1. Andrej Ficnar Columbia University
Falling strings and Light quark jet quenching at LHC
Andrej Ficnar
Columbia University
Hard Probes 2012 May 28, 2012

2. Outline Introduction: AdS/CFT and light quarks
Energy loss in time-dependent string configurations
Light quark energy loss
Extracting RAA
Higher derivative corrections
Work in progress: JP metric, …
Conclusions
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3. AdS/CFT in a nutshell
AdS/CFT conjecture: equivalence of (3+1)-dim SYM and type IIB string theory on
In this way, one can study strongly coupled gauge theories ( ) by studying classical two-derivative (super)gravity
Introduce finite temperature by a black hole in
Quark of mass is dual to a string in the bulk with an endpoint attached to a D7-brane ending at
Maldacena, 1998
holographic dictionary
take ‘t Hooft limit
Witten, 1998 D7
Karch & Katz, 2002
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4. Light quarks in AdS/CFT
For light quarks, approaches  D7 brane fills all of the AdS-BH geometry  falling strings
Maximum stopping distance:
Cannot be used for extracting instantaneous energy loss
Chesler et al., 2009
Gubser et al., 2008
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5. Time-dep. strings & energy loss
AF, 2012
Dynamics of the string governed by the classical Polyakov action
Spacetime momentum currents:
Flux of the momentum through some curve on the worldsheet:
For a constant- curve (in parametrization):
To use this formula, therefore, we must be in a coordinate system where the coordinate of the points (on the string) we want to evaluate the energy loss on, does not change in time
Energy loss
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6. Time-dep. strings & energy loss
Write this in coordinate system in which those points have a constant coordinate and express it in terms of coordinates where those points are described by (e.g. the radial coordinate):
For example, for falling strings, we could choose:
AF, 2012
true energy loss
‘apparent’ energy loss
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7. Falling strings energy loss
For a falling string in : no ‘Bragg peak’
This correction does not affect the maximum stopping distance
‘uncorrected’
true
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8. Extracting RAA
motivated by Horowitz, Gyulassy, 2011
Model phenomenologically relevant part of the energy loss as:
Stopping distance:
Then:
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9. Extracting RAA
For different initial conditions, keeping the energy constant:
For and :
Preliminary numerics suggest:
Looks like pQCD
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10. Extracting RAA
Compute RAA in a dynamical, expanding plasma with Glauber initial conditions:
Here:
We know so for we would need
Correct shape, but jet quenching seems to be too strong
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11. Higher derivative corrections
Model generic higher derivative corrections to the gravity sector of AdS with, for example, the Gauss-Bonnet term:
Analytic solution for the metric is known:
Because of this: and
Cai, 2002
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12. Higher derivative corrections
Shear viscosity to all orders in
Hint: negative might work, indeed:
Perturbative expansion of stopping distance:
Myers et al., 2008
(to avoid causality violations)
but
(energy positivity)
Hofman & Maldacena, 2008
magnitude increase
(collection of small effects)
new scaling?
AF, Noronha, Gyulassy, to appear
Falling strings and Light quark jet quenching at LHC| Andrej Ficnar | Hard Probes 2012
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13. Higher derivative corrections
What do numerics say:
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14. Work in progress – JP metric
Janik & Peschanski, 2006
Janik – Peschanski metric, dual to perfect fluid hydrodynamics:
Trailing strings (heavy quarks):
Falling strings (light quarks):
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15. Conclusions
Formalism for treating energy loss in an arbitrary string configuration
Light quarks in AdS/CFT might look like in pQCD
Model for extracting RAA
seems to have a correct shape, but the magnitude is too low
Higher derivative corrections can increase it by a factor of ~2
How to make RAA higher; or, how to make calculations more realistic:
Janik-Peschanski metric
Phenomenological parameters
Alternative scalings
Non-conformal geometry
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