We study the process $pp \to Z(\ell^+ \ell^-)h(b\bar b)$ in the Standard Model Effective Field Theory (SMEFT) at high energies using subjet techniques to reconstruct the Higgs boson. We show that at high energies this process probes four directions in the dimension 6 EFT space, namely the operators that contribute to the four contact interactions, $hZ_��\bar{f}��^��f$, where $f=u_L, u_R,d_L$ and $d_R$. These four directions are, however, already constrained by the $Z$-pole and diboson measurements at LEP. We show that by utilising the energy growth of this process in the SMEFT and the accuracy that can be achieved by using subjet techniques at the High Luminosity LHC, one can obtain bounds on these operators that are an order of magnitude better than existing LEP bounds.

v2: 9 pages, 2 figures and 4 tables; some equations, expressions and numbers corrected; conclusions unchanged; version accepted for publication in PRD