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Zero th 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. A Talk in Two Parts. pQCD vs. AdS/CFT Drag
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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
A Talk in Two Parts pQCD vs. AdS/CFT Drag 0th Order Production Radiation WWND 2008
arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions) Testing pQCD vs. AdS/CFT Drag Energy Loss Mechanisms(In Five Slides) 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 • 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 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 • 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 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 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 WWND 2008
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 WWND 2008
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 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 • 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 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 c b M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003 WWND 2008
0th Order % Differences WWND 2008
William Horowitz Columbia University Frankfurt Institute for Advanced Studies (FIAS) February 9, 2008 arXiv:0706.2336 (LHC predictions) arXiv:0710.0703 (RHIC predictions) With many thanks to Miklos Gyulassy and Simon Wicks Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss 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: Y. Akiba for the PHENIX collaboration, hep-ex/0510008 (circa 2005) • 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 • e- RAA too small • Hydro h/s too small • v2 too large A. Drees, H. Feng, and J. Jia, Phys. Rev. C71:034909 (2005) (first by E. Shuryak, Phys. Rev. C66:027902 (2002)) M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006) D. Teaney, Phys. Rev. C68, 034913 (2003) • wQGP not ruled out, but what if we try strong coupling? 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: AdS/CFT S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:0706.0213 J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393 PHENIX, Phys. Rev. Lett. 98, 172301 (2007) • Mach wave-like structures • sstrong=(3/4) sweak, similar to Lattice • h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD • e- RAA ~ p, h RAA; e- RAA(f) 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 = pl1/2T2/2Mq WWND 2008
Energy Loss Comparison D7 Probe Brane t x v Q, m 3+1D Brane Boundary zm = 2pm / l1/2 D3 Black Brane (horizon) zh = pT Black Hole z = 0 • 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 y=0 RHIC LHC • 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) WWND 2008
Looking for a Robust, Detectable Signal erad~as L2 log(pT/Mq)/pT • 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. eAdSindep of pT!! • dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST eST~ 1 - Exp(-m L), m = pl1/2T2/2Mq 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 • 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 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 - asn(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
Not So Fast! x5 “z” • 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 Worldsheet boundary Spacelikeif 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 y=0 RHIC LHC • Future detector upgrades will allow for identified c and b quark measurements • RHIC production spectrum significantly harder than 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 • Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well WH, M. Gyulassy, arXiv:0710.0703 [nucl-th] WWND 2008
RHIC Rcb Ratio • Wider distribution of AdS/CFT curves due to large n: 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 [nucl-th] 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 AdS/CFT here • 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: WWND 2008