Zeroth Order Heavy Quark Photon/Gluon Bremsstrahlung William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) April 9, 2008 With many thanks to Miklos Gyulassy, Simon Wicks, Ivan Vitev, Hendrik van Hees WWND 2008

pQCD vs. AdS/CFT Drag 0th Order Production Radiation A Talk in Two Parts pQCD vs. AdS/CFT Drag 0th Order Production Radiation WWND 2008

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

(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 WWND 2008

LHC c, b RAA pT Dependence WH, M. Gyulassy, arXiv:0706.2336 Naïve expectations met in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST Significant rise in RAA(pT) for pQCD Rad+El Large suppression leads to flattening Use of realistic geometry and Bjorken expansion allows saturation below .2 LHC Prediction Zoo: What a Mess! Let’s go through step by step Unfortunately, large suppression pQCD similar to AdS/CFT WWND 2008

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] WWND 2008

RHIC Rcb Ratio pQCD pQCD AdS/CFT AdS/CFT WH, M. Gyulassy, arXiv:0710.0703 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 WWND 2008

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 WWND 2008

Some Investigations of 0th Order Production Radiation WWND 2008

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 WWND 2008

New Fragmentation g Data A. Hanks, QM2008 WWND 2008

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 WWND 2008

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

Previous Calculation of Ter-Mikayelian M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003 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: WWND 2008

Compare Classical E&M to “pQCD” Recall Jackson: Soft photon limit => Note charge conserved Usual pQCD approach Charge explicitly not conserved => Ward identity ( ) violated WWND 2008

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: WWND 2008

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 WWND 2008

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 WWND 2008

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 WWND 2008

LO Gluon Production Radiation 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 Prefactor => 50-150% effect Implications for in-medium radiative loss? Filling in dead code => 5-20% WWND 2008

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 WWND 2008

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? WWND 2008

Backups WWND 2008

Reasonable Consistency with Magda M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003 WWND 2008

0th Order % Differences WWND 2008

Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) February 9, 2008 With many thanks to Miklos Gyulassy and Simon Wicks arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions) WWND 2008

Motivation Many heavy quark energy loss models Hope to distinguish between two broad classes: Standard Model pQCD AdS/CFT Drag Comparison difficult: nontrivial mapping of AdS/CFT to QCD predictions for LHC Look for robust signal WWND 2008

pQCD Success at RHIC: (circa 2005) Consistency: RAA(h)~RAA(p) Y. Akiba for the PHENIX collaboration, hep-ex/0510008 Consistency: RAA(h)~RAA(p) Null Control: RAA(g)~1 GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dNp/dy WWND 2008

Trouble for wQGP Picture v2 too large A. Drees, H. Feng, and J. Jia, Phys. Rev. C71:034909 (2005) (first by E. Shuryak, Phys. Rev. C66:027902 (2002)) Trouble for wQGP Picture wQGP not ruled out, but what if we try strong coupling? e- RAA too small M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006) D. Teaney, Phys. Rev. C68, 034913 (2003) Hydro h/s too small WWND 2008

Intro to AdS/CFT Large Nc limit of d-dimensional conformal field theory dual to string theory on the product of d+1-dimensional Anti-de Sitter space with a compact manifold 3+1 SYM z = 0 WWND 2008

Strong Coupling Calculation The supergravity double conjecture: QCD  SYM  IIB IF super Yang-Mills (SYM) is not too different from QCD, & IF Maldacena conjecture is true Then a tool exists to calculate strongly-coupled QCD in classical SUGRA WWND 2008

Qualitative AdS/CFT Successes: h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD e- RAA ~ p, h RAA; e- RAA(f) sstrong=(3/4) sweak, similar to Lattice Mach wave-like structures J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393 AdS/CFT PHENIX, Phys. Rev. Lett. 98, 172301 (2007) S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:0706.0213 T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006) WWND 2008

AdS/CFT Energy Loss Models Langevin model Collisional energy loss for heavy quarks Restricted to low pT pQCD vs. AdS/CFT computation of D, the diffusion coefficient ASW model Radiative energy loss model for all parton species pQCD vs. AdS/CFT computation of Debate over its predicted magnitude ST drag calculation Drag coefficient for a massive quark moving through a strongly coupled SYM plasma at uniform T not yet used to calculate observables: let’s do it! WWND 2008

AdS/CFT Drag Model heavy quark jet energy loss by embedding string in AdS space dpT/dt = - m pT m = pl1/2 T2/2Mq WWND 2008

Energy Loss Comparison t x Q, m v D7 Probe Brane D3 Black Brane (horizon) 3+1D Brane Boundary Black Hole z = 0 zh = pT zm = 2pm / l1/2 AdS/CFT Drag: dpT/dt ~ -(T2/Mq) pT Similar to Bethe-Heitler dpT/dt ~ -(T3/Mq2) pT Very different from LPM dpT/dt ~ -LT3 log(pT/Mq) WWND 2008

RAA Approximation Above a few GeV, quark production spectrum is approximately power law: dN/dpT ~ 1/pT(n+1), where n(pT) has some momentum dependence We can approximate RAA(pT): RAA ~ (1-e(pT))n(pT), where pf = (1-e)pi (i.e. e = 1-pf/pi) y=0 RHIC LHC WWND 2008

Looking for a Robust, Detectable Signal Use LHC’s large pT reach and identification of c and b to distinguish between pQCD, AdS/CFT Asymptotic pQCD momentum loss: String theory drag momentum loss: Independent of pT and strongly dependent on Mq! T2 dependence in exponent makes for a very sensitive probe Expect: epQCD 0 vs. eAdS indep of pT!! dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST erad ~ as L2 log(pT/Mq)/pT eST ~ 1 - Exp(-m L), m = pl1/2 T2/2Mq S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006 WWND 2008

Model Inputs AdS/CFT Drag: nontrivial mapping of QCD to SYM “Obvious”: as = aSYM = const., TSYM = TQCD D 2pT = 3 inspired: as = .05 pQCD/Hydro inspired: as = .3 (D 2pT ~ 1) “Alternative”: l = 5.5, TSYM = TQCD/31/4 Start loss at thermalization time t0; end loss at Tc WHDG convolved radiative and elastic energy loss as = .3 WHDG radiative energy loss (similar to ASW) = 40, 100 Use realistic, diffuse medium with Bjorken expansion PHOBOS (dNg/dy = 1750); KLN model of CGC (dNg/dy = 2900) WWND 2008

LHC c, b RAA pT Dependence WH, M. Gyulassy, arXiv:0706.2336 Naïve expectations met in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST Significant rise in RAA(pT) for pQCD Rad+El Large suppression leads to flattening Use of realistic geometry and Bjorken expansion allows saturation below .2 LHC Prediction Zoo: What a Mess! Let’s go through step by step Unfortunately, large suppression pQCD similar to AdS/CFT WWND 2008

An Enhanced Signal But what about the interplay between mass and momentum? Take ratio of c to b RAA(pT) pQCD: Mass effects die out with increasing pT Ratio starts below 1, asymptotically approaches 1. Approach is slower for higher quenching ST: drag independent of pT, inversely proportional to mass. Simple analytic approx. of uniform medium gives RcbpQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27 Ratio starts below 1; independent of pT RcbpQCD(pT) ~ 1 - as n(pT) L2 log(Mb/Mc) ( /pT) WWND 2008

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] WWND 2008

Worldsheet boundary Spacelike if g > gcrit Not So Fast! Speed limit estimate for applicability of AdS drag g < gcrit = (1 + 2Mq/l1/2 T)2 ~ 4Mq2/(l T2) Limited by Mcharm ~ 1.2 GeV Similar to BH LPM gcrit ~ Mq/(lT) No Single T for QGP smallest gcrit for largest T T = T(t0, x=y=0): “(” largest gcrit for smallest T T = Tc: “]” D7 Probe Brane Q “z” x5 Worldsheet boundary Spacelike if g > gcrit Trailing String “Brachistochrone” D3 Black Brane WWND 2008

LHC RcAA(pT)/RbAA(pT) Prediction (with speed limits) WH, M. Gyulassy, arXiv:0706.2336 [nucl-th] T(t0): (O), corrections unlikely for smaller momenta Tc: (|), corrections likely for higher momenta WWND 2008

Measurement at RHIC Future detector upgrades will allow for identified c and b quark measurements RHIC production spectrum significantly harder than LHC y=0 RHIC LHC NOT slowly varying No longer expect pQCD dRAA/dpT > 0 Large n requires corrections to naïve Rcb ~ Mc/Mb WWND 2008

RHIC c, b RAA pT Dependence WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well WWND 2008

RHIC Rcb Ratio pQCD pQCD AdS/CFT AdS/CFT WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] Wider distribution of AdS/CFT curves due to large n: increased sensitivity to input parameters Advantage of RHIC: lower T => higher AdS speed limits WWND 2008

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 WWND 2008

Backups WWND 2008

Geometry of a HI Collision Medium density and jet production are wide, smooth distributions Use of unrealistic geometries strongly bias results S. Wicks, WH, M. Djordjevic, M. Gyulassy, Nucl.Phys.A784:426-442,2007 1D Hubble flow => r(t) ~ 1/t => T(t) ~ 1/t1/3 M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005 WWND 2008

Langevin Model Langevin equations (assumes gv ~ 1 to neglect radiative effects): Relate drag coef. to diffusion coef.: IIB Calculation: Use of Langevin requires relaxation time be large compared to the inverse temperature: AdS/CFT here WWND 2008

But There’s a Catch (II) Limited experimental pT reach? ATLAS and CMS do not seem to be limited in this way (claims of year 1 pT reach of ~100 GeV) but systematic studies have not yet been performed ALICE Physics Performance Report, Vol. II WWND 2008

LHC p Predictions Our predictions show a significant increase in RAA as a function of pT This rise is robust over the range of predicted dNg/dy for the LHC that we used This should be compared to the flat in pT curves of AWS-based energy loss (next slide) We wish to understand the origin of this difference WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation WWND 2008

Asymptopia at the LHC Asymptotic pocket formulae: DErad/E ~ a3 Log(E/m2L)/E DEel/E ~ a2 Log((E T)1/2/mg)/E WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation WWND 2008

K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) WWND 2008

Pion RAA Is it a good measurement for tomography? Yes: small experimental error Claim: we should not be so immediately dis-missive of the pion RAA as a tomographic tool Maybe not: some models appear “fragile” WWND 2008

Fragility: A Poor Descriptor All energy loss models with a formation time saturate at some RminAA > 0 The questions asked should be quantitative : Where is RdataAA compared to RminAA? How much can one change a model’s controlling parameter so that it still agrees with a measurement within error? Define sensitivity, s = min. param/max. param that is consistent with data within error WWND 2008

Different Models have Different Sensitivities to the Pion RAA GLV: s < 2 Higher Twist: DGLV+El+Geom: AWS: s ~ 3 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation WWND 2008

WWND 2008 T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007) WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation WWND 2008

A Closer Look at ASW The lack of sensitivity needs to be more closely examined because (a) unrealistic geometry (hard cylinders) and no expansion and (b) no expansion shown against older data (whose error bars have subsequently shrunk (a) (b) K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) WWND 2008

Surface Bias vs. Surface Emission Surface Emission: one phrase explanation of fragility All models become surface emitting with infinite E loss Surface Bias occurs in all energy loss models Expansion + Realistic geometry => model probes a large portion of medium A. Majumder, HP2006 S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076 WWND 2008

A Closer Look at ASW Difficult to draw conclusions on inherent surface bias in AWS from this for three reasons: No Bjorken expansion Glue and light quark contributions not disentangled Plotted against Linput (complicated mapping from Linput to physical distance) A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005) WWND 2008