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NDOF (effective). R. Seto May 29 (fixed using mike Ts answer) dEt/dy~1.25dEt/deta add calculation using s/T 3. Plan. use dEt/dy to get energy density use dN/dy to get entropy density (see lines of thought from muller/Rajagopal (hep-ph/0502174v1 and Enterria/Peressounko nucl-th/0503054v3) - PowerPoint PPT Presentation

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NDOF (effective) R. SetoMay 29(fixed using mike Ts answer)dEt/dy~1.25dEt/detaadd calculation using s/T3

Planuse dEt/dy to get energy densityuse dN/dy to get entropy density (see lines of thought from muller/Rajagopal (hep-ph/0502174v1 and Enterria/Peressounko nucl-th/0503054v3)use Tmeas(photons)~ 245 MeVfit models of Tinit using Tmeas as a function of this fit allows us to eliminate some sensitivity to Tget the values for /T4, 3s/4T3 and compare to lattice values (multiply by 30/2 to get an effective ndof)Now in a sQGP I am not sure a dof is well defined, but the , s, and T are. I just think of them as effective DOF. Maybe a model of resonances can approximate the DOF in an sQGP?Hope look for consistency with the lattice and some lower limit on NDof

CommentsThis is a quintessentially PHENIX measurement we wanted to measure low mass photons and dileptons, and ET (and dN/dy). We now have them lets make use of themStatements from Muller Rajagopal hep-ph/0502174v1 (2005)The challenge of demonstrating that the matter produced in heavy ion collisions is a deconfined quark-gluon plasma, as predicted by lattice QCD calculations, is the challenge of measuring the number of thermodynamic degrees of freedom /T4 at the time t0 at which the matter comes into approximate local thermal equilibrium and begins to behave like a hydrodynamic fluid. Data from experiments done at the Relativistic Heavy Ion Collider have been used to estimate t0 and to put a lower bound on the energy density (t0). However, measuring has seemed out of reach, because no current data serve even as qualitative proxies for the temperature T(t0).an experimental demonstration of deconfinement cannot be seen as the answer to some yes/no question, but must instead involve the measurement of some physical property of the matter created in heavy ion collisions that can also be predicted by controlled theoretical calculations, and which takes on quite different values below and above the crossover between a hadron gas and a quark-gluon plasma.A measurement of the temperatures of the quark-gluon plasma presumed to be present at early times is one of the goals of studies of direct photon and dilepton emission in heavy ion collisions but, so far, no evidence for thermal photon or dilepton radiation has been observed at RHIC.

Preliminariestheory you knowandphenix data

Can we melt the hadrons and liberate quark and gluon degrees of freedom?Energy density for g massless d.o.f. (bosons)Hadronic Matter: quarks and gluons confinedFor T ~ 200 MeV, 3 pions with spin=0Quark Gluon Matter:8 gluons;2(3) quark flavors, antiquarks,2 spins, 3 colors37 (48) !a first guess: Degrees of Freedom

The Critical temperatureLattice: TC~190 MeV (C ~ 1 GeV/fm3)Phase transition- fast cross overto experimentalist: 1st order

difference between S-B and lattice interactions(in hindsight)

Energy DensitypR22ctPHENIX: Central Au-Au yields

Energy density far above transition value predicted by lattice.R~5.5fmwhere did this number come from?

QuestionHow were these values derivedif I use dEt/deta=600 GeVR=6.8 and Tau=.35I get =12 GeV/fm3 (not 15)I need an R~6fm to get 15ANSWER from mikedEt/dy=1.25*dEt/deta I fixed this and I get this plotNote: to go from dN/deta to s(entropy)there is a factor of ~7.9=1.1*7.25/1.04see Mueller, Rajagopalhep-ph/0502174v1

Mike Leitch - PHENIX*Initial State & Temperature - PhotonsNearly real photons extracted from shape of low-mass e+e- spectrum

Shows large enhancement above scaled p+p in low-pT thermal region Fit to the pT slope in central collisions yields Tavg = 221 23 18 MeV Using models for the expansion Tavg = 221 Tinit > 300 MeVTalk: Y. Yamaguchi (4C, Thu)arXiv:0804.4168v1 [nucl-ex]Tavg = 221 MeV?

Tinit > Tc !To unfold hydro evolution:Compare to photon spectrum from hydro modelsT decreasing with timeTinit ~ 300-600 MeVTc ~ 170 MeVDEnterria & Peressounko, EPJ C46 (2006) 451G. David

NDOF? a Sanity check

hadron gasQGP choose 0 ~0.5-0. 6 fm/c good

Now do it more carefully

what do we expect?for 2 flavors12 (ndof=36)9.5 (ndof=29)37=ndof(effective 3 flavor)7.5 (ndof=23)

tauT(MeV) in fm/cfit

NDOF using /T4e.g NDOF= 39(0.6)0.9= 25

NDOF using s/T3e.g NDOF= 22(0.6)0.425= 18from 1.1*7.25/1.04

fits for a range of valuesTemps from models1.18(npart/2)1/3Ndof(tau)NDOF for reasonable values of tau0-5% centraldEt/dy=dEt/deta*1.25from mike

fmNDOFpion gas0.350.6from v2 considerationscanonical 2 flavor qgp value2520Tinit/10(MeV)ndof from e/T4ndof from s/T3energy densityentropy dens/10

- CommentsPretty hard to get NDOF=3 (i.e. need tau
more comments/caveatsIf you look at p 3 of the Mueller/Raj article they point out to exclude the resonance gas we need to exclude Ndof~10 (I dont clearly understand this statement when I look at the figure). I am not sure we know that yet. It seems to be, but I would still like to understand the errors better. the energy density is a average of the transverse dimension, where the T is the max. but that implies that the real energy density is higher so that would drive ndof higherAll the models used to extrapolate back to Tinit are hydro models with a QGP EOS. (note that some of them have a first order transition. I would like to understand if the system sits at Tc in a mixed phase) So the argument is a bit circular. On the other hand you can just use Tmeasured and you still get a large ndof. What you would need is for the Tinit to be much larger (>1 GeV), i.e. to have a much steeper time dependence. That does not seem reasonable to me. this does not actually tell you WHAT the DOF are. (again, the DOF may not be well defined in an sQGP) For all we know, perhaps they are some variant of resonances. We already know some modified J/psi continues to live at above Tc, so maybe that is the same of other particles.

If its OK with the collaboration, I would like to say something like what I have presented here at the AGS/Users meeting where I have to give a talk. However, if its decided that I cannot I can live with it.

excel

ndof

tauT

0.15590

0.17580

0.2525

0.33370

0.5300

0.6350

using ndof=e/T^4Tinit(tau)0.8210.7160.3950.3060.240

centNpartRdET/detadET/dye*tauetau/.35etau/.6NDOF/tau^0.9tau0.0750.100.350.601.00

0-5351.46.616067585.5215.779.2038.673.764.8715.0324.4238.67

0-10325.26.44549.56875.2715.068.7836.923.594.6514.3523.3136.92

0-20279.96.13457.255724.8513.858.0833.953.304.2713.2021.4433.95

using ndof=s/T^3Tinit(tau)0.8210.7160.3950.3060.240

centNpartRdN/detads/dys*taustau/.35stau/.6NDOF/tau^0.425tau0.0750.100.350.601.00

0-5351.46.61687542739.55113.0065.9224.938.299.3715.9620.0724.93

0-10325.26.44624493037.83108.0863.0523.857.938.9615.2619.1923.85

0-20279.96.13519410034.7799.3557.9521.927.298.2414.0317.6421.92

Expectaions

ndof(sb)e/T^4(sb)3s/4T^3(sb)e/T^4(lattice)3s/4T^3(lattice)ndof(effective)3s/4T^3(near Tc)ndof(effective)

3 flavor4816.001612.512.538.010.0030.4

2 flavor3712.00129.59.528.97.5022.8

Sheet2

Sheet3

from dET/dy paper 200 GeV AuAu

centralitytable for AuAuReygers

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