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

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

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

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

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

6. 6 Heavy Quark E-loss cont’d. Energy distribution of radiated gluons: Energy distribution of radiated gluons: Radiation vanishes for  >  1 because then formation time exceeds length of medium: Radiation vanishes for  >  1 because then formation time exceeds length of medium: Typical transverse momentum of radiated gluon k T ^2 = √(  *q), characteristic angle Typical transverse momentum of radiated gluon k T ^2 = √(  *q), characteristic angle

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

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

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

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

11. 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. 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. Collisional e-loss should not be neglected: significant for heavy quarks. This is because heavy quarks not ultra-relativistic. This is because heavy quarks not ultra-relativistic. Even for light quarks, collisional e-loss may be half as strong as radiative e-loss. Even for light quarks, collisional e-loss may be half as strong as radiative e-loss.

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

13. 13 Collisional E-loss Comparison 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). WHDG 2008

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