Measuring the temperature

3. Measuringthetemperature • Thermometer (directcontact) • dilatation • air pressure • mechanicalorelectricstress • Chemistry (mixture) • color • massratios • hadroniccomposition • Spectra (telemetrics) • astronomy (photons) • pTspectra of light and heavyparticles • multiplicityfluctuations

4. Measuringthetemperature • Thermometer (directcontact) • dilatation • air pressure • mechanicalorelectricstress • Chemistry (mixture) • color • massratios • hadroniccomposition • Spectra (telemetrics) • astronomy (photons) • pTspectra of light and heavyparticles • multiplicityfluctuations

5. Interpretingthetemperature • Thermodynamics (universality of equilibrium) • zeroththeorem (Biro+Van PRE 2011) • derivative of entropy • Boyle-Mariottetypeequation of state • Kinetictheory (equipartition) • energy / degree of freedom • fluctuation - dissipation • otheraveragevalues • Spectralstatistics (abstract) • logarithmicslopeparameter • observedenergyscale • dispersion / power-laweffects

6. Tsallis quark matter + transverse flow + quark coalescence fits to hadron spectra with Károly Ürmössy RHIC data JPG: SQM 2008, Beijing

7. Tsallis quark matter + transverse flow + quark coalescence fits to hadron spectra with Károly Ürmössy RHIC data JPG: SQM 2008, Beijing

8. arXiV: 1111.4817 -> PLB: Unruh gamma radiationat RHIC ? with Miklós Gyulassy and Zsolt Schram Constantacceleration* is aliketemperature… Softbremsstrahlung: high k_T exp, low k_T 1 / square; longacceleration: Bjorken shortacceleration: Landauhydro * Whataboutnon-constant, non time-symmetricacceleration? Mimickingthermalsources byUnruhradiation T.S.Biró¹, M.Gyulassy² and Z.Schram³ ¹ MTA KFKI RMKI  MTA Wigner Research Centre RMI ²University of Columbia, ³University of Debrecen Exploring QCD Frontiers: from RHIC and LHC to EIC, Jan. 30. – Feb. 03. 2012, Stellenbosch, Republic of South-Africa

9. Whydostatisticswork ? • Independentobservation over 100M events • Universallawsforlargenumbers • Steadynoiseinenvironment: ‚reservoir’ • Phasespacedominance • Bychancethedynamicsmimicsthermalbehavior

10. Canonical distribution with Rényi entropy This cut power-law distribution is an excellent fit to particle spectra in high-energy experiments!

11. Fit and physicswith Rényi entropy The cut power-law distributionis an excellentfit, butitgivessmallervaluesfortheparameter hat(T) atthesameTthanthe Boltzmann form!

12. NBD = Euler ○ PoissonPower Law = Euler ○ Gibbs S u p e r s t a t i s t i c s

13. Arxiv: 1111.4817 Phys.Lett. B, 2012 Ourview

14. Experimentalmotivation: apparentlythermalphotons RHIC: PHENIX

15. Theoreticalmotivation • Decelerationduetostopping • Schwingerformula + Newton +Unruh= Boltzmann Satz, Kharzeev, …

16. WhyPhotons (gammas) ? • Zeromass: flow – Doppler, easykinematics • Colorneutral: escapesstronginteraction • Couplestocharge: Z / A sensitive • Classicalfieldtheoryalsopredictsspectra

17. Soft bremsstrahlung • Jackson formula for the amplitude: With , and the retarded phase

18. Soft bremsstrahlung • Covariant notation: IR div, coherenteffects Feynmangraphs The Unruheffectcannot be calculatedbyanyfinitenumber of Feynmangraphs!

19. Kinematics, source trajectory • Rapidity: Trajectory: Let us denote by in the followings!

20. Kinematics, photon rapidity • Angle and rapidity:

21. Kinematics, photon rapidity • Doppler factor: Phase: Magnitude of projected velocity:

22. Intensity, photon number Amplitude as an integral over rapidities on the trajectory: Here is a characteristic length.

23. Intensity, photon number Amplitude as an integral over infinite rapidities on the trajectory (velocity goes from –c to +c): With K1 Bessel function! Flatinrapidity !

24. Photon spectrum, limits Amplitude as an integral over infinite rapidities on the trajectory (velocity goes from –c to +c): for for

25. Photonspectrumfrom pp backgroound, PHENIX experiment

26. Apparent temperature • High - infinite proper time acceleration: Connection to Unruh: proper time Fourier analysis of a monochromatic wave

27. Unruh temperature • Entirely classical effect • Special Relativity suffices Unruh Constant ‚g’ acceleration in a comoving system: dv/d = -g(1-v²) Max Planck

28. Unruh temperature Planck-interpretation: The temperature in Planck units: The temperature more commonly:

29. Unruh temperature On Earth’ surface ist is 10^(-19) eV, while at room temperature about 10^(-3) eV.

30. Unruh temperature Braking from +c to-cin a Compton wavelength: kT ~ 150 MeV if mc² ~ 940 MeV (proton)

31. Connection to Unruh Fourier component for the retarded phase:

32. Connection to Unruh Fourier component for the projected acceleration: Photon spectrum in the incoherent approximation:

33. Connection to Unruh Fourier component for the retarded phase at constant acceleration: KMS relation and Planck distribution:

34. Connection to Unruh KMS relation and Planck distribution:

35. Connection to Unruh Note: It is peaked around k = 0, but relatively wide! (an unparticle…)

36. Transverse flow interpretation Mathematica knows: ( I derived it using Feynman variables) Alike Jüttner distributions integrated over the flow rapidity…

37. Finite time (rapidity) effects = with Short-timedeceleration Non-uniform rapiditydistribution;  Landauhydrodynamics Long-timedeceleration uniform rapiditydistribution;  Bjorkenhydrodynamics

38. Short time constant acceleration Non-uniform rapidity distribution;  Landau hydrodynamics

39. Analytic results x(t), v(t), g(t), τ(t), 𝒜, dN/kdkd limit

46. Glauber model

47. Glauber model

48. Summary • Semiclassical radiation from constant accelerating point charge occursrapidity-flat and thermal • The thermal tail develops at highenough k_perp • At low k_perp the conformal NLO result emerges • Finite time/rapidity acceleration leads to peakedrapiditydistribution, alikeLandau - hydro • Exponentialfitstosurplus over NLO pQCDresultsreveal a ’’pi-timesUnruh-’’ temperature

49. Is acceleration a heatcontainer?