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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 Dnipropetrovsk. Introduction.

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

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  1. 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

  2. Introduction • 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

  3. SU(2)-gluodynamics in external field - QCD Lagrangian - Ghostfields

  4. 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

  5. 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:

  6. Corresponding Feynman diagrams

  7. 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.

  8. SU(3)-gluodynamics Lagrangian in background gauge - SU(3) group structure constants. Let’s switch to charged basis:

  9. SU(3)-gluodynamics Lagrangian in charged basis

  10. 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)

  11. 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.

  12. 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)

  13. Debye mass of neutral gluons Debye mass slightly grows at high temperature:

  14. Vertex term of the Lagrangian

  15. 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

  16. Charged gluons Debye mass Expressions for Debye mass: Dependence on temperature:

  17. Conclusions • 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.

  18. Thank you for attention!

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