Transverse diffusion at weak coupling

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Transverse diffusion ( ) at weak coupling

• S. Caron-Huot (McGill)

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0. Outline of talk

• 1.1. Motivation for this NLO calculation
• 2. Whats ? (jet quenching parameter)
• 2.1. is an Euclidean quantity !
• 2. Its NLO calculation
• 3. Results
• 4. Conclusion

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1.1. Motivation for NLO calculation

• Classical, nonabelian plasma physics (HTL) is not
  well understood perturbatively.
• Corrections sizeable even at s 0.1
• Pressure, thermal masses, heavy quark
  diffusion...
• Classical effects expansion parameter is
• Is sensitive to this physics?

? Yes! But...
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1.2.Whats ? (Jet quenching param.) ?

• Dynamics of high-energy jets is slow. Many
  collisions occur during their splitting (LPM
  effect)

? Mock them up using a momentum diffusion
coefficient
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1.2. Whats ? (II)
(Guy D. Moore, private comm.)
2) Classical (soft q) contribution always there,
no cut-off needed.
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2.1. Space-like correlatorsEuclidean !

• Consider a space-like correlator, x3gtx0

• Boost along x3 to the frame with x000

• Go Euclidean Matsubara freqs.

• Boost back to the plasma frame

Twisted freqs.
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2.1.But, C(q?) is a space-like correlator!!

• Particles move with v ¼ 1

• Points on different trajectories are space-like
  separated
• Points on a given line are borderline-separated.

Classically, the limit v? 1 should be smooth.
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2.1. C(q?) is space-like! (application)

• At leading order
• All points are space-like separated.Sum over
  Matsubara freqs. and keep only n0(equivalent to
  classical approx. nB(q0)¼ T/q0)

Aurenche, Gelis Zaraket (hep-ph/0204146).
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2.2. Analogy with the pressure

• In principle, calculable within real-time HTL
  theory
• But it can be calculated in Euclidean space!

• Approaches related by sum rules (analyticity in
  q0) Here need analyticity in q.

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2.3.Gauge-invariant definition of C(q?)

• Look at dipole amplitude (Wilson loop)

?
Note dipole is only strictly valid for photon
splitting, q?qg gluon bremsstrahlung would
require evolution of 3 charges,e.g. a qggtltq
state, NOT a dipole.
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2.3. Soft contribution to C(q?)

• Classical physics drop n? 0.
• 3D effective theory (3D gauge field scalar
  A0)
• Wilson line runs along x3, and couples to
  (A3A0)

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2.3. Diagrams
W
With

• The gauge dependence cancels between diagrams
• The NLO correction is proportional to CA.
  It vanishes in the Abelian theory.

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3.1.Result ( _at_ T0.4GeV, s(2¼T)0.3)
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3.2.Result ( _at_ T15GeV, s(2¼T)0.12)
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3.3. Results some numbers
(_at_ T0.4 GeV, s0.3)

• Leading order
• NLO

Note qmax E1/4T3/4 in LPM regime
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Summary

• O(g) corrections to C(q?) (and ) have been
  calculated, and are sizeable.

Future directions

• The classical (soft) piece of C(q?) is
  Euclidean. Investigate it via 3D, Euclidean,
  lattice simulations?
• Calculate O(g2) quantum (hard) contributions?
• (? Systematic effective field theory approach?)
• Clarify the importance of v1 vs. v1 (this
  calculation v1)