What about the chiral phase transition or where does mass hadronic come from
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What about the chiral phase transition or Where 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 T c ?

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

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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?


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


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

    •  (?)


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-


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


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


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


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%)


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


Some rate estimates

Lave=3x1026 (design:2x1026)

40% “duty factor”

Rate

Guestimates

Vacuum values

no enhacement


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.


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


/ 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


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


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-


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


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


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?


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”


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


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