Exploring sizable triple Higgs couplings in the 2HDM

<jats:title>Abstract</jats:title><jats:p>An important task at future colliders is the measurement of the triple Higgs coupling. Depending on its size relative to the Standard Model (SM) value, certain collider options result in a higher experimental accuracy. Within the framework of Two Higgs Doublet Models (2HDM) types I and II we investigate the allowed ranges for all triple Higgs couplings involving at least one light, SM-like Higgs boson. We take into account theoretical constraints (unitarity, stability), experimental constraints from direct Higgs-boson searches, measurements of the SM-like Higgs-boson properties, flavor observables and electroweak precision data. We find that the SM-type triple Higgs coupling w.r.t. its SM value, <jats:inline-formula><jats:alternatives><jats:tex-math>$$\lambda _{hhh}/\lambda _{\mathrm {SM}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mi>hhh</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>SM</mml:mi> </mml:msub> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>, can range between <jats:inline-formula><jats:alternatives><jats:tex-math>$$\sim -0.5$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mo>-</mml:mo> <mml:mn>0.5</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\sim 1.5$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>1.5</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>. Depending on which value is realized, the HL-LHC can compete with, or is clearly inferior to the ILC. We find the 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> between <jats:inline-formula><jats:alternatives><jats:tex-math>$$\sim -1.5$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mo>-</mml:mo> <mml:mn>1.5</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\sim 1.5$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>1.5</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>. Triple Higgs couplings involving two heavy Higgs bosons, <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>, <jats:inline-formula><jats:alternatives><jats:tex-math>$$\lambda _{hAA}$$</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>hAA</mml:mi> </mml:mrow> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\lambda _{hH^+H^-}$$</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>h</mml:mi> <mml:msup> <mml:mi>H</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>H</mml:mi> <mml:mo>-</mml:mo> </m ...