QCD corrections to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Z</mml:mi><mml:mi>Z</mml:mi></mml:mrow></mml:math> production in gluon fusion at the LHC

We compute the next-to-leading-order QCD corrections to the production of two $Z$-bosons in the annihilation of two gluons at the LHC. Being enhanced by a large gluon flux, these corrections provide a distinct and, potentially, the dominant part of the ${\mathrm{N}}^{3}\mathrm{LO}$ QCD contributions to $Z$-pair production in proton collisions. The $gg\ensuremath{\rightarrow}ZZ$ annihilation is a loop-induced process that receives the dominant contribution from loops of five light quarks, that are included in our computation in the massless approximation. We find that QCD corrections increase the $gg\ensuremath{\rightarrow}ZZ$ production cross section by $\mathcal{O}(50%--100%)$ depending on the values of the renormalization and factorization scales used in the leading-order computation and the collider energy. The large corrections to the $gg\ensuremath{\rightarrow}ZZ$ channel increase the $pp\ensuremath{\rightarrow}ZZ$ cross section by about 6% to 8%, exceeding the estimated theoretical uncertainty of the recent next-to-next-to-leading-order QCD calculation.

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