Leading two-loop corrections to the Higgs boson self-couplings in models with extended scalar sectors
Johannes Braathen, Shinya Kanemura
Abstract
Abstract We compute the dominant two-loop corrections to the Higgs trilinear coupling $$\lambda _{hhh}$$ <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> and to the Higgs quartic coupling $$\lambda _{hhhh}$$ <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> 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 $$\overline{{\mathrm{MS}}}$$ <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> 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 $$\overline{{\mathrm{MS}}}$$ <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> 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 $$\lambda _{hhh}$$ <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> 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.