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Xin-Jian Wen (温新建 )
2015-9-22 CCNU
Shanxi University
Efrain J. Ferrer & Vivian de la Incera University of Texas at El Paso
Anisotropic structure of the running coupling constant in a strong magnetic field
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Outline
Vacuum polarization and running coupling without magnetic field
QCD coupling constant in a strong magnetic field
Anisotropic pressure and critical temperature
summary
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23/4/21 J.D.Griffiths, Introduction to Elementary particle
Screening effect by a dielectric medium
1 vacuum polarization and running coupling without magnetic field
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QED
Comparization of QED and QCD
QCD
Electron and positron are half-integer spin and ruled by Pauli exclusion principle. QED vacuum has normal diamagnetic properties and is screening.
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.
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Renormalized running coupling constant
Color electric permitivity
QCD asymptotic freedom and antiscreening are dominated by the one-loop contribution in vacuum polarization tensor
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(a) Vacuum polarization
(b) Fermion self energy
(c) Vertex correction
Renormalized QCD coupling constant—dimensional regularization
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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.
2 QCD coupling constant in a strong magnetic field
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Preceding work on coupling constant depending on magnetic field
In 2002, Miransky, hep-ph/0208180
In 2013, Andreichikov, Orlovsky, Simonov, PhysRevLett.110.162002
Meson mass
1) Analytical expression at ultra-strong magnetic field
Magnetic field is of the order of the energy scale of the Fermions
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Since there is no LQCD data for , they do the fit to reproduce
2) Fit the Lattice QCD result for any value of magnetic field
In 2014, Ferreira, PRD89, 116011 (2014)
Preceding work on coupling constant depending on magnetic field
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Quark-loop contribution to gluon self energy
Coordinate space
Transform it into momentum space with the help of Ritus eigenfunction method
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Ritus eigenfunctions method
the parabolic cylinder functions
The fermion self-energy operator is a function of the operators
and
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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.
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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.
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Ferrer, Incera, Wen PRD,91 (2015) 054006
Anisotropic structure of coupling constant
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3 Anisotropic pressure and critical temperature
Anisotropic pressure in nuclear matter or quark matterreflects the breaking of the rotational symmetry by the magnetic field.
2|| P P H MH
Isayev & Yang PLB 707 (2012) 163 Wen PRD 88707 (2013) 034031Ferrer et.al, PRD82 (2010) 065802
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23/4/21Ferrer, Incera, Wen PRD,91 (2015) 054006
Magnetic field dependent coupling constant is used to interpret the inverse magnetic catalysis.
is the spin operator.1 2[ , ]
2 3
i
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Summary1. 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!