Double Higgs boson production via vector boson fusion in SMEFT

While gluon fusion dominates Higgs pair production at the LHC, vector boson fusion (VBF) offers a unique window into beyond the Standard Model (BSM) physics through its distinctive kinematic features and direct sensitivity to Higgs-vector boson interactions. We perform a comprehensive analysis of double Higgs production via VBF in the Standard Model effective field theory (SMEFT), systematically investigating how dimension-6 and dimension-8 bosonic operators—particularly those involving field derivatives—can enhance the production rate. We identify the most relevant Wilson coefficients (WCs) affecting the trilinear Higgs coupling (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>h</a:mi><a:mi>h</a:mi><a:mi>h</a:mi></a:math>) and Higgs-vector boson interactions (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>h</c:mi><c:mi>V</c:mi><c:mi>V</c:mi></c:math>, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>h</e:mi><e:mi>h</e:mi><e:mi>V</e:mi><e:mi>V</e:mi></e:math>). Using constraints from global fits and interpolating fit results for unconstrained WCs with naive dimensional analysis, we assess their effects on the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>V</g:mi><g:mi>V</g:mi><g:mo stretchy="false">→</g:mo><g:mi>h</g:mi><g:mi>h</g:mi></g:math> (<j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:mrow><j:mi>V</j:mi><j:mo>=</j:mo><j:mi>W</j:mi></j:mrow><j:mo>,</j:mo><j:mrow><j:mi>Z</j:mi></j:mrow></j:mrow></j:math>) scattering amplitudes and cross sections. Our analysis includes a study of EFT convergence and validity in models with scalar extensions of the SM. Numerical simulations for the planned High-Luminosity LHC experiment (HL-LHC) in general reveal only a modest and challenging to detect enhancement of the VBF di-Higgs production rate over the SM prediction. However, we show that in optimistic scenarios, such a process could be observed at the HL-LHC. In certain cases, when the enhancement is dominated by the dimension-6 or dimension-8 operators containing field derivatives (and thus leading to stronger energy-dependent effects), this channel becomes competitive with di-Higgs production via gluon fusion. This work highlights the role of VBF di-Higgs production as a complementary channel for probing anomalous Higgs couplings and their impact on BSM physics.