UCD Responses to Collaborator questions on the Longitudinal Flow Manuscript

The following are the major questions and concerns raised about the manuscript. Gulshan provided a fax copy of the paper with his comments. Answers to these are largely addressed within these responses and occasionally specifically indicated.

Dave Krofcheck:

1) 0n one plot in Fig 1!, i feel like an astronomer!). I feel okay with the analysis, do we need some more description of error analysis in "eta_max" in Table I?

The error is that which comes from the CERN fitting routines. Is there a need for more discussion?

2) Consider this rewording "...leaving a hot, high-energy density region from which a Quark_Gluon Plasma..." instead of using the term "dense vacuum" on p.1

Okay, changed.

3) Fig. 1 caption, needs subscripts for mt and m0; typing error "rapidity" Fig. 2 caption , "+2" in the 2and 6AGeV plots overlaps with "-2" from 4 and 8 AGeV plots. Fig. 3 caption, (_L) needs a capital "L" in the subscript.

Okay. Fixed all of these captions.

4) Is the straight line in Figure 3 a chi^2 best fit, following the reanalyzed FOPI data? Are we saying that our data supports this steeper slope, or has the line been drawn to "guide the eye", and it just happens to have a slope 2.5 times larger than before?

Your second interpretation is the one which describes the figure. The original Stachel reference drew a "guide the eye" line. based on the line, the conclusion was that the SPS was anomalous. Our data changes the trend, so I included the reference to the increased slope. I modified the text where necessary to say "linear with the logarithm of beam energy". If you have another suggestion let me know. I don't have reliable error bars for some of the values collected from other experiments, so I wouldn't know how to produce a fit that makes sense.

5) Comment: "eta" on p.3 is normally defined as the pseudorapidity. granted that Schnedermann, Sollfrank and Heinz used "eta" as rapidity in their paper, but should we worry that this is not "standard"? should we change "eta" in this paper to some less commonly used greek letter?

Yeah, I know it could be confusing, but since I heavily reference their paper, I thought I should stick to their labeling, however bad. I could add a statement explaining that this is not pseudorapidity, but i haven't been able to come up with wording that doesn't sound patronizing.

6) What are the "mid-rapidity slope parameter" values , used in the model for longitudinal flow on p3? refer to Table I T_0 values?

Okay, I added reference to table.

7) Explicitly call radial flow velocity on p. 4 ?

Do you mean rather than isotropic? The variable used in the FOPI paper is , but since they use a spherical model, I think they mean radial literally. In solely mid-rapidity analyses, the expansion is often called "radial" but it should really be called "transverse", because there is no longitudinal component. Of course then you introduce confusion with the label for directed flow, which is often called transverse flow. I prefer to leave it as is. It is just a semantics issue. Radial is a poorly defined word in the English language in that we use radial for both cylindrical and spherical coordinate systems. In solely mid-rapidity analysis, one can easily also call this radial in a cylindrical sense with no loss of accuracy.

8) Is =0.38 c really supposed to be _L=0.38c "longitudinal flow velocity" on p. 4?

Again, it's the "isotropic" label. They (FOPI) never explicitly say themselves that the longitudinal velocity is 0.38c, but they say that the dndy can be described by a spherical model which includes their radial flow value. They did not include the fit function (to the dndy) in the paper, so I can't tell exactly how they did this.
Stachel took their and, I guess, interpreted the "radial" to mean "isotropic" and arrived at the longitudinal flow value which makes the trend that doesn't fit with ours. The point is that we need to make an apples to apples comparison, so the FOPI data have to be fit with the same model as ours and everyone else's. Otherwise an excitation function of derived quantities makes no sense. So I tried to say that it may be valid to analyze the data in the way they did, but that for this comparison, we reanalyzed with the SSH model to be able to compare the flow values.

9) Should not begin a sentence with a reference "[17] reported good agreement..."; instead consider rewording "Good agreement [17] was reported between the Au+Au..."

Good point, I changed the wording.

10) Again, p.4, is used, does this really mean (_L with a capital "subscript "L"?

Oops. I went through and did a consistency check so that all "l"'s are now "L"'s.

11) In the final paragaph, perhaps summarize the physical assumptions of the model used to fit our data in Fig.2, and how the renormaization of the FOPI result supports this model?

There were some significant changes to the new draft, solet me know if you still think this point needs more work.

Chris Pinkenburg:

1) The data look really neat, and just for consistency, are the 4 pi proton yields you get by integrating over dN/dy reasonable (do we approximately conserve the total charge)?

Yes, they are reasonable, but no, they do not approximately conserve total charge by themselves. At 2 Gev, I see a 4pi yield of approximately 116 protons, at 8 GeV approximately 154. I believe the deficit would be made up (on average) by adding in the 4pi yields of the deuterons, tritons and helions.

2) For fig 1, I might have misunderstood the caption but as far as I understand it midrapidity should be in the middle and forward scaled up by factors of 10, backward scaled down by factors of 10, while the figurejust scales both of them down (which is fine by me).

The caption came from the old way of plotting the data. I have changed it to reflect the figure as plotted.

3) BTW, If you do a set dmod 1 in your draw kumac the lines will always stay full not go from full to dashed to dotted to dash dotted back to full.

THANK YOU!!!! The paw manual and the CERN web pages were totally unhelpful with this annoying plotting problem. The only advice available was to change the ltyp. This is completely ignored by PAW.
Just when I'm learning all the tricks, we are moving to ROOT. Grrr. Using this handy bit 'o widsom, I have also fixed the dndy plot so that the figure is consistent with the caption.

4) The reason the fits don't really follow the data at midrapidity is radial flow?

Yes. The thermal fit is basically a straight line, so it overshoots at low mt-m0, where radial flow causes the spectra to turn over. This is mostly ignored by people who use a thermal spectrum model - often because their measured mt-m0 spectra don't go down far enough to see a significant departure from the straight line fit. At one point, I looked into how off the integrated yield is compared to a fit that goes through all the data points and found that the difference was smaller than the error bars on the yield. I included a statement in the text to this effect.

5) Fig 3 doesn't present a linear dependance but a logarithmic one (it's linear due to the log scale for the beam energy).

True. Basically I changed the wording to "linear with the logarithm of beam energy". I don't know if that's better or worse but it's more correct. I know everyone is going to plotting in sqrt(s), but I was trying to stay consistent with the published data and the published trend I compare with.

6) Now on to the text... Abstract is the same like fig 3 with the linear dependance. Maybe some rephrasing in terms of "overshoot of the cern data is gone" instead of line slope would be better.

The line slope sentence is gone.

7) I am not sure what to make out of the first paragraph of the introduction. Where is the connection to longitudinal flow and how did NA49 got longitudinal flow out of a double hump structure? That sounds like the recipe you use to extract beta is not applicable for sps energies since it doesn't describe the data.

First point - duh. You're right, this is not the right intro for the paper. The intro has therefore been substantially revised. Please read and comment.

8) The last sentence promises a substantially different result, but I couldn't find that discussion.

That sentence has been removed.

9) As far as I understand our tracking, we don't take the momentum from the radius of the curvature but track the particle through the magnetic field figuring out the momentum somehow. (I think leaving out the radius, just saying we figure it from the curvature describes it).

Okay. Just curvature.

10) I don't see a place where you need the impact parameter in fm, why don't we just stick to 5% centrality?

Okay. It's gone.

11) The analysis section refers to two manuscripts in preparation I haven't seen so far. But then it becomes pretty specific on what was done, so I don't know what these refs could add to that.

Ok. These are now pointing to my thesis, which is a finished document, available, should anyone want more details on the analysis.

12) Our GEANT version is 3.21 (at least it claims that when you start it up).

Oops. The manual on my desk is 3.16, but the code compiled into the simulator is 3.21. I have fixed this.

13) Are there any errors assigned to the efficiency correction which propagate to the presented spectra?

No. The statistical error on the correction is significantly larger than the statistical error on the data. We fit the corrections with an empirical form to reduce the fluctuations and we smoothed the results with respect to rapidity. All of these result in an uncharacterized systematic error. So the correct answer is: "No, there are no errors assigned to the efficiency correction." The fuller answer is that it is simply impossible to accurately characterize the systematic error associated with the efficiency correction. The forward backward symmetry of the dN/dy provides the best estimate of this error.

14) I would be careful with the "unusual" good forward/backward symmetry that doesn't go well with experiments with the usual lousy symmetry preservation.

I changed "unusual" to "very" (also Gulshan's suggestion).

15) How different is the longitudinal flow when you treat forward/backward seperately?

I have not done this. In principle it could be done and if the results are outside the error bars, than I guess the error could be expanded to encompass this. But doing this wouldn't change the physics message.

16) The line of argument in the result section would gain from some little reordering. E.g. The sentence the effect of the chemical potential... does not affect Eq.2, would fit better after you introduce eq.2. The fitted T(y) probably has an error associated with it, how does this affect the fit, plotting a band instead of a line would accomodate for that (same for the full blown longitudinal flow inclusion). To make the Schnedermann approach clearer (at least I got confused) leave out the plural in "For this second analysis...". I kind of mixed the multiple sources mentioned previously with dealing with multiple beam energies you probably talk about here. dN_th/dy is Eq. 2 (maybe is calculated/extracted) m is the mass of the emitted particle. That should go in the explanation of eq 2.

I made some changes at Gulshan's suggestion. Hopefully the new draft will satisfy your question. If not, let me know.

17) Can you put the errors on beta in the table? In fig 3 there is an error bar.

Well, that will clutter up the table. Since eta_max is the actual fitted parameter I thought it was more correct to quote the error on that. It's straightforward to figure out the error on a function of a single variable if you know the error on the variable. If you want to know the values for your own use I can provide them, but I don't think they need to be in the paper.

18) The conclusion and my own figuring basically says that the previous slope was based on using a FOPI value which was calculated using a different formalism. Chances are we get a FOPI referee so I would leave out this "may be a valid interpretation" - Willi Reisdorf may go ballistic here and - on a more serious note - a lot of effort went into that FOPI analysis and it is probably more sophisticated than the simple "more than one source" idea which is presented here. The plot you refer to shows that quite clearly (the original is from Stachel NPA 610, the other ones are just copies of this one). But certainly more points at more energies help make a convincing argument.

I took that out. I don't want to ruffle their feathers. My intent was to point out Stachel's misinterpretation.

19) But now what did we learn, why did we bother to look at longitudinal flow? Some concluding remarks should be included. The previous systematic was interpreted in terms of reduced stopping at sps energies. Can we say anything more about this with the new data (like no change in stopping) and how valid is the sps value in light of the double humps (you are member of NA49 not so)?

I am not a member of NA49, so I can't comment on that. In my thesis I tested whether the pions could also be fit with the thermal + longitudinal flow using the same flow velocity as was found for the protons. They are consistent, so I think we have substantial stopping at our energies too. The dndy of protons at our energies cannot distinguish between transparency/stopping and flow. This analysis shows a consistency with the flow picture, but doesn't rule out the possibility of a change in the transparency. This is where we really need the 40 AGeV and the 80 AGeV CERN data. I added a statement to that effect in the conclusion. But maybe it needs more punch.

20) One other general thing, which is more for Declan I suppose. I am confused about the different authos lists we seem to use. Can we agree to a current list of authors? On my qm contribution I asked spefically for everyone to check the author list (no response) but it certainly is different from yours.

Well, Daniel pointed out the following:
"The variations in the E895 author list are quite interesting. And probably a final word should come from the Spokesman concerning this. As this effects no UCD authors, we shall leave this issue to the reps and spokesman to resolve. There are basically three variables that we find in the Author lists:
1) Most SUNY-SB publications include C.Law, most other institutions do not.
2) All OSU publications include R. Wells. Most others do not.
3) All KSU publications include S. Wang. Most others do not."

21) In the pid section you mention that beyond 8GeV/c p/d/t should disentangle again and blame it on statistical errors that we don't see that. From looking at our pid plots, I doubt that we can see the relativistic rise or would be able to disentangle anything there even if we had all the stats we want. On the other hand how many d/t are there anyway? Just taking the proton cut a'la Paul looks very exponential. I assume we would see a change in slope if the d/t would seperate again from the protons.

The method we employ is more sensitive than the "by-eye" or graphical cuts that are usually used. These particles are all hitting their various minimum ionizing at different momenta. So the bands separate at different points and there is a region in which our PID is sensitive to the re-separation. All of the particles have low statistics by this point, so even if there aren't that many d/t, there also aren't that many protons. And even if there are fewer d/t, they preferentially populate the high momentum region.

22) Do you have the momentum resolution at these high momenta?

I looked into this with my simulations at one point. The web page is http://nuclear.ucdavis.edu/~jklay/e895/sim/resolution.html

Last updated:22-Oct-2001