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Advanced Energy Density Estimates in LHC P+P Collisions: Correcting the Bjorken Estimate

This presentation discusses the initial energy density in LHC proton-proton collisions, correcting the classic Bjorken estimate. The work highlights the significance of acceleration in determining energy density, with advanced calculations suggesting a corrected initial density of approximately 1.14 GeV/fm³. This density is crucial in understanding the conditions leading to potential quark-gluon plasma formation. Various parameters, uncertainties, and their effects on initial conditions are considered, drawing comparisons with RHIC and emphasizing new insights from experimental data.

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Advanced Energy Density Estimates in LHC P+P Collisions: Correcting the Bjorken Estimate

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  1. ZIMÁNYI SCHOOL 2012 December 3-7. Budapest, Hungary INITIAL energydensityin LHC P+Pcollisions M. Csanád &T. Csörgő 04 Dec2012

  2. 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)

  3. An advancedestimate • Fact: dn/dynotflat • Finiteness & acceleration • Needacceleratingsolution of relativistichydro • Twomodifications: • yh & hfinal hinitial • Correctedinitialenergydensity: • Workneededtoaccelerate! • Correctionw.r.t. EoS:

  4. 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)

  5. 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)

  6. 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!

  7. Correctionfrominitialacceleration • Initialaccelerationpushesoutervolumeelements • Thismodifiesthedn/dhdistribution • Estimateaccelerationfromit! • l = 1: no acceleration • TOTEM fit: l = 1.0730.0010.004 • WithoutEoS: 20%

  8. 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

  9. Dependenceonparticlenumber • Severalmultiplicityclasses, 6-20, even 30 seen!

  10. Initialtemperatureestimate • Temperaturefrome~T4

  11. 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

  12. Systematicuncertainties • Allsources of uncertainties: • Conclusion: • eini= (1.14  0.01(syst) +0.21-0.16 (syst)) GeV/fm3

  13. 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?

  14. 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

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