ILC phenomenology of the $$Z_3$$ symmetric type-Z three Higgs doublet model

Abstract The Three-Higgs-Doublet Model (3HDM) extends the Standard Model by introducing two additional scalar doublets, leading to a rich spectrum of new particles: three neutral CP-even Higgs bosons $$(h_1,$$ ( h 1 , $$H_2,$$ H 2 , $$H_3),$$ H 3 ) , two neutral CP-odd Higgs bosons $$(A_2,$$ ( A 2 , $$A_3),$$ A 3 ) , and two charged Higgs bosons $$(H_2^+,$$ ( H 2 + , $$H_3^+).$$ H 3 + ) . In this work, we present a phenomenological study of the 3HDM at the future International Linear Collider (ILC) with a center-of-mass energy of $$\sqrt{s} = 1000\,\text {GeV}.$$ s = 1000 GeV . Applying a comprehensive set of theoretical and experimental constraints, we identify promising new physics signals with sufficiently large production cross-sections. Our analysis shows that $$e^+e^- \rightarrow H_2 A_2,$$ e + e - → H 2 A 2 , $$e^+e^- \rightarrow H_2 H_2 Z,$$ e + e - → H 2 H 2 Z , $$A_2 A_2 Z,$$ A 2 A 2 Z , $$H_2 H_2^{\pm } W^{\mp },$$ H 2 H 2 ± W ∓ , $$A_2 H_2^{\pm } W^{\mp }$$ A 2 H 2 ± W ∓ and $$H_1 H_2 A_2$$ H 1 H 2 A 2 are among the most sensitive channels to probe this extended Higgs sector. We demonstrate that a future ILC would offer a powerful platform to test these interactions and discover these heavier Higgs bosons thus providing evidence of physics beyond the Standard Model.