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The measurement of Higgs self-coupling is one of the most crucial physics goals at the future colliders. At the LHC, the di-Higgs production is a main way to measure the Higgs trilinear coupling. As a complementary to the di-Higgs production, t t ¯ h h $$ t\overline{t}hh $$ process may open a new avenue to measure di-Higgs physics at the LHC and a future 100 TeV pp collider or a high energy e + e − collider since the extra t t ¯ $$ t\overline{t} $$ in the final states may efficiently suppress the backgrounds. However, such a kind of process is also controlled by the top-Higgs coupling. In this work, we investigate the impact of CP-violating top-Higgs coupling on t t ¯ h h $$ t\overline{t}hh $$ production at the LHC, e + e − and a 100 TeV hadron collider under the current Higgs data. Within 2σ Higgs data allowed parameter region, we find that the cross section of t t ¯ h h $$ t\overline{t}hh $$ at the LHC-14 TeV, e + e − -1 TeV and VHE-LHC/SPPC-100 TeV can be enhanced up to 2.1 times the SM predictions. The future precise measurement of Higgs coupling will reveal the nature of top-Higgs interaction and improve the sensitivity of the determination of Higgs self-coupling through t t ¯ h h $$ t\overline{t}hh $$ production

Enhancing t t ¯ h h $$ t\overline{t}hh $$ production through CP-violating top-Higgs interaction at the LHC and future colliders