STAR Flow, Chirality and Vorticity PWG

["Junyi Han" <jyhan AT mails.ccnu.edu.cn>]

Dear Prof. ShinIchi,

Thank you for your careful explanations and nice suggestions! I have added some content and explanations and placed them in the attachment. Firstly, the studies are based on the 7.7 GeV collider mode.

(1) For the q-vector calculations in EPD planes, I used the eta weight and tile weighted as I showed in Page 5 of my slides. The charged hadrons raw v1 as a function of eta and the eta weight factor I used are also in Page 2, 3 and 4.

(2) As I mentioned above, I used eta weight and tile weight when I calculated the q-vector in EPD planes. As the eta weight factors I showed in Page 3, I fitted the distribution of v1 vs. eta with EPD eta range(eastern: [-5.1, -2.1]). As for TPC q-vector calculations, I only used particle pT as weight without eta weight. 

Before I combine the q-vector in east and west EPD, I flip the eastern q-vector as you guessed. As the same, I flip the eastern q-vector in TPC before I combined them. And we can see in the Page 1, the distribution of charged hadrons raw v1 as a function of eta did show s-shape and it is more significant in the peripheral collisions.

(3) Thank you for your correction! It should be EPD(A) instead TPC(A). In the Page 4, I expanded the range of the x-axis, and this range is around the eta range of eastern EPD-CD(eta:[-2.8, -2.1]). Because it is easy to find the value of eastern EPD-A (eta:[-5.1, -3.5]) is negative.

 

(4)(5) Thank you again for your suggestions and explanations! I have already updated the figures with grid lines and change the range of y-axis and I hope it is helpful to look clearly. 

(6) The eta range of TPC(a) and TPC(b) are |eta|<0.7 and 0.8<|eta|<1.5. I have also updated the figures and put them in the slides. And the minimum value in the left bottom pad is located around bin5 as you expected.

Thank you again and Best regards,

Junyi

 

------------------ Original ------------------

From:  "ShinIchi Esumi"<esumi.shinichi.gn AT u.tsukuba.ac.jp>;

Date:  Sun, Oct 29, 2023 11:39 AM

To:  "韩君仪"<jyhan AT mails.ccnu.edu.cn>;

Cc:  "STAR Flow, Chirality and Vortici"<star-fcv-l AT lists.bnl.gov>; "Zuowen Liu"<liuzw AT mails.ccnu.edu.cn>;

Subject:  Re: [Star-fcv-l] mom.-cons. effect in 2-sub e.p. resolution estimation...

 

Dear Junyi

Thank you very much for the investigation. I see the results tells that the various methods that I’ve proposed seems to be not vary easy, nor works very well, but I would like to ask a few more questions in the following before we give up, in order for us to understand the feature of our data. By the way, is this done at 7.7GeV collider mode, right?

(1) I first like to ask you what kind of weighting factor you have used for EPD planes, since we know the v1 changes the sign in the middle of EPD, so you might have applied the weighting factor (that is mostly proportional to the v1, so as a function of eta or ring number) in order to maximize the resolution, is that right? If you have the weighting factors (in numbers or in plots), please show that to me, too.

(2) I understand you flip the sign of Q-vector (east or west plane), when you combine east and west. However since your EPD(east)-EPD(west) correlation is already positive, so one of them should have been flipped (just for the single plane), so please tell me which one is flipped. I’m guessing you have flipped the east (eta<0, z<0) side, so that TPC-EPD correlation is always negative in peripheral collisions, assuming you’ve used “eta” as a weighting factor for the TPC Q-vector, or you flipped the sign for particles at the negative eta region. This is based on our understanding that the v1 of charged particle has opposite-sign slope as a function of eta at mid-rapidity compared to forward/backward-rapidity, such as s-shape like v1 behavior (or anti-flow in the mid-rapidity), which is more significant in the peripheral collisions. While the TPC-EPD correction become positive in the central collisions, which might be due to the “physical” auto-correlation between TPC and EPD, or the mid-rapidity v1 slope does indeed change to have positive slope with respect to the forward/backward plane (No more s-shape like behavior in central collisions, that could also be interesting, which is also visible in my slide P2-P3 at LBNL collaboration meeting in March).

(3) Your TPC(A) in your slide P4 (for top-right panel axis labels for both cos and sin term) would be EPD(A), right? Assuming that is the case, the fact we observe always positive correlation between EPD(A) and EPD(CD) tell me that you do have reasonable weighting factor in EPD that is proportional to v1 depending on eta region or ring. I would just like to confirm that you do have negative weighting factor for EPD(CD: outer rings, smaller eta) region and positive for EPD(A: inner ring, larger eta) in the EPD west (positive eta) case.

(4) We do see in your P4 the similar feature of vanishing s-shape like v1-behavior in central collision in TPC-EPD correlation both EPD(A) and EPD(CD), although it is weaker (less significant) for EPD(CD) that would be understood by the worse EP resolution compared to EPD(A), which might tell us the above mentioned other possibility of “physical” auto-correlation is less likely, since it does not increase with reducing the eta-gap.

(5) On your TPC(east) or TPC(west) in your slide P5, one of them are flipped again (or I might have to say it is automatically flipped by “eta” as weighting factor, therefore we see always positive value in the bottom panel, and we see a clear (or pure) momentum conservation effect in the bottom panel without any peak-like feature at the mid-rapidity, that we would expect, if this has any flow-like signal originated from the centrality dependence of v1 and multiplicity. I would have the same vertical scale for the top 2 panels, though. (and/or please overlaid them with dashed line at zero level or grid lines for all the plots especially the ones with crossing zero in all other pages...)

(6) Your TPC(a) and TPC(b) in your slide P6 are done with |eta|<0.7 and 0.8<|eta|<1.5 according to your E-mail, right? I would like to have the same vertical scale again for the top 2 panels, where we now clearly see the different magnitude with similar shape, that I would also like to see them overlaid with grid lines. I would especially like to see the bottom panel with very much expanded vertical scale, where I expect minimum in the mid-central around bin 5, where the top 2 panels cross zero around the same bin 5.

Thanks again for your great studies for us to get full picture.

Best regards, ShinIchi

2023/10/28 22:10、Junyi Han <jyhan AT mails.ccnu.edu.cn>のメール:

Dear Prof. ShinIchi,

Thank you very much for your reply and nice suggestions!

I have used the proper method via chi extraction to estimate the combined event plane resolution for the 2-sub event method. When I combined forward and backward event planes, I flipped the sign of eastern q-vector before I adding them for TPC and EPD(east and west), but no TPC a(east_a and west_a) and b(east_b and west_b). So I corrected it and get the new results. The direct correlation values between two planes I have showed in the attachment. For the question of the enhancement at about 30% in the resolution plot, I do not have a clearly idea about it. Maybe due to the reversion of the direct correlation values between TPC and EPD in the figure I showed in the attachment. Then, I will check the reason about this enhancement.

Thank you again and Best regards,

Junyi

 

 

------------------ Original ------------------

From:  "ShinIchi Esumi"<esumi.shinichi.gn AT u.tsukuba.ac.jp>;

Date:  Wed, Oct 25, 2023 09:16 PM

To:  "韩君仪"<jyhan AT mails.ccnu.edu.cn>;

Cc:  "STAR Flow, Chirality and Vortici"<star-fcv-l AT lists.bnl.gov>; "Zuowen Liu"<liuzw AT mails.ccnu.edu.cn>;

Subject:  Re: [Star-fcv-l] mom.-cons. effect in 2-sub e.p. resolution estimation...

 

Dear Junyi (and Zuowen)

Thank you very much for your studies.

Do you now use the proper method via chi extraction to get a combined resolution

for the 2-sub method without the sqrt(2) approximation? It is reasonable to see

this red points are very close to the green (4-sub) points which include the same

correlation between EpdE and EpdW, but do you understand the small step (deviation)

at about 30%? There also seems to be significant steps at about 30% in the other

resolutions for the blue and light-brown (both triangle) points. So could you please

show the direct correlation between 2 planes (average cos and sin values) for each

of the 3-sub (and 4-sub) cases, where you seem to take absolute value to solve the

equation, therefore I would first like to see all these 3 (or 4) positive and negative

correlation values (average cos terms) for each of the 3-sub (or 4-sub) cases before

taking the absolute values. If it’s not too much for you. When you combine forward

and backward event planes, you would need to flip the sign of the q-vector before

adding them (especially for EPD_inner/outer as well as for TPC_a/b cases), that I

hope you do, right? Thanks again for your efforts on this.

Best regards, ShinIchi

2023/10/25 17:56、Junyi Han <jyhan AT mails.ccnu.edu.cn>のメール:

Dear Prof. Shinlchi,

Thank you very much for your nice suggestions and patient explanations!

After discussions with Zuowen, we conducted the test based on your recommendations, and the results are in the attachment. The EPD(east)-EPD(west) used traditional 2-sub method, and for EPD inner and outer defined by EPD-CD and EPD-A(eta gap is EPD-B here). Similarly, the definitions of TPC (a) and (b) are |eta|<0.7 and 0.8<|eta|<1.5. The results of EPD(east)-EPD(west) and TPC(full)-EPD(east)-EPD(west)-EPD(full) are similarly at different centrality bins. But the other results vary significantly.

Thanks again and Best regards,

Junyi

 

 

------------------ Original ------------------

From:  "STAR Flow, Chirality and Vortici"<star-fcv-l AT lists.bnl.gov>;

Date:  Tue, Oct 24, 2023 12:45 PM

To:  "ShinIchi Esumi"<esumi.shinichi.gn AT u.tsukuba.ac.jp>; "STAR Flow, Chirality and Vortici"<star-fcv-l AT lists.bnl.gov>;

Cc:  "Zuowen Liu"<liuzw AT mails.ccnu.edu.cn>;

Subject:  Re: [Star-fcv-l] mom.-cons. effect in 2-sub e.p. resolution estimation...

 

Dear Prof. ShinIchi,

I am very appreciate your nice and instructive suggestions.

I agree that we should avoid the p-cons. effect, for much wider eta coverage of upgraded EPD in particularly. The formula you write would tell us how much would the p-cons. bring, it's worthy to test it. I think I know how to do this for now.

The formula I wrote (1) R1( TPC-EPD(full) ) = ...

please just forget it, I misunderstood the symbol "-" as connector but not subtraction.

Thanks again for your kind help.

Best regards,

Zuowen

 

 

------------------ Original ------------------

From:  "ShinIchi Esumi"<esumi.shinichi.gn AT u.tsukuba.ac.jp>;

Date:  Fri, Oct 20, 2023 09:38 PM

To:  "star-fcv-l"<star-fcv-l AT lists.bnl.gov>;

Cc:  "Zuowen Liu"<liuzw AT mails.ccnu.edu.cn>;

Subject:  Re: [Star-fcv-l] mom.-cons. effect in 2-sub e.p. resolution estimation...

 

Dear Zuowen

There was a typo, "with change” should have been “with charge” at the end of

the 1st paragraph. One can also do (a) with |eta|<0.5 (<0.75) and (b) with |eta|>0.5

(>0.75 for BES2 case) in order to make both (a) and (b) be rapidity symmetric

just like EPD inner and outer cases.

For the 2-sub case, they need to be similar as you say, and it is always be better

to be less affected by p-cons nor non-flow etc...

Best regards, ShinIchi

2023/10/21 2:47、EsumiShinIchi via Star-fcv-l <star-fcv-l AT lists.bnl.gov>のメール:

Dear Zuowen

I can re-write the full EPD resolution for these four "3-sub" from (1)

to (4) cases in my previous E-mail as attached png file, we could

also call (1) and (2) as 4-sub, since we use the 4 terms (4 planes)

to get the full EPD plane. The notations are the followings. We also

have usual 2-sub just with EPD_east and EPD_west in order to get

EPD_full plane via sqrt(2) times the chi value of single plane, which

we can call (0) that I’ve not listed here. For TPC(a/b), one can

define in “any” rapidity symmetric way like randomly or with many

small eta slices or with change (in case of high energy) etc.

E          : EPD full

Ee/Ew  : EPD east/west

Ei/Eo    : EPD inner/outer

T           : TPC full

Te/Tw    : TPC east/west

Ta/Tb    : TPC a/b (charge, many eta slices, random)

We need to worry about p-cons effect for cases (1) and (3) as well as

(0), since they all contain the east - west correlation. While we do not

need to worry about p-cons effect for (2) and (4), since all planes are

defined in rapidity symmetric way such that the p-cons effects cancel out

in all the terms. But we need to worry about non-flow coming from the

small or no-eta gap in (2) and (4) and most likely also in (3), since 2 TPC

planes would be close. We might also not be able to neglect the non-flow

between TPC and EPD depending on the eta (nHitFit) cuts and z-vertex

selections for all the cases.

You wrote a formula (1) R1( TPC-EPD(full) ) = ... that I could not follow

what you wanted to say as I attached in the 2nd png file without (number).

It’s not wrong, but...

Best regards, ShinIchi

<ForZuowen0.png>

<ForZuowen2.png>

2023/10/20 22:14、Zuowen Liu <liuzw AT mails.ccnu.edu.cn>のメール:

Dear Prof. ShinIchi,

Thank you very much for your patient and detailed explanation.

If I understand correctly, 2-sub method require 2 similar EP, while the EPD cover high and low rapidity, correlation between east and west EPD would be affected by p-cons. , e.g. high rapidity at west EPD correlated with low y at east EPD.

Sorry for the four combinations you provided here, I want to make sure, could the 3-sub resolution could be expressed as follow:

(1)  R1( TPC-EPD(full) ) = sqrt{ (TPC-EPD(full) TPC-EPD(east)) * (TPC-EPD(full) TPC-EPD(west)) / (TPC-EPD(east) TPC-EPD(west)) }

(2),(3)....

(4) what's the meaning of TPC (a) and (b) here?

Thanks again for the great help and professional suggestion you always gived.

Best regards,

Zuowen

 

------------------ Original ------------------

From:  "ShinIchi Esumi"<esumi.shinichi.gn AT u.tsukuba.ac.jp>;

Date:  Wed, Oct 18, 2023 02:08 AM

To:  "Zuowen Liu"<liuzw AT mails.ccnu.edu.cn>;

Cc:  "star-fcv-l"<star-fcv-l AT lists.bnl.gov>;

Subject:  Re: [Star-fcv-l] mom.-cons. effect in 2-sub e.p. resolution estimation...

 

Dear Zuowen

Thank you very much for the reply.

v1 = v1_raw / resolution

The “v1_raw" can be measured without p-cons effect, because of the symmetric

rapidity acceptance of EPD with respect to TPC as you have also mentioned,

however the “resolution” could be still affected by p-cons between 2 EPD planes,

especially if it is determined with 2-sub method, which uses the correlation between

the forward and backward EPD planes. So in this case, “v1_raw” is OK, but “resolution”

could be overestimated by p-cons, therefore the final “v1”could be smaller than the truth.

That is why we need to think about 3-sub method or some other ways to take this into

account, for example, one could try to do a few things.

(1) TPC-EPD(east)-EPD(west) and TPC-EPD(full)

(2) TPC-EPD(inner)-EPD(outer) and TPC-EPD(full)

(3) TPC(east)-TPC(west)-EPD(full)

(4) TPC(a)-TPC(b)-EPD(full)

With these A-B-C and A-D for the cases (1) and (2), one could get resolution of D

= (AD)/sqrt(AB*AC/BC). For the case (1), I would think it gives a similar resolution

from the current 2-sub, because of the same p-cons effect existing in B-C. For the

case (2), all A,B and C are free from p-cons because of the symmetric choice, but

we now need to worry about non-flow and eta-gap in B-C. For the case (3), we also

need to worry about non-flow and p-cons in A-B. For the case (4), if we take both

TPC(a) and (b) to be symmetric in rapidity, we are free from the p-cons, but we still

need to care about non-flow between (a) and (b)… If we could have 3 independent

and rapidity symmetric planes (without non-flow and de-correlation), it would be

good. Thank you very much again for the discussion.

Best regards, ShinIchi

On Oct 18, 2023, at 3:39, Zuowen Liu <liuzw AT mails.ccnu.edu.cn> wrote:

Dear Prof. ShinIchi,

Thanks a lot for your nice suggestions.

Junyi and I have talked about the approximation on sqrt(2).

We agree that the approximation is not appropriate, and it would be corrected.

For the mom. cons. effect, I agree if we reconstruct EP with one arm of EPD, we would face the p cons. effect due to the asymmetry. But I don't understand why we need to worry about p cons. if we used 2-sub event, where the mom is conserved "naturally" due to the symmetric track direction. While Junyi and I could take a quick cross-check for the

single and two EPDs.

Thanks and Best regards,

Zuowen

 

------------------ Original ------------------

From:  "EsumiShinIchi via Star-fcv-l"<star-fcv-l AT lists.bnl.gov>;

Date:  Tue, Oct 17, 2023 11:14 AM

To:  "star-fcv-l"<star-fcv-l AT lists.bnl.gov>;

Cc:  "ShinIchi Esumi"<esumi.shinichi.gn AT u.tsukuba.ac.jp>;

Subject:  [Star-fcv-l] mom.-cons. effect in 2-sub e.p. resolution estimation...

 

Dear Zuowen (and Junyi)
I mentioned to Junyi about the approximation on sqrt(2), so I hope you can
communicate with Junyi on this. As I’ve also written in the chat window, I
send you the same (following) message just in case you might have missed,
that is about the mom.-cons. effect in 2-sub e.p. resolution estimation.

I should have asked this to Zuowen, who is doing similar 2 sub-event methods
for estimating e.p. resolution, I think we need to think about p-conservation
between 2-subs, by including and/or comparing the 3-sub or other methods in
order to understand the possible contribution from p-cons effect in the current
e.p. resolution estimation. While for measuring raw v1, it is canceled, since you
use the combined E.P. from e/w EPDs, but as long as you are based on the
2-sub method between E-W event planes for the E.P. resolution estimation,
we are affected by the momentum conservation effect, that we would like
to subtract, as we could clearly see the effect using the single arm EPD plane
E or W, that is the p-cons effect between TPC and single EPD, which would be
different from the one between two EPDs...
Best regards, ShinIchi

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<EPD_mom_cons.pdf>

<EP_mom_cons.pdf>

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