Ⅱ-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 50 (2017)

Transport coeﬃcients of quark-gluon plasma in strong magnetic ﬁeld
H. -U. Yee∗1,∗2
The quark-gluon plasma (QGP) created in relativistic heavy-ion collisions is subject to a strong magnetic
ﬁeld produced by heavily charged projectiles, whose
scale is comparable to the temperature of the plasma.
The question whether the magnetic ﬁeld stays longenough to be able to induce interesting eﬀects, such as
chiral magnetic eﬀect, on the plasma observables canbe answered by realistic simulations of magneto hydrodynamics (MHD) that are planned, for example, in theBeam Energy Scan Theory collaboration (BEST). Oneof the key parameters in MHD simulations is electric
conductivity, that should be rotationally asymmetricdue to the magnetic ﬁeld. Other key transport coefﬁcients of the magnetized QGP that aﬀect high energy probes such as jets and heavy quarks include jet
quenching parameter q̂ and heavy quark momentum
diﬀusion constant κ. We report our attempts on computing them in complete leading order of perturbative
QCD1–3) , and for some cases, also in strong couplingby AdS/CFT correspondence2) .
We work in the perturbative regime of αs eB T 2  eB, where the ﬁrst inequality turns out to be essential to have a consistent Hard Thermal Loop (HTL)
power counting scheme, and the second inequality
brings us a simpliﬁcation of working in the lowest Landau level (LLL) approximation for the quarks1) . The
LLL quarks are eﬀectively 1+1 dimensional and carry
only longitudinal currents ﬂowing along the magneticﬁeld direction. Their thermal density is ∼ (eB) × T ,a product of transverse and longitudinal density ofstates, that dominates over the thermal density ofhard gluons ∼ T 3 . This implies that the dominant
HTL self-energy for gluons comes from the 1-loop LLL
hard quark contribution that is of order Σ ∼ αs eB,
which sets a scale of dynamical screening m2D ∼ αs eB.
Since m2D  T 2 due to our assumption, hard particles of typical momentum T keep their free dispersion
relation at leading order, while the soft gluons thatare exchanged in infrared-sensitive scattering processes
should include re-summation of HTL self-energy Σ:
this gives us a consistent HTL power counting scheme
we use for our leading order computations1) .
Electric conductivity in a magnetized plasma isasymmetric, with longitudinal conductivity being
dominant over transverse one due to 1+1 dimensional
nature of LLL states. Since the transverse dynamics
is intrinsically quantum, we can use a semi-classicalpicture of kinetic theory of LLL quarks valid in leading order computation for only longitudinal conductivity3) . In a massless quark limit, neglecting higher∗1∗2

Department of Physics, University of Illinois
RIKEN Nishina Center- 123 -order eﬀects from QCD sphalerons, the chiral anomaly
dictates that a parallel electric and magnetic ﬁeld imply a diverging longitudinal electric current, and hence
an inﬁnite longitudinal conductivity. The key dynamics taming this is the axial charge relaxation with therate γA ∼ αs m2q /T , and the longitudinal conductivity
is parametrically given as σL ∼ e2 (eB)2 /(χγA ) whereχ is the charge susceptibility which grows linearly in
B in LLL approximation χ ∼ (eB), giving us an estimate3) σL ∼ e2 (eB)T /(αs m2q ). Our detailed computation reveals that the leading process in the collision
term in the eﬀective kinetic theory is 1-to-2 gluon decay into quark-antiquark pair and vice versa: g ↔ q+q̄,
which results in σL ∼ e2 (eB)T /(αs m2q log(T /mq )) inmq /T  1 limit.
1)
For the heavy quark momentum diusion
diﬀusionconstantconstant1)2)2)andandthethejetjetquenchingquenchingparameterparameter ,, wewe computecomputethem for both transverse and longitudinal directions
with respect to magnetic ﬁeld: κ⊥, and q̂⊥, . The
leading order process is the t-channel 2-to-2 scatterings of heavy quark/energetic jet with hard LLL
quarks via soft gluon exchange, that are enhanced
by infrared divergence tamed by the HTL self-energy
Σ. This is true for κ⊥ and q̂⊥, , giving us the re3
sults of κ⊥ ∼ αs2 (eB)T log(1/αs ), q̂⊥ ∼ αs2 (eB) 2 +222αs (eB)T log(T /αs eB) and q̂ ∼ αs (eB)T log(1/αs ),respectively. It should be noted that q̂⊥ does not vanish even at zero temperature: this is because a QCD
gluon ﬁeld from a jet can create a LLL quark-antiquark
pair from the vacuum, which is consistent with 1+1 dimensional kinematics of LLL states2) . The physics issimilar to the Schwinger mechanism of pair creation.
However, the longitudinal momentum diﬀusion κturns out to vanish at this order in massless quark limit
due to 1+1 dimensional kinematics of LLL states1) :only a light-like, longitudinal exchanged momentum ispossible, q 0 = ±q 3 , and since κ is proportional to thestatic gluon spectral density at q 0 = 0, a longitudinal
momentum transfer vanishes. The ﬁrst non-vanishing
contribution comes either from the t-channel scatterings with hard gluons or the eﬀect of a ﬁnite quark
mass mq , the former being κ ∼ αs2 T 3 log(1/αs ) and1
the latter κ ∼ αs (αs eB) 2 m2q , respectively1) .
References
1) K. Fukushima, K. Hattori, H. U. Yee and Y. Yin, Phys.
Rev. D 93, no. 7, 074028 (2016).
2) S. Li, K. A. Mamo and H. U. Yee, Phys. Rev. D 94, no.
8, 085016 (2016).
3) K. Hattori, S. Li, D. Satow and H. U. Yee, Phys. Rev.
D 95, no. 7, 076008 (2017).