Leading two-loop corrections to the Higgs boson self-couplings in models with extended scalar sectors

<jats:title>Abstract</jats:title><jats:p>We compute the dominant two-loop corrections to the Higgs trilinear coupling <jats:inline-formula><jats:alternatives><jats:tex-math>$$\lambda _{hhh}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>λ</mml:mi><mml:mrow><mml:mi>hhh</mml:mi></mml:mrow></mml:msub></mml:math></jats:alternatives></jats:inline-formula> and to the Higgs quartic coupling <jats:inline-formula><jats:alternatives><jats:tex-math>$$\lambda _{hhhh}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>λ</mml:mi><mml:mrow><mml:mi>hhhh</mml:mi></mml:mrow></mml:msub></mml:math></jats:alternatives></jats:inline-formula> in models with extended Higgs sectors, using the effective-potential approximation. We provide in this paper all necessary details about our calculations, and present general <jats:inline-formula><jats:alternatives><jats:tex-math>$$\overline{{\mathrm{MS}}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>MS</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math></jats:alternatives></jats:inline-formula> expressions for derivatives of the integrals appearing in the effective potential at two loops. We also consider three particular Beyond-the-Standard-Model (BSM) scenarios – namely a typical scenario of an Inert Doublet Model (IDM), and scenarios of a Two-Higgs-Doublet Model (2HDM) and of a Higgs Singlet Model (HSM) without scalar mixing – and we include all the necessary finite counterterms to obtain (in addition to <jats:inline-formula><jats:alternatives><jats:tex-math>$$\overline{{\mathrm{MS}}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>MS</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math></jats:alternatives></jats:inline-formula> results) on-shell scheme expressions for the corrections to the Higgs self-couplings. With these analytic results, we investigate the possible magnitude of two-loop BSM contributions to the Higgs self-couplings and the fate of the non-decoupling effects that are known to appear at one loop. We find that, at least as long as pertubative unitarity conditions are fulfilled, the size of two-loop corrections remains well below that of one-loop corrections. Typically, two-loop contributions to <jats:inline-formula><jats:alternatives><jats:tex-math>$$\lambda _{hhh}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>λ</mml:mi><mml:mrow><mml:mi>hhh</mml:mi></mml:mrow></mml:msub></mml:math></jats:alternatives></jats:inline-formula> amount to approximately 20% of those at one loop, implying that the non-decoupling effects observed at one loop are not significantly modified, but also meaning that higher-order corrections need to be taken into account for the future perspective of precise measurements of the Higgs trilinear coupling.</jats:p>