Paul Romatschke CU Boulder amp CTQM based on arXiv180206804 Source code for all new results http githubcom paro8929Eremitic Prologue Data Trend changes qualitatively around pT34 ID: 812103
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Slide1
Azimuthal Anisotropies at High Momentum
Paul RomatschkeCU Boulder & CTQM
based on
arXiv:1802.06804
Source code for all new results:
http://
github.com
/paro8929/Eremitic
Slide2Prologue
Slide3Data: Trend
changes qualitatively around pT~3-4 GeV
Slide4Can we explain it?
It’s not hydro: hydro stops working well below 4 GeVIs it jets (e.g. [1609.05171])?If not, what is it?
Slide5Challenge for Jet explanation: p+Pb
Same trends as in
Pb+Pb
, but no apparent jet modifications observed
Slide6Proposed explanation: non-hydrodynamic transport
Modern formulation of hydrodynamics in terms of effective theory of long-lived (hydrodynamic) modes [New Textbook, based on 1712.05815, to appear summer ‘19 w/ Cambridge University Press]
Main message: competition between hydro modes and non-hydro modes; hydro works as long as non-hydro modes loose
However, even if hydro has broken down, there is still transport; this transport is now due to non-hydrodynamic modes and may be qualitatively different from usual hydro transport
Slide7A look at non-hydro transport: kinetic theory
Model for transport at different scales: Boltzmann equation w/ relaxation time approximation; relaxation time encodes interaction strength
Classical particles
Note: These model assumptions are not essential and can be relaxed if needed
Slide8Energy-momentum tensor in and out of equilibrium
Note: Velocity and energy density defined in and out of equilibrium, as is the “pseudo”-temperature T defined above
Slide9Approximation of small mean free path
(well-known)
Slide10Near equilibrium (hydro expansion)
Strong interactions -> small relaxation time tR T<<1
Small relaxation time implies f close to equilibrium
Zeroth order hydro expansion!
Slide11Near equilibrium (hydro expansion)
Collective modes (hydro modes) are sound and shear modesWell known how to extend hydro expansion to higher ordersHydro expansion small parameter is tR
times gradient
Approximation breaks down at LARGE
t
R
and/or momentum
p
T
Slide12Near equilibrium (hydro expansion)
Hydro equations of motion may be solved for anisotropies, find
Hydro
v
n’
s
rise with
p
T
Slide13Approximation of LARGE mean free path
(not-so-well-known)
Slide14Near ballistic (eremitic expansion)
Weak interactions -> large relaxation time tR T>>1
Large relaxation time implies collision kernel close to zero
Zeroth order eremitic expansion (free streaming)
Slide15Near ballistic (eremitic expansion)
Free-streaming equation can be solved by method of characteristics, leading toNote: leads to vn=0, but in non-trivial way. Hadronic
afterburner can recover non-zero
v
n
’s
(see e.g. 1504.02529)
Note: evolution quite far away from equilibrium, but local velocity, energy-density (and pseudo-temperature) well defined for classical particles
Slide16Near ballistic (eremitic expansion)
Corrections to free-streaming: particles rarely (but nevertheless occasionally) interactLike hermit crabs: hence the name “eremitic” expansionFirst order eremetic expansion:
Solution in terms of characteristics
Slide17Near ballistic (eremitic expansion)
Collective modes (non-hydro modes) are branch cuts [1512.02641]Known how to extend eremitic expansion to higher orders [1802.06804] and some applications exist [1012.0899, 1802.06804, 1803.02072, 1811.05195]; maybe related to “escape mechanism”?
Eremitic expansion parameter is inverse
t
R
times integral
Approximation breaks down at
SMALL
t
R
and/or momentum
p
T
Slide18Hydro vs. Eremitic Expansion
Equations of motion may be solved for anisotropies, find
Hydro
v
n
’s
rise with
p
T
Non-hydro
v
n
’s
fall with
p
T
Slide19Hydro vs. Eremitic expansion
Two opposite limits of momentum range: low (hydro) and high (eremitic); qualitatively different behaviorDifferent collective modes: sound/shear pole (hydro), branch cut (eremitic)Full theory (kinetic theory) always has both, but they presumably dominate at low/high momentum, respectively
Slide20A guess for full kinetic theory
Pade approximant using hydro and eremitic results
Hydro
v
n
’s
rise with
p
T
Non-hydro
v
n
’s
fall with
p
T
Pade
as a guess to full kinetic theory
Slide21Hydro+Eremitic captures qualitative behavior in
Pb+Pb...
Slide22...and in p+Pb
!!!
Slide23Summary and Conclusions
Transport at high momentum is non-hydrodynamic and in kinetic theory can be captured by simple approximation scheme (“eremitic expansion”)Applied to nuclear collisions, non-hydro transport gives “unusual” qualitative behavior of azimuthal anisotropies falling with pTNon-hydro transport approximation fails at LOW momenta (opposite to hydro)
So far only model results with massless
partons
, classical statistics, no
hadronization
. Good opportunity to get involved!!!!
Slide24Bonus Material
Slide25vn
ratios: approximately constant at high pT