superrenormierbare

Superrenormalizable is a term used in quantum field theory to describe a type of quantum field theory where the coupling constants relevant to the theory have mass dimensions that are negative. This contrasts with renormalizable theories, where coupling constants are dimensionless or have positive mass dimensions. In superrenormalizable theories, the divergences that appear in calculations at higher loop orders do not grow indefinitely with energy. Instead, they are suppressed by powers of the mass scale associated with the coupling constant. This suppression means that the theory is well-behaved at high energies, or equivalently, at short distances.

The concept of superrenormalizability is important because it implies a certain degree of predictability for the theory at all energy scales, up to the Planck scale in some cases. While traditional renormalizable theories require renormalization procedures to absorb infinities, superrenormalizable theories have divergences that are less severe. This can simplify calculations and sometimes suggest that the theory is a low-energy effective field theory that will eventually be superseded by a more fundamental theory at higher energies. Examples of theories that exhibit superrenormalizable behavior can be found in certain models of condensed matter physics and in some extensions of the Standard Model of particle physics. The presence of negative mass dimension coupling constants often hints at a breakdown of the theory's validity at very high energies.