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Heavy Quark Radiative Energy Loss in QCD Matter

Magdalena Djordjevic, Miklos Gyulassy

TL;DR

The paper extends the GLV opacity expansion to heavy quarks by incorporating finite mass $M$ and gluon plasmon mass $m_g$, revealing a universal energy shift $oxed{ oldsymbol{ abla olinebreak oxed{oldsymbol{ abla} ext{Ω}_{(m,...,n)} = oldsymbol{ abla} ext{ω}_{(m,...,n)} + rac{m_g^2 + M^2 x^2}{2 x E}}}$ that modifies all radiative amplitudes. It demonstrates that heavy-quark radiative energy loss is markedly closer to the incoherent (Bethe-Heitler-like) limit than for light partons, with the formation-time effects weakened by mass and a long radiation length $L_{ ext{rad}}$ that often exceeds nuclear dimensions, implying volume rather than surface domination. Numerical results for RHIC and LHC indicate charm and bottom losses are substantial yet moderated by the Ter-Mikayelian effect and dead-cone suppression, scaling roughly with $L/ ext{λ}_g$ and jet energy, and showing a gradual transition from incoherent to partially coherent behavior as energy and medium density vary. Overall, heavy-quark tomography emerges as a promising tool to map QGP properties, complementing light-parton jet quenching measurements.

Abstract

Heavy quark medium induced radiative energy loss is derived to all orders in opacity, $(L/λ_g)^n$. The analytic expression generalizes the GLV opacity expansion for massless quanta to heavy quarks with mass $M$ in a QCD plasma with a gluon dispersion characterized by an asymptotic plasmon mass, $m_g=gT/\sqrt{2}$. Remarkably, we find that the general result is obtained by simply shifting all frequencies in the GLV series by $(m_g^2+x^2 M^2)/(2 x E)$. Numerical evaluation of the first order in opacity energy loss shows that both charm and bottom energy losses are much closer to the incoherent radiation limit than light partons in nuclear collisions at both RHIC and LHC energies. However, the radiation lengths of heavy quarks remain large compared to nuclear dimensions and hence high $p_T$ heavy quark production is volume rather than surface dominated.

Heavy Quark Radiative Energy Loss in QCD Matter

TL;DR

The paper extends the GLV opacity expansion to heavy quarks by incorporating finite mass and gluon plasmon mass , revealing a universal energy shift that modifies all radiative amplitudes. It demonstrates that heavy-quark radiative energy loss is markedly closer to the incoherent (Bethe-Heitler-like) limit than for light partons, with the formation-time effects weakened by mass and a long radiation length that often exceeds nuclear dimensions, implying volume rather than surface domination. Numerical results for RHIC and LHC indicate charm and bottom losses are substantial yet moderated by the Ter-Mikayelian effect and dead-cone suppression, scaling roughly with and jet energy, and showing a gradual transition from incoherent to partially coherent behavior as energy and medium density vary. Overall, heavy-quark tomography emerges as a promising tool to map QGP properties, complementing light-parton jet quenching measurements.

Abstract

Heavy quark medium induced radiative energy loss is derived to all orders in opacity, . The analytic expression generalizes the GLV opacity expansion for massless quanta to heavy quarks with mass in a QCD plasma with a gluon dispersion characterized by an asymptotic plasmon mass, . Remarkably, we find that the general result is obtained by simply shifting all frequencies in the GLV series by . Numerical evaluation of the first order in opacity energy loss shows that both charm and bottom energy losses are much closer to the incoherent radiation limit than light partons in nuclear collisions at both RHIC and LHC energies. However, the radiation lengths of heavy quarks remain large compared to nuclear dimensions and hence high heavy quark production is volume rather than surface dominated.

Paper Structure

This paper contains 17 sections, 89 equations.

Table of Contents

  1. Introduction
  2. The one gluon associated radiation
  3. First order radiative energy loss
  4. Higher orders in opacity energy loss
  5. Heavy quark generalization of GLV to all orders
  6. The Incoherent, Short Formation Time Limit
  7. Numerical estimates
  8. Heavy quark energy loss at RHIC
  9. Heavy quark energy loss at LHC
  10. Summary
  11. Apendix: Assumptions
  12. Diagrams $M_{1,0,0}$, $M_{1,1,0}$ and $M_{1,0,1}$
  13. Diagram $M_{2,0,3}$
  14. Diagrams $M_{2,0,0}$ and $M_{2,2,0}$
  15. Diagrams $M_{2,0,1}$ and $M_{2,0,2}$
  16. ...and 2 more sections