STAR Correlations and Fluctuations PWG

[Roy Lacey <roy.lacey AT stonybrook.edu>]

A more relevant variable for tracking phase transitions (first- or second-order) is the root_s (\mu_B T) dependence of the transverse expansion speed related to the sound speed.

That is, phase transitions lead to a softening of the equation of state, resulting in a minimum in the sound speed. Fig, 1b in https://arxiv.org/pdf/1512.09152.pdf shows the expected 

minimum corresponding to the maximum shown in Fig. 1a. The finite-size scaling in Fig. 5 aids a distinction of the order of a possible phase transition.

Thanks

Roy

On Mon, Aug 23, 2021 at 11:37 AM Lisa, Michael via Star-cf-l <star-cf-l AT lists.bnl.gov> wrote:

Hi Helen,

 

Thanks for the message.  Indeed, I would expect an extended lifetime to affect both systems.  As for “lifetime,” that word is overused (like “error”), so it’s worthwhile to expand a bit.

 

For the Rout/Rside, we are talking about the emission duration, which has been associated with the “cooling time,” a dynamic timescale that may correlate with the time for the phase change to occur.  To get an absolute *lower limit*, one might assume a spherical source with no flow or (producing the same effect) opacity.  In that case, tau = sqrt(Rout^2-Rside^2)/(pT/mT).  For the peak shown in our paper, this would be something like sqrt(8 fm^2)/0.9 ~ 3 fm/c.  That’s pretty low, but keep in mind it ignores flow, which we know is pretty big.  For anything more serious, one needs to turn to the blast wave, which we showed how to do in quite some detail in https://arxiv.org/pdf/nucl-th/0312024.pdf  STAR applied this formalism to its *top energy* data in this paper https://arxiv.org/pdf/nucl-ex/0411036.pdf  There, we found an emission duration of 3 fm/c, even when Rout/Rside ~unity.  This shows the importance of (radial) flow.  My preliminary estimate (paper in process) is that STARs result at 20 GeV gives about 10 fm/c.  All of these estimates ignore opacity; including opacity would increase the lifetime estimate.

 

Now, “lifetime” is sometimes used to refer to the “evolution time” of the system.  Here, we see no peaking, just a slow growth of the evolution time with collision energy.  This is based on Rlong and a formulation that assumes boost-invariance (whose validity deteriorates at low energy, of course), and strong flow.  In figure 10 of STAR’s later paper https://arxiv.org/pdf/1403.4972.pdf  you see a value of something like 7 fm/c at BES energies, and 11 fm/c at LHC.  This should be the time between the onset of boost-invariant flow and the peak of emission.  It should likewise be considered a lower limit.

 

You said you had not seen any attempt of this in a long time.  I would like to point to one more paper that deals extensively with timescales probed by HBT.  It is in my opinion (as author, ahem) quite good: https://arxiv.org/pdf/1607.06188.pdf  It shows a completely different analysis that combines anisotropic HBT of the transverse radii (Rout and Rside) with the evolution time given by the longitudinal radius (Rlong).  The very interesting result is that these analyses give consistent results for evolution time.  I think that is so cool!  Check out section 5.2 and figure 10.

 

 

Very good, so much for HBT.  Above I gave some quantitative estimates/limits for the timescales that might be indicated.  Dilepton measurements are probably sensitive to the evolution time.  What quantitative estimates does one extract from this data?  That is the only way to tell whether the two measurements give a consistent picture.  In other words, how much increase in lifetime would be required to produce a non-flat structure in the dileptons?

 

Thanks,

Mike

 

 

 

-- 

Michael Lisa

Professor of Physics

The Ohio State University

 

 

From: Star-cf-l <star-cf-l-bounces AT lists.bnl.gov> on behalf of Helen Caines via Star-cf-l <star-cf-l AT lists.bnl.gov>
Reply-To: Helen Caines <helen.caines AT yale.edu>, STAR Correlations and Fluctuations PWG <star-cf-l AT lists.bnl.gov>
Date: Friday, August 20, 2021 at 10:46 AM
To: "star-cf-l AT lists.bnl.gov" <star-cf-l AT lists.bnl.gov>
Subject: [Star-cf-l] Extracting Timescales with HBT

 

Hi All,

 

  At this week’s LBNL BES workshop there was a brief discussion triggered by the difference in shapes of our reported HBT R_out^2 - R_side^2 vs sqrt(s) which might be related to an extended emission duration due passing through a first order phase transition, and the excess dilepton yield per pion which is also theoretically related to the lifetime of the source.

 

The HBT result shows a wide peak around 20 GeV while the dilepton results appear flat. See for example slides 18 and 20 of my presentation here: https://drupal.star.bnl.gov/STAR/files/STARPlansBES-II_0.pdf

 

I know that the two measurements measure different timescales so the absolute values don’t need to agree, but I thought both should be sensitive to potential extended freeze-outs generated via a first order phase transition. I was therefore wondering of this group if we see this HBT peaking in other species? Or rather, since the BES-II data are only just coming in, will we have the statistic to look at this and is someone currently planning to make the measurements?

 

Also, at the start of RHIC/STAR there were measurements of “total time of collision” being extracted from HBT+ spectra blast wave fits. I haven’t seen anyone attempting this in quite some time. Is it still considered a valid analysis technique? If so and we perform the study do we see a similar peaking? 

 

Thanks

 

Helen

 

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