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Debye screening in external field in SU(3) gluodynamics

M. Khandoga, V.V. Skalozub Dnipropetrovsk National University. Debye screening in external field in SU(3) gluodynamics. The Actual Problems of Microworld Physics Gomel, July 22 - August 2, 2013. Introduction. Motivation

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Debye screening in external field in SU(3) gluodynamics

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  1. M. Khandoga, V.V. SkalozubDnipropetrovsk National University Debye screening in external field in SU(3) gluodynamics The Actual Problems of Microworld Physics Gomel, July 22 - August 2, 2013

  2. Introduction Motivation • Magnetic field of order is spontaneously generated in QCD vacuum at high temperatureSuperdaisyresummations: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 (Shin'ichiro Ando and Alexander Kusenko 2010 ApJ 722 L39). • Peripheral collisions of heavy ions: magnetic field is generated by parts of nuclei, travelling by sides • Recent studies have shown the significant role of screening masses in the understanding of QCD properties at high temperature

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

  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 obviously 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 Electrical potential 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 theLagrangian

  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. Comparison

  18. 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

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