Relevance of fermion loops for <math><mrow><msup><mrow><mi>W</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>W</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> scattering at the LHC

We study the one-loop corrections to W+W− elastic scattering within the framework of effective theories. Rescattering via intermediate electroweak would-be-Goldstone bosons dominate at high energies, as the corresponding loop diagrams with these intermediate bosons scale like O(s2/v4) in the chiral effective counting. In the present article, we focus our attention on the usually neglected fermion-loop corrections which scale like O(Mfer2s/v4) in the Higgs effective field theory (HEFT). Although this dependency is formally suppressed for s→∞ with respect to the ones from boson loops, the large top mass can lead to a numerical competition between fermion and boson loops at intermediate energies of the order of a few TeV. The central goal of the present study is to assess the importance of these fermion loops. For this, since the fermion contribution scales with the mass of the fermions, we have calculated the imaginary part induced by loops of the heaviest fermions, top and bottom quarks, in W+W−→W+W− elastic scattering and compared them with the loop contributions from purely bosonic loops, as a large imaginary part would be a clear indicator of large fermion-loop effects. We have examined the dependence of both amplitudes on the effective couplings, allowing an O(10%) deviation from the Standard Model. In some cases, boson loops dominate over top and bottom corrections, as expected. However, we find that there are regions in the space of effective parameters that yield a significant—and even dominant—imaginary contribution from fermion loops. In addition to our conclusions for the general HEFT, we also provide analyses particularized to some benchmark points in the SO(5)/SO(4) minimal composite Higgs model.