Narrow Results

After the gauge invariant gluon condensation, gluons remain as massless excitations. When the effective theory describing the condensation and the excitation is constructed, a constraint has to be imposed for the vacuum to be stable. The constraint implies the perfect dia-electricity and assures the solution of color flux tube when quarks are introduced. Thus the dia-electric model of Kogut–Susskind and 't Hooft is derived by the stability of the condensed vacuum.

The gluon condensation (GC)-effects in high energy cosmic rays are investigated. After a brief review of the GC, several examples including gamma-, electron- and positron-spectra in a broad $\mathrm{\text{GeV}}\sim \mathrm{\text{TeV}}$ region can be explained by the GC-effects. We find that the GC may break the power-law of the cosmic ray spectra if the energy of accelerated protons exceeds the GC-threshold. The GC is a new phenomenon that is not yet known, it provides a new window to understand the high energy cosmic ray spectra.

Using the gluon condensation (GC) model, we predict a possible connection of the broken power phenomenon between the energy spectra of electron and proton. We find that once the GC occurs, large amount of gluons accumulate near the GC threshold. This phenomenon provides a possible source of the power rule, broken in the energy spectra of cosmic rays, and even predicts the connection between them.