Role of dynamic geometry in jet tomography
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Role of Dynamic Geometry in Jet Tomography. William Horowitz Columbia University December 12, 2005. In conjunction with Simon Wicks, Magdalenda Djordjevic, and Miklos Gyulassy. Motivation. Past tomographic models simplified the calculation by neglecting either: Multigluon fluctuations

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Role of Dynamic Geometry in Jet Tomography

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Role of dynamic geometry in jet tomography

Role of Dynamic Geometry in Jet Tomography

William Horowitz

Columbia University

December 12, 2005

In conjunction with Simon Wicks, Magdalenda Djordjevic, and Miklos Gyulassy

Heavy Flavor Productions Workshop


Motivation

Motivation

  • Past tomographic models simplified the calculation by neglecting either:

    • Multigluon fluctuations

    • Path length fluctuations

  • For fixed-length calculations, reasonable but unjustifiable length L~5 fm used

Heavy Flavor Productions Workshop


Significance of nuclear profile

Significance of Nuclear Profile

  • Simpler densities create a surface bias

Hard Cylinder

Hard Sphere

Woods-Saxon

Heavy Flavor Productions Workshop

Toy model for purely geometric radiative loss from Drees, Feng, Jia, Phys. Rev. C.71:034909


Edgy geometry

Edgy Geometry

  • We use the Woods-Saxon nuclear geometry, which has a fuzzy “edge”

  • There is no unique, natural LWS definition

    • Two examples (of many possibilities):

  • We will use the latter formula

Heavy Flavor Productions Workshop


Partonic r aa model

Partonic RAA Model

  • where Pincoherently convolves DGLV energy loss (including multigluon fluctuations) with the infinite-time elastic energy loss for fixedas

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Momentum Jacobian as survival probability; see, e.g., Gyulassy, nucl-th/0403032


Volume emission of partons

Volume Emission of Partons

  • fixed pT = 15 GeV, yT = f = 0, and as = .3

Heavy Flavor Productions Workshop


Average lengths of emission

Average Lengths of Emission

  • Dynamic volume depends on partonic species and pT

    • For pT = 5, 10, 15, 20 GeV, as = .3

    • <Lg> = 1.74, 1.93, 2.16, 2.41 fm

    • <Lu> = 3.83, 4.21, 4.47, 4.62 fm

    • <Lc> = 4.65, 4.43, 4.48, 4.50 fm

    • <Lb> = 6.17, 5.69, 5.43, 5.29 fm

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The results

Electrons

Pions

The Results

as = .3

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The results1

Electrons

Pions

The Results

as = .4

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Conclusions

Conclusions

  • There are several large effects that must be taken into account in any energy loss model:

    • Multigluon fluctuations

    • Path length fluctuations

    • Collisional energy loss

    • Running as

Heavy Flavor Productions Workshop


Future work

Future Work

  • Find more accurate analytic formulae for collisional loss

    • Molnár’s parton cascade provides exact numerical answer

  • Simultaneously treat elastic and inelastic energy loss

    • Find a more natural L?

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Future work cont d

Future Work (cont’d)

  • Allow as to run

    • Nonzero lower bound to theoretical error

  • Use even more accurate medium density

    • Hirano’s CGC-initial condition 3+1 D evolving hydro background

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Let s eat

Let’s Eat!

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Role of dynamic geometry in jet tomography

Heavy Flavor Productions Workshop


Role of dynamic geometry in jet tomography

Heavy Flavor Productions Workshop


Role of dynamic geometry in jet tomography

Heavy Flavor Productions Workshop


Partonic r aa model1

Partonic RAA Model

  • Exploit the power law production rate to use the momentum Jacobian to define the probability of escape, (1-e)n

    • pT, final = e pT, initial

    • n is simply related to the exponent of the power law

    • Assumes a slowly changing power law

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Combining models

Combining Models

  • Find a fixed L that reproduces the dynamical length-generated partonic RAA using proper initial spectra followed by fragmentation into pions and electrons

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Vary a s

Vary as

  • We expect a big change since

  • DErad ~ as3

  • DEelas ~ as2

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Finding fixed l

Heavies

Lights

Finding Fixed L

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Heavies alph 4 bt and tg

Heavies alph=.4 BT and TG

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Theoretical error from length uncertainty

Theoretical Error from Length Uncertainty

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Volume emission for a s 4

Volume Emission foras = .4

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Volume emission for a s 4 cont d

Volume Emission for as = .4 (cont’d)

Heavy Flavor Productions Workshop


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