2021/09/24 QCD相転移やQGP生成のモデル化による重イオン衝突の時空発展の理解に向けた理論・実験共同研究会

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Y. Kanakubo et al., arXiv:2108.07943

金久保優花
上智大

SOPHIA
HADRONPHYSICS
GROUP

IntroductionPowerful tool to tease out QGP properties
from exp. data
Fundamentaltheory

Experimental data/phenomena
Phenomenologicaldynamical framework

As a bridge between experiment and fundamental theory
Accurate studies of QGP properties!
e.g., Bayesian parameter estimation with hydro-based frameworks

Call for a hydro-based framework that is capable ofaccounting for experimental data

Remaining basic issues in hydro-based framework
AALocal equilibrium for awhole system?
Conservation of beamenergy-momentum?

pA/pp

Incorporation of jet
production in hydro?
Hydro description in low
multiplicity event?

Hydro-based MC event generator- Respect beam energy (as a MC event generator)- Both equilibrated and non-equilibrated matter➔ From low to high 𝒑𝑻 , from pp to AA

Y. Kanakubo et al., PTEP 2018 12, 121D01 (2018);

Core: fluids(equilibrated matter)

Corona: nonequilibrated partonsDynamical generation of QGP fluids based on the core-corona picture

Description of entire system generated in a collision
as a MC event generator from pp to AA

Phys. Rev. C 101 2, 024912 (2020); arXiv:2108.07943

Hydro-based MC event generator

Dynamical Core-Corona
Initialization model 2
Y. Kanakubo et al., arXiv:2108.07943

PYTHIA8
Stringfragmentation

iS3D
Sampling via
Cooper-FryeiS3D: M. McNelis et al., Comput. Phys.Commun.258, 107604 (2021)

JAM: Y. Nara et al.,Phys. Rev. C61, 024901 (2000)

Final state hadrons

Hadronic afterburner

JAM

with source terms(3+1)-D hydroInitial partonsPYTHIA8/PYTHIA8 Angantyr

PYTHIA:T. Sjöstrand et al., Comput. Phys. Commun. 191, 159 (2015)
C. Bierlich et al., JHEP 1610 139 (2016)

Model flowchart of DCCI2 Y. Kanakubo et al., arXiv:2108.07943

Dynamical initialization framework➔ Dynamical generation of hydro initial conditions
Conventional hydro𝝉𝝉Hydrowith dynamical initialization

𝝏𝝁 𝑻𝝁𝝂 = 𝟎𝝏𝝁 𝑻𝝁𝝂 = 𝑱𝝂𝝉𝟎𝜼𝒔
→ Put initialcondition at fixed 𝝉𝟎𝜼𝒔→ Generate initial condition
locally through sources 𝑱𝝁Dynamical initialization framework (cont’d)M. Okai et al., Phys. Rev. C 95,054914 (2017)

Assumption 1. Initial partons are generated just after a collision of nuclei

Assumption 2. Instant equilibration of deposited energy and momentum

Continuum eq. for fluid+parton𝝁𝝂𝝁𝝂

𝝏𝝁 𝑻𝐟𝐥𝐮𝐢𝐝 + 𝑻𝐩𝐚𝐫𝐭𝐨𝐧 = 𝟎fluids
partons

Hydrodynamic eq. with source term𝝁𝝂𝝏𝝁 𝑻𝐟𝐥𝐮𝐢𝐝 = 𝑱𝝂Assuming Gaussian profile and straight trajectory for a parton
𝝂 𝒕𝒅𝒑𝒊
𝑱𝝂 → − ෍𝑮 𝒙 − 𝒙𝒊 𝒕
𝒅𝒕𝒊

Total system“Sources of fluids” =“Four-momentum
deposition from partons”

𝑮: Gaussian function
𝝁𝒑𝒊 : Four-momentum of the 𝒊𝐭𝐡 parton

Dynamical core-corona initialization
Core-corona picture∼ EoM with a drag force due to secondary scatterings

𝑑𝑝𝑖 𝜇𝑑𝜏𝑁scat= − ෍ 𝜌𝑖,𝑗 𝜎𝑖,𝑗 𝑣rel,𝑖,𝑗 𝑝𝑖 𝜇𝑗

Defined at a co-moving
frame with 𝜼𝒔,𝒊

Note 1. Energy and momentum ➔ direct conversion into fluids
Note 2. Phenomenological model to capture dynamical aspect of core-corona
Low 𝒑𝑻 and/or dense region
Core (fluids)
High 𝒑𝑻 and/or dilute region
Corona (non-equilibrated partons)

Dynamical core-corona initialization
Core-corona picture∼ EoM with a drag force due to secondary scatterings

𝑑𝑝𝑖 𝜇𝑑𝜏𝑁scat= − ෍ 𝜌𝑖,𝑗 𝜎𝑖,𝑗 𝑣rel,𝑖,𝑗 𝑝𝑖 𝜇
𝑗- Collision criterion
𝝈𝒊,𝒋𝒃𝒊,𝒋 ≤𝝅→Geometrical interpretation of a cross-section- Parametrized cross-section of aparton-parton scattering
𝝈𝟎𝝈𝒊,𝒋 =𝟐𝒔𝒊,𝒋 /[𝐆𝐞𝐕 ] →Collision at a CM frame

Defined at a co-moving
frame with 𝜼𝒔,𝒊- Density of non-equilibrated partons
𝝆𝒊,𝒋 ∝ 𝐞𝐱𝐩 −𝒙⊥,𝒊 − 𝒙⊥,𝒋𝟐𝝈𝟐𝒙⊥𝟐−𝜼𝒊 − 𝜼𝒋𝟐𝟐𝝈𝟐𝜼

→Gaussian profile of a parton

𝑁scat : # of (non-equilibrated andequilibrated) partons scatteredwith ith parton

Thermal parton sampling in dynamical core-corona
initialization
𝑑𝑝𝑖 𝜇𝑑𝜏𝑁scat= − ෍ 𝜌𝑖,𝑗 𝜎𝑖,𝑗 𝑣rel,𝑖,𝑗 𝑝𝑖 𝜇𝑗➔ Applied to both core (QGP fluids) and corona (non-equilibrated partons)
Sampling ofequilibrated
partons at
each time step*with mass-less ideal gas approximation

Demonstration of dynamical core-corona initialization
Transverse plane

PbPb 2.76 TeV
𝒙 − 𝜼𝒔 plane (𝒚 ∼ 𝟎)

Initial partons fromPYTHIA8/PYTHIA8 Angantyr

Demonstration of dynamical core-corona initialization
Transverse plane

PbPb 2.76 TeV
𝒙 − 𝜼𝒔 plane (𝒚 ∼ 𝟎)

Demonstration of dynamical core-corona initialization
pp 7 TeV
Transverse plane𝒙 − 𝜼𝒔 plane (𝒚 ∼ 𝟎)

Initial partons fromPYTHIA8/PYTHIA8 Angantyr

Demonstration of dynamical core-corona initialization
pp 7 TeV
Transverse plane𝒙 − 𝜼𝒔 plane (𝒚 ∼ 𝟎)

Energy budget in dynamical core-corona initialization
Dynamical energy conversion from initial partons (corona) to fluids (core)PbPb

pp- Starting from vacuum 𝑇𝜇𝜈 = 𝟎 for fluids- Energy & momentum conservation as total system
Characteristic of DCCI2?

Dynamical realization of core-corona picture

Corona components from string modification𝝉𝒔 < 𝝉 < 𝝉𝐟𝐨𝝉𝒔 = 𝟎. 𝟑 𝐟𝐦

String cutting
String modification caused by ..
・Spatial overlap of strings and medium
・Completely fluidized partonsParton-pairing

1. Discard dead partons
2. Find hypersurface boundaries 𝑻𝐬𝐰
3. Sample partons using Fermi/Bose distribution& boost with 𝒗𝐟𝐥𝐮𝐢𝐝 at the boundary(recreation of color singlet )Corona components from string modification (cont’d)𝝉𝒔 = 𝟎. 𝟑 𝐟𝐦

𝝉𝒔 < 𝝉 < 𝝉𝐟𝐨String cutting
String modification caused by ..
・Spatial overlap of strings and medium
・Completely fluidized partonsParton-pairing
4. Surviving partons traverse medium
5. Make a pair for a parton coming out frommedium*Sampling of thermal partons: Bose/Fermi (massive)*𝒑𝑻,𝐜𝐮𝐭: threshold to/not to modify a string

Corona components from string modification (cont’d)𝝉𝒔 = 𝟎. 𝟑 𝐟𝐦

𝝉𝒔 < 𝝉 < 𝝉𝐟𝐨String cutting

Parton-pairing

String modification caused by ..
・Spatial overlap of strings and medium
・Completely fluidized partons

Hadronized via string fragmentation➔ Corona components

PYTHIA8Stringfragmentation

iS3D
Sampling via
Cooper-FryeiS3D: M. McNelis et al., Comput. Phys.Commun.258, 107604 (2021)

JAM: Y. Nara et al.,Phys. Rev. C61, 024901 (2000)

Final state hadrons

Hadronic afterburner

JAM

with source terms(3+1)-D hydroInitial partonsPYTHIA8/PYTHIA8 Angantyr

PYTHIA:T. Sjöstrand et al., Comput. Phys. Commun. 191, 159 (2015)
C. Bierlich et al., JHEP 1610 139 (2016)

Model flowchart of DCCI2 Y. Kanakubo et al., arXiv:2108.07943

Space-time distribution of direct hadrons PbPb 2.76 TeV
1 sampled event

Probability distribution ( 𝜼 < 𝟎. 𝟓)

Double peaks of hadron vertices fromcore and corona before hadronic
rescatterings

Space-time distribution of direct hadrons
1 sampled event

pp 7 TeV

Probability distribution ( 𝜼 < 𝟎. 𝟓)- Short lifetime of hydro (∼ 𝟏 𝐟𝐦) in pp- Direct hadrons from core and corona➔ closely produced in space-time coordinateSpace-time distribution of direct hadrons
1 sampled event

pp 7 TeV

Probability distribution ( 𝜼 < 𝟎. 𝟓)- Short lifetime of hydro (∼ 𝟏 𝐟𝐦) in pp- Direct hadrons from core and corona➔ closely produced in space-time coordinate

Results from DCCI2

B. Abelev et al. (ALICE Collaboration), Phys. Lett. B 728, 216-227 (2014); erratum 734, 409-410(2014)

J. Adam et al., (ALICE Collaboration), Nature Phys. 13 535-539 (2017)

𝛀/𝝅 ratio from pp and PbPb
Parameter fixing with 𝛀/𝝅Smooth enhancement of
the ratio➔ smooth increase of core
contribution

Input

QGP fluids➔ Forced to be generated
to describe strangenessenhancement from pp toPbPb

Particle yield ratios from pp and PbPb
Effects ofhadronic
rescatterings➔
Suppress particle
yield ratios(dissociation/annihilation)➔ Reproductionof qualitativebehavior inexp.data

J. Adam et al., (ALICE Collaboration), Nature Phys. 13 535-539 (2017)

pp 7 TeVPbPb 2.76 TeV

・pp: Excess of core contribution at the highest multiplicity class (0-0.95%)
・PbPb: ∼ 𝟐𝟎% fraction of corona in intermediate central events (40-60%)➔ Need both of core and corona in pp and AA!

K. Aamodt et al., (ALICE Collaboration), Phys. Rev. Lett. 106 032301 (2011)

Core/corona fraction in multiplicity/centrality classFraction of core and corona vs. 𝒅𝑵𝐜𝐡 /𝒅𝜼 from pp to PbPb

Clear scaling withmultiplicity
Change of dominant
contribution at𝒅𝑵𝐜𝐡 /𝒅𝜼 ∼ 𝟏𝟖

ppPbPbSmooth description from low to high 𝒑𝑻
G. Aad et al., (ATLAS Collaboration), New J. Phys. 13 053033 (2011)

pp 7 TeV (MB)PbPb 2.76 TeV (MB)pp: Dominant corona contribution for all 𝒑𝑻 range
PbPb: Dominant contribution flips at ∼ 𝟓. 𝟓 GeV.
Non-negligible corona contribution (∼ 𝟐𝟎%) at very low 𝒑𝑻 (< 𝟏 GeV)

Keep in mind soft from corona!

Origin of corona contribution at low 𝒑𝑻

Input

Fragmentation function in PYTHIAPoS LHCP2019 (2019) 050

𝒑𝑻 distribution of partons (corona)
PbPb 2.76 TeV (MB)OutputDynamical deposition of 𝒑𝑻 ➔ shift of 𝒑𝑻➔ Low 𝒛 (soft) production
should appear

Lack of low 𝒑𝑻 yield from Hydro
ALICE Collaboration, Phys.Rev.C 88 (2013) 044910

Comparisons between exp. dataand hydro models➔ Lack of (very) low 𝒑𝑻 yield inhydro models
Be careful withsemi-log plot!

Other sources to compensate
the low 𝒑𝑻 yield?
Phys.Rev.C 103 (2021) 5, 054909

Comparisons of charged 𝒑𝑻 spectra between DCCI and exp. data
ALICE Collaboration, JHEP 11 (2018) 013

0-5%40-50%

70-80%

Pure hydro results cannot reproduce the slopes of spectra obtainedin experimental data
Possible compensation of low 𝒑𝑻 production with corona contribution

Corona correction in PbPb
∼ 𝟓 − 𝟏𝟏 %∼ 𝟏𝟓 − 𝟑𝟖 %Corona contribution∼ “Far from” equilibrium
correction to hydro!

Even PbPb needs corona
to properly extract
transport coefficients(?)

Summary
Dynamical core-corona initialization model (DCCI2)- Respect beam energy (as a MC event generator)- Both equilibrated and non-equilibrated matter➔ From low to high 𝒑𝑻 , from pp to AA
Extraction of core/corona fraction in multiplicity/centrality classes➔ Excess of core contribution over corona contribution at𝒅𝑵𝐜𝐡 /𝒅𝜼 ∼ 𝟏𝟖 regardless of collision systems or energy.
Non-negligible contribution of corona at very low 𝒑𝑻 (< 𝟏 𝐆𝐞𝐕) in PbPb
➔ Corona dilutes 𝒑𝑻 by ∼ 𝟓 − 𝟏𝟏% and 𝒗𝟐 𝟐 by ∼ 𝟏𝟓 − 𝟑𝟖%.

Towards accurate study of QGP properties!
➔ Importance of interplay between core and corona

Outlooks- Extension to viscous (& fluctuating) hydro- Process to local equilibrium- Jet quenching- Charge conservation……

A ton of work to do. Stay tuned!Thank you!