Vices and virtues of Higgs effective field theories at large energy

We study constraints on new physics from Higgs production at the LHC in the context of an effective field theory (EFT), focusing on Higgs searches in $HV$ ($V=W,Z$) associated production which are particularly sensitive to the high-energy behavior of certain dimension-six operators. We show that analyses of these searches are generally dominated by a kinematic region where the generic EFT expansion breaks down, and we establish under which conditions they can nevertheless be meaningful. For example, constraints from these searches on the Wilson coefficients of operators whose effects grow with energy can be established in scenarios where a particular combination of fermions and the Higgs are composite and strongly coupled: then, bounds from Higgs physics at high energy are complementary to LEP1 and competitive with LEP2.

Figure 1

To illustrate the UV behavior of the operator ${\mathcal{O}}_W-{\mathcal{O}}_B$, these plots contrast the LO distributions of $p_T(V)$ and $\mathrm{\Delta }R(b,\overline{b})$ ($pp\to ZH@8\mathrm{TeV}$) for the SM and $\mathrm{SM}+\mathcal{O}$ with a large Wilson coefficient. No cutoffs are applied.

Figure 2

The impact of the operators ${\mathcal{O}}_{WW}$ and ${\mathcal{O}}_W$ on the cross section and kinematics of $pp\to Wh$ at the LHC8. Shown is $\sigma /{\sigma }_{\mathrm{SM}}$ (LEFT) and $\sigma /{\sigma }_{\mathrm{SM}}(p_T>200)$ (RIGHT). The net effect of ${\mathcal{O}}_{WW}$ on the signal strength is subdominant in the region $p_T(W)>200\mathrm{GeV}$. We assume that the EFT is valid up to the unitarity cutoff.

Figure 3

The $c_W$ dependence of the $u\overline{d}\to h{W}^{+}$ cross section at different fixed c.o.m. energies $\sqrt{\widehat{s}}=400,500,1200$ as described in the text. All orders of $c_W$ are included in the squared amplitude for the solid lines. The dashed lines represent the linearized signal strengths.

Figure 4

The combined expected (left) and observed (right) 1-parameter fit $\mathrm{\Delta }{\chi }^2$ contours in the coefficient $c_W(m_W^2/{\mathrm{\Lambda }}^2)=-c_B(m_W^2/{\mathrm{\Lambda }}^2)$ from Higgs searches in the $b\overline{b}+0l,1l,2l$ final states in ATLAS. We assume all other operators in the basis to be negligible and employ various UV cutoff prescriptions. The dashed contours are for fixed UV cuts $\sqrt{\widehat{s}}<500,550,\dots \mathrm{GeV}$, while the solid contours are for parameter-dependent cutoffs $\widehat{s}<{\mathrm{\Lambda }}^2/c_W$ (blue, lowest lying curve), $2{\mathrm{\Lambda }}^2/c_W$ (purple, next-to lowest curve), $4{\mathrm{\Lambda }}^2/c_W$ (yellow, next-to-steepest curve) and $4\pi {\mathrm{\Lambda }}^2/c_W$ (green, steepest curve) inspired by our discussion of UV completions and perturbativity. We assume that the main source of error is statistical and treat the theoretical errors as nuisances.

Figure 5

The 95% C.L. (solid) and 99% C.L. (dashed) combined observed limits on the coefficients $c_W$ and $c_{\overline{HB}}$ (with $c_B=-c_W$ and all other operators set to zero) from our analysis of Higgs searches in the $b\overline{b}+0l,1l,2l$ final states in ATLAS. We employ a cut $\sqrt{\widehat{s}}<1.2\mathrm{TeV}$. We compare the exclusion with LEP2 limits on TGCs (red contour).