God Parent Committee for the paper on "Global polarization measurement in Au+Au collisions"

GPC members:

• Hal Spinka (Chair)
• Aihong Tang (PWG representative)
• Ilya Selyuzhenkov (PA representative)
• Evan Finch
• Mark Heinz
• Ernst Sichtermann
• Steve Vigdor (English/grammar QA)

Main GPC comments

1. (Ernst Sichtermann) The uncertainty in polarization caused by feed-down contribution should presumably be presented as a possible offset instead of a percentage.

   We report the systematic errors on feed down from multi strange hyperon assuming the same polarization as for direct lambdas. Therefore we report the relative systematic error in percents.

2. (Evan Finch) The systematic error from acceptance is not naturally a relative error, right?

   Second line in equation (9) of the paper draft shows that both acceptance function A^(0,2) contribute together with polarization expansion coefficients P_H^(0,2). If polarization is zero (all P_H^(n) = 0), the acceptance effects in A^(0,2) are not contribute. This allows us to treat the deviation in A^(0,2) of 20% from perfect acceptance case as a relative uncertainty.

3. (Hal Spinka) In Figs. 5 and 8, there are points with centrality 0-5%. I would have naively thought that you couldn't define a reaction plane for these events (or maybe have a reaction plane with such large uncertainty as to be meaningless). In any case, I suspect that the polarization should vanish as the centrality (and p_T) goes to zero.

   We do expect the polarization and anisotropic flow (which defines the event plane) are goes to zero only for b=0. Centrality region 0-5% corresponds to a relatively large range of impact parameters. Although the systematic uncertainties are larger, we still are able to reconstruct reaction plane angle and measure the polarization in this centrality region.

4. (Mark Heinz) The lowest p_T point on the figures 3 and 6. The efficiency for reconstructing the lowest p_T point - was this ever resolved?

   Large error bars for lowest p_t points are showing the increase in uncertainty to reconstruct hyperons in this p_t region and we left these points in figures to indicate this effect.

5. (Evan Finch) The 0.15 sigma0/lambda ratio referred to is Gene's d+Au; for Au+Au the predictions are (as he notes) 2-3 times this big.

   We estimate systematic errors from Sigma^0 feed-down based on results for dAu collisions and exactly this estimate is given in the paper draft. Since we do not have such a measurement for AuAu collisions, we only mention that it is possible for this uncertainty to be larger for AuAu collisions.

6. (Ernst Sichtermann) I do agree with Evan's comment that the repeated "Data points are not acceptance corrected" in the figure captions is not (longer) needed - it is clear enough from the text and can be viewed as just one source of systematic uncertainty. If you want to keep the message in the caption, I would probably phrase it as "The indicated uncertainties are statistical only. The systematic uncertainties include acceptance and other effects, and are estimated to be smaller as discussed in sec IIC."

   Replaced in the paper draft Version 11

7. (Ernst Sichtermann) Reference [28], Y.J. Pei hep-ph/9703243 - have you considered F. Becattini and U. Heinz, ZPC 76 (1997) 269?

   Added with corresponding discussions in the paper draft Version 11

8. (Ernst Sichtermann) Last, I would like to suggest some (other) minor rewording:
   On page 5, "This estimate takes into account ... Au+Au collisions (this can affect the estimated uncertainty)." How about: This estimate takes into account the average polarization transfer from Σ0 to Λ, which we estimate to be -1/3 [26, 27], neglecting the possible effect from non-uniform acceptance of the daughter Λ. The production ratio of Σ0/Λ is measured to be 0.15 for d+Au collisions [29]. Our uncertainty estimate takes into account that it can be 2-3 times higher for Au+Au collisions.

   There is a confusion here. Please see corresponding comment by Steve Vidgor at this page.

    

Recent GPC comments

1. (Hal Spinka)
   PACS - you only have the PACS for collective flow. Perhaps include 24.70.+s for polarization, or maybe others for hyperon production? Sorry I didn't notice this before.
   page 8, left col., line 7 and beyond paragraph. I make a suggestion for this paragraph, but think some improvement is still needed. -> "To check the reconstruction code, Monte Carlo simulations with sizable linear ... spectra have been performed. Both the sign and magnitude of the reconstructed polarization agreed with the input values (within statistical uncertainties?)."

   Added PACS numbers:
   23.20.En Angular distribution and correlation measurements 24.70.+s Polarization phenomena in reactions 25.75.-q Relativistic heavy-ion collisions 25.75.Ld Collective flow 14.20.Jn Hyperons 25.75.Gz Particle correlations 25.75.Dw Particle and resonance production
   Paragraph discussing simulation results is replaced by what Hal suggested: "To check the reconstruction code, Monte Carlo simulations with sizable linear transverse momentum dependence of hyperon global polarization and hydrodynamic p_t^H spectra have been performed. Both the sign and magnitude of the reconstructed polarization agreed with the input values within statistical uncertainties."

2. (Steve Vidgor)
   1) In a number of places the text refers to colors (red vs. black, etc.) in describing figures. Since the colors will likely not appear in the journal, choose different descriptions (e.g., darker vs. lighter shading in Fig. 2; open circles vs. filled squares in Figs. 3-8), and modify the text accordingly.
   2) Since the discussion of feed-down comes quite a bit before the discussion of systematic errors, the reader is left hanging a bit at the end of the feed-down discussion, as to what will be made of these estimates. So I would suggest adding a sentence in the 2nd paragraph, left column on page 5:
   "...decaying via strong interactions. THE EFFECT OF THESE FEED-DOWNS, ESTIMATED AS DESCRIBED BELOW, IS INCORPORATED IN OUR SYSTEMATIC ERRORS IN SEC. II C. Under the assumption..." 3) Under eq. (4), the sentence that begins "The direction of the system..." will be clearer if the final parenthetical "(event plane)" is removed, and the earlier description in that sentence modified to say: "...defined to be along the normal to the EVENT plane spanned by..."
   4) I find the addition of the average values of trigonometric functions in eqs. (9-11) helps quite a bit in thinking about the acceptance non- uniformities. However, I find the added sentence "The stronger deviation from unity of A_0 at smaller p_t^H..." still not very illuminating. I would suggest a slightly longer description along the following lines -- I don't know if my explanation is correct, but it sounds plausible. If you have a better understanding of the behavior, please describe that in somewhat more detail than the present version.
   "The deviation of this function from unity is small and it reflects losses of the daughter protons or pions from the STAR detector acceptance, primarily at small angles with respect to the beam direction. Proton losses and pion losses dominate in different regions of phase space, since in the detector frame the protons follow the parent Lambda direction much more closely than do the pions. When the Lambda momentum is itself near the acceptance edges ($|\eta| \approx 1$), then the primary losses come from protons falling even closer to the beam direction. This disfavoring of small $\theta_p*$ tends to increase $\overline{\sin \theta_p*}$, hence $A_0$, with respect to uniform acceptance. In contrast, when the Lambda is near mid- rapidity or at high $p_t^H$, the daughter protons are constrained to stay within the detector acceptance. Then the primary losses arise from forward-going daughter pions, preferentially correlated with large $\sin \theta_p*$, tending to reduce $A_0$ from unity. In any case, the corresponding corrections to the absolute value of the global polarization are estimated to be less than 20\% of the extracted polarization values."
   5) Some grammatical corrections in the last paragraph on page 9: "The hyperon directed flow is defined as THE first-order coefficient in THE Fourier expansion of THE hyperon azimuthal..." Later: "...of the same order of magnitude as FOR charged particles ($\leq 10\%$), the effects of such interference HAVE been found...due to both the hyperon reconstruction procedure and IMPERFECTION of the reaction plane determination..."
   6) The 0.02 limit appears for the first time in the conclusions. I would suggest foreshadowing this appearance at the very end of section IIC: "...less than a factor of 2--2.5. TAKING ALL THESE POSSIBLE CORRECTION FACTORS INTO ACCOUNT, OUR RESULTS SUGGEST THAT THE GLOBAL LAMBDA AND LABMDA-BAR POLARIZATIONS ARE <= 0.02 IN MAGNITUDE."

   All figures are modified and only filled circles and oped squares symbols are used
   sentences added
   This para added. The only changes were made are (see page 9, left column): protons -> protons (anti-protons) Lambda -> Lambda (Anti-Lambda)
   "factor of 2" replaced by "factor of 2-2.5"

3. (Evan Finch)

   I would take the statement "Data points are not acceptance corrected" out of the figure captions, It's clear now in the text and I think it will just confuse people who skim the text and look at the figures.
   Left as is. This sentence was added as the result of previous GPC comments. We are ready to remove it if other GPC members agreed on this too.

   The statement on strong feed down/string fragmentation model would benefit from mentioning what fraction of the indirect lambdas come from strong feed down (in the model) as opposed to sources you've already accounted for.
   Left as is. This fraction of indirect hyperons from strong decay depends on both, our estimate of weak decay feed-downs and on the fraction of direct hyperons. Since the latter one is not measured with STAR, providing such a model dependent number without detailed explanation can potentially confuse the reader.

   Is it possible to replace 'negligible' with a real number for the effect of spin precession? If you have a number at hand, it would be better to include it.
   The relative uncertainty from this effect is < 0.1%. This number is added to the text and the Table 1.

   In the acceptance section, I might replace "A() is a function to account for detector acceptance" with "A() is the fraction of lambdas which are accepted as a function of hyperon and daughter momentum".
   Left as is. This statement will be difficult to understand together with the normalization of this function to unity. We can modified it as follows: "A() is a function to account for detector acceptance which is proportional to the fraction of accepted hyperons." In this form it is just a repetition of what we understand under detector acceptance.

   And some minor grammar points... From the first line in page 3, I would remove "the". Also, take out the last occurence of "the" in that same paragraph.
   Removed

   Remove "in distance" from "at least 6cm in distance" on page 4. In that same paragraph, replace "choose" with "chose" to stay in the past tense.
   Removed and replaced

   Page 5, first column, I would add "in" to "Based on the results in [30].
   Added