4 research outputs found
Fermion family recurrences in the Dyson-Schwinger formalism
We study the multiple solutions of the truncated propagator Dyson-Schwinger
equation for a simple fermion theory with Yukawa coupling to a scalar field.
Upon increasing the coupling constant , other parameters being fixed, more
than one non-perturbative solution breaking chiral symmetry becomes possible
and we find these numerically. These ``recurrences'' appear as a mechanism to
generate different fermion generations as quanta of the same fundamental field
in an interacting field theory, without assuming any composite structure. The
number of recurrences or flavors is reduced to a question about the value of
the Yukawa coupling, and has no special profound significance in the Standard
Model. The resulting mass function can have one or more nodes and the
measurement that potentially detects them can be thought of as a collider-based
test of the virtual dispersion relation for the charged
lepton member of each family. This requires three independent measurements of
the charged lepton's energy, three-momentum and off-shellness. We illustrate
how this can be achieved for the (more difficult) case of the tau lepton
QCD Corrections to QED Vacuum Polarization
We compute QCD corrections to QED calculations for vacuum polarization in
background magnetic fields. Formally, the diagram for virtual loops
is identical to the one for virtual loops. However due to
confinement, or to the growth of as decreases, a direct
calculation of the diagram is not allowed. At large we consider the
virtual diagram, in the intermediate region we discuss the role of
the contribution of quark condensates \left and at the
low-energy limit we consider the , as well as charged pion
loops. Although these effects seem to be out of the measurement accuracy of
photon-photon laboratory experiments they may be relevant for -ray
burst propagation. In particular, for emissions from the center of the galaxy
(8.5 kpc), we show that the mixing between the neutral pseudo-scalar pion
and photons renders a deviation from the power-law spectrum in the
range. As for scalar quark condensates \left and
virtual loops are relevant only for very high radiation density
and very strong magnetic fields of order .Comment: 15 pages, 4 figures; Final versio