A derivation of the source term A derivation of the source term induced by a fast parton frinduced by a fast parton from the om the quark energy-momentum tensorquark energy-momentum tensor

Bryon Neufeld, LANLBryon Neufeld, LANLWinter Workshop on Nuclear Dynamics 2011Winter Workshop on Nuclear Dynamics 2011

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Timeline of experimental Timeline of experimental relativistic heavy-ion programsrelativistic heavy-ion programs

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1992 - BNL AGS1992 - BNL AGS10 GeV/A, T = 190 MeV10 GeV/A, T = 190 MeV

1994 - CERN SPS1994 - CERN SPS158 GeV/A, T = 245 MeV158 GeV/A, T = 245 MeV

2000 - 2000 - BNL RHICBNL RHIC200 GeV/A, T = 410 MeV200 GeV/A, T = 410 MeV

2010 - 2010 - CERN LHCCERN LHC5.5 TeV/A, T = 800 MeV5.5 TeV/A, T = 800 MeV

http://www.aps.org/publications/apsnews/201002/newsmakers.cfmhttp://www.aps.org/publications/apsnews/201002/newsmakers.cfm

APS listed discovery of QGP APS listed discovery of QGP in heavy-ion collisions in heavy-ion collisions

as one of top 10 physics as one of top 10 physics newsmakers of the last decadenewsmakers of the last decade

What are the properties of QCD matter at What are the properties of QCD matter at high temperature and or baryon density?high temperature and or baryon density?

Jets as a probe of the QGPJets as a probe of the QGPHigh pT partons can be produced in hard scattering High pT partons can be produced in hard scattering events in the early stages of a heavy-ion collisionevents in the early stages of a heavy-ion collision

The modification of The modification of energetic partons due to energetic partons due to the interaction with the the interaction with the medium is a sensitive probe medium is a sensitive probe of medium density, Debye of medium density, Debye scale, strong coupling, scale, strong coupling, transport coefficients. A transport coefficients. A similar statement can be similar statement can be made for the modification made for the modification of the medium due to an of the medium due to an energetic parton.energetic parton.

partonparton

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Jets as a probe of the QGPJets as a probe of the QGPHigh pT partons can be produced in hard scattering High pT partons can be produced in hard scattering events in the early stages of a heavy-ion collisionevents in the early stages of a heavy-ion collision

The modification of The modification of energetic partons due to energetic partons due to the interaction with the the interaction with the medium medium is a sensitive probe is a sensitive probe of medium density, Debye of medium density, Debye scale, strong coupling, scale, strong coupling, transport coefficients. A transport coefficients. A similar statement can be similar statement can be made for the modification made for the modification of the medium due to an of the medium due to an energetic parton.energetic parton.

partonparton

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Jets as a probe of the QGPJets as a probe of the QGPHigh pT partons can be produced in hard scattering High pT partons can be produced in hard scattering events in the early stages of a heavy-ion collisionevents in the early stages of a heavy-ion collision

The modification of The modification of energetic partons due to energetic partons due to the interaction with the the interaction with the medium is a sensitive probe medium is a sensitive probe of medium density, Debye of medium density, Debye scale, strong coupling, scale, strong coupling, transport coefficients. A transport coefficients. A similar statement can be similar statement can be made for the made for the modification modification of the medium due to an of the medium due to an energetic partonenergetic parton..

partonparton

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Evidence for strong jet quenching:Evidence for strong jet quenching: Large leading particle Large leading particle

suppression strong suppression strong evidence for formation evidence for formation of QGP in HICof QGP in HIC

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Mike Tannenbaum, Review Article, 2006Mike Tannenbaum, Review Article, 2006

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Jet quenching confirmed at LHC:Jet quenching confirmed at LHC:

ALICE Collaboration, Phys.Lett. B696, 2011ALICE Collaboration, Phys.Lett. B696, 2011

First results from heavy-ion First results from heavy-ion program at LHC are becoming program at LHC are becoming available. Results from ALICE available. Results from ALICE collaboration confirm results on jet collaboration confirm results on jet quenching, and extend to higher pTquenching, and extend to higher pT

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The medium response to jets - The medium response to jets - PHENIX

Au-Au at 200 GeV c.m. energy di-hadron Au-Au at 200 GeV c.m. energy di-hadron correlations (PHENIX): Per-trigger yield correlations (PHENIX): Per-trigger yield distributiondistribution

Dihadron correlations at RHIC energies may Dihadron correlations at RHIC energies may show conical flow indicative of a show conical flow indicative of a shockwave, but the statistics are not good shockwave, but the statistics are not good enough to be sure. As with jet quenching, enough to be sure. As with jet quenching, the LHC program will probably greatly the LHC program will probably greatly improve the situation.improve the situation.

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LHC already shows great opportunity LHC already shows great opportunity to study medium response:to study medium response:

ATLAS Collaboration, PRL, 2011ATLAS Collaboration, PRL, 2011

This result shows an asymmetric di-jet This result shows an asymmetric di-jet in a very central collision. Away-side in a very central collision. Away-side appears to show energy distributed in appears to show energy distributed in the underlying medium…stay tunedthe underlying medium…stay tuned

Doesn’t Doesn’t

have to be have to be double-double-peaked, the peaked, the broadening broadening itself is itself is interesting interesting to consider.to consider.

Results presented by Ed Wenger suggest ‘lost’ Results presented by Ed Wenger suggest ‘lost’ energy transferred to the underlying medium:energy transferred to the underlying medium:

Medium induced gluon radiation doesn’t automatically Medium induced gluon radiation doesn’t automatically get transferred to the medium, requires additional get transferred to the medium, requires additional interactions. It is non-trivial to say that energy is interactions. It is non-trivial to say that energy is transferred to the medium.transferred to the medium.

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Such an investigation was performed for a Such an investigation was performed for a strongly coupled AdS/CFT plasmastrongly coupled AdS/CFT plasma Friess, Gubser, Michalogiorgakis and Pufu, PRD, (2007) Friess, Gubser, Michalogiorgakis and Pufu, PRD, (2007)

Ideally, to theoretically investigate the Ideally, to theoretically investigate the medium’s response to an energetic parton medium’s response to an energetic parton one would appeal directly to the underlying one would appeal directly to the underlying

field theory for the full solutionfield theory for the full solution

Plot from Chesler and Yaffe, PRD, (2008)Plot from Chesler and Yaffe, PRD, (2008)

They solved for the They solved for the

stress tensor in the stress tensor in the presence of an presence of an asymptotically asymptotically propagating quark, propagating quark, solving the full solving the full dynamics from the dynamics from the underlying field underlying field theory. theory.

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The medium response to jets in QCD The medium response to jets in QCD –– theory theory

At a fundamental level the At a fundamental level the medium is described by an medium is described by an energy-momentum tensor energy-momentum tensor (EMT) (will consider a (EMT) (will consider a medium of quarks here)medium of quarks here)

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At a fundamental level the At a fundamental level the medium is described by an medium is described by an energy-momentum tensor energy-momentum tensor (EMT) (will consider a (EMT) (will consider a medium of quarks here)medium of quarks here) In principle, the medium In principle, the medium response to hard partons response to hard partons can be completely can be completely determined using the EMTdetermined using the EMT The fast parton is here The fast parton is here coupled to the Lagrangian to coupled to the Lagrangian to create an additional create an additional interaction terminteraction term

J is input by hand, can J is input by hand, can be of very general formbe of very general form

The medium response to jets in QCD The medium response to jets in QCD –– theory theory

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In practice, cannot evaluate In practice, cannot evaluate directly (real-time problem), must directly (real-time problem), must resort to perturbation theoryresort to perturbation theory

The medium response to jets in QCD The medium response to jets in QCD –– theory theory

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In practice, cannot evaluate In practice, cannot evaluate directly (real-time problem), must directly (real-time problem), must resort to perturbation theoryresort to perturbation theory

At this point, have two options:At this point, have two options:

Directly evaluate Directly evaluate components of EMT in components of EMT in pert. theory, obtain pert. theory, obtain information about information about medium response near medium response near source chargesource charge

Evaluate source of energy and Evaluate source of energy and momentum, let effective theory take momentum, let effective theory take it from thereit from there

The medium response to jets in QCD The medium response to jets in QCD –– theory theory

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In this presentation, I will In this presentation, I will consider this option:consider this option:

Evaluate source of energy and Evaluate source of energy and momentum, let effective theory take momentum, let effective theory take it from thereit from there

In this approach, the In this approach, the problem is reduced to two problem is reduced to two

separate pieces: separate pieces: a) the calculation of the a) the calculation of the distribution J from first distribution J from first

principles, and principles, and b) solving the hydro b) solving the hydro

equations coupled to J for equations coupled to J for some initial conditionssome initial conditions

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Several authors have emphasized solving the hydrodynamic Several authors have emphasized solving the hydrodynamic

equations, using schematic forms for J, see for example:equations, using schematic forms for J, see for example:

Rigorous attempts to solve for J have also been performed:Rigorous attempts to solve for J have also been performed:

Medium response with hydrodynamics: Medium response with hydrodynamics:

Betz et al, (2008 - 2010)Betz et al, (2008 - 2010)

Casalderrey-Solana et al, (2005)Casalderrey-Solana et al, (2005) Chaudhuri and Heinz, (2006)Chaudhuri and Heinz, (2006)

Neufeld, Muller and Ruppert, (2008)Neufeld, Muller and Ruppert, (2008)Neufeld and Muller, (2009)Neufeld and Muller, (2009)

Qin, Majumder, Song and Heinz, (2009)Qin, Majumder, Song and Heinz, (2009)

Using the source term Using the source term derived in Neufeld et al, derived in Neufeld et al, (2008), authors solved (2008), authors solved the linearized hydro the linearized hydro

equations and plotted equations and plotted the resultsthe results

Neufeld, PRD (2011)Neufeld, PRD (2011)

Neufeld and Renk, (2010)Neufeld and Renk, (2010)

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Deriving the source term from the Deriving the source term from the fundamental EMT of QCD: fundamental EMT of QCD:

Begin with a medium of quarks only, to Begin with a medium of quarks only, to

simplify the calculationsimplify the calculation

Neufeld, PRD, accepted (2011)Neufeld, PRD, accepted (2011)

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Deriving the source term from the Deriving the source term from the fundamental EMT of QCD: fundamental EMT of QCD:

Begin with a medium of quarks only, to Begin with a medium of quarks only, to

simplify the calculationsimplify the calculation

Neufeld, PRD, accepted (2011)Neufeld, PRD, accepted (2011)

Advantage of going directly to Advantage of going directly to

underlying field theory is that one underlying field theory is that one can obtain the full spatial can obtain the full spatial distribution for both soft and hard distribution for both soft and hard momentum exchange with the momentum exchange with the medium. Previous approaches medium. Previous approaches have only considered soft have only considered soft exchange. Also, there is direct exchange. Also, there is direct access to components of EMT for access to components of EMT for short distance response.short distance response.

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Deriving the source term from the Deriving the source term from the fundamental EMT of QCD: fundamental EMT of QCD:

Begin with a medium of quarks only, to Begin with a medium of quarks only, to

simplify the calculationsimplify the calculation

The energetic parton couples to the medium The energetic parton couples to the medium

via an interaction term in the Lagrangianvia an interaction term in the Lagrangian

Neufeld, PRD, accepted (2011)Neufeld, PRD, accepted (2011)

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Deriving the source term from the Deriving the source term from the fundamental EMT of QCD: fundamental EMT of QCD:

Begin with a medium of quarks only, to Begin with a medium of quarks only, to

simplify the calculationsimplify the calculation

The energetic parton couples to the medium The energetic parton couples to the medium

via an interaction term in the Lagrangianvia an interaction term in the Lagrangian

Neufeld, PRD, accepted (2011)Neufeld, PRD, accepted (2011)

This coupling can be made quite This coupling can be made quite

general to consider hard partons general to consider hard partons created in an initial scattering created in an initial scattering and also to incorporate medium and also to incorporate medium induced radiation. Here I will induced radiation. Here I will consider asymptotic fast parton. consider asymptotic fast parton.

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Deriving the source term from the Deriving the source term from the fundamental EMT of QCD: fundamental EMT of QCD:

Begin with a medium of quarks only, to Begin with a medium of quarks only, to

simplify the calculationsimplify the calculation

The energetic parton couples to the medium The energetic parton couples to the medium

via an interaction term in the Lagrangianvia an interaction term in the Lagrangian

Neufeld, PRD, accepted (2010)Neufeld, PRD, accepted (2010)

Additionally, must incorporate Feynman rule Additionally, must incorporate Feynman rule

for EMT:for EMT:

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Deriving the source term from the Deriving the source term from the fundamental EMT of QCD: fundamental EMT of QCD:

Once the rule for the source and EMT are extracted, the Once the rule for the source and EMT are extracted, the

calculation proceeds via standard rules for real-time finite T calculation proceeds via standard rules for real-time finite T

perturbation theory (must extract T dependent part) perturbation theory (must extract T dependent part)

Neufeld, PRD, accepted (2010)Neufeld, PRD, accepted (2010)

The result is shown here in integral form:The result is shown here in integral form:

The result is complicated looking, but the underlying The result is complicated looking, but the underlying

physics can be seen in the Green’s functions physics can be seen in the Green’s functions

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What does the result mean?What does the result mean?

Rather than consider the full Rather than consider the full spatial distribution here, spatial distribution here, consider a simplified form consider a simplified form that makes direct contact that makes direct contact with a previous study:with a previous study:

Neufeld and Renk, PRC (2010)Neufeld and Renk, PRC (2010)

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Deriving the source term from the Deriving the source term from the fundamental EMT of QCD: fundamental EMT of QCD:

Primary result:Primary result:

Neufeld, PRD, accepted (2010)Neufeld, PRD, accepted (2010)

Although this result is complicated, Although this result is complicated,

can be simplified by considering how can be simplified by considering how

strongly it couples to sound modesstrongly it couples to sound modes

Figure shows the strength of coupling Figure shows the strength of coupling

to the sound mode decreases as to the sound mode decreases as

energy increasesenergy increases

Implication that Mach cone less likely Implication that Mach cone less likely

to be observed in experiment for higher to be observed in experiment for higher

parton energy within approximation parton energy within approximation

considered hereconsidered here

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Derived source term for medium response Derived source term for medium response directly from EMT directly from EMT ––

direct theory of QCD at high temperaturedirect theory of QCD at high temperature

Result suggests a trend of pT dependence of Result suggests a trend of pT dependence of possible Mach cone/broadening observation in possible Mach cone/broadening observation in experimentexperiment

In progress and future work (with I. Vitev): In progress and future work (with I. Vitev): include gluons in medium and consider source include gluons in medium and consider source created in initial hard scattering, consider created in initial hard scattering, consider importance of medium induced radiationimportance of medium induced radiation

Summary and Outlook:Summary and Outlook:

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