Resolving gluon fusion loops at current and future hadron colliders

TL;DR

The paper tackles the degeneracy in Higgs-gluon fusion between long-distance top-quark loop effects and short-distance new physics by adopting a two-operator EFT and evaluating multiple exclusive probes (ttH, boosted, off-shell, and double-Higgs) at HL-LHC and FCC-hh. It extends the EFT to include top-Z couplings, analyzes their impact on off-shell gg→ZZ, and uses a vector-like quark toy model to study EFT validity. The results show that exclusive channels provide complementary sensitivity to $c_t$ and $c_g$, with off-shell Higgs additionally constraining top-Z corrections; EFT validity at high energy is nuanced and may require nonlinear or UV-complete treatments. These insights inform strategies for future colliders and have implications for composite-Higgs scenarios and top-partner phenomenology.

Abstract

Inclusive Higgs measurements at the LHC have limited resolution on the gluon fusion loops, being unable to distinguish the long-distance contributions mediated by the top quark from possible short-distance new physics effects. Using an Effective Field Theory (EFT) approach we compare several proposed methods to lift this degeneracy, including $t\bar{t}h$ and boosted, off-shell and double Higgs production, and perform detailed projections to the High-Luminosity LHC and a future hadron collider. In addition, we revisit off-shell Higgs production. Firstly, we point out its sensitivity to modifications of the top-$Z$ couplings, and by means of a general analysis we show that the reach is comparable to that of tree-level processes such as $t\bar{t}Z$ production. Implications for composite Higgs models are also discussed. Secondly, we assess the regime of validity of the EFT, performing an explicit comparison for a simple extension of the Standard Model containing one vector-like quark.

Figures (7)

• Figure 1: Left panel:$95\%$ (solid) and $68\%$ (dashed) exclusion contours in the $(c_y,\,c_g)$ plane obtained from HL-LHC projections: inclusive Higgs measurements (blue), $t\bar{t}h$ (purple), off-shell (red), boosted (gray), and double Higgs production (orange). The $h\gamma\gamma$ effective interaction in Eq. \ref{['eq:photon']} is included. Right panel: Same as in the left panel, but without the $h\gamma\gamma$ effective interaction in Eq. \ref{['eq:photon']}.
• Figure 2: $95\%$ (solid) and $68\%$ (dashed) exclusion contours in the $(c_y, c_g)$ plane obtained from FCC projections. Red corresponds to off-shell, gray to boosted and orange to double Higgs production, while the purple band indicates the $68\%$ region from $t \bar{t}h$.
• Figure 3: Representative subset of the Feynman diagrams for $gg\to ZZ$ that involve the couplings $c_t, c_g, c_V$ and $c_A$. The fermion lines correspond to top quarks.
• Figure 4: Top left panel: In red, $99,95$ and $68\%$ credibility exclusion contours in the $(\delta c_A, c_g)$ plane from off-shell Higgs measurements at the HL-LHC. The purple dotted line indicates the estimate of the weakest direction of the fit as obtained from a simple analytical expansion, see text for details. The blue line shows the prediction of the singlet top partner model. The grey area is the $95\%$ CL$_s$ constraint from $gg\to hZ$ production as given in Ref. Englert:2016hvy, see Section \ref{['sec:comparison']}. Top right panel: The same plot, zoomed in near the SM point and overlayed with points showing the predictions of composite Higgs models. Black circles and brown triangles were obtained using the full Lagrangian in Eq. \ref{['eq:ch']}, while green diamonds and blue squares correspond to the predictions of the ${\bf M4_5}$ and ${\bf M1_5}$ simplified models DeSimone:2012fs, respectively. See Section \ref{['sec:eftCH']}. Bottom left panel: The red (blue) solid line shows the $68\%$ credibility contour based on the bin with $\sqrt{\hat{s}}\in[400,600]\,([1100,1500])$ GeV. The red (blue) dashed line shows, for illustration, an isocontour of the approximate matrix element squared in Eq. \ref{['leadingamp']}, computed for $\sqrt{\hat{s}}=500\,(1200)$ GeV. Bottom right panel: Exclusion contours in the $(\delta c_A, c_g)$ plane from off-shell Higgs measurements at the FCC. The purple dotted and blue lines indicate the analytical estimate of the weakest direction of the fit and the prediction of the singlet top partner model, respectively.
• Figure 5: The ratio of the minimal partonic energy for which the EFT description becomes invalid to the mass $M_T$ of the vector-like top partner, as function of $M_T$. Several values of the Yukawa coupling $Y_*$ are considered: $Y_* = 2,3,4,5$ are indicated by the blue, red, yellow and green curves, respectively. The solid lines correspond to the dimension-$6$ EFT, whereas the dashed lines correspond to the nonlinear parameterization where the full modifications to the $h \bar{t}t, Z \bar{t}t$ and $hgg$ couplings are retained.