Two-Higgs-doublet model fitting and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi><mml:mover accent="true"><mml:mi>t</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>b</mml:mi><mml:mover acc

One of the most straightforward extensions of the standard model (SM) is having an additional Higgs doublet to the SM, namely the two-Higgs-doublet models. In the type-I model, an additional Higgs doublet is introduced that does not couple to any fermion via the Yukawa interaction in the original Lagrangian. Considering various theoretical and phenomenological constraints, we have found the best-fitted parameter set in the type-I model using the minimum <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>χ</a:mi><a:mn>2</a:mn></a:msup></a:math> method by scanning the model’s parameter space. We show that this optimal parameter set can be tested by precisely analyzing the decay processes <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msubsup><c:mi>D</c:mi><c:mi>s</c:mi><c:mo>+</c:mo></c:msubsup><c:mo stretchy="false">→</c:mo><c:msup><c:mi>τ</c:mi><c:mo>+</c:mo></c:msup><c:msub><c:mi>ν</c:mi><c:mi>τ</c:mi></c:msub></c:math>, <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msup><f:mi>D</f:mi><f:mo>+</f:mo></f:msup><f:mo stretchy="false">→</f:mo><f:msup><f:mi>μ</f:mi><f:mo>+</f:mo></f:msup><f:msub><f:mi>ν</f:mi><f:mi>μ</f:mi></f:msub></f:math>, and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>B</i:mi><i:mn>0</i:mn></i:msup><i:mo stretchy="false">→</i:mo><i:msup><i:mi>K</i:mi><i:mo>*</i:mo></i:msup><i:msup><i:mi>μ</i:mi><i:mo>+</i:mo></i:msup><i:msup><i:mi>μ</i:mi><i:mo>−</i:mo></i:msup></i:math>. Moreover, the decay channels <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>h</l:mi><l:mo stretchy="false">→</l:mo><l:mi>γ</l:mi><l:mi>γ</l:mi></l:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>Z</o:mi><o:mi>γ</o:mi></o:math> can be used to distinguish the model from the SM. For a direct search of the model at future colliders, we have proposed an investigation of the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msup><q:mi>e</q:mi><q:mo>+</q:mo></q:msup><q:msup><q:mi>e</q:mi><q:mo>−</q:mo></q:msup><q:mo stretchy="false">→</q:mo><q:mi>t</q:mi><q:mover accent="true"><q:mi>t</q:mi><q:mo stretchy="false">¯</q:mo></q:mover><q:mi>b</q:mi><q:mover accent="true"><q:mi>b</q:mi><q:mo stretchy="false">¯</q:mo></q:mover></q:math> process at the International Linear Collider to detect the new physics of the model. Considering the initial state radiation correction and applying appropriate background cuts, the calculation result of the scattering cross section shows that it is feasible to observe a clear and unique signal in the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi>t</x:mi><x:mover accent="true"><x:mi>b</x:mi><x:mo stretchy="false">¯</x:mo></x:mover></x:math> invariant mass distribution corresponding to the charged Higgs pair creations.