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M. Khandoga , V. Skalozub. Gluon Polarization Tensor in external field in SU(3) theory. New Physics and Quantim Chromodynamics at External Conditions 2011 May 5 Dnipropetrovsk. Introduction.

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gluon polarization tensor in external field in su 3 theory

M. Khandoga, V. Skalozub

Gluon Polarization Tensor in external field in SU(3) theory

New Physics and Quantim Chromodynamics at External Conditions 2011

May 5


  • Magnetic field of order is spontaneously generated in QCD vacuum at high temperatureSuperdaisy resummations:A. O. Starinets, A. V. Vshivtsev, V. Ch. Zukovskii. Phys. Lett. B 322, 403 (1994)Lattice simulations:N.O. Agasian (2003), V. Demchik (2008).
  • Cosmological proof: Fermi-LAT Collaborationfound out, that relict intergalactic magnetic fields of order ~ 10-15 Gare observed (Science, Vol. 328. no. 5979, pp. 725 – 729, April 2010).
  • Peripheral collisions of heavy ions: magnetic field is generated by parts of nuclei, travelling by sides
su 2 gluodynamics in external field
SU(2)-gluodynamics in external field

- QCD Lagrangian

- Ghostfields

background gauge
Background gauge

Field potential А(х) is divided into external field B(x)andquantum fluctuations Q(x):

External field is chosen in the following form:

Lagrangian in background gauge:

Ghost Lagrangian

charged basis
Charged basis

Since external field is directed along 3rd axis in the color space, it is convenient to introduce the following basis, which is called charged:

su 3 gluodynamics in external field
SU(3)-gluodynamics in external field

Spatial structure remains unchanged

Now we have 8 degrees of freedom instead of 3 which results in 8 gauge particles.

One more external field is added, it has same spatial orientation and directed along 8th axis in color space.

su 3 gluodynamics lagrangian in background gauge
SU(3)-gluodynamics Lagrangian in background gauge

- SU(3) group structure constants.

Let’s switch to charged basis:

neutral gluons sector
Neutral gluons sector

Neutral gluons do not interact with each other. We can write interaction Lagrangians of both neutral gluons as a combination of SU(2)-like Lagrangians:

Every interaction Lagrangian has a structure, identical to SU(2) case.

Thus the polarization operator of neutral gluons in SU(3) theory can be brought to SU(2) case, already researched by M.Bordag, V. Skalozub, Phys. Rev. D 75, 125003 (2007)

In the recent paper (V.Skalozub, A. Strelchenko (2004)) it was found out, that two fields are generated. After reaching the deconfinement phase two fields are generated:

Spontaneous generation of magnetic fields at high temperature

But after reaching some temperature only one field remains:

Hence the behavior of field-dependant quantities differs significantly at high temperature. Let’s illustrate it on Debye mass.

debye mass
Debye mass

If electrical potential is surrounded by plasma, it has a limited reach:

Sometimes it is convenient to use an inverted quantity:

In QFT Debye screening is caused by vacuum polarization. Debye mass can be obtained from polarization operator:

In finite-temperature QCD there is a well-known result:

O. Kalashnikov (1984)

debye mass of neutral gluons
Debye mass of neutral gluons

Debye mass slightly grows at high temperature:

charged gluons sector
Charged gluons sector

In SU(3) theory charged gluons do interact with each other:

SU(2) case was researched in paper by M. Bordag and V. Skalozub Phys. Rev. D 77, 105013 (2008)

For polarization operators of charged gluons we get

charged gluons debye mass
Charged gluons Debye mass

Expressions for Debye mass:

Dependence on temperature:

  • Gluon polarization operator in external field is obtained in SU(3) case. Significant differences with SU(2) gluodynamics are observed.
  • The spontaneously generated external field appears to reduce Debye mass.
  • Obtained result may be used for further research, finding gluon spectra and magnetic masses.