bayesian analysis of oxygen-oxygen collisions · 2021. 2. 4. · trajectum for 2010.15130, we used...

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



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

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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]

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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]

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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

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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.

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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]

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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.

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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’.

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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

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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

]


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



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}


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)

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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 .

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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.

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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.

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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 · 2021. 2. 4. · trajectum for 2010.15130, we used...

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