Heavy quark diffusion in strong magnetic fields at weak coupling and implications for elliptic flow
In this paper, we compute the momentum diffusion coefficients of heavy quarks, κ _{∥} and κ _{⊥}, in a strong magnetic field B along the directions parallel and perpendicular to B, respectively, at the leading order in QCD coupling constant α _{s}. We consider a regime relevant for the relativistic heavy ion collisions, α _{s}eB << T ^{2} << eB, so that thermal excitations of light quarks are restricted to the lowest Landau level (LLL) states. In the vanishing lightquark mass limit, we find κ ^{LO} _{⊥} ∝ α ^{2} _{s}TeB in the leading order that arises from screened Coulomb scatterings with (1+1)dimensional LLL quarks, while κ _{∥} gets no contribution from the scatterings with LLL quarks due to kinematic restrictions. We show that the first nonzero leading order contributions to κ ^{LO} _{∥} come from the two separate effects: 1) the screened Coulomb scatterings with thermal gluons, and 2) a finite lightquark mass m _{q}. The former leads to κ ^{LO,gluon} _{∥} ∝ α ^{2} _{s}T ^{3} and the latter to κ ^{LO,massive} _{∥} ∝ α _{s}(α _{s}eB) ^{1/2}m ^{2} _{q}. Based on our results, we propose a new scenario for the large value of heavyquark elliptic flow observedmore »
 Authors:

^{[1]};
^{[2]};
^{[3]};
^{[4]}
 The Univ. of Tokyo, Tokyo (Japan)
 Brookhaven National Lab. (BNL), Upton, NY (United States); Nishina Center, RIKEN, Saitama (Japan)
 Univ. of Illinois, Chicago, IL (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Publication Date:
 Report Number(s):
 BNL1121362016JA
Journal ID: ISSN 24700010; PRVDAQ; R&D Project: PO3
 Grant/Contract Number:
 SC00112704; SC0012704
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 93; Journal Issue: 7; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Riken BNL Research Center
 OSTI Identifier:
 1254122
 Alternate Identifier(s):
 OSTI ID: 1248250
Fukushima, Kenji, Hattori, Koichi, Yee, Ho Ung, and Yin, Yi. Heavy quark diffusion in strong magnetic fields at weak coupling and implications for elliptic flow. United States: N. p.,
Web. doi:10.1103/PhysRevD.93.074028.
Fukushima, Kenji, Hattori, Koichi, Yee, Ho Ung, & Yin, Yi. Heavy quark diffusion in strong magnetic fields at weak coupling and implications for elliptic flow. United States. doi:10.1103/PhysRevD.93.074028.
Fukushima, Kenji, Hattori, Koichi, Yee, Ho Ung, and Yin, Yi. 2016.
"Heavy quark diffusion in strong magnetic fields at weak coupling and implications for elliptic flow". United States.
doi:10.1103/PhysRevD.93.074028. https://www.osti.gov/servlets/purl/1254122.
@article{osti_1254122,
title = {Heavy quark diffusion in strong magnetic fields at weak coupling and implications for elliptic flow},
author = {Fukushima, Kenji and Hattori, Koichi and Yee, Ho Ung and Yin, Yi},
abstractNote = {In this paper, we compute the momentum diffusion coefficients of heavy quarks, κ∥ and κ⊥, in a strong magnetic field B along the directions parallel and perpendicular to B, respectively, at the leading order in QCD coupling constant αs. We consider a regime relevant for the relativistic heavy ion collisions, αseB << T2 << eB, so that thermal excitations of light quarks are restricted to the lowest Landau level (LLL) states. In the vanishing lightquark mass limit, we find κLO⊥ ∝ α2sTeB in the leading order that arises from screened Coulomb scatterings with (1+1)dimensional LLL quarks, while κ∥ gets no contribution from the scatterings with LLL quarks due to kinematic restrictions. We show that the first nonzero leading order contributions to κLO∥ come from the two separate effects: 1) the screened Coulomb scatterings with thermal gluons, and 2) a finite lightquark mass mq. The former leads to κLO,gluon∥ ∝ α2sT3 and the latter to κLO,massive∥ ∝ αs(αseB)1/2m2q. Based on our results, we propose a new scenario for the large value of heavyquark elliptic flow observed in RHIC and LHC. Namely, when κ⊥ >> κ∥, an anisotropy in drag forces gives rise to a sizable amount of the heavyquark elliptic flow even if heavy quarks do not fully belong to an ellipsoidally expanding background fluid.},
doi = {10.1103/PhysRevD.93.074028},
journal = {Physical Review D},
number = 7,
volume = 93,
place = {United States},
year = {2016},
month = {4}
}