5/2/08 William Horowitz Yale-Columbia Fest 2008 1 Zero th Order Heavy Quark Photon/Gluon Bremsstrahlung William Horowitz Columbia University Frankfurt.

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Presentation transcript:

5/2/08 William Horowitz Yale-Columbia Fest Zero th Order Heavy Quark Photon/Gluon Bremsstrahlung William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) May 2, 2008 With many thanks to Miklos Gyulassy, Simon Wicks, Ivan Vitev, Hendrik van Hees

5/2/08 William Horowitz Yale-Columbia Fest A Talk in Two Parts pQCD vs. AdS/CFT Drag 0 th Order Production Radiation

5/2/08 William Horowitz Yale-Columbia Fest Testing pQCD vs. AdS/CFT Drag Energy Loss Mechanisms (In Five Slides) arXiv: (LHC predictions) arXiv: (RHIC predictions)

5/2/08 William Horowitz Yale-Columbia Fest (Proper) Subset of Mechanisms DGLV, AdS/CFT Drag, Diffusion… Use heavy quark R AA to test these two dp T /dt ~ -(T 2 /M q ) p T LPM: dp T /dt ~ -LT 3 log(p T /M q )

5/2/08 William Horowitz Yale-Columbia Fest –LHC Prediction Zoo: What a Mess! –Let’s go through step by step –Unfortunately, large suppression pQCD similar to AdS/CFT–Large suppression leads to flattening –Use of realistic geometry and Bjorken expansion allows saturation below.2 –Significant rise in R AA (p T ) for pQCD Rad+El–Naïve expectations met in full numerical calculation: dR AA (p T )/dp T > 0 => pQCD; dR AA (p T )/dp T ST LHC c, b R AA p T Dependence WH, M. Gyulassy, arXiv:

5/2/08 William Horowitz Yale-Columbia Fest LHC R c AA (p T )/R b AA (p T ) Prediction Recall the Zoo: –Taking the ratio cancels most normalization differences seen previously –pQCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates) –AdS/CFT ratio is flat and many times smaller than pQCD at only moderate p T WH, M. Gyulassy, arXiv: [nucl-th]

5/2/08 William Horowitz Yale-Columbia Fest RHIC R cb Ratio Wider distribution of AdS/CFT curves at RHIC due to large n power law production: increased sensitivity to input parameters Advantage of RHIC: lower T => higher AdS speed limits WH, M. Gyulassy, arXiv: pQCD AdS/CFT pQCD AdS/CFT

5/2/08 William Horowitz Yale-Columbia Fest Conclusions AdS/CFT Drag observables calculated Generic differences (pQCD vs. AdS/CFT Drag) seen in R AA –Masked by extreme pQCD Enhancement from ratio of c to b R AA –Discovery potential in Year 1 LHC Run Understanding regions of self- consistency crucial RHIC measurement possible

5/2/08 William Horowitz Yale-Columbia Fest Some Investigations of 0 th Order Production Radiation

5/2/08 William Horowitz Yale-Columbia Fest Motivation Previous work: test pQCD or AdS/CFT energy loss –Heavy quark R Q AA and R c AA /R b AA Future goal: additional energy loss test using photon bremsstrahlung Zero th Order Calculation –Recent p + p fragmentation  data –Good warm-up and test problem Investigate running , low-p T, etc. –Reevaluate magnitude of Ter-Mikayelian

5/2/08 William Horowitz Yale-Columbia Fest New Fragmentation  Data A. Hanks, QM2008

5/2/08 William Horowitz Yale-Columbia Fest Motivating Example: Running  s –Fixed  s is simplification to speed up code Not a free parameter –Running  s will most likely introduce a large error –Want to understand systematics in 0 th Order S. Wicks, WH, M. Djordjevic, M Gyulassy, Nucl.Phys. A783 : ,2007

5/2/08 William Horowitz Yale-Columbia Fest Quark mass => Dead cone –Ultrarelativistic “searchlight” rad. pattern Gluon mass => Longitudinal modes, QCD Ter-Mikayelian –Reduction of production radiation compared to vacuum Alters DGLAP kernel Quark and Gluon/Photon Mass Effects  ~ M q /E Y. Dokshitzer and D. Kharzeev, Phys.Lett. B519 : ,2001 M. Djordjevic and M. Gyulassy, Phys.Rev. C68 :034914,2003

5/2/08 William Horowitz Yale-Columbia Fest Previous Calculation of Ter-Mikayelian Reduction of E-loss for charm quarks by ~ 30% E-loss from full HTL well approx. by fixed m g = m ∞ Small- x pQCD 0 th Order result: M. Djordjevic and M. Gyulassy, Phys.Rev. C68 :034914,2003

5/2/08 William Horowitz Yale-Columbia Fest Compare Classical E&M to “pQCD” –Classical E&M Recall Jackson: Soft photon limit => –Note charge conserved –Usual pQCD approach –Charge explicitly not conserved => Ward identity ( ) violated

5/2/08 William Horowitz Yale-Columbia Fest Classical/QFT Inconsistency –For m Q = m g = 0 and in the small x, large E + limit, both are equal: –For m Q, m g ≠ 0 and the small x, large E + limit, they differ:

5/2/08 William Horowitz Yale-Columbia Fest Not a Classical Error –Wrong classical calculation? Plugged in massive 4-vectors into massless formulae Rederive classical result using Proca Lagrangian –After several pages of work… Identical to

5/2/08 William Horowitz Yale-Columbia Fest Error from QFT Ward Violation Identical expressions are not a surprise QFT Calculation –Photon momentum carried away crucial for cancellation of photon mass Classical case neglects both; effects cancel

5/2/08 William Horowitz Yale-Columbia Fest Resulting Expression –To lowest order in 1/E + –New: (1- x ) 2 prefactor: naturally kills hard gluons m g 2 in numerator: fills in the dead cone!?! –What are the sizes of these effects? Call this LO

5/2/08 William Horowitz Yale-Columbia Fest LO Gluon Production Radiation Prefactor => % effect –Implications for in-medium radiative loss? Filling in dead code => 5-20% –Numerics includes k T and x limits » x large enough to create m g » x small enough that E Jet > M q –Fixed  =.5 GeV and  s =.5 »Similar to Magda full HTL propagator with running  s

5/2/08 William Horowitz Yale-Columbia Fest LO vs. All Orders Production Rad. Ter-Mikayelian similar for both Different normalizations –0-60% effect All orders calculation self-regulates for m g = 0 and p T → 0

5/2/08 William Horowitz Yale-Columbia Fest Conclusions No single satisfactory energy loss model Search for tests sensitive to mechanism –Ratio of charm to bottom R AA for pQCD vs. AdS/CFT –Future tests using photon bremsstrahlung Inclusion of away-side jet fills in dead cone –Ultimately leads to a relatively small (5-20%) effect Radiative calculations integrate over all x ; importance of large x behavior?

5/2/08 William Horowitz Yale-Columbia Fest Backups

5/2/08 William Horowitz Yale-Columbia Fest Reasonable Consistency with Magda b c M. Djordjevic and M. Gyulassy, Phys.Rev. C68 :034914,2003

5/2/08 William Horowitz Yale-Columbia Fest th Order % Differences