Heavy Quark Energy Loss

1. Heavy Quark Energy Loss Tatia Engelmore Journal Club 7/21

2. Types of Energy Loss • Radiative • Fast partons interact in a color field, radiate gluons • Collisional • Elastic Scattering of partons off other partons in the medium • Initially radiative energy loss was thought to dominate, but collisional energy loss is actually of similar magnitude

3. Energy Loss Models • DGLV • Radiative e-loss, expanded in opacity • Debye-screened color potential • N≤3 scatterings • BDMPS • Also radiative, well-separated scattering centers • Applies to infinite matter (N»1) • WHDG • DGLV + collisional e-loss and path length fluctuations • AdS/CFT calculations • Many others

4. Commonly Used Parameters in Energy Loss Calculations •  = mean free path in medium = 1/ •  = opacity = L/ (L = size of medium) • q = transport coefficient = ^2/ where  = characteristic momentum transfer •  = energy of radiated gluon

5. Energy Loss of Heavy Quarks (Dokshitzer and Kharzeev) • Radiated gluons have formation time tform = /kT^2, typical momentum kT^2=^2*tform/. • Number of scattering centers = tform/ =√(/*^2) • Energy spectrum for emitted gluons (scattering centers far apart, use Bethe-Heitler limit): • q = ^2/

6. Heavy Quark E-loss cont’d. • Energy distribution of radiated gluons: • Radiation vanishes for >1 because then formation time exceeds length of medium: • Typical transverse momentum of radiated gluon kT^2 = √(*q), characteristic angle

7. Heavy Quark E-loss cont’d. • Power spectrum of gluon radiation: • Modified from light quark spectrum by factor: • If <0, radiation is suppressed - heavy quarks lose less energy than light quarks.

8. How do Heavy Quarks Actually Behave? • PHENIX single electron data from Run 4 Au+Au (D and B meson decays) • Fit to FONLL curve from p+p data (assume binary scaling). • Data match at low pt but seem to be suppressed at high pt.

9. Large Heavy Flavor Suppression • Left, compare inclusive single e, high pt e (heavy flavor), 0 data • Inclusive e is weighted more toward lower pt (only half charm/bottom) • Heavy flavor suppressed almost as much as light quarks. PHENIX final 2007

10. PHENIX + STAR single e Dong 2005 PHENIX and STAR results consistent, radiative energy loss model fails to explain the data.

11. Collisional e-loss • If using radiative e-loss alone, need either a very large transport coefficient (q=14) or almost no contribution of b-quarks to single e spectrum. • Collisional e-loss should not be neglected: significant for heavy quarks. • This is because heavy quarks not ultra-relativistic. • Even for light quarks, collisional e-loss may be half as strong as radiative e-loss.

12. WHDG • Radiative + elastic collisional e-loss • Initial + final state e-loss • Includes path length fluctuation effects, rather than assuming entire length of medium traversed. • Given initial starting point, parton completes random walk: variety of lengths traversed in medium.

13. Collisional E-loss Comparison WHDG 2008 Above left, comparison between radiative e-loss vs. e-loss from radiative + collisional + path length fluctuations. Above left, comparison of scales of radiative vs. collisional e-loss for light and heavy quarks. (Wicks, Horowitz, Djordjevic and Gyulassy 2008).

14. Future of Heavy Quark E-loss • More realistic modeling of the medium is leading to better consistency with data • Other methods being tested • Energy loss through resonance formation (van Hees) • AdS/CFT drag • LHC should shed light on e-loss in a new energy regime, potentially verifying or falsifying current theories.