heavy quark energy loss in pqcd and sym plasmas
DESCRIPTION
Heavy quark energy loss in pQCD and SYM plasmas. Cyrille Marquet. Columbia University. based on F. Dominguez, C. Marquet, A. Mueller, B. Wu and B.-W. Xiao, arXiv:0803.3234, Nucl. Phys. A811 (2008) 197. Outline. - PowerPoint PPT PresentationTRANSCRIPT
Heavy quark energy loss in pQCD and SYM plasmas
Cyrille Marquet
Columbia University
based on F. Dominguez, C. Marquet, A. Mueller, B. Wu and B.-W. Xiao, arXiv:0803.3234, Nucl. Phys. A811 (2008) 197
Outline
• Heavy quark energy loss in pQCDmedium induced gluon radiation and dead cone effectthe saturation scale of the pQCD plasma
• Heavy quark energy loss in SYM theorythe AdS/CFT correspondencethe trailing string picturethe saturation scale of the strongly coupled SYM plasma
• DIS off the SYM plasmathe structure functions and the saturation scale
• Quarkonium dissociation in the SYM plasmathe screening length and the saturation scale
Heavy quark energy loss in a weakly-coupled QCD plasma
The heavy quark wave function
its transverse momentum is denoted
• consider a heavy quark of mass M and energy E
the heavy quark wave function at lowest order
the energy of the gluon is denoted
the virtuality of the fluctuations is measured by their lifetime or coherence time
short-lived fluctuations are highly virtual
the probability of this fluctuation is
Lorentz factor of the heavy quark
• the dead cone effectcompared to massless quarks, the fluctuation with are suppressed
absence of radiation in a forward cone
Medium induced gluon radiation
only property of the medium needed
• multiple scattering of the radiated gluon
this is how the virtual gluon in the heavy quark wave function is put on shell
it becomes emitted radiation if it picks up enough transverse momentum
the accumulated transverse momentum picked up by a gluon of coherence time
mean free path
average pT picked up
in each scattering
only the fluctuations which pick up enough transverse momentum are freed
this discussion is also valid for light quarks
• the saturation scale of the pQCD plasma
Heavy quark energy loss
for heavy quarks, the radiated gluons which dominate the energy loss have
• the case of infinite extend matter
and
this allows to express Qs in terms of T and E/M only
and
the relevant fluctuations in the wave function have a smaller energy
• the case of finite extend matter of length
the maximum transverse momentum that gluons can pick-up is
the radiated gluons which dominate the energy loss have
and the heavy quark energy loss is
Indications from RHIC data
suppression similar to light
hadron suppression at high pT
PHENIX, PRL 172301 (2007)PHENIX, PRL 172301 (2007)
STAR, PRL 192301 (2007)STAR, PRL 192301 (2007)
• light-quark energy loss
• heavy-quark energy loss
comparisons between models and data indicate the need for
however, for a weakly-coupled pQCD plasma we expect
Heavy quark energy loss in astrongly-coupled SYM plasma
Motivations• it is unclear if the perturbative QCD approach can describe the
suppression of high-pT particles in Au+Au collisions at RHIC, in particular for heavy-quark energy loss:
high-pT electrons from c and b decays indicate similar suppression for light and heavy quarks, while the dead-cone effect in pQCD
implies a weaker suppression for heavier quarks
this motivates to think about a strongly-coupled plasma
• for the N=4 SYM theory, the AdS/CFT correspondence allows to investigate the strong coupling regime
limited tools to address the QCD dynamics at strong coupling
the results for SYM may provide insight on strongly-coupled gauge theories, some aspects may be universal
in this work, we consider the trailing string picture of heavy-quark energy lossby Herzog et al., and address the question of finite-extend matter
The AdS/CFT correspondence
strong coupling means ‘t Hooft limit in gauge theory:
• the N=4 SYM theory: 1 gauge field, 4 fermions, 6 scalars, all adjoint
in the large Nc limit, the ‘t Hooft coupling λ controls the theory
classical gravity is a good approximation
• the equivalent string theory in AdS5 x S5 : weak coupling and small curvature
fifth dimension
curvature radius of AdS5
T = Hawking temperature of the black
hole = temperature of the SYM plasma
the SYM theory lives on the boundary at r = infinity
horizon
• the AdS5 black-hole metric
quantum fluctuations in the SYM theory are mapped onto the 5th dimension
• a heavy quark lives on a brane atwith a string attached to it, hanging down to the horizon
• points on the string can be identified to quantum fluctuationsin the quark wave function with virtuality ~ u
• the string dynamics is given by the Nambu-Goto action:
A heavy quark in the plasma
induced metric on the worldsheetarea of the string worldsheet
equation of motion:
rate at which energy flows down the string:
• parameterization:
The trailing string solutionassume the quark is being pulled at a constant velocity v:
solution (known as the trailing string) :
Herzog et al (2006)Gubser et al (2006)Liu et al (2006)
corresponding rate of energy flow down the string:
this is naturally understood after this key observation:the part of string above is genuinely part of heavy quarkthe part of string below is emitted radiation
limiting velocity: the picture is valid for meaning
one has, similarly to the weak-coupling result:
Energy loss in the partonic picture
• this picture is obtained from several results - the part of the string below Qs is not causally connected with the part of the string above: Qs corresponds to a horizon in the rest frame of the string
- when computing the stress-tensor on the boundary:
the trailing string is a source of metric perturbations in the bulk which give
the energy density is unchanged around the heavy quark up to distances ~ 1/Qs
one gets forGubser et al (2006), Chesler and Yaffe (2007)
the radiated partons in the wavefunction have transverse momentum and energy
giving the maximum (dominant) values and
and therefore a coherence time
• simple derivation of the energy loss:
thenthis does not give the overall coefficient
but it gets the right v and T dependences
The case of finite-extend matterwe would like to know the medium length L dependence of the energy loss
exact calculation difficult to set up, need another scale in the metric
using the partonic picture, we can get the L dependence
the heavy quark is bare when produced and then builds its wave function while interacting with the medium, how to set this up in AdS ?
describe the creation with a brief acceleration to the desired speed
then stopping the acceleration triggers the building of the wavefunctionour proposal:
key issue: the time it takes for the heavy quark to build the partonic fluctuations which will be freed and control the energy loss
if the ones that dominate in the infinite matter case have time to build before
the heavy quark escapes the plasma, then the result is as before:
if not, the hardest fluctuations which could be build dominate, and one finds:
The accelerating string
a can be interpreted as the acceleration
of the quark solution
the equation of motion at zero temperature:
the acceleration acts like an effective temperature (Unruh effect): the part of string below u =a is not causally connected with the part of the string above
at finite T, this separation is not affected, provided T << a
Xiao (2008)
when stopping the acceleration, this separation goes down as :the heavy quark is building its wavefunction
when the time it takes to build the fluctuations which dominate the energy loss in the infinite matter case), the separation crosses Qs, hence:
a
v
if , the result is as before
if , then softer fluctuations dominate:
with
for , only soft components contributeto the heavy quark
Summary
infinite matter or
finite matter with
QCD at weak coupling SYM at strong coupling
heavy-quark energy loss
results for energy loss
coherence time
- same parametric form for the energy loss in pQCD and SYM at strong coupling !
- first estimate of the plasma length dependence of heavy quark energy loss
- one easily gets the infinite matter result which is non trivial to get with a direct calculation
About pT broadening
- same parametric form for the pT broadening in pQCD and SYM at strong coupling !
- in the finite matter case, (at weak-coupling: )
Gubser (2007), Solana and Teaney (2007)
results for pT broadening
- at strong coupling: no multiple scattering with local transfer of momentum no equivalent of
- again, similar to radiative pT broadening in pQCD
for infinite or finite length plasma
DIS off the SYM plasmaY. Hatta, E. Iancu and A. Mueller, arXiv:0710.5297, JHEP 0801 (2008) 063
DIS off the SYM plasma• the retarded current-current correlator
its imaginary part gives the plasma structure functions
the current-plasma interaction is described by the propagation
of a vector field which obeys Maxwell equations in AdS5
R-current, equivalent of EM
current for SYM theory
• properties of the current
it probes plasma fluctuations with energy fraction
assume high energy high virtuality:
coherence time of the current
The saturation scale
structure functions exponentially small, no large-x partons
for , the vector field is prevented to penetrate AdS space by a potential barrier
decreasing x at fixed Q2, the barrier disappears for
structure functions saturated, all the partons at small x
• a partonic picture
• the saturation scale
consistent with what we found in the energy loss case
• the energy density
dominates
for a given , all partons in the plasma have
Quarkonium dissociationin the SYM plasma
H. Liu, K. Rajagopal and U.A. Wiedemann, hep-ph/0612168, JHEP 0703 (2007) 066
The quark-antiquark potential• the quark and antiquark live on a brane at
each hooked to the end of a string hanging down in the fifth dimension
• the string dynamics is given by the Nambu-Goto action
parameterization:
for small L, there is string connecting the
pair, hanging down in the fifth dimension
quark-antiquark potential
substraction of S0 so that
at small L
obtained from implicit equation
The screening length
the transition between the two regimes defines the screening length
the quark and antiquark are screened from each other when the string breaks
for large L, there is no solution , and the minimum of the
action is obtained with two strings hanging down to the horizon
consistent with what we found in the energy loss case
up a to a distance ~ 1/Qs away from the quark, the plasma is not felt
in fact before the string breaks, it doesn’t tilt in the direction of motion of the pair
forone finds
Conclusions• same parametric form for the heavy quark energy loss and pT
broadening when written in terms of the saturation scale Qs
• only the saturation scale differs between pQCD and SYM theories
• the plasma length L dependence is stronger in SYM compared to pQCD, for both the energy loss and pT broadening
• Qs appears in other calculations, deep inelastic scattering and quarkonium dissociation