Higgs self-coupling measurement at the International Linear Collider

The Higgs sector of particle physics is still largely uncovered, where establishing the Higgs mechanism is central to advance the field. The Higgs self-coupling is the key ingredient missing and an important puzzle piece for potentially uncovering new physics beyond the standard model. With the energy reach and precision reach of linear $e^+e^-$ colliders, the Higgs self-coupling can be measured directly and precisely enough that certain BSM scenarios can be evaluated. A new analysis of the capability to measure the Higgs self-coupling at the International Linear Collider (ILC) is ongoing and have identified aspects concerning the reconstruction tools which are expected to improve precision reach and are presented. This ongoing analysis intends to update the state-of-the-art projections for measuring the Higgs self-coupling at ILC which was previously evaluated at a centre-of-mass energy of 500 GeV. Additionally, the ongoing analysis intends to evaluate the choice of centre-of-mass energy and how it influences the reachable precision, as well as to consider how BSM effects might influence the reachable precision.