PoS - Proceedings of Science
Volume 376 - Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019) - Workshop on Connecting Insights in Fundamental Physics: Standard Model and Beyond
Necessity and Insufficiency of Scale Invariance for solving Cosmological Constant Problem
T. Kugo
Full text: pdf
Published on: August 18, 2020
A scenario based on the scale invariance for explaining the vanishing
cosmological constant (CC) is discussed. I begin with a notice on
the miraculous fact of the CC problem that the vacuum energies
totally vanish at each step of hierarchical and successive
spontaneous symmetry breakings. I then argue that the classical scale
invariance is a {\it necessary} condition for the calculability of
the vacuum energy.

Next, I discuss how {\it sufficient} the scale invariance is for
solving the CC problem. First in the framework of classical field
theory, the scale invariance is shown to give a natural mechanism
for realizing the miracle of vanishing vacuum energies at every
step of spontaneous symmetry breakings. Then adopting Englert-
Truffin-Gastmans' prescription to maintain the scale invariance
in quantum field theory, I point out that the quantum scale
invariance alone is not yet sufficient to avoid the superfine
tuning of coupling constants for realizing vanishingly small
cosmological constant, whereas the hierarchy problem may be solved.
Another symmetry or a mechanism is still necessary which protects
the flat direction of the potential against the radiative corrections.
DOI: https://doi.org/10.22323/1.376.0071
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