Effective quantum kinetic theory for spin transport of fermions with collsional effects
- PDF / 841,203 Bytes
- 52 Pages / 595.276 x 841.89 pts (A4) Page_size
- 59 Downloads / 170 Views
Springer
Received: February Revised: May Accepted: June Published: July
15, 28, 18, 10,
2020 2020 2020 2020
Effective quantum kinetic theory for spin transport of fermions with collsional effects
a
Faculty of Science and Technology, Keio University, Yokohama 223-8522, Japan b Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan c RIKEN Nishina Center, RIKEN, Wako, Saitama 351-0198, Japan d RIKEN iTHEMS, RIKEN, Wako, Saitama 351-0198, Japan
E-mail: [email protected], [email protected], [email protected] Abstract: We systematically derive the collision term for the axial kinetic theory, a quantum kinetic theory delineating the coupled dynamics of the vector/axial charges and spin transport carried by the massive spin-1/2 fermions traversing a medium. We employ the Wigner-function approach and propose a consistent power-counting scheme where the axial-charge distribution function, a non-conserved quantity for massive particles, is accounted as the first-order quantity in the ~ expansion, while the vector-charge distribution function the zeroth-order quantity. This specific power-counting scheme allows us to organize a reduced ~ expansion for the collision term and to formally identity the spindiffusion effect and the spin-polarization effect at the same order. We confirm that the obtained collisional axial kinetic theory smoothly reduces to the chiral kinetic theory in the massless limit, serving as a consistency check. In the absence of electromagnetic fields, we further present the simplified axial kinetic equations suitable for tracking dynamical spin polarization of heavy and light fermions, respectively. As an application to the weakly coupled quark-gluon plasma at high temperature, we compute the spin-diffusion term for massive quarks within the leading-log approximation. The formal expression for the firstorder terms provides a path toward evaluation of the spin polarization effect in quantum chromodynamics. Keywords: Heavy Ion Phenomenology, QCD Phenomenology ArXiv ePrint: 2002.02612
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)070
JHEP07(2020)070
Di-Lun Yang,a Koichi Hattorib and Yoshimasa Hidakac,d
Contents 1 Introduction
1
2 Wigner-function approach with collisions 2.1 Full master equations 2.2 Setting the power-counting scheme 2.3 Effective master equations and constrains
3 3 7 9 11 11 14 15 16
4 Example: spin diffusion of quarks in weakly coupled QGP 4.1 Scattering between massive fermions and a medium 4.2 Weakly coupled QGP and hard-thermal-loop approximation 4.3 SKE and AKE with diffusion effects in the leading-log approximation 4.3.1 Results 4.3.2 Nonrelativistic limit 4.3.3 Consistency checks
17 17 19 21 22 23 23
5 Concluding remarks and outlook
24
A Derivation of the master equations A.1 Spinor decomposition A.2 Eliminating S, P and Sµν
26 26 30
B Angular-momentum decomposition for fermions and spin polarization
31
C Decomposition of the collision term in AKE
32
D Derivation of t
Data Loading...
