A How to add higher dimensional operator at higher energy in SM?

[zaman786]

TL;DR

how to add higher dimensional operator to SM

Hi, I Learned that we can add higher dimensional operator but they are non-renormalizable - but effect of higher dimensional operator is vanishes at low energy - my question is than how can we add higher dimensional operator at higher energy - like dimension 5 operator ( weinberg operator) which is non- renormalizable.

 

[Orodruin]

TL;DR Summary: how to add higher dimensional operator to SM

Hi, I Learned that we can add higher dimensional operator but they are non-renormalizable - but effect of higher dimensional operator is vanishes at low energy - my question is than how can we add higher dimensional operator at higher energy - like dimension 5 operator ( weinberg operator) which is non- renormalizable.

These effective operators are typically the result of integrating out some degrees of freedom at a higher scale. The actually UV complete theory can contain only d=4 operators.

As an example, for the Weinberg operator there are essentially three ways of UV completing the theory:

• With SM singlet fermions - aka right-handed neutrinos.
• With a SU(2) triplet scalar.
• With a SU(2) triplet fermion.

These are the type I, type II, and type III seesaw mechanisms. When you integrate out any of these from the theory, you obtain the Weinberg operator as the d=5 operator (and other operators at higher d).