the results that were prompted via our studies of the systematic effects on the yield extraction. Since this paper deals with cross sections and with nuclear-modification factors, both of which involve obtaining the yields of the Upsilon states, this change affects all the results in the paper. We therefore wanted to discuss this change first. Please note that the magnitude of these effects do not change the overall message of the paper.

We wanted to alert the referees up-front about this important change before we proceeded into the detailed responses. This study was indirectly prompted by one of the questions from Referee 2 regarding systematic effects from yield extraction.

In the process of investigating the systematic difference between extracting the upsilon yield through simultaneous fitting compared to background subtraction as requested by the referee, we also studied the effects of chi^2 fits (specifically of Modified Least-Squares fits) compared to maximum-likelihood fits. We used chi^2 fits in our original submission. We were aware that extracting yields using a chi^2 fit introduces a bias (e.g see Glen Cowan's "Statistical Data Analysis", Sec. 7.4). The size of the bias is proportional to the value of the chi^2 of the fit. In the case of the Modified Least-squares fit, when fitting a histogram including the total yield as a fit parameter, the yield will on average be lower than the true yield by an amount equal to chi^2. The relative bias, i.e. the size of the bias divided by the extracted yield, goes to zero in the large yield limit, which is why for cases with large statistics this effect can be negligible. We had attempted to mitigate the effects of this bias by using the integral of the data, since this removes the bias completely in the signal-only case. But a bias remains in the case where there are both signal and background present. For our case, the yield extracted from the fit for the background is also biased toward lower values, and since we used this background estimate to subtract from the integral of the data in the extraction of the Upsilon yields, these biased the Upsilon yields towards higher values. Through simulation studies, where we include signal and 3 background components as in our analysis, we were able to quantify these effects. Given that in some cases the biases could be of order 10-20%, the fits needed to be redone in order to remove the bias. The solution is straightforward since the extraction of yields using a maximum-likelihood fit is unbiased. We have studied the difference of a modified-least squares fit and a maximum-likelihood fit and confirmed that the yield extraction in the latter method is essentially unbiased. We therefore have redone all the fits to extract the Upsilon yields via maximum-likelihood fits. The revised results are now quoted in the paper. The overall message of the paper is not affected by these changes.

We proceed next to answer the specific points raised by the reviewers.

Reviewer #1: This paper reports results on Y production in pp, dAu, and AuAu

collisions at top RHIC energy. It contains original and important

results and clearly qualifies for publication in PLB. However, there

are many aspects of the paper which need attention and/or improvement

prior to publication. They are detailed below:

1. the introduction is carelessly written. For example, the value

quoted for the pseudo-critical temperature near mu = 0 of 173 MeV is

taken from an old publication in 2003. Recent lattice results from the

Wuppertal-Budapest group (PoS LATTICE2013 (2013) 155) and the Hot QCD

Collaboration (Phys.Rev. D81 (2010) 054504) imply much lower T values

near 150 MeV and are far superior in terms of lattice sizes and spacing.

the results from the Hot QCD collaboration (Phys.Rev. D81 (2010) 054504) do not imply

much lower T values. In that paper, in section IV "Deconfinement and Chiral aspects of the QCD transition", when discussing the deconfinement transition temperature range the authors write:

"...we have seen that the energy density shows a rapid rise in the temperature interval T = 170–200. MeV. This is usually interpreted to be due to deconfinement, i.e., liberation of many new degrees of freedom".

Therefore, this does not indicate T values near 150 MeV. In addition, they also mention this range when discussing their results for the renormalized Polyakov loop, which

is the parameter most closely related to the deconfiment transition, being that it is the exact order parameter in the pure

gauge case:

"The renormalized Polyakov loop rises in the temperature interval T = 170–200 MeV where we also see the rapid increase of the energy density."

Therefore, the results from the Hot QCD collaboration do not imply T values near 150 MeV.

In addition, in reference 9 of the Wuppertal-Budapest group (JHEP 1009 (2010) 073 arXv:1005.3508), which is a paper comparing the various results for Tc between the Wuppertal-Budapest and HotQCD groups, again the results for the renormalized Polyakov loop (figure 7, right) indicate a broad transition region in the region T=160-200 MeV. They do have a table discussing values of Tc of about 147 MeV, but that is for the chiral transition, which is not the most relevant one for quarkonium suppression.

When they look at the trace anomaly (e-3p)/T^4, they see 154 MeV for the Tc value. They in addtion make the point that the transition is a broad crossover, which is something we also say in our paper. The fact that the transition is a broad crossover leads to differences in the estimates of the pseudo-critical temperatures depending on which observable is used. As an example, in the caption of Table 2, where they give the values of Tc for many observables, they mention that the Bielefeld-Brookhaven-Columbia-Riken Collaboration obtained Tc=192. They also note "It is more informative to look at the complete T dependence of observables, than

just at the definition-dependent characteristic poins of them." So given the above, we will modify the paper to give a range of temperatures, 150-190, and cite the papers from the

Wuppertal-Budapest and HotQCD collaborations.

probe..' does not get to any of the real issues, such as the complex

feeding pattern in the Y sector and the crucial question of whether Y

mesons reach equilibrium in the hot fireball as required to interpret

the apparent sequential melting pattern in terms of 'break-up'

temperatures.

The reviewer also mentions that there is a crucial question as to whether the Upsilon mesons reach equilibrium with the fireball as a requirement to interpret the sequential melting pattern. We respectfully disagree with the referee in this matter. The Upsilon is by definition not in equilibrium. The only requirement of course is that the medium is deconfined. In lattice QCD studies only the medium is thermalized; the potential between the heavy quarks is screened independent of whether the Upsilon is in equilibrium or not. We discussed this issue with lattice expert Peter Petreczky who confirmed our view.

furthermore, statistical recombination is not a 'complication' but a

direct measure of deconfinement. And the smallness of off-diagonal

terms in the recombination matrix does not imply absence of

recombination as the diagonal terms can be substantial.

Also the newest results on p-Pb collisions from the LHC are entirely

ignored, see, e.g., arXiv:1308.6726.

2. section on experimental methods

no detail is given concerning the crucial momentum resolution but it

is stated at the end of this section that cuts were adjusted for

different systems such that 'tracking and electron id would be the

same across the 3 data sets'. On the other hand, already in Fig. 1 we

see a strong dependence of the mass resolution on the system even for

low multiplicities as in pp and p-Pb. The effect must be much stronger

in Pb-Pb as is indeed visible in Fig. 4. Especially in view of the

importance of resolution for the separation of excited Y states this

referee has to be convinced that the systematic errors are under

control for momentum and pid measurements as a function of

multiplicity. Also how the systematic errors for the separation of Y'

and Y'' from Y are determined as a function of multiplicity needs to

be demonstrated explicitely.

3. Fig. 2b

even at y = 0 the difference between data and models is less than 2

sigma, taking uncertainties due to the pp reference into account and I

don't believe it makes sense to argue about effects beyond shadowing

and initial state parton energy loss in these data.

4. in Fig. 3 the size of the systematic errors should be indicated.

5. in Fig. 5 it is demonstrated that the observed suppression near

midrapidity is independent of system size (N_part). This could imply

that the higher Y states are already disappeared in dAu

collisions. This is mentioned briefly in the conclusion, but could be

stressed more.

6. At LHC energy, the anisotropic model of Strickland reproduces well

the centrality dependence of R_AA but not the rapidity dependence,

see, e.g. the final session of the recent hard probes meeting in South

Africa.

7. The presentation in Fig. 6 on the quantitative evaluation of

different model assumptions compared to data depends again strongly on

the size of the systematic errors, see the comment in section 2.

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Reviewer #2: I have read the manuscript PLB-D-13-01645 submitted to me for review.

The authors present a detail analysis on the suppression of Y production in d+Au and Au+Au collisions at sqrt(s_NN)=200 GeV using the STAR detector at RHIC. The article is very well written and deserves publication. However, I would like to suggest considering the following remarks to improve the understandability of the article:

1. Page 1, column 1, paragraph 1: The now accepted value for the critical temperature (chiral transition) is Tc = 150 - 160 MeV (depending on the exact definition of the observables). Reference 3 is outdated and should be replaced by more recent publications, i.e. arXiv:1005.3508 [hep-lat]

2. Page 2, column 2, paragraph 1: Please quantify the corrections due to the trigger bias w.r.t. the event centrality. Same for the tracking efficiency as a function of N_part. How does acceptance times efficiency for detecting Y as a function of rapidity and N_part looks like?

3. Page 3, column 1, paragraph 1: statement "some information will be lost" is too general! What are the systematic uncertainties arising from the different methods (same-event like-sign CB, fit to the CB) of the combinatorial background subtraction? What is the signal significance, in particular in the d+Au measurement? How does the signal looks like after CB and physical background subtraction? Systematic errors should be clearly mentioned.

We have studied these effects through various MC simulations in order to extract the biases. The likelihood fits have negligible biases. Furthermore, and to get back to the original question posed by the referee, in these simulations we obtained the variance of our results when doing simultaneous fits when compared to background-subtracted fits. We found a reduction in the variance when using simultaneous fits which was our original impetus. We also found no systematic effect in the expectation values of the yields obtained by the two different fitting methods. However, given the reduction in the variance of the extracted yield (i.e. in their error) in the simultaneous fit, we favor this method since it introduces a smaller uncertainty. We have redone all of our fits using the likelihood method and we corrected for any extraction biases seen through simulation.

Regarding signal significance, in all cases we see significant signals in d+Au. This can be infered by examining Fig. 3a and comparing the size of the statistical+fit error bars to the measured value of the cross section. This ratio is a good indicator of the statistical significance of our signal. For example, the dAu signal at |y|<0.5 has a significance of 11.7/3.2 = 3.7 sigma.

Since the referee also asked about systematic uncertainties, we have added a full table covering all measured sources of systematic uncertainty and added additional comments about the main sources in the text.

4. Fig 1: It would be easier for reader if the range of the y axis would be the same in Fig 1a and Fig 1b. Why is the explanation of the grey curves in the figure discussed in this complicated way, to my understanding the gray band simply shows the pp yield scaled by the number of binary collisions? If so, the label could read simply pp*<N_coll>.

5. Fig 1a: From where the line shape for pp comes from? It seems NOT to fit experimental data, i.e. all data points around 9 GeV/c^2 and below. Is it then evident to take as a cross section the integral of the data points?

6. Page 3, column 2, paragraph 1: How was the measured Y(1S+2S+3S) yield transformed to cross section?

7. Page 3, column 2, paragraph 3 (wording): "Hence, averaging between forward and reverse rapidities is not warranted as it is in

p+p." --> "Hence, averaging between forward and backward rapidities is not justified as it is in p+p." sounds more understandable.

8. Page 4: Try to arrange the placement of Figs such that there will not be a single line of the text within one column.

9. Fig 2: also here Fig a and Fig b could be presented with the same range on the Y axis, e.g. from -3 to 3.

10. Fig 2a : what is shown here is Y(1S+2S+3S), moreover PHENIX results on Y -> mu+mu- are shown in the same plot, that is why the figure label should be changed, i.e. Y->e+e- should be replaced by Y(1S+2S+3S)

11. Page 4, column 2, paragraph 2: <N_coll> (not <N_bin>) is commonly used as notation for the number of binary collisions. Sigma_AA is sigma^tot_AA (same for pp). It is important to indicate in the text the values for the total inelastic cross sections in pp, dA and AA and <N_coll> used to calculate R_AA.

12. Page 4, column 2, paragraph 3: In view of the discussion would it be helpful to also show R_AuAu vs. Rapidity?

13. Page 6, column 1, paragraph 1: Which function has been used to fit the CB - exponential? Again, what are the systematic uncertainty arising from the different methods (same-event like-sign CB, fit to the CB) of the combinatorial background subtraction. See also comment 4. concerning the label.

The function used to model the CB is now discussed in the text. Systematics from the fit methods are summarized in Tab. I.

14. Page 6, column 1, paragraph 2: The statement "Similar suppression is found by CMS in PbPb collisions (37)" should be moved to the paragraph 4 where the authors discuss Y(1S) suppression. Actually, for the same value of N_part=325 R_AuAu=0.54+-0.09 as for R_PbPb=0.45

Done.

15. Page 6, column 1, paragraph 4: How did the authors derived: R_AA(1S+2S+3S) = R_AA(1S)*0.69?

We had aimed to keep the text brief, since we were mindful of the space constraints, but given this question, we have added a few more sentences and references to clarify the R_AA(1S+2S+3S)=R_AA(1S)*0.7 statement, and also reduced our significant figures, quoting only a factor of 0.7.

16. Page 6, column 2, paragraph 2: What are the uncertainties on Drell-Yan and bbbar cross sections and how does it influence the significance of the signal.

Various normalizations are used in the fit. This is accounted for in the correllation

17. http://arxiv.org/pdf/1109.3891.pdf reports on the first measurement of the Y nuclear modification factor with STAR. It is probably worth to mention this work in the ms.

18. The R_AA of J/psi (p_T > 5 GeV), Y(1S) and an upper limit on the R_AA (2S+3S) was obtained in STAR. I would like to suggest to add a plot showing R_AA as a function of binding energy as a summary figure (also as a key figure to the long discussion on the extraction of the upper limit on R_AA(2S+3S)).

In summary, this ms. contains very interesting results and I propose publication in Phys. Letter B after the authors have taken care of the remarks above.

We thank the referee for her/his comments and remarks, which have helped improve the paper. We hope that we have addressed the issues raised, and adequately answered the questions posed, and look forward to the publication of the paper.

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