What about the chiral phase transition or Where does mass (hadronic) come from?

1. What about the chiral phase transition orWhere does mass (hadronic) come from? • Do we understand the relationship between the chiral and deconfinement transitions? • Can we see the ? • Are there reliable calculations of mass? (see duality) • Shift up, shift down, broadening, exist above Tc? • Not yet (maybe Rapp Wambach) – but there will be (unquenched lattice) • BR (e+e-) /BR () sensitive to Chiral restoration? (rescattering of K’s) • We will make a first crack at this for QM (?) • If this is radically different (say larger), what does it mean? • K mass shifted up •  mass shifted down • K’s from inside fireball got scattered out of  peak • Can we use the  as a clock? • Of what – mixed phase? High density phase? – how good is it?

2. DOF? duality • Is there a right set of degrees of freedom? • <<Tc (hadrons); < Tc (?); >Tc (?): >> Tc(quarks/gluons) • Various approaches: Assumptions of • Brown-Rho scaling: assumption that hadron masses scale as the quark condensate - essentially from a quark degrees of freedom point of view • Rapp-Wambach: Rescattering and cross sections – from a hadronic degrees of freedom point of view • This always puzzled me. • Duality?: hadronic  quark degrees of freedom •  (Vector) and A1(Axial-Vector) become degenerate in hadronic model – I.e. chiral symmetry is restored. • To actually prove this is not possible at the moment. • Theorists will depend on experiment (or the lattice?) to help define the right “degrees of freedom” to use

3. How do you see this?Vector Meson mass shifts in the dilepton channel e+  e- • “Light” Vector mesons are ideal probes (,,) • Short lifetime ~ few fm/c • Decay inside the medium • Electrons (and muons) are ideal messengers • Don’t interact strongly (e.g. neutrinos from the sun) • Like putting a scale to measure mass inside the fireball •  (?)

4. What measurements are possible?     e+   e- • Problem – background from dalitz decays and conversions • What can we do now? • Future : Dalitz rejection via electron ID in a field free region. • Critically important to see vacuum values to prove mass resolution is good – I.e. you want to see a “peak” • New Calculations by Rapp (PRC(63) 2001 954907) • Specific to RHIC • Uses hadronic degrees of freedom • Modification of hadronic resonances (chiral restoration) • Strong enhancement of the  (mixed and hadron gas phase) •  have a very short mean free path in the hadronic gas •  has a very short lifetime (<1 fm)   e+e-  e+e-  e+e-  e+e-  e+e-

5. Experimental “Knobs” Signal should increase with centrality Signal should be enhanced at low pT Central Peripheral Central- “High” PT Me+e Me+e Central- “Low” PT Me+e Me+e

6. Spectra (theory) Rapp/Wambach • Spectral functions (this is where the interesting stuff is) • Many of the medium effects of interest come from interactions with Baryons • Verification on Lattice? – needs unquenched • At RHIC these baryons are mostly from thermal excitations of baryon-antibaryon pairs

7. Time evolution • Rapp’s model has • Spectral functions (this is where the interesting stuff is) • Many of the medium effects of interest come from interactions with Baryons • At RHIC these baryons are mostly from thermal excitations of baryon-antibaryon pairs • Above Tc use quark DOF • Time evolution • Rapp provides us with • Mass and pt distribution from inside medium QGP mixed hadronic

8. The “Experiment” -Exodus generator • R. Averback has put together a dilepton generator for phenix. • Includes • sources of dileptons VM(,,,J/,), , ’, Charm(singles), dalitz decays, (conversions assumed as scaled dalitz) • Acceptance • Momentum resolutions effects • “Standard” Exodus produces vacuum decays, Rapp spectra govern “in medium” decays. • Normalization Checked vs calculation by Rapp. • PHENIX (Y. Akiba) has made some first measurements of the di-electron background. • Strategy • Incorporate Rapp’s model into Exodus • Check backgrounds against early PHENIX measurement (rescale) • Assume that a mixed event subtraction will work. • Assume ~ 109 Central events ~4 months perfect running (1-2 yrs) • Ignore Systematics, Triggering problems, Assume efficiency is ~100% (It is now ~24% - realistically it may reach 80%)

9. An example (simulation) • Assume ~ 109 Central events • Note: This running period int Lum=42 b-1 ~ 180M events18M central, • Next run (x10)  ~200M Central • so change binning by 5 • Look at spectra assuming a perfect mixed event subtraction Raw e+e- inv mass       Combinatorial dalitz background After background subtraction

10. Some rate estimates Lave=3x1026 (design:2x1026) 40% “duty factor” Rate Guestimates Vacuum values no enhacement

11. Input Pt spectra Hot vector mesons from fireball “ordinary” Vector mesons Arbitrary normalization Pt (GeV) • Pt spectra of “in medium” decays is much softer. The cuts are • Pt<0.2 – low pt • Pt > 0.8 – “high pt” –the signal is down by a factor of 10.

12. Pt and centrality dependence of the Exodus+Rapp model High pt (>0.8GeV) Low pt (<0.2 GeV) Central 0-10% Decayed in Vacuum From inside the fireball  Peripheral 60-80%  • The signal for “in medium” effects is strongest for central, low pt events • Peripheral low pt events, show a substantial enhancement of the  from the hadron gas stage 

13. / region We should be able to identify this if the enhancement is as strong as predicted. (remember change bin by 5) But is it a “hot qgp” or a cold hadron gas? • The is complicated since it sits on the  -nevertheless it should be broadened. • Even if there is no QGP, Rapp predicts a strong enhancement of the. (which in itself would be interesting to see – remember the “clock”?) • correlated charm pairs are not yet in Charm, in many scenarios, is also expected to be enhanced – we already know some limits Low pt central High pt peripheral Charm- low pt central Charm-high pt peripheral

14. Model comparison – with and w/o “in medium effects” In the case of a hadron gas, though strongly enhanced the  should have its ordinary width. The  and  will be separable. In the case of “in medium” effects both the  and  will be strongly broadened. Probably not next run Hot “qgp” Cold Hadron Gas Mee 109 central events pt<0.2 Gev Charm

15. Dalitz background? Can we get rid of it? w/ 90% datitz rejection e+e- • Problem – background from dalitz decays and conversions • Simulation for 109 Central events • Central events pt<0.2 GeV (red) compared to • high pt peripheral renormalized (black) • Critically important to see vacuum values to prove mass resolution is good – I.e. you want to see a “peak” Good momentum resolution • NEED Dalitz rejection via electron ID in a field free region. No datitz rejection e+e-

16. The future: RHIC IIStrategy for Low Mass Pair Measurement e- p e+ p V0 e- TPC/HBD p measured in outer PHENIX detectors (Pe > 200 MeV/c) e+ • Operate PHENIX with low inner B field • to optimize measurement of low • momentum tracks • Identify signal electrons (r,w,f, …) and • background electrons with p>200 MeV in • outer PHENIX detectors • Identify low momentum electrons (p<200 • MeV) using dE/dx from TPC and/or • Cherenkov light in HBD • Calculate effective mass (or opening • angle) between all opposite sign tracks • identified as electrons • (eelectron > 0.9, prej > 1:200) • Reject pair if mass < 140 MeV • (or q< 200 mrad) B~0 dalitz/conversion has ~ zero opening angle Must provide sufficient Dalitz rejection (>90%) while preserving the true signal

17. PHENIX Inner Detector TPC tracking coverage Df=2p -0.7<|h|<0.7 dpT/pT ~ 0.02 Inner Coil creates a “field free” (∫Bdl=0) region inside the Central Magnet

18. Conclusions • This was an exercise to get a feeling for what is possible – and assumed a particular model. • Assuming Rapp’s Calculation • If the  is strongly enhanced Phenix should be able to see it. We may be lucky enough to see the first hints of chiral symmetry restoration in the //. • However, the clear signature of chiral symmetry restoration - the detection of width broadening will need very high statistics and/or dalitz rejection • Can we make a clear interpretation of whatever we see?

19. Spectra (theory) Note strong broadening of  • May be possible to see broadening of  since at low pt, a large fraction of the spectrum is from “in medium” decays Pt<0.2 GeV Free  In Medium  Pt<0.2 GeV Black-total Red- “in medium”

20. Theory • Old • Sum rules, Eff. Lagrangians, small lattices • New • More complete effective degrees of freedom (Rapp-Wambach) • Lattice Calculations • Reliable calculations coming- large lattice-entropy method • Mass shifts/broadening • My understanding-large effects • Gradual with net baryon density (B) • Sharp with T if no quark/anti-quarks (I.e. baryons- quenched approx for the lattice) • Rapp and Wambach- mass shift/broadening are large and gradual since