Gauge-invariant scalar and vector operators in the SU( 2) × U( 1) Higgs model: Ward identities and renormalization

In this work, we investigate the renormalization of the gauge-invariant scalar and vector composite operators proposed in Dudal et al. (Eur Phys J C 83(11):1091, 2023) to describe the SU(2)× U(1) S U ( 2 ) × U ( 1 ) Higgs model from a gauge-invariant perspective. To establish the relationship between the counterterms, we use the algebraic renormalization approach (Piguet et al. in Lect Notes Phys Monogr 28:1–134, 1995, https://doi.org/10.1007/978-3-540-49192-7 ). Therefore, we also derive the set of Ward identities of the model after introducing these composite operators. Using these Ward identities, we demonstrate important exact relations between the correlation functions of elementary fields and composite fields.