Two-loop scale-invariant scalar potential and quantum effective operators

Understand

Spontaneous breaking of quantum scale invariance may provide a solution to the hierarchy and cosmological constant problems.

• In a scale-invariant regularization, we compute the two-loop potential of a higgs-like scalar $\phi$ in theories in which scale symmetry is broken only spontaneously by the dilaton ($\sigma$).
• Its vev $\langle\sigma\rangle$ generates the DR subtraction scale ($\mu\sim\langle\sigma\rangle$), which avoids the explicit scale symmetry breaking by traditional regularizations (where $\mu$=fixed scale).
• The two-loop potential contains effective operators of non-polynomial nature as well as new corrections, beyond those obtained with explicit breaking ($\mu$=fixed scale).