Search for Stochastic GW Signal as a Complementary Approach to Multi-Higgs Productions at the Hadron Colliders to Probe Dimension Six Operator

We have considered an effective field theory framework in which the Standard Model is extended by a non-renormalizable dimension six operator ($\frac{1}{\Lambda^2}(H^{\dagger}H)^3$) respecting the symmetries of the Standard Model. Such an operator can affect the dynamics of Higgs field and the electroweak phase transition. Presence of such term modifies the triple Higgs coupling which is already under the lens from di-Higgs searches in various channels at the LHC. Constraint on the scale parameter $\Lambda$ is obtained from the di-Higgs data at the LHC Run II. Additionally, such dimension six terms will give rise to additional couplings which will affect tri-Higgs and four-Higgs productions at future high energy, high luminosity hadron colliders. The shape of the scalar potential also gets modified due to such higher dimensional term composed of Higgs field. It is worthwhile to study the impact of such higher-dimensional operators at suitable gravitational wave (GW) interferometry experiments since GW astronomy has become a good probe for new physics searches. Bounds obtained on the scale parameter $\Lambda$ from the allowed first-order electroweak phase transition is $450 \lesssim \Lambda \lesssim 590$~GeV. On the other hand, di-Higgs results from the LHC Run II put a lower bound on $\Lambda \gtrsim 340$~GeV.