Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Bayesian Analysis of Oxygen-Oxygen Collisions
Govert Nijs
February 5, 2021
Based on:
GN, van der Schee, Gursoy, Snellings, arXiv:2010.15130
GN, van der Schee, Gursoy, Snellings, arXiv:2010.15134
GN, van der Schee, arXiv:21xx.xxxxx
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Second order transport coefficients
We want to use Bayesian analysis to decide betweenmicroscopic theories.
We have mild constraints, but not enough to decide.
parameter 2010.15130 AdS/CFT kinetic theory
τπsTη
1 6.5 120
0.1
0.2
τπsT/η
4.5±2.1
4− log(4) ≈ 2.61 5
τππτπ
0.8 2 3.20
0.45
0.9
τππ/τπ
2.27±0.50
8835(2−log 2) ≈ 1.92 10
7 ≈ 1.43
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
A pT -differential fit to data
In 2010.15130, we fit to pT -differential observables, leading toextra constraints.
π± (*1/2) K± p h
±ET (*2)
PbPb, sNN =2.76 TeV
0 10 20 30 40 50 60 70
510
50100
5001000
5000
centrality [%]
dN dy,dN
ch
dη,dE
T
dη[GeV
]
PbPb, sNN =2.76 TeV π±
K±
p
0.5 1.0 1.5 2.0 2.5 3.00.1
1
10
100
1000
pT [GeV]
dN/N
ev
dpTdy
[GeV
-1]
PbPb, sNN =2.76 TeVπ±
K±
p
0.5 1.0 1.5 2.00.00
0.05
0.10
0.15
0.20
pT [GeV]
v2(2)
PbPb, sNN =5.02 TeV
v2 (2)
v2 (4)
v3 (2)
v4 (2)
0 10 20 30 40 50 60 700.00
0.02
0.04
0.06
0.08
0.10
0.12
centrality [%]
vn(k)
pPb, sNN =5.02 TeV π±
K±
p
0 10 20 30 40 50 600.4
0.6
0.8
1.0
1.2
1.4
centrality [%]
⟨pT⟩[GeV
]
pPb, sNN =5.02 TeV
v2 (2) v3 (2)
0 1 2 3 4 5
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
Nch / ⟨Nch⟩
vn(k)
[ALICE, 2010–2018; ATLAS, 2017]
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Trajectum
For 2010.15130, we used the new heavy ion code Trajectum:
We use TRENTo with substructure for initial conditions.
We use free streaming with a variable speed as apre-hydrodynamic stage.
We use temperature-dependent specific shear and bulkviscosities (η/s)(T ), (ζ/s)(T ).
We vary 3 second order transport coefficients: τπsT/η,τΠsT (1/3− c2
s )2/ζ and τππ/τπ.
For particlization, we use the Pratt-Torrieri-Bernhard (PTB)prescription.
We use SMASH as a hadronic afterburner.
[Bernhard, Moreland, Bass, 2019]
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Small bulk viscosity
In 2010.15130, we found asmaller bulk viscosity thanprevious studies. We couldidentify 3 causes:
Addition of pPb data.
Addition of extraparameters.
Addition of pT -differentialobservables.
PbPb 2.76 & 5.02Obs: pT-diffPara: This work
0.15 0.20 0.25 0.30 0.350.00
0.01
0.02
0.03
0.04
0.05
T [GeV]
ζ/s
PbPb 2.76 & 5.02pPb 5.02Para: This work
Obs: pT-diff
0.15 0.20 0.25 0.30 0.350.00
0.01
0.02
0.03
0.04
0.05
T [GeV]
ζ/s
PbPb 2.76 & 5.02Para: DukeObs: Duke
0.15 0.20 0.25 0.30 0.350.00
0.01
0.02
0.03
0.04
0.05
T [GeV]
ζ/s
PbPb 2.76 & 5.02Para: Duke pPb 5.02Obs: Duke
0.15 0.20 0.25 0.30 0.350.00
0.01
0.02
0.03
0.04
0.05
T [GeV]
ζ/s
PbPb 2.76 & 5.02Para: This work pPb 5.02Obs: Duke
0.15 0.20 0.25 0.30 0.350.00
0.01
0.02
0.03
0.04
0.05
T [GeV]
ζ/s
PbPb 2.76 & 5.02Para: Duke pPb 5.02Obs: pT-diff
0.15 0.20 0.25 0.30 0.350.00
0.01
0.02
0.03
0.04
0.05
T [GeV]
ζ/s
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Goals and outline
Goals of this project:
Use the PbPb posteriors to make predictions for OO.
Investigate impact of potential OO experiments on posteriors.
Outline of this talk:
Our setup.
OO predictions for various observables.
Bayesian analysis using OO mock data.
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Setup: Trajectum
For this project, the following things were changed in the model:
The Pb nucleus is modeled by a Saxon-Woods potential withminimal distance dmin, whereas O is modeled using two- andthree-nucleon potentials. See also talk by Broniowski.
We use a ‘continuous’ number of constituents nc in TRENTo.
We vary 2 second order transport coefficients instead of 3:τπsT/η and τππ/τπ.
We use UrQMD instead of SMASH as a hadronic afterburner.
[Lonardoni, Lovato, Pieper, Wiringa, 2017]
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Setup: bayesian analysis
For the emulator, we have the following settings:
system # design points # events/design point
PbPb 750 15k
pPb 1500 100k
OO 1500 40k
For Markov Chain Monte Carlo (MCMC), we use the ptemceecode.
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Studying Oxygen-Oxygen collisions
How do we study the potential impact of OO experiments withoutavailable experimental data?
Sample 10 random sets of parameters from the PbPbposterior.
Perform high statistics OO runs for the chosen parameter sets.This yields OO predictions based on known constraints.
Perform MCMC using the high statistics OO runs as ‘data’ inaddition to PbPb data.
Compare posterior distributions with and without OO ‘data’.
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Dependence of v2 in OO on parameters
We define v2{2} ≡ sgn(v2{2}2)|v2{2}|.0-1 2-3 3-4
OO
8 19 300.05
0.075
0.1
N PbPb2.76 [fm-1]
v2{2}
0-1 2-3 3-4
OO
40 70 1000.06
0.08
0.1
σNN PbPb 2.76 TeV [mb]
0-1 2-3 3-4
OO
0.4 0.8 1.20.05
0.085
0.12
w [fm]
0-1 2-3 3-4
OO
140 152.5 1650.06
0.08
0.1
Tswitch [MeV]
0-1 2-3 3-4
OO
-0.4 0 0.40.05
0.075
0.1
p
OO
0 0.75 1.50.06
0.08
0.1
dmin [fm]
v2{2}
OO
0.2 0.8 1.40.04
0.07
0.1
σfluct
OO
1 4.5 80.06
0.08
0.1
nc
OO
0 0.5 10.04
0.07
0.1
χstruct
OO
0.1 0.8 1.50.05
0.07
0.09
τfs [fm/c]
OO
0 0.1 0.20.03
0.09
0.15
(η/s)min
v2{2}
OO
0 1.5 30.04
0.08
0.12
(η/s)slope [GeV-1]
OO
-1 0 10.05
0.075
0.1
(η/s)crv
OO
0 0.02 0.040.05
0.075
0.1
(ζ/s)max
OO
0 0.15 0.30.06
0.08
0.1
(ζ/s)width [GeV]
OO
0.14 0.195 0.250.06
0.08
0.1
(ζ/s)T0 [GeV]
v2{2}
OO
1 6.5 120.06
0.08
0.1
τπsT/η
OO
0.8 2 3.20.06
0.08
0.1
τππ/τπ
OO
0.6 0.8 10.06
0.08
0.1
vfs
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
High statistics OO runs: pT -integrated observables
(Identified) particle yields, identified 〈pT 〉 and vn{k}:π ± (*1/2) K
± p h±
ET (*2)
OO, sNN =7 TeV
0 20 40 60 80
0.5
1
5
10
50
100
500
centrality [%]
dN dy
,d
Nch
dη
,d
ET
dη[G
eV]
π ± K± p
OO, sNN =7 TeV
0 20 40 60 800.4
0.6
0.8
1.0
1.2
1.4
centrality [%]
⟨pT⟩[G
eV/c]
v2{2} v2{4} v3{2} v4{2}
OO, sNN =7 TeV
0 10 20 30 40 50 60 700.00
0.02
0.04
0.06
0.08
0.10
centrality [%]
vn{k}
π± (*1/2) K± p h
±ET (*2)
PbPb, sNN =2.76 TeV
0 10 20 30 40 50 60 70
510
50100
5001000
5000
centrality [%]
dN dy,dN
ch
dη,dE
T
dη[GeV
]
PbPb, sNN =2.76 TeV π±
K±
p
0 10 20 30 40 50 600.4
0.6
0.8
1.0
1.2
1.4
1.6
centrality [%]
⟨pT⟩[GeV
/c]
PbPb, sNN =5.02 TeV
v2 (2)
v2 (4)
v3 (2)
v4 (2)
0 10 20 30 40 50 60 700.00
0.02
0.04
0.06
0.08
0.10
0.12
centrality [%]
vn(k)
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
High statistics OO runs: pT -differential observables
Identified particle spectra and identified v2{2}(pT ):
π± K± p
OO, sNN =7 TeV
0-5%
40-50% (*0.1)
0.5 1.0 1.5 2.0 2.5 3.0
0.001
0.010
0.100
1
10
100
pT [GeV/c]
dN/N
ev
dpT
dy[G
eV-
1c]
π± K± p
OO, sNN =7 TeV
20-30%
0-5%
0.5 1.0 1.5 2.0 2.50.00
0.05
0.10
0.15
0.20
pT [GeV/c]
v2{2}
PbPb, sNN =2.76 TeV π±
K±
p
0.5 1.0 1.5 2.0 2.5 3.00.1
1
10
100
1000
pT [GeV]
dN/N
ev
dpTdy
[GeV
-1]
PbPb, sNN =2.76 TeVπ±
K±
p
0.5 1.0 1.5 2.00.00
0.05
0.10
0.15
0.20
pT [GeV]
v2(2)
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Posterior distributions including OO ‘data’
We perform a Bayesiananalysis using each of thehigh statistics OO runs as‘data’.
We show the resultingposterior distributions forthe nucleon width w .
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Improvements in PbPb + OO compared to PbPb alone
We define the improvement in terms of the standard deviations ofthe posteriors: I = σPbPb/〈σPbPb + OO〉OO runs − 1.
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Correlations between observables
OO causes a 43% improvementin dmin, however OO does notdepend on dmin. How is thispossible?
dmin and σfluct are stronglycorrelated.
σfluct improves by 46% whenincluding OO.
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions
Introduction Setup OO predictions Impact of OO on posteriors Conclusions and outlook
Conclusions and outlook
Conclusions:
We predict various observables for the Oxygen-Oxygen system.
PbPb + OO appears to improve uncertainties over PbPb.
Outlook:
We will analyze the PbPb + OO results in more depth.
In addition to PbPb + OO, we will study PbPb + pPb + OO.
Govert Nijs
Bayesian Analysis of Oxygen-Oxygen Collisions