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Measurement of the Gluon Magnetic Mass in external Abelian magnetic field

Measurement of the Gluon Magnetic Mass in external Abelian magnetic field. S.S. Antropov , V.I. Demchik, V.V. Skalozub. Measurement of the Gluon Magnetic Mass S.S. Antropov , V.I. Demchik, V.V. Skalozub in external Abelian magnetic field. Introduction.

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Measurement of the Gluon Magnetic Mass in external Abelian magnetic field

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  1. Measurement of the Gluon Magnetic Mass in external Abelian magnetic field S.S. Antropov, V.I. Demchik, V.V. Skalozub

  2. Measurement of the Gluon Magnetic Mass S.S. Antropov, V.I. Demchik, V.V. Skalozub in external Abelian magnetic field • Introduction. • Action on a lattice. • Data and simulation analysis. • Discussion. • Conclusions.

  3. Measurement of the Gluon Magnetic Mass S.S. Antropov, V.I. Demchik, V.V. Skalozub in external Abelian magnetic field Introduction • The goal of our study is to measure a gluon magnetic mass which appears as an inverse screening length in a system in colour external magnetic field. • The object of our study is SU(2) gluon fields on a lattice. • For our purposes we used method of Monte-Carlo calculation.

  4. We start with associating link variables (which is SU(2) matrixes) with a vector potential of gluon field as follows: where x ̶ coordinates of the side, ̶ shift in -th direction, a ̶ lattice spacing, g0 ̶ coupling constant, P ̶ mere. • The Wilson lattice action reads where is inverse temperature. Measurement of the Gluon Magnetic Mass S.S. Antropov, V.I. Demchik, V.V. Skalozub in external Abelian magnetic field Action on a lattice

  5. Measurement of the Gluon Magnetic Mass S.S. Antropov, V.I. Demchik, V.V. Skalozub in external Abelian magnetic field • To represent Abelian external magnetic field the following boundary conditions were used* * it is published in paper: • G. 't Hooft (1979).

  6. Measurement of the Gluon Magnetic Mass S.S. Antropov, V.I. Demchik, V.V. Skalozub in external Abelian magnetic field • Three possibilities exist: • magnetic flux tubes are formed (Meissner effect), • magnetic fields have Coulomb behavior, • magnetic fields are screened. In case of flux tubes plaquette average* for cubic spatial part of the lattice (with linear size NS) has to show an effect proportional to . If magnetic fields are Coulombic ̶ proportional to , for screening ̶ to , where m - magnetic mass. *Plaquette average have sense of internal energy.

  7. Measurement of the Gluon Magnetic Mass S.S. Antropov, V.I. Demchik, V.V. Skalozub in external Abelian magnetic field Data and simulation analysis. Monte-Carlo data and fit curves for Abelian magnetic field.

  8. Measurement of the Gluon Magnetic Mass S.S. Antropov, V.I. Demchik, V.V. Skalozub in external Abelian magnetic field Fit results for Abelian magnetic field. • Many possible fit has been tested. • Bestfits for dependences , and . • We see that for case of Abelian magnetic field the magnetic mass is 0 and the screening is absent.

  9. Measurement of the Gluon Magnetic Mass S.S. Antropov, V.I. Demchik, V.V. Skalozub in external Abelian magnetic field Discussion. • For Abelian magnetic field: • Best fits for dependences , and corresponds to appearance of a magnetic flux tubes with increasing field strength. • Because values of for best dependences is almost equal and because the screening parameters for that dependences are small we can conclude that magnetic mass is 0 for that case.

  10. Conclusions. • For Abelian magnetic field: • Magnetic flux tubes with increasing field strength appear. • Magnetic mass is equal to 0.

  11. Thank you for your attention

  12. Fit results for non-Abelian magnetic field. 3 points Fit results for non-Abelian magnetic field. 17 points

  13. Fit results for Abelian magnetic field

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