Implementing a Flow Afterburner for sHIJING

Javier Orjuela-KoopUniversity of Colorado

sPHENIX Jet Structure MeetingJun. 25, 2018

sHIJING

HepMC FileEvent Record

Flow Afterburner

Modified HepMCEvent Record

Statement of the Problem

• We want to write an afterburner that takes sHIJINGoutput, in the form of a HepMC text file, and modifiesthe uniform azimuthal distribution of particles to haveflow modulations.

• This needs to be done in a pT- and centrality-dependentmanner.

• Local correlations (like jets) need to be preserved

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(Mathematical) Statement of the Problem

Let the azimuthal angle φ of particles at a given pT be a random variable distributed uniformly in [0, 2π]

We want to find a mapping y :φ à φ’ where φ’ is a new random variable distributed according to

Such a mapping guarantees that local particle correlations (e.g., jets) are preserved, while constructinga global flow correlation of strength v2.

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(Mathematical) Statement of the Problem

The probability of φ being between values a and b is given by:

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(Mathematical) Statement of the Problem

The probability of φ being between values a and b is given by:

But, given the mapping y :φ à φ’, it should also be equal to the probability of φ’ being between y(a) and y(b)

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Transforming Probability Density Distributions

The probability of φ being between values a and b is given by:

But, given the mapping y :φ à φ’, it should also be equal to the probability of φ’ being between y(a) and y(b)

This is akin to integration bysubstitution of variables

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Transforming Probability Density Distributions

Comparing the integrands of the expressions in the previous slide, we see that the probability distributions and the mapping should satisfy the following differential equation, which must be solved for φ’(φ)

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In our case, with ,, we obtain the following transcendental equation

which can be solved numerically for φ’, as shown below for v2 = 0.4:

Transforming Probability Density Distributions: A Toy Problem

φà φ’ φ’- φ

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Transforming Probability Density Distributions: A Toy Problem

The mapping is applied to every single particle, originally with uniform azimuthal distribution, obtainingthe new azimuthal distribution shown on the right.

1 + 2 x 0.4 x Cos(2φ)

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Centrality-Dependent v2 for Identified Pions in Au+Au Collisions

PHENIX has published centrality-dependent v2 for identified pionsin Phys. Rev. C 88, 064910, as shown on the right. Let us consideronly the most central category for now

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Centrality-Dependent v2 for Identified Pions in Au+Au Collisions

PHENIX has published centrality-dependent v2 for identified pionsin Phys. Rev. C 88, 064910, as shown on the right. Let us consideronly the most central category for now

0-20%

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Centrality-Dependent v2 for Identified Pions in Au+Au Collisions

PHENIX has published centrality-dependent v2 for identified pionsin Phys. Rev. C 88, 064910, as shown on the right. Let us consideronly the most central category for now

0-20%

What to do in thisenergy loss region?

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Testing the Afterburner on sHIJING Output

We apply the afterburner on sHIJING events with b=0, following the v2(pT) parameterization shown previously

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BEFORE AFTER

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To-Do List

• Parameterize published central v2 at high pT

• Parameterize v2(pT) in all published centrality categories

• Run sHIJING to create a mapping between impact parameter and centrality class

• Commit afterburner to code repository