Precise predictions for double Higgs production in association with a vector boson in Effective Field Theory

We present next-to-next-to-leading order (NNLO) QCD predictions for Higgs boson pair production in association with a weak gauge boson, $pp \to Vhh$ with $V=W^\pm,Z$, in effective field theory descriptions of new physics. We consider both the Standard Model Effective Field Theory (SMEFT), truncated at dimension six, and the Higgs Effective Field Theory (HEFT) at leading order in the chiral expansion. The calculation builds on the factorisation of the quark-induced production process into Drell-Yan production of an off-shell vector boson and its subsequent decay into $Vhh$, supplemented in the $Zhh$ channel by the loop-induced $gg \to Zhh$ contribution that first enters at NNLO QCD. We provide inclusive predictions at $\sqrt{s}=13.6$ and $14.0$ TeV, including scale, PDF, and $\alpha_s$ uncertainties, and express the results in terms of numerical coefficients that allow fast evaluations for arbitrary EFT parameters in the considered ranges. We find that, for $W^\pm hh$ production, QCD corrections largely factorise from the EFT dependence, leading to almost flat $K$-factors. In contrast, $Zhh$ production shows a stronger dependence on the EFT coefficients because of the gluon-induced component.