Shock geometry and particle acceleration timescales in gradual SEP events e.g., 1/20/05 event
Shock Treatment: Heavy Quark Energy Loss in a Novel Geometry
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Transcript of Shock Treatment: Heavy Quark Energy Loss in a Novel Geometry
Quark Matter 2009 14/3/09
William Horowitz
Shock Treatment: Heavy Quark Energy Loss in a Novel
GeometryWilliam HorowitzThe Ohio State University
April 3, 2009
With many thanks to Yuri Kovchegov and Ulrich Heinz
Quark Matter 2009 24/3/09
William Horowitz
pQCD Success in High-pT at RHIC:
– Consistency: RAA()~RAA()
– Null Control: RAA()~1
– GLV Calculation: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dN/dy
Y. Akiba for the PHENIX collaboration, hep-ex/0510008
(circa 2005)
Quark Matter 2009 34/3/09
William Horowitz
Trouble for High-pT wQGP Picture– v2 too small – NPE supp. too large
STAR, Phys. Rev. Lett. 98, 192301 (2007)
0 v2
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
NPE v2
Pert. at LHC energies?
C. Vale, QM09 Plenary (analysis by R. Wei)
WHDG
Quark Matter 2009 44/3/09
William Horowitz
Motivation for High-pT AdS• Why study AdS E-loss models?
– Many calculations vastly simpler• Complicated in unusual ways
– Data difficult to reconcile with pQCD– pQCD quasiparticle picture leads to
dominant q ~ ~ .5 GeV mom. transfers=> Nonperturbatively large s
• Use data to learn about E-loss mechanism, plasma properties– Domains of self-consistency crucial for
understanding
Quark Matter 2009 54/3/09
William Horowitz
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
Quark Matter 2009 64/3/09
William Horowitz
AdS/CFT Energy Loss Models I– Langevin Diffusion
• Collisional energy loss for heavy quarks
• Restricted to low pT
• pQCD vs. AdS/CFT computation of D, the diffusion coefficient
– ASW/LRW model• Radiative energy loss model for all parton
species• pQCD vs. AdS/CFT computation of• Debate over its predicted magnitude
Moore and Teaney, Phys.Rev.C71:064904,2005Casalderrey-Solana and Teaney, Phys.Rev.D74:085012,2006; JHEP 0704:039,2007
BDMPS, Nucl.Phys.B484:265-282,1997Armesto, Salgado, and Wiedemann, Phys. Rev. D69 (2004) 114003Liu, Ragagopal, Wiedemann, PRL 97:182301,2006; JHEP 0703:066,2007
Quark Matter 2009 74/3/09
William Horowitz
AdS/CFT Energy Loss Models II
String Drag calculation– Embed string rep. quark/gluon in AdS geom.– Includes all E-loss modes (difficult to
interpret)– Gluons and light quarks– Empty space HQ calculation– Previous HQ: thermalized QGP plasma, temp.
T,
Gubser, Phys.Rev.D74:126005,2006Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013, 2006
Kharzeev, arXiv:0806.0358 [hep-ph]
Gubser, Gulotta, Pufu, Rocha, JHEP 0810:052, 2008Chesler, Jensen, Karch, Yaffe, arXiv:0810.1985 [hep-th]
Quark Matter 2009 84/3/09
William Horowitz
Energy Loss Comparison
– AdS/CFT Drag:dpT/dt ~ -(T2/Mq) pT
– Similar to Bethe-HeitlerdpT/dt ~ -(T3/Mq
2) pT
– Very different from LPMdpT/dt ~ -LT3 log(pT/Mq)
tx
Q, m v
D7 Probe Brane
D3 Black Brane(horizon)
3+1D Brane Boundary
Black Holez =
zh = 1/T
zm = 1/2/2m
z = 0
Quark Matter 2009 94/3/09
William Horowitz
LHC RcAA(pT)/Rb
AA(pT) Prediction
• Individual c and b RAA(pT) predictions:
– 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
– Distinguish rad and el contributions?WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
Quark Matter 2009 104/3/09
William Horowitz
Universality and Applicability
• How universal are th. HQ drag results?– Examine different theories– Investigate alternate geometries
• Other AdS geometries– Bjorken expanding hydro– Shock metric
• Warm-up to Bj. hydro• Can represent both hot and cold nuclear
matter
Quark Matter 2009 114/3/09
William Horowitz
New Geometries
Albacete, Kovchegov, Taliotis,JHEP 0807, 074 (2008)
J Friess, et al., PRD75:106003, 2007
Constant T Thermal Black Brane
Shock GeometriesNucleus as Shock
Embedded String in Shock
DIS
Q
vshock
x
zvshock
x
zQ
Before After
Bjorken-Expanding Medium
Quark Matter 2009 124/3/09
William Horowitz
Standard Method of Attack• Parameterize string worldsheet
– X(, )
• Plug into Nambu-Goto action
• Varying SNG yields EOM for X
• Canonical momentum flow (in , )
Quark Matter 2009 134/3/09
William Horowitz
New in the Shock• Find string solutions in HQ rest
frame– vHQ = 0
• Assume static case (not new)– Shock wave exists for all time– String dragged for all time
• X = (t, x(z), 0,0, z)
• Simple analytic solutions:– x(z) = x0, x0 ±
½ z3/3
Quark Matter 2009 144/3/09
William Horowitz
Shock Geometry Results• Three t-ind. solutions (static gauge):
X = (t, x(z), 0,0, z)
– x(z) = x0, x0 ± ½ z3/3
• Constant solution unstable• Time-reversed negative x solution unphysical• Sim. to x ~ z3/3, z << 1, for const. T BH
geom.
x0 ½ z3/3 x0 ½ z3/3
x0
vshock
Qz = 0
z = x
Quark Matter 2009 154/3/09
William Horowitz
HQ Momentum Loss
Relate to nuclear properties– Use AdS dictionary
• Metric in Fefferman-Graham form: ~ T--/Nc2
– T’00 ~ Nc2 4
• Nc2 gluons per nucleon in shock
• is typical mom. scale; typical dist. scale
x(z) = ½ z3/3 =>
Quark Matter 2009 164/3/09
William Horowitz
Frame Dragging• HQ Rest Frame • Shock Rest Frame
vshMq
1/
vq = -vsh
Mq
i i vsh = 0vq = 0
– Change coords, boost T into HQ rest frame:
• T-- ~ Nc2 4Nc
2 4 (p’/M)2
• p’ ~ M: HQ mom. in rest frame of shock
– Boost mom. loss into shock rest frame
– 0t = 0:
Quark Matter 2009 174/3/09
William Horowitz
Put Together• This leads to
• We’ve generalized the BH solution to both cold and hot nuclear matter E-loss
–Recall for BH:–Shock gives exactly the same drag as BH for = T
Quark Matter 2009 184/3/09
William Horowitz
Shock Metric Speed Limit• Local speed of light (in HQ rest frame)
– Demand reality of point-particle action
• Solve for v = 0 for finite mass HQ– z = zM = ½/2Mq
– Same speed limit as for BH metric when = T
Quark Matter 2009 194/3/09
William Horowitz
Conclusions and Outlook– Use data to test E-loss mechanism
• RcAA(pT)/Rb
AA(pT) wonderful tool
– Calculated HQ drag in shock geometry• For = T, drag and speed limit identical to BH• Generalizes HQ drag to hot and cold nuclear matter
– Unlike BH, quark mass unaffected by shock• Quark always heavy from strong coupling dressing?• BH thermal adjustment from plasma screening IR?
– Future work:• Time-dependent shock treatment• AdS E-loss in Bjorken expanding medium
Quark Matter 2009 204/3/09
William Horowitz
Backup Slides
Quark Matter 2009 214/3/09
William Horowitz
Canonical Momenta
Quark Matter 2009 224/3/09
William Horowitz
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-(pT))n(pT),
where pf = (1-)pi (i.e. = 1-pf/pi)
y=0
RHIC
LHC
Quark Matter 2009 234/3/09
William Horowitz
– 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: pQCD 0 vs. AdS indep of pT!!
• dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
rad s L2 log(pT/Mq)/pT
Looking for a Robust, Detectable Signal
ST 1 - Exp(- L), = T2/2Mq
S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006
Quark Matter 2009 244/3/09
William Horowitz
Model Inputs– AdS/CFT Drag: nontrivial mapping of QCD to SYM
• “Obvious”: s = SYM = const., TSYM = TQCD
– D 2T = 3 inspired: s = .05– pQCD/Hydro inspired: s = .3 (D 2T ~ 1)
• “Alternative”: = 5.5, TSYM = TQCD/31/4
• Start loss at thermalization time 0; end loss at Tc
– WHDG convolved radiative and elastic energy loss• s = .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)
Quark Matter 2009 254/3/09
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 and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
Quark Matter 2009 264/3/09
William Horowitz
• 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
An Enhanced Signal
RcbpQCD(pT) 1 - s n(pT) L2 log(Mb/Mc) ( /pT)
Quark Matter 2009 274/3/09
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
– Distinguish rad and el contributions?WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
Quark Matter 2009 284/3/09
William Horowitz
Additional Discerning Power
– Adil-Vitev in-medium fragmentation rapidly approaches, and then broaches, 1» Does not include partonic E-loss, which will be nonnegligable as ratio goes to unity
– Higgs (non)mechanism => Rc/Rb ~ 1 ind. of pT
– Consider ratio for ALICE pT reachmc = mb = 0
Quark Matter 2009 294/3/09
William Horowitz
• Speed limit estimate for applicability of AdS drag– < crit = (1 + 2Mq/1/2 T)2
~ 4Mq2/(T2)
• Limited by Mcharm ~ 1.2 GeV
• Similar to BH LPM– crit ~ Mq/(T)
• No single T for QGP
Not So Fast!Q D7 Probe Brane
Worldsheet boundary Spacelikeif > crit
TrailingString
“Brachistochrone”
z
x
D3 Black Brane
Quark Matter 2009 304/3/09
William Horowitz
LHC RcAA(pT)/Rb
AA(pT) Prediction(with speed limits)
– T(0): (, highest T—corrections unlikely for smaller momenta
– Tc: ], lowest T—corrections likely for higher momenta
WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
Quark Matter 2009 314/3/09
William Horowitz
Derivation of BH Speed Limit I
• Constant HQ velocity– Assume const. v kept by F.v
– Critical field strength Ec = M2/½
• E > Ec: Schwinger pair prod.
• Limits < c ~ T2/M2
– Alleviated by allowing var. v• Drag similar to const. v
z = 0
zM = ½ / 2M
zh = 1/T
EF.v = dp/dt
dp/dt
Q
Minkowski Boundary
D7
D3
v
J. Casalderrey-Solana and D. Teaney, JHEP 0704, 039 (2007)
Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013 (2006)z =
Quark Matter 2009 324/3/09
William Horowitz
Derivation of BH Speed Limit II• Local speed of light
– BH Metric => varies with depth z• v(z)2 < 1 – (z/zh)4
– HQ located at zM = ½/2M
– Limits < c ~ T2/M2
• Same limit as from const. v
– Mass a strange beast• Mtherm < Mrest
• Mrest Mkin
– Note that M >> T
z = 0
zM = ½ / 2M
zh = 1/T
EF.v = dp/dt
dp/dt
Q
Minkowski Boundary
D7
D3
v
S. S. Gubser, Nucl. Phys. B 790, 175 (2008)
z =
Quark Matter 2009 334/3/09
William Horowitz
Trouble for High-pT wQGP Picture– v2 too small – NPE supp. too large
STAR, Phys. Rev. Lett. 98, 192301 (2007)
0 v2
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
NPE v2
Pert. at LHC energies?
C. Vale, QM09 Plenary (analysis by R. Wei)
WHDG dN/dy = 1400
Quark Matter 2009 344/3/09
William Horowitz
Measurement at RHIC– Future detector upgrades will allow for
identified c and b quark measurements
y=0
RHIC
LHC
• • NOT slowly varying
– No longer expect pQCD dRAA/dpT > 0
• Large n requires corrections to naïve
Rcb ~ Mc/Mb
– RHIC production spectrum significantly harder than LHC
Quark Matter 2009 354/3/09
William Horowitz
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]
Quark Matter 2009 364/3/09
William Horowitz
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
WH, M. Gyulassy, arXiv:0710.0703 [nucl-th]
pQCD
AdS/CFT
pQCD
AdS/CFT
Quark Matter 2009 374/3/09
William Horowitz
HQ Momentum Loss in the Shock
• Must boost into shock rest frame:• Relate to nuclear properties
– Use AdS dictionary• Metric in Fefferman-Graham form: ~ T--/Nc
2
– T00 ~ Nc2 4
• Nc2 gluons per nucleon in shock
• is typical mom. scale; typical dist. Scale
– Change coords, boost into HQ rest frame:• T-- ~ Nc
2 4(p/M)2
=> = 4(p/M)2
x(z) = ½ z3/3 =>
Quark Matter 2009 384/3/09
William Horowitz
HQ Momentum Loss in the Shock
Relate to nuclear properties– Use AdS dictionary: ~ T--/Nc
2
– T-- = (boosted den. of scatterers) x (mom.)
– T-- = Nc2 (3 p+/) x (p+)
• Nc2 gluons per nucleon in shock
• is typical mom. scale; typical dist. scale• p+: mom. of shock gluons as seen by HQ• p: mom. of HQ as seen by shock
=> = 2p+2
x(z) = ½ z3/3 =>
Quark Matter 2009 394/3/09
William Horowitz
HQ Drag in the Shock• HQ Rest Frame • Shock Rest Frame
vshMq
1/
vq = -vsh
Mq
i i vsh = 0vq = 0
–Recall for BH:–Shock gives exactly the same drag as BH for = T
Quark Matter 2009 404/3/09
William Horowitz
HQ Momentum Loss
Relate to nuclear properties– Use AdS dictionary
• Metric in Fefferman-Graham form: ~ T--/Nc2
– T’00 ~ Nc2 4
• Nc2 gluons per nucleon in shock
• is typical mom. scale; typical dist. scale
– Change coords, boost into HQ rest frame:• T-- ~ Nc
2 4Nc2 4 (p’/M)2
• p’ ~ M: HQ mom. in rest frame of shock
x(z) = ½ z3/3 =>
Quark Matter 2009 414/3/09
William Horowitz
Shocking Drag• HQ Rest Frame • Shock Rest Frame
vshMq
1/
vq = -vsh
Mq
i i vsh = 0vq = 0
–Recall for BH:–Shock gives exactly the same drag as BH for = T
• Boost mom. loss into shock rest frame
• Therefore– 0t = 0: