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Zero th Order Heavy Quark Photon/Gluon Bremsstrahlung

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. A Talk in Two Parts. pQCD vs. AdS/CFT Drag

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Zero th Order Heavy Quark Photon/Gluon Bremsstrahlung

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  1. Zeroth 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 Yale-Columbia Fest 2008

  2. A Talk in Two Parts pQCD vs. AdS/CFT Drag 0th Order Production Radiation Yale-Columbia Fest 2008

  3. arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions) Testing pQCD vs. AdS/CFT Drag Energy Loss Mechanisms(In Five Slides) Yale-Columbia Fest 2008

  4. (Proper) Subset of Mechanisms • DGLV, AdS/CFT Drag, Diffusion… • Use heavy quark RAA to test these two LPM: dpT/dt ~ -LT3 log(pT/Mq) dpT/dt ~ -(T2/Mq) pT Yale-Columbia Fest 2008

  5. LHC c, b RAA pT Dependence WH, M. Gyulassy, arXiv:0706.2336 • 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 RAA(pT) for pQCD Rad+El • Naïve expectations met in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST Yale-Columbia Fest 2008

  6. LHC RcAA(pT)/RbAA(pT) Prediction • Recall the Zoo: WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] • 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 pT WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] Yale-Columbia Fest 2008

  7. RHIC Rcb 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 pQCD pQCD AdS/CFT AdS/CFT WH, M. Gyulassy, arXiv:0710.0703 Yale-Columbia Fest 2008

  8. Conclusions • AdS/CFT Drag observables calculated • Generic differences (pQCD vs. AdS/CFT Drag) seen in RAA • Masked by extreme pQCD • Enhancement from ratio of c to b RAA • Discovery potential in Year 1 LHC Run • Understanding regions of self-consistency crucial • RHIC measurement possible Yale-Columbia Fest 2008

  9. Some Investigations of 0th Order Production Radiation Yale-Columbia Fest 2008

  10. Motivation • Previous work: test pQCD or AdS/CFT energy loss • Heavy quark RQAA and RcAA/RbAA • Future goal: additional energy loss test using photon bremsstrahlung • Zeroth Order Calculation • Recent p + p fragmentation g data • Good warm-up and test problem • Investigate running a, low-pT, etc. • Reevaluate magnitude of Ter-Mikayelian Yale-Columbia Fest 2008

  11. New Fragmentation g Data A. Hanks, QM2008 Yale-Columbia Fest 2008

  12. Motivating Example: Running as • Fixed as is simplification to speed up code • Not a free parameter • Running as will most likely introduce a large error • Want to understand systematics in 0th Order S. Wicks, WH, M. Djordjevic, M Gyulassy, Nucl.Phys.A783:493-496,2007 Yale-Columbia Fest 2008

  13. Quark and Gluon/Photon Mass Effects q ~ Mq/E • 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 • Y. Dokshitzer and D. Kharzeev, Phys.Lett.B519:199-206,2001 M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003 Yale-Columbia Fest 2008

  14. Previous Calculation of Ter-Mikayelian • Reduction of E-loss for charm quarks by ~ 30% • E-loss from full HTL well approx. by fixed mg = m∞ • Small-x pQCD 0th Order result: M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003 Yale-Columbia Fest 2008

  15. 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 Yale-Columbia Fest 2008

  16. Classical/QFT Inconsistency • For mQ = mg = 0 and in the small x, large E+ limit, both are equal: • For mQ, mg ≠ 0 and the small x, large E+ limit, they differ: Yale-Columbia Fest 2008

  17. 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 Yale-Columbia Fest 2008

  18. 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 Yale-Columbia Fest 2008

  19. Resulting Expression • To lowest order in 1/E+ • New: • (1-x)2 prefactor: naturally kills hard gluons • mg2 in numerator: fills in the dead cone!?! • What are the sizes of these effects? Call this LO Yale-Columbia Fest 2008

  20. LO Gluon Production Radiation • Prefactor => 50-150% effect • Implications for in-medium radiative loss? • Filling in dead code => 5-20% • Numerics includes kT and x limits • x large enough to create mg • x small enough that EJet > Mq • Fixed m = .5 GeV and as = .5 • Similar to Magda full HTL propagator with running as Yale-Columbia Fest 2008

  21. LO vs. All Orders Production Rad. • Ter-Mikayelian similar for both • Different normalizations • 0-60% effect • All orders calculation self-regulates for mg = 0 and pT → 0 Yale-Columbia Fest 2008

  22. Conclusions • No single satisfactory energy loss model • Search for tests sensitive to mechanism • Ratio of charm to bottom RAA 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? Yale-Columbia Fest 2008

  23. Backups Yale-Columbia Fest 2008

  24. Reasonable Consistency with Magda c b M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003 Yale-Columbia Fest 2008

  25. 0th Order % Differences Yale-Columbia Fest 2008

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