Download Anisotropic structure of the running coupling constant in a strong

Anisotropic structure of the running coupling
constant in a strong magnetic field
Xin-Jian Wen (温新建)
Shanxi University
Efrain J. Ferrer & Vivian de la Incera
University of Texas at El Paso
2015-9-22 CCNU
Outline
 Vacuum polarization and running coupling without magnetic
field
QCD coupling constant in a strong magnetic field
Anisotropic pressure and critical temperature
summary
1 vacuum polarization and running coupling without magnetic field
Screening effect by a dielectric medium
2017/5/3
J.D.Griffiths, Introduction to Elementary particle
Comparization of QED and QCD
QED
Electron and positron are half-integer spin
and ruled by Pauli exclusion principle.
QED vacuum has normal diamagnetic
properties and is screening.
QCD
Gluons are integer. Gluon behave like a
paramagnetic medium. And this implies
antiscreening.
But if the test charges are close together,
they can penetrate each others’ particle
cloud and will not feel any screening or
antiscreening.
Renormalized running coupling constant
Color electric permitivity
QCD asymptotic freedom and antiscreening are dominated by the one-loop
contribution in vacuum polarization tensor
Renormalized QCD coupling constant
—dimensional regularization
(a) Vacuum polarization
(b) Fermion self energy
(c) Vertex correction
2 QCD coupling constant in a strong magnetic field
Our motivation is to explain how the magnetic field
enters into the coupling constant and to investigate
the anisotropic structure of QCD matter under
strong magnetic field.
Preceding work on coupling constant depending on magnetic field
1) Analytical expression at ultra-strong magnetic field
Magnetic field is of the order of the energy scale of the Fermions
In 2002, Miransky, hep-ph/0208180
In 2013, Andreichikov, Orlovsky, Simonov, PhysRevLett.110.162002
Meson mass
Preceding work on coupling constant depending on magnetic field
2) Fit the Lattice QCD result for any value of magnetic field
In 2014, Ferreira, PRD89, 116011 (2014)
Since there is no LQCD data for
, they do the fit to reproduce
Quark-loop contribution to gluon self energy
Coordinate space
Transform it into momentum space with the help of
Ritus eigenfunction method
Ritus eigenfunctions method
The fermion self-energy operator is a function of the operators
and
the parabolic cylinder functions
Quark loop to the gluon self-energy
In the low energy region, fermions in the LLL only contribute to the longitudinal
components of the polarization tensor.
Approximation
To satisfy the asymptotic limits
Quark loop contribution will produce the anisotropic structure. Quarks in
the LLL will contribute to the coupling constant in longitudinal direction.
Anisotropic structure of coupling constant
Ferrer, Incera, Wen PRD,91 (2015) 054006
3 Anisotropic pressure and critical temperature
Anisotropic pressure in nuclear matter or quark
matterreflects the breaking of the rotational
symmetry by the magnetic field.
P  P||  H2  MH
Ferrer et.al, PRD82 (2010) 065802
Isayev & Yang PLB 707 (2012) 163
Wen PRD 88707 (2013) 034031
Magnetic field dependent coupling constant
is used to interpret the inverse magnetic
catalysis.
i 1 2
  [ ,  ]
2
3
2017/5/3
is the spin operator.
Ferrer, Incera, Wen PRD,91 (2015) 054006
Summary
1. A magnetic field affects the color Coulomb
potential through quark loops with gluon external
legs.
2. If the field is strong enough to force the quarks
to remain in the LLL. The degeneracy factor is
propotional to eB. The dynamics is dimensionally
reduced to D-2.
3. The loops of these LLL quarks will lead to a
significant anisotropy in the gluon self-energy and
hence in the coupling because these loops only
contribute to the longitudinal components of the
self-energy.
Thank you!