STAR Flow, Chirality and Vorticity PWG

[EsumiShinIchi <esumi.shinichi.gn AT u.tsukuba.ac.jp>]

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

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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