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

Yale-Columbia Fest 2008

15/2/08

William Horowitz

Zeroth Order Heavy Quark Photon/Gluon

Bremsstrahlung

William HorowitzColumbia University

Frankfurt Institute for Advanced Studies (FIAS)May 2, 2008

With many thanks to Miklos Gyulassy, Simon Wicks, Ivan Vitev, Hendrik van Hees


25/2/08

William Horowitz

A Talk in Two Parts

pQCD vs. AdS/CFT Drag

0th Order Production Radiation


35/2/08

William Horowitz

Testing pQCD vs. AdS/CFT Drag Energy Loss Mechanisms

(In Five Slides)

arXiv:0706.2336 (LHC predictions)arXiv:0710.0703 (RHIC predictions)


45/2/08

William Horowitz

(Proper) Subset of Mechanisms

• DGLV, AdS/CFT Drag, Diffusion…

• Use heavy quark RAA to test these twodpT/dt ~ -(T2/Mq) pTLPM: dpT/dt ~ -LT3 log(pT/Mq)


55/2/08

William Horowitz

– 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

LHC c, b RAA pT Dependence

WH, M. Gyulassy, arXiv:0706.2336


65/2/08

William Horowitz

LHC RcAA(pT)/Rb

AA(pT) 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 pT

WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]

WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]


75/2/08

William Horowitz

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

WH, M. Gyulassy, arXiv:0710.0703

pQCD

AdS/CFT

pQCD

AdS/CFT


85/2/08

William Horowitz

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


95/2/08

William Horowitz

Some Investigations of 0th Order Production Radiation


105/2/08

William Horowitz

Motivation• Previous work: test pQCD or

AdS/CFT energy loss– Heavy quark RQ

AA and RcAA/Rb

AA

• Future goal: additional energy loss test using photon bremsstrahlung

• Zeroth Order Calculation– Recent p + p fragmentation data– Good warm-up and test problem

• Investigate running , low-pT, etc.

– Reevaluate magnitude of Ter-Mikayelian


115/2/08

William Horowitz

New Fragmentation Data

A. Hanks, QM2008


125/2/08

William Horowitz

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 0th Order

S. Wicks, WH, M. Djordjevic, M Gyulassy, Nucl.Phys.A783:493-496,2007


135/2/08

William Horowitz

• 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

~ Mq/E

Y. Dokshitzer and D. Kharzeev, Phys.Lett.B519:199-206,2001

M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003


145/2/08

William Horowitz

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:



155/2/08

William Horowitz

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


165/2/08

William Horowitz

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:


175/2/08

William Horowitz

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


185/2/08

William Horowitz

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


195/2/08

William Horowitz

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


205/2/08

William Horowitz

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 = .5 GeV and s = .5» Similar to Magda full HTL

propagator with running s


215/2/08

William Horowitz

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


225/2/08

William Horowitz

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?


235/2/08

William Horowitz

Backups


245/2/08

William Horowitz

Reasonable Consistency with Magda

b

c



255/2/08

William Horowitz

0th Order % Differences

Documents

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