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ZIMÁNYI SCHOOL 2012. December 3-7. Budapest, Hungary. INITIAL energy density in LHC P+ P collisions. M. Csanád &T. Csörgő. 04 Dec 2012. The Bjorken-estimate. The original idea: energy density based on dE / dy QGP critical e :  1 GeV /fm 3 ( from e c =6-8  T c 4 )

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initial energy density in lhc p p collisions

ZIMÁNYI SCHOOL 2012

December 3-7. Budapest, Hungary

INITIAL energydensityin LHC P+Pcollisions

M. Csanád &T. Csörgő

04 Dec2012

the bjorken estimate
The Bjorken-estimate
  • The original idea: energydensitybasedondE/dy
  • QGP criticale: 1 GeV/fm3 (fromec=6-8Tc4)
  • Result (1900x cited)
  • Needscorrection!
  • Ref.: Phys.Rev. D27 (1983)
an advanced estimate
An advancedestimate
  • Fact: dn/dynotflat
  • Finiteness & acceleration
  • Needacceleratingsolution

of relativistichydro

  • Twomodifications:
    • yh & hfinal hinitial
  • Correctedinitialenergydensity:
  • Workneededtoaccelerate!
  • Correctionw.r.t. EoS:
a solution of relativistic hydro
A solution of relativistichydro
  • Velocity: tanh(lh)
  • Acceleration: l1
  • Density: (t/t0)l
  • dn/dycalculable!
  • Comparethisto RHIC data!
  • dn/dymeasurementyieldsadvancedinitialeestimate
  • Significantcorrectionat RHIC!
  • Reference: Phys.Lett. B663 (2008) 306-311 (nucl-th/0605070)
initial energy density at rhic
Initialenergydensityat RHIC
  • Bjorkenestimatefrom BRAHMS: 5 GeV/fm3
  • Advanced estimategives:
  • Correction: 2-3x, result 15 GeV/fm3, QCD agreement!
  • Correspondsto Tini 2Tc  340 MeV
  • Confirmedbyphotonspectraat PHENIX, published 2010
  • Referencee.g.: J.Phys.G35 (2008) 104128 (arXiv:0805.1562)
initial energy density at lhc
Initialenergydensityat LHC
  • RoughestimatepossibleviatheBjorken formula
    • Number of particlesatmidrapidity: 5.89 (CMS, ALICE)
    • Averageenergy: mt=0.562 GeV (CMS)
    • Initialradius of thesystem R: ~1.081 fm (TOTEM, sinel)
    • Formationtimet0: 1 fm/c (conservativeestimate)
  • Energydensityfromthis:
  • Justbelowcritical? Importantquestion!
correction from initial acceleration
Correctionfrominitialacceleration
  • Initialaccelerationpushesoutervolumeelements
  • Thismodifiesthedn/dhdistribution
  • Estimateaccelerationfromit!
  • l = 1: no acceleration
  • TOTEM fit: l =

1.0730.0010.004

  • WithoutEoS: 20%
advanced estimate
Advanced estimate
  • Fit result: l=1.073
  • Conservatively: cs2=0.1
  • ~25% correction
  • Input parameters:
    • dN/dyatmidrap.: 5.89
    • Averagemt: 0.562 GeV
    • Area: 3.67 fm2
      • Fromcrosssections
    • Freeze-outtime / form. time: atleast 2
  • Bjorkenresult: 0.90 Gev/fm3
  • Correctedresult: 1.14 GeV/fm3
dependence on particle number
Dependenceonparticlenumber
  • Severalmultiplicityclasses, 6-20, even 30 seen!
initial temperature estimate
Initialtemperatureestimate
  • Temperaturefrome~T4
sources of uncertainties
Sources of uncertainties
  • Forthecorrectionfactore/eBj:
    • Fit parameterl
    • Statisticalerror (fromthedata)
    • Speed of sound cs2
    • Durationtf/ti
  • FortheoriginalBjorken-estimate:
    • Main uncertaintysource: multiplicityatmidrapiditydN/dy
    • Area (iftakenfromcross-section): veryprecise
    • Formationtime
    • Averagetransversemass
systematic uncertainties
Systematicuncertainties
  • Allsources of uncertainties:
  • Conclusion:
    • eini= (1.14  0.01(syst) +0.21-0.16 (syst)) GeV/fm3
is it unprecedented consequences
Is itunprecedented? Consequences?
  • Bjorken and Landau worked out hydro for pp and pA
  • Success of hydro to describe h+p, with <n> = 7-8... Phys.Lett. B422 (1998) 359-368
  • Bjorken: it is not hadrons that play billiard balling
  • If p+p is a complexsystem:
    • Radial flow
    • V2 scaling
    • HBT radiiscaling
    • Lowmassdileptonenhancement?
    • Directphotonenhancement?
  • RAAmightnot be thebestmeasure: dividebylengthscale?
summary
Summary
  • ExperimentallywidelyusedBjorken est.
  • Advanced estimate: accelerationwork, fromdn/dh
  • Resultsontheinitialefor cs2=0.1, attf/tini=2
  • From TOTEM data: eini= (1.14  0.01  0.2) GeV/fm3
    • ThisatdN/dy=6 & linearlyriseswithmultiplicity!
  • Criticalenergydensity: 1 GeV/fm3
  • Resultsnotincompatiblewithsupercrit. sQGP phase