Thermometer direct contact dilatation a ir pressure m echanical or electric stress Chemistry mixture color mass ratios hadronic composition ID: 796049
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Slide1
Slide2Slide3Measuring the temperature
Thermometer (
direct contact)
dilatationa
ir pressuremechanical
or electric stress
Chemistry
(
mixture
)
color
mass
ratios
hadronic compositionSpectra (telemetrics)astronomy (photons)pT spectra of light and heavy particlesmultiplicity fluctuations
Slide4Measuring the temperature
Thermometer (
direct contact)
dilatationa
ir pressuremechanical
or electric stress
Chemistry
(
mixture
)
color
mass
ratios
hadronic compositionSpectra (telemetrics)astronomy (photons)pT spectra of light and heavy particlesmultiplicity fluctuations
Slide5Interpreting the temperature
Thermodynamics (
universality of equilibrium)
zeroth theorem (Biro
+Van PRE 2011)derivative of entropy
Boyle-Mariotte type
equation
of
state
Kinetic
theory
(
equipartition
)
energy / degree of freedom fluctuation - dissipation other average valuesSpectral statistics (abstract)logarithmic slope parametero
bserved energy scale
dispersion / power -law
effects
Slide6Tsallis quark matter + transverse flow + quark coalescence fits to hadron spectra
JPG: SQM 2008,
Beijing
with Károly Ürmössy
RHIC data
Slide7Tsallis quark matter + transverse flow + quark coalescence fits to hadron spectra
with Károly Ürmössy
RHIC data
JPG: SQM 2008,
Beijing
Slide8Blast wave fits and quark coalescence
SQM 2008, Beijing
with Károly Ürmössy
arXiV: 1011.3442
Slide9All particle types follow power-law
E
L(E)
G O
O
D
B E T
T
E R !
with Károly Ürmössy
Slide10Mimicking
thermal
sources
by Unruh
radiation
T.S.Biró
¹
, M.Gyulassy
²
and Z.Schram
³
¹
MTA KFKI RMKI
MTA Wigner Research Centre
RMI²University of Columbia, ³University of DebrecenarXiV: 1111.4817 -> PLB:
Unruh gamma
radiation
at RHIC ?
w
ith
Miklós
G
yulassy
and Zsolt
Schram
Constant
acceleration
* is
alike
temperature
…
Soft
bremsstrahlung
:
high
k_T
exp
, low k_T 1 /
square
;
long
acceleration
:
Bjorken
s
hort
acceleration
:
Landau
hydro
*
What
about
non-constant
, non
time-symmetric
acceleration?
Exploring
QCD
Frontiers
:
from
RHIC and LHC
to
EIC, Jan. 30. –
Feb
. 03. 2012,
Stellenbosch
,
Republic
of
South-Africa
Slide11Why do
statistics work ?
Independent
observation over 100M eventsUniversal
laws for large
numbersSteady
noise
in
environment
: ‚
reservoir
’
Phase space dominanceBy chance the dynamics mimics thermal behavior
Slide12Canonical distribution with Rényi entropy
This cut power-law distribution is
an
excellent
fit to particle spectra
in high-energy experiments!
12
Slide13Fit and physics with Rényi entropy
The
cut power-law
distribution
is an excellent
fit, but
it
gives
smaller
values
for
the parameter hat(T) at the same T than the Boltzmann form!
13
Slide14NBD = Euler ○ PoissonPower Law = Euler ○ Gibbs
S u p e r s t a t i s t i c
s
Slide15Arxiv
: 1111.4817
Phys.Lett
. B, 2012
Our view
Slide16Experimental
motivation
:
apparently
thermal
photons
RHIC: PHENIX
Slide17Theoretical motivation
Deceleration due to stopping
Schwinger formula + Newton +
Unruh = Boltzmann
Satz
,
Kharzeev
, …
Slide18Why Photons
(gammas) ?
Zero mass
: flow – Doppler, easy kinematics
Color neutral: escapes
strong interactionCouples
to
charge
: Z / A
sensitive
Classical
field
theory also predicts spectra
Slide19Jackson formula for the amplitude:
With
,
a
nd the retarded phase
Soft bremsstrahlung
Slide20Covariant notation:
Soft bremsstrahlung
Feynman
graphs
IR
div
,
coherent
effects
The
Unruh
effect
cannot
be
calculated
by
any
finite
number
of
Feynman
graphs
!
Slide21Kinematics, source trajectory
Rapidity:
Trajectory:
Let us denote
by
in the followings!
Slide22Kinematics, photon rapidity
Angle and rapidity:
Slide23Kinematics, photon rapidity
Doppler factor:
Phase:
Magnitude
of projected velocity:
Slide24Intensity, photon number
Amplitude as an integral over rapidities on the trajectory:
Here
is a
characteristic
length.
Slide25Intensity, photon number
Amplitude as an integral over infinite rapidities on the trajectory (velocity goes from –c to +c):
With K1 Bessel
function
!
Flat
in
rapidity
!
Slide26Photon spectrum, limits
Amplitude as an integral over infinite rapidities on the trajectory (velocity goes from –c to +c):
for
for
Slide27Photon spectrum from pp
backgroound, PHENIX experiment
Slide28Apparent temperature
High -
infinite proper time acceleration:
Connection to Unruh:
proper time Fourier analysis of a monochromatic wave
Slide29Unruh temperature
Entirely classical effectSpecial Relativity suffices
Unruh
Max Planck
Constant ‚g’ acceleration in a comoving system: dv/d
= -g(1-v
²
)
29
Slide30Unruh temperature
Planck-interpretation:
The temperature in
Planck
units:
The temperature
m
ore commonly:
30
Slide31Unruh temperature
On Earth’ surface ist is 10
^(-19)
eV, while at room temperature about 10^(-3) eV.
31
Slide32Unruh temperature
Braking
from
+c
to
-c
in
a
Compton
wavelength:
kT ~ 150 MeV
if
mc
² ~ 940 MeV (proton)32
Slide33Connection to Unruh
Fourier component for the retarded phase:
Slide34Connection to Unruh
Fourier component for the projected acceleration:
Photon spectrum in the incoherent approximation:
Slide35Connection to Unruh
Fourier component for the retarded phase at constant acceleration:
KMS relation and Planck distribution:
Slide36Connection to Unruh
KMS relation and Planck distribution:
Slide37Connection to Unruh
Note:
It is peaked around k = 0, but relatively wide! (an unparticle…)
Slide38Transverse flow interpretation
Mathematica knows: ( I derived it using Feynman variables)
Alike Jüttner distributions integrated over the flow rapidity…
Slide39Finite time (rapidity) effects
=
with
Short-time
deceleration
Non-uniform
rapidity
distribution
;
Landau
hydrodynamics
Long-time
deceleration
uniform
rapidity
distribution
;
Bjorken
hydrodynamics
Slide40Short time constant acceleration
Non-uniform rapidity distribution;
Landau hydrodynamics
Slide41Analytic results
x(t), v(t), g(t), τ(t), 𝒜,
dN/kdkd
limit
Slide42Slide43Slide44Slide45Slide46Slide47Slide48Large
pT: NLO QCD
Smaller
pT:
plus direct gammas
Slide49Glauber
model
Slide50Glauber
model
Slide51Slide52Summary
Semiclassical radiation from constant accelerating point charge occurs rapidity-flat and
thermal The thermal tail develops at high enough k_
perpAt low k_perp the conformal NLO result
emergesFinite time/rapidity acceleration leads to peaked rapidity
distribution, alike Landau -
hydro
Exponential
fits
to
surplus
over NLO
pQCD
results reveal a ’’pi-times Unruh-’’ temperature
Slide53Is
acceleration
a
heat
container
?