A derivation of the source term induced by a fast parton from the quark energy-momentum tensor Bryon Neufeld, LANL Winter Workshop on Nuclear Dynamics Neufeld

Timeline of experimental relativistic heavy-ion programs 2Neufeld BNL AGS 10 GeV/A, T = 190 MeV CERN SPS 158 GeV/A, T = 245 MeV BNL RHIC 200 GeV/A, T = 410 MeV CERN LHC 5.5 TeV/A, T = 800 MeV APS listed discovery of QGP in heavy-ion collisions as one of top 10 physics newsmakers of the last decade What are the properties of QCD matter at high temperature and or baryon density?

Jets as a probe of the QGP High pT partons can be produced in hard scattering events in the early stages of a heavy-ion collision The modification of energetic partons due to the interaction with the medium is a sensitive probe of medium density, Debye scale, strong coupling, transport coefficients. A similar statement can be made for the modification of the medium due to an energetic parton. The modification of energetic partons due to the interaction with the medium is a sensitive probe of medium density, Debye scale, strong coupling, transport coefficients. A similar statement can be made for the modification of the medium due to an energetic parton.parton E 3Neufeld

Jets as a probe of the QGP High pT partons can be produced in hard scattering events in the early stages of a heavy-ion collision The modification of energetic partons due to the interaction with the medium is a sensitive probe of medium density, Debye scale, strong coupling, transport coefficients. A similar statement can be made for the modification of the medium due to an energetic parton. The modification of energetic partons due to the interaction with the medium is a sensitive probe of medium density, Debye scale, strong coupling, transport coefficients. A similar statement can be made for the modification of the medium due to an energetic parton.parton E 4Neufeld

Jets as a probe of the QGP High pT partons can be produced in hard scattering events in the early stages of a heavy-ion collision The modification of energetic partons due to the interaction with the medium is a sensitive probe of medium density, Debye scale, strong coupling, transport coefficients. A similar statement can be made for the modification of the medium due to an energetic parton. The modification of energetic partons due to the interaction with the medium is a sensitive probe of medium density, Debye scale, strong coupling, transport coefficients. A similar statement can be made for the modification of the medium due to an energetic parton.parton E 5Neufeld

Evidence for strong jet quenching: Large leading particle suppression strong evidence for formation of QGP in HIC 6Neufeld Mike Tannenbaum, Review Article, 2006

Neufeld7 Jet quenching confirmed at LHC: ALICE Collaboration, Phys.Lett. B696, 2011 First results from heavy-ion program at LHC are becoming available. Results from ALICE collaboration confirm results on jet quenching, and extend to higher pT

Neufeld8 The medium response to jets - PHENIX Au-Au at 200 GeV c.m. energy di-hadron correlations (PHENIX): Per-trigger yield distribution Dihadron correlations at RHIC energies may show conical flow indicative of a shockwave, but the statistics are not good enough to be sure. As with jet quenching, the LHC program will probably greatly improve the situation. Dihadron correlations at RHIC energies may show conical flow indicative of a shockwave, but the statistics are not good enough to be sure. As with jet quenching, the LHC program will probably greatly improve the situation.

Neufeld9 LHC already shows great opportunity to study medium response: ATLAS Collaboration, PRL, 2011 This result shows an asymmetric di-jet in a very central collision. Away-side appears to show energy distributed in the underlying medium…stay tuned Doesn’t have to be double- peaked, the broadening itself is interesting to consider. Doesn’t have to be double- peaked, the broadening itself is interesting to consider.

Results presented by Ed Wenger suggest ‘lost’ energy transferred to the underlying medium: Medium induced gluon radiation doesn’t automatically get transferred to the medium, requires additional interactions. It is non-trivial to say that energy is transferred to the medium.

11Neufeld Such an investigation was performed for a strongly coupled AdS/CFT plasma Friess, Gubser, Michalogiorgakis and Pufu, PRD, (2007) Ideally, to theoretically investigate the medium’s response to an energetic parton one would appeal directly to the underlying field theory for the full solution Plot from Chesler and Yaffe, PRD, (2008) They solved for the stress tensor in the presence of an asymptotically propagating quark, solving the full dynamics from the underlying field theory. They solved for the stress tensor in the presence of an asymptotically propagating quark, solving the full dynamics from the underlying field theory.

R.B. Neufeld 12 The medium response to jets in QCD – theory  At a fundamental level the medium is described by an energy-momentum tensor (EMT) (will consider a medium of quarks here)

R.B. Neufeld 13  At a fundamental level the medium is described by an energy-momentum tensor (EMT) (will consider a medium of quarks here)  In principle, the medium response to hard partons can be completely determined using the EMT  The fast parton is here coupled to the Lagrangian to create an additional interaction term J is input by hand, can be of very general form The medium response to jets in QCD – theory

R.B. Neufeld14  In practice, cannot evaluate directly (real-time problem), must resort to perturbation theory The medium response to jets in QCD – theory

R.B. Neufeld15  In practice, cannot evaluate directly (real-time problem), must resort to perturbation theory At this point, have two options:  Directly evaluate components of EMT in pert. theory, obtain information about medium response near source charge  Evaluate source of energy and momentum, let effective theory take it from there The medium response to jets in QCD – theory

R.B. Neufeld16 In this presentation, I will consider this option:  Evaluate source of energy and momentum, let effective theory take it from there In this approach, the problem is reduced to two separate pieces: a) the calculation of the distribution J from first principles, and b) solving the hydro equations coupled to J for some initial conditions

17Neufeld Several authors have emphasized solving the hydrodynamic equations, using schematic forms for J, see for example: Rigorous attempts to solve for J have also been performed: Medium response with hydrodynamics: Betz et al, ( ) Casalderrey-Solana et al, (2005) Chaudhuri and Heinz, (2006) Neufeld, Muller and Ruppert, (2008) Neufeld and Muller, (2009) Qin, Majumder, Song and Heinz, (2009) Using the source term derived in Neufeld et al, (2008), authors solved the linearized hydro equations and plotted the results Neufeld, PRD (2011) Neufeld and Renk, (2010)

Neufeld18 Deriving the source term from the fundamental EMT of QCD: Begin with a medium of quarks only, to simplify the calculation Neufeld, PRD, accepted (2011)

Neufeld19 Deriving the source term from the fundamental EMT of QCD: Begin with a medium of quarks only, to simplify the calculation Neufeld, PRD, accepted (2011) Advantage of going directly to underlying field theory is that one can obtain the full spatial distribution for both soft and hard momentum exchange with the medium. Previous approaches have only considered soft exchange. Also, there is direct access to components of EMT for short distance response. Advantage of going directly to underlying field theory is that one can obtain the full spatial distribution for both soft and hard momentum exchange with the medium. Previous approaches have only considered soft exchange. Also, there is direct access to components of EMT for short distance response.

Neufeld20 Deriving the source term from the fundamental EMT of QCD: Begin with a medium of quarks only, to simplify the calculation The energetic parton couples to the medium via an interaction term in the Lagrangian Neufeld, PRD, accepted (2011)

Neufeld21 Deriving the source term from the fundamental EMT of QCD: Begin with a medium of quarks only, to simplify the calculation The energetic parton couples to the medium via an interaction term in the Lagrangian Neufeld, PRD, accepted (2011) This coupling can be made quite general to consider hard partons created in an initial scattering and also to incorporate medium induced radiation. Here I will consider asymptotic fast parton. This coupling can be made quite general to consider hard partons created in an initial scattering and also to incorporate medium induced radiation. Here I will consider asymptotic fast parton.

Neufeld22 Deriving the source term from the fundamental EMT of QCD: Begin with a medium of quarks only, to simplify the calculation The energetic parton couples to the medium via an interaction term in the Lagrangian Neufeld, PRD, accepted (2010) Additionally, must incorporate Feynman rule for EMT:

Neufeld23 Deriving the source term from the fundamental EMT of QCD: Once the rule for the source and EMT are extracted, the calculation proceeds via standard rules for real-time finite T perturbation theory (must extract T dependent part) Neufeld, PRD, accepted (2010) The result is shown here in integral form: The result is complicated looking, but the underlying physics can be seen in the Green’s functions

Neufeld24 What does the result mean? Rather than consider the full spatial distribution here, consider a simplified form that makes direct contact with a previous study: Neufeld and Renk, PRC (2010)

Neufeld25 Deriving the source term from the fundamental EMT of QCD: Primary result: Neufeld, PRD, accepted (2010) Although this result is complicated, can be simplified by considering how strongly it couples to sound modes Figure shows the strength of coupling to the sound mode decreases as energy increases Implication that Mach cone less likely to be observed in experiment for higher parton energy within approximation considered here

Neufeld26 Derived source term for medium response directly from EMT – direct theory of QCD at high temperature Result suggests a trend of pT dependence of possible Mach cone/broadening observation in experiment In progress and future work (with I. Vitev): include gluons in medium and consider source created in initial hard scattering, consider importance of medium induced radiation Summary and Outlook:

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