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Resonance properties and transport coefficients in SMASH
Hannah Petersen
16.04.18, NED 2018, Varadero, Cuba
Hannah Petersen NED 2018 16.04.18
The QCD Phase Diagram• Main goals of heavy ion research
•Understand the structures in the phase diagram •Investigate the properties of the quark-gluon plasma •Focus in this talk: Hadron/Resonance dynamics and
transport coefficients (η/s and electric conductivity)
!2
•Questions to be answered: – What is the temperature and the
density? What are the relevant degrees of freedom?
– Phase transition, critical point? – What are the transport properties?
(η/s)(T,µB) and (ζ/s)(T,µB)
Hannah Petersen NED 2018 16.04.18
Transport Approaches
•Theoretical models are essential to gain insights about the properties of the hot and dense stage of the reaction
!3
Fundamental field theory of strong interactions (QCD)
Measurements in the detector
(CBM@FAIR)
Dynamical description of heavy ion reactions
Hannah Petersen NED 2018 16.04.18
Outline• Hadronic transport approach
– SMASH: content and validation – Bulk observables at GSI-SIS energies – Strangeness production at threshold – Dilepton production and resonance properties
• Transport coefficients of the hadron gas – Green-Kubo formalism and its application – Shear viscosity over entropy ratio – Electric conductivity in simple systems
• Summary and Outlook
!4
Hannah Petersen NED 2018 16.04.18
Dynamical Description of Heavy Ion Collisions• Two regimes with well-established approaches
!5
FAIR
Hannah Petersen NED 2018 16.04.18
Dynamical Description of Heavy Ion Collisions• Two regimes with well-established approaches
!6
FAIR
‚Standard model‘ at high energies ( = 39 GeV-5.5 TeV+):
•Non-equilibrium initial evolution •Viscous hydrodynamics •Hadronic transport
—> Refinement and Bayesian multi-parameter analysis
psNN
Hannah Petersen NED 2018 16.04.18
Dynamical Description of Heavy Ion Collisions• Two regimes with well-established approaches
!7
FAIR
At very low beam energies ( < 3 GeV):
•Hadronic transport approaches •Resonance dynamics •Nuclear potentials
—> High density phase? Multi-particle interactions?
psNN
Hannah Petersen NED 2018 16.04.18
Dynamical Description of Heavy Ion Collisions• Two regimes with well-established approaches
!8
FAIR
• How to interpolate between the two? Transport with hydro bubbles? Hydro with transport corona?
• How to model the phase transition/critical point?
Hadron transport at very low beam energies ( < 3 GeV)psNN
‚Standard model‘ at high energies ( = 39 GeV-5.5 TeV+)psNN
Hannah Petersen NED 2018 16.04.18
SMASH* •Hadronic transport approach:
– Includes all mesons and baryons up to ~2 GeV – Geometric collision criterion – Binary interactions: Inelastic collisions through
resonance excitation and decay – Infrastructure: C++, Git, Redmine, Doxygen, (ROOT)
!10
J. Weil et al, PRC 94 (2016)
* Simulating Many Accelerated Strongly-Interacting Hadrons
Hannah Petersen NED 2018 16.04.18
Detailed Balance• Inverse absorption cross section calculated from
production cross section • Conservation of detailed balance (only 1 <—> 2 or
2 <—> 2 processes)
• Test: Full hadron gas indicating most violating processes!11
⇡ � ⇢� � �Box
Hannah Petersen NED 2018 16.04.18
Elementary Cross Sections• Total cross section for
pp/pπ collisions • Parametrised elastic
cross section • Many resonance
contributions to inelastic cross section
• Reasonable description of data up to 4 - 4.5 GeV
• String excitation by PYTHIA: work in progress
!12
Hannah Petersen NED 2018 16.04.18
Analytic Solution•Comparison to analytic solution of Boltzmann
equation within expanding metric
•Perfect agreement proves correct numerical implementation of collision algorithm
!13
J. Tindall, J. M. Torres-Rincon, J.-B. Rose and HP, PLB 770 (2017)
Bulk observables at GSI-SISJ. Weil et al, arXiv:1606.06642, PRC 94 (2016)
M. Mayer et al in preparation
Hannah Petersen NED 2018 16.04.18
Pion Production in Au+Au
• Potentials decrease pion production, while Fermi motion increases yield
• Slightly too high pion multiplicities
!15
J. Weil et al, PRC 94 (2016)
Hannah Petersen NED 2018 16.04.18
Collective Behaviour•Potentials in SMASH
– Basic Skyrme and symmetry potential
– Describes interactions between nucleons, repulsive at high densities
– Default values according to recent transport code comparison
!16
USkyrme = ↵(⇢/⇢0) + �(⇢/⇢0)⌧
J. Xu et al., PRC 93 (2016)
USymmetry = ±2SPot⇢I3⇢0
Hannah Petersen NED 2018 16.04.18
Elliptic Flow
Coordinate space asymmetry à momentum space anisotropy
Second coefficient of the Fourier expansion of the azimuthal particle distribution:
v2 =
* p2x � p2y
p2T
!+
Flow is sensitive to the pressure as a function of time
-> equation of state of nuclear matter? !17
Hannah Petersen NED 2018 16.04.18
Collective Flow -v2
• Directed and elliptic flow are compared to available data from FOPI and HADES
• SMASH agrees well with previous UrQMD calculation for v2 excitation function
!18
HP
et a
l, P
hys.
Rev.
C74
(20
06)
0649
08
by Markus Mayer
Hannah Petersen NED 2018 16.04.18
Φ/Ξ yields at SIS-18•UrQMD hadronic transport approach with
additional high mass resonances
•Sub-threshold Φ and Ξ production is visible •Decay channels of high N* resonances unknown
J. Steinheimer and M. Bleicher. JPG43 (2016)
!20
Hannah Petersen NED 2018 16.04.18
Φ Production in SMASH• Independent data sets to constrain production cross-
section from dileptons and elementary reactions
• Work in progress: prediction for Φ production in heavy ion collisions
!21
HADES, Phys.Lett. B715 (2012)
Hannah Petersen NED 2018 16.04.18
Φ Production in SMASH• Independent data sets to constrain production cross-
section from dileptons and elementary reactions
• Work in progress: prediction for Φ production in heavy ion collisions
!22
HADES, Phys.Lett. B715 (2012)
Hannah Petersen NED 2018 16.04.18
Strangeness Production• Elementary cross-sections
provide constraints
!23
Hannah Petersen NED 2018 16.04.18
Strangeness Production•Kaons and Lambdas in heavy ions:
• Ongoing work: Centrality dependence, predictions for pion beam and hyperon potentials
!24
Kaons Λ’s
Hannah Petersen NED 2018 16.04.18
Dileptons in SMASH• Dileptons produced by resonance
decays
• Direct and Dalitz dilepton decay channels
• Rare e.m. decays —> Time-Integration-Method / Shining
– Continuously perform dilepton decays and weight them by taking their decay probability into account (better statistics)
• Acceptance correction for HADES detector possible
!26
Dilepton Decays⇢ ! e+e�
! ! e+e�
� ! e+e�
⇡ ! e+e��⌘ ! e+e��⌘0 ! e+e��! ! e+e�⇡0
� ! e+e�⇡0
�+ ! e+e�p�0 ! e+e�n0
1
Hannah Petersen NED 2018 16.04.18
Elementary Collisions•Contributions of vector meson spectral
functions below hadronic thresholds
•Very nice agreement with HADES measurement
!27
Hannah Petersen NED 2018 16.04.18
Vacuum Properties•Hadron transport with collisional broadening
sufficient for C+C collisions
•For larger systems (ArKCl) excess in intermediate mass region
!28
Hannah Petersen NED 2018 16.04.18
Dilepton Production
• SMASH and UrQMD compare very similar to data • Different vector meson thresholds
!29
+ Stephan plot
UrQMD
S. Endres et al., J.Phys.Conf.Ser. 426 (2013)
HADES, PRL 98 (2007)
J. Staudenmaier et al, arXiv: 1711.10297
SMASH
Hannah Petersen NED 2018 16.04.18
Medium Modifications•Medium modified spectral functions are applied
on a coarse-grained transport evolution
•Very nice agreement with HADES data •Waiting for Au+Au results..
!30
Transport coefficientsJ.-B. Rose, J. M. Torres-Rincon, A. Schäfer, D. Oliinychenko and HP,
arXiv: 1709.00369 and 1709.03826 and J. Hammelmann et al, in preparation
Hannah Petersen NED 2018 16.04.18
Transport Coefficients• Within hydrodynamics/hybrid approaches the shear
viscosity is an input parameter
• Application of Bayesian techniques allows extraction of temperature dependence
!32
J. Bernhard et al, Phys.Rev. C94 (2016)
RHIC
Whi
te p
aper
, 20
12
Hannah Petersen NED 2018 16.04.18
Existing Results - Discrepancy
•Long standing question: Why are the results so different from each other?
!33
N. Demir and S.A. Bass, Phys.Rev.Lett. 102 (2009)
Green-Kubo formalism UrQMD
Discrepancy with hydro-inspired B3D and VISHNU
Hannah Petersen NED 2018 16.04.18
Shear Viscosity over Entropy Density• Box with periodic boundary condition in chemical and
thermal equilibrium • Entropy is calculated via Gibbs formula from
thermodynamic properties • The shear viscosity is extracted following the Green-
Kubo formalism:
!34
⌘ =V
T
Z 1
0Cxy(t)dt Cxy(t) =
1
N
NX
s
T xy(s)T xy(s+ t)
Tµ⌫ =1
V
NpartX
i
pµi p⌫i
p0i⌘ =
V Cxy(0)⌧
T
Cxy(t) ' Cxy(0) exp
✓� t
⌧
◆
0.1 0.12 0.14 0.16 0.18Τ (GeV)
0
0.2
0.4
0.6
0.8
η (G
eV fm
⁻²)
SMASH normal lifetimeSMASH zero lifetimeChapman-Enskog
Hannah Petersen NED 2018 16.04.18
Resonance Dynamics• Energy-dependence of cross-sections is modelled via
resonances • Point-like in analytic calculation and finite lifetime in
transport approach
• Agreement recovered by decreasing ρ meson lifetime
!35
Hannah Petersen NED 2018 16.04.18
Comparison to Literature
• Closest similarity to Bass/Demir result as expected
!36
1 10 100τ (fm)
1
10
100
τ
(fm
)
Full SMASHFull SMASH + 10 mb elastic
Temperaturerela
x
mft
0.1 0.12 0.14 0.16 0.18T (GeV)
0.1
1
η/s
Pratt, Baez & Kim [B3D]Full SMASHFull SMASH + 10mb elastic
Hannah Petersen NED 2018 16.04.18
Point-like Interactions• Adding a constant elastic cross section leads to agreement
with B3D result
• Approximately linear relationship between relaxation time and mean free time is recovered
!37
Hannah Petersen NED 2018 16.04.18
Electric Conductivity•Comparison to linear response kinetic theory to
validate our approach
•Infinite matter with constant σ = 30 mb
!38
�el =V
T
Z 1
0hji(0)ji(t)idt �el =
V C(0)⌧
T
Greif et al, Phys.Rev. D93 (2016)
T (GeV)0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
/ T
elσ
0
0.01
0.02
0.03
0.04
SMASH
Kinetic approach
SMASH
Kinetic approach
SMASH
Kinetic approach
T (GeV)0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
/ T
elσ
0
0.01
0.02
0.03
0.04
SMASH
Kinetic approach
π only π, K, P
Hannah Petersen NED 2018 16.04.18
Effect of Lifetime• ρ-π system is again affected by the lifetime
• Work in progress: Understand the differences between analytic calculation and SMASH results
!39
T (GeV)0.1 0.12 0.14 0.16 0.18 0.2
/T elσ
0
0.01
0.02
0.03
0.04
0.05SMASH, nonzero lifetime
SMASH, zero lifetime
Kinetic approach
SMASH, nonzero lifetime
SMASH, zero lifetime
Kinetic approach
SMASH, nonzero lifetime
SMASH, zero lifetime
Kinetic approach
SMASH, nonzero lifetime
SMASH, zero lifetime
Kinetic approach
Hannah Petersen NED 2018 16.04.18
Summary and Outlook• SMASH has been developed as a new hadronic transport
approach – Bulk observables are in reasonable agreement with
experimental data – Strangeness production based on cross-section from
elementary reactions – Electromagnetic observables are integrated
• Shear viscosity and electric conductivity have been calculated via Green-Kubo formalism – Comparison to analytic results are used for validation – Resonance lifetimes have large impact on relaxation
dynamics in both cases • Future: Afterburner calculations at RHIC/LHC
!40
Hannah Petersen NED 2018 16.04.18
General Setup• Transport models provide an effective solution of the
relativistic Boltzmann equation
• Particles represented by Gaussian wave packets • Geometric collision criterion
• Test particle method
!42
Hannah Petersen NED 2018 16.04.18
Resonances•Spectral function
– All unstable particles („resonances“) have relativistic Breit-Wigner spectral functions
•Decay widths – Particles stable, if
width < 10 keV
– Treatment of Manley et al
!43
(⇡, ⌘, K, ...)
D. M. Manley and E. M. Saleski, Phys. Rev. D 45, 4002 (1992)
N*(1440)
Hannah Petersen NED 2018 16.04.18
Collision Term• In few GeV energy regime decay and excitation of
resonances dominate hadronic cross section
• No string fragmentation yet
!44
Inelastic Scattering Decays
Elastic scattering 2 —> 1 processes
Hannah Petersen NED 2018 16.04.18
Treatment of Manley
•Scaling of on-shell decay width:
•Definiton of rho-funtion:
•Hadronic Form Factor:
!45
M. Post, S. Leupold, U. Mosel, Nucl. Phys. A 741, 81 (2004)
D. M. Manley and E. M. Saleski, Phys. Rev. D 45, 4002 (1992)
…
Blatt Weisskopf functions
Hannah Petersen NED 2018 16.04.18
Correlation Function Systematics
•Important details: – Fixed intercept and 6% cut-off agree best with analytic expectations
!460.1 0.12 0.14 0.16 0.18
Τ (GeV)
0
0.1
0.2
0.3
0.4
0.5
η (G
eV fm
⁻²)
Chapman-Enskog2%4%6%10%5fm
0.08 0.1 0.12 0.14 0.16 0.18 0.2T (GeV)
0.0001
0.001
0.01
Cˣʸ
(0)⋅
V (G
eV² f
m⁻³)
Fixed interceptFloating interceptAnalytic result
0 2 4 6 8t (fm)
1x10-9
1x10-8
1x10-7
1x10-6
1x10-5
Cˣʸ(
t) (G
eV² f
m⁻⁶)
π-ρ, zero lifetime
σ=20 mb, T=200 MeV, π only
J.-B
. Ro
se e
t al
, ar
Xiv:
1709
.003
69