Zeroth Order Heavy Quark PhotonGluon Bremsstrahlung William Horowitz

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 5/2/08 Yale-Columbia Fest 2008 William Horowitz 1

A Talk in Two Parts p. QCD vs. Ad. S/CFT Drag 0 th Order Production Radiation 5/2/08 Yale-Columbia Fest 2008 William Horowitz 2

Testing p. QCD vs. Ad. S/CFT Drag Energy Loss Mechanisms (In Five Slides) ar. Xiv: 0706. 2336 (LHC predictions) ar. Xiv: 0710. 0703 (RHIC predictions) 5/2/08 Yale-Columbia Fest 2008 William Horowitz 3

(Proper) Subset of Mechanisms • DGLV, Ad. S/CFT Drag, Diffusion… LPM: dp. T/dt ~ -LT 3 log(p. T/Mq) dp. T/dt ~ -(T 2/Mq) p. T • Use heavy quark RAA to test these two 5/2/08 Yale-Columbia Fest 2008 William Horowitz 4

LHC c, b RAA p. T Dependence WH, M. Gyulassy, ar. Xiv: 0706. 2336 – Naïve expectations met in full numerical calculation: LHC Prediction Zoo: What a Mess! Unfortunately, large suppression p. QCD similar to Ad. S/CFT Large suppression leads to flattening Significant rise in R AA(p. T) for p. QCD Rad+El – Use of realistic geometry and Bjorken expansion allows saturation below. 2 d. R Let’s go through step by step AA(p. T)/dp. T > 0 => p. QCD; d. RAA(p. T)/dp. T < 0 => ST 5/2/08 Yale-Columbia Fest 2008 William Horowitz 5

c LHC R b AA(p. T)/R AA(p. T) Prediction • Recall the Zoo: WH, M. Gyulassy, ar. Xiv: 0706. 2336 [nucl-th] – Taking the ratio cancels most normalization differences seen previously – p. QCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates) WH, M. Gyulassy, ar. Xiv: 0706. 2336 [nucl-th] – Ad. S/CFT ratio is flat and many times smaller than p. QCD at only moderate p T 5/2/08 Yale-Columbia Fest 2008 William Horowitz 6

cb RHIC R Ratio p. QCD Ad. S/CFT WH, M. Gyulassy, ar. Xiv: 0710. 0703 • Wider distribution of Ad. S/CFT curves at RHIC due to large n power law production: increased sensitivity to input parameters • Advantage of RHIC: lower T => higher Ad. S speed limits 5/2/08 Yale-Columbia Fest 2008 William Horowitz 7

Conclusions • Ad. S/CFT Drag observables calculated • Generic differences (p. QCD vs. Ad. S/CFT Drag) seen in RAA – Masked by extreme p. QCD • Enhancement from ratio of c to b RAA – Discovery potential in Year 1 LHC Run • Understanding regions of self-consistency crucial • RHIC measurement possible 5/2/08 Yale-Columbia Fest 2008 William Horowitz 8

Some Investigations of 0 th Order Production Radiation 5/2/08 Yale-Columbia Fest 2008 William Horowitz 9

Motivation • Previous work: test p. QCD or Ad. S/CFT energy loss – Heavy quark RQAA and Rc. AA/Rb. AA • 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-p. T, etc. – Reevaluate magnitude of Ter-Mikayelian 5/2/08 Yale-Columbia Fest 2008 William Horowitz 10

New Fragmentation g Data A. Hanks, QM 2008 5/2/08 Yale-Columbia Fest 2008 William Horowitz 11

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 0 th Order S. Wicks, WH, M. Djordjevic, M Gyulassy, Nucl. Phys. A 783: 493 -496, 2007 5/2/08 Yale-Columbia Fest 2008 William Horowitz 12

Quark and Gluon/Photon Mass Effects • Quark mass => Dead cone – Ultrarelativistic “searchlight” rad. pattern q ~ Mq/E Y. Dokshitzer and D. Kharzeev, Phys. Lett. B 519: 199 -206, 2001 • Gluon mass => Longitudinal modes, QCD Ter-Mikayelian M. Djordjevic and M. Gyulassy, Phys. Rev. C 68: 034914, 2003 – Reduction of production radiation compared to vacuum • Alters DGLAP kernel 5/2/08 Yale-Columbia Fest 2008 William Horowitz 13

Previous Calculation of Ter-Mikayelian M. Djordjevic and M. Gyulassy, Phys. Rev. C 68: 034914, 2003 • Reduction of E-loss for charm quarks by ~ 30% • E-loss from full HTL well approx. by fixed mg = m∞ • Small-x p. QCD 0 th Order result: 5/2/08 Yale-Columbia Fest 2008 William Horowitz 14

Compare Classical E&M to “p. QCD” – Classical E&M • Recall Jackson: • Soft photon limit => – Note charge conserved – Usual p. QCD approach – Charge explicitly not conserved => Ward identity ( ) violated 5/2/08 Yale-Columbia Fest 2008 William Horowitz 15

Classical/QFT Inconsistency – For m. Q = mg = 0 and in the small x, large E+ limit, both are equal: – For m. Q, mg ≠ 0 and the small x, large E+ limit, they differ: 5/2/08 Yale-Columbia Fest 2008 William Horowitz 16

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 Yale-Columbia Fest 2008 William Horowitz 17

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 Yale-Columbia Fest 2008 William Horowitz 18

Resulting Expression – To lowest order in 1/E+ – New: • (1 -x)2 prefactor: naturally kills hard gluons • mg 2 in numerator: fills in the dead cone!? ! – What are the sizes of these effects? Call this LO 5/2/08 Yale-Columbia Fest 2008 William Horowitz 19

LO Gluon Production Radiation – Numerics includes k. T and x limits » x large enough to create mg » x small enough that EJet > Mq – Fixed m =. 5 Ge. V and as =. 5 » Similar to Magda full HTL propagator with running as • Prefactor => 50 -150% effect – Implications for in-medium radiative loss? • Filling in dead code => 5 -20% 5/2/08 Yale-Columbia Fest 2008 William Horowitz 20

LO vs. All Orders Production Rad. • Ter-Mikayelian similar for both • Different normalizations • All orders calculation selfregulates for mg = 0 and p. T → 0 – 0 -60% effect 5/2/08 Yale-Columbia Fest 2008 William Horowitz 21

Conclusions • No single satisfactory energy loss model • Search for tests sensitive to mechanism – Ratio of charm to bottom RAA for p. QCD vs. Ad. S/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 Yale-Columbia Fest 2008 William Horowitz 22

Backups 5/2/08 Yale-Columbia Fest 2008 William Horowitz 23

Reasonable Consistency with Magda c b M. Djordjevic and M. Gyulassy, Phys. Rev. C 68: 034914, 2003 5/2/08 Yale-Columbia Fest 2008 William Horowitz 24

th 0 Order % Differences 5/2/08 Yale-Columbia Fest 2008 William Horowitz 25