# Effective theories and dimension six operators

What is the importance of dimension six operators in the study of physics beyond the Standard Model? Are these operators more relevant than dimension five operators like $HHFF$ or operators with derivative couplings?

I often see lagrangians with dimension six operators in effective studies of the standard model, but I do not understand this choice. An example is the paper arXiv:1304.1151, where they have defined: $$\mathcal{L}_{\rm eff}= \sum_n \frac{g_n}{\Lambda^2}\mathcal{O_n},$$ whit $g_n$ being the corresponding couplings and $\mathcal{O}_n$ the dimension six operators.

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Minor comment to the post (v1): In the future please link to abstract pages rather than pdf files, e.g., arxiv.org/abs/1304.1151 –  Qmechanic Apr 20 '14 at 5:03

The only dimension-five operators allowed by the SM are neutrino masses, $(HL_i)(HL_j)$. So we mostly talk about dimension-six operators because for almost any question they're the first higher-dimension operators that can appear.