The Higgs potential is written as $V(\phi) = -\mu^2 |\phi|^2 + \lambda^2 |\phi|^4$, where $|\phi|^2 = \phi^\dagger \phi $ and $ \phi $ is a complex scalar doublet. My question is: why do we not include a $|\phi|^3$ term, which is also gauge invariant? Is it because this term is non-polynomial $(|\phi|^2)^{3/2}$ which can lead to infinite series in Taylor expansion?
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- 1$\begingroup$ Are you surveying renormalizable systems? $\endgroup$Cosmas Zachos– Cosmas Zachos2025-11-20 16:31:49 +00:00Commented Nov 20 at 16:31
- $\begingroup$ @CosmasZachos I thought of it as a renormalizable system, as the potential doesn't include higher-order terms. $\endgroup$Ayush Fotedar– Ayush Fotedar2025-11-20 17:37:41 +00:00Commented Nov 20 at 17:37
- $\begingroup$ So his cockeyed cubic spoils the broth... No? $\endgroup$Cosmas Zachos– Cosmas Zachos2025-11-20 17:49:12 +00:00Commented Nov 20 at 17:49
- $\begingroup$ @CosmasZachos So cubic term is not renormalizable here? $\endgroup$Martin– Martin2025-11-21 05:26:04 +00:00Commented Nov 21 at 5:26
- 1$\begingroup$ The square root interaction appears dangerous. $\endgroup$Cosmas Zachos– Cosmas Zachos2025-11-21 12:29:12 +00:00Commented Nov 21 at 12:29
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