Abstract
The result of removing of heavy non-equal mass particles from the theory can be described, at low energy, by the effective action, which is a series in inverse-square powers of the mass. We propose a new efficient tool to calculate the leading terms of this series based on the Schwinger proper-time method. Unequal masses give rise to a large number of effective vertices describing the explicit flavor symmetry breaking effects with well-defined coupling constants. Our method is pertinent to the theory with explicit and spontaneous chiral symmetry breaking, chiral gauge theory, standard and beyond standard model effective field theory, the theory of critical phenomena, cosmology, etc.
Highlights
The proper-time method [1,2,3,4] is an efficient tool to study quantum corrections in many areas of theoretical physics: in quantum gravity [5,6,7,8], in QCD, in chiral gauge theories [11], in cosmology [12], in QED (Casimir energies and forces [13]), etc
I propose a new proper-time based algorithm to derive the effective action in the theory with heavy virtual fermions of unequal masses belonging to some representation of the symmetry group G
The effects of flavor symmetry breaking are currently important in many physical applications: in studies of physics beyond standard model to construct the low energy effective action by integrating out the heavy degrees of freedom [21, 22]; in two Higgs doublet models [23] to address the problem of almost degenerate Higgs states at 125GeV [24, 25]; in the low energy QCD to study the SU (3) and isospin symmetry breaking [26]
Summary
The proper-time method [1,2,3,4] is an efficient tool to study quantum corrections in many areas of theoretical physics: in quantum gravity [5,6,7,8], in QCD (effective meson Lagrangians [9, 10]), in chiral gauge theories [11], in cosmology [12], in QED (Casimir energies and forces [13]), etc. The result is the inverse mass series for the one-loop effective action, where I explicitly calculate the two leading contributions This powerful tool opens a promising avenue for studying explicit flavor symmetry breaking effects in many effective field theories. The effects of flavor symmetry breaking are currently important in many physical applications: in studies of physics beyond standard model to construct the low energy effective action by integrating out the heavy degrees of freedom [21, 22]; in two Higgs doublet models [23] to address the problem of almost degenerate Higgs states at 125GeV [24, 25]; in the low energy QCD to study the SU (3) and isospin symmetry breaking [26].
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