Implications of vector boson scattering unitarity in composite Higgs models

The strong nature of composite Higgs models manifests at high energies through the growing behavior of the scattering amplitudes of longitudinally polarized weak bosons that leads to the formation of composite resonances as well as nonresonant strong effects. In this work the unitarity of these scattering amplitudes is used as a tool to assess the profile of the composite spectrum of the theory, including nonresonant enhancements, vector resonances and the $CP$-even scalar excitation. These three signatures are then studied in realistic scattering processes at hadron colliders, aiming to estimate the potential to exclude dynamically motivated scenarios of composite Higgs models.

Figure 1

Unitarity violation [Eq. (23)] scale of $a_{A0}(s)$ as a function of $\widehat{L_A}(8\mathrm{TeV})$ for $\sin \theta =0.2$ at NLO (blue solid line) and LO (black solid line). Also shown are the regions of lost of perturbativity $K\equiv |a^{\mathrm{NLO}}(s)|/|a^{\mathrm{LO}}(s)|-1>50\%$ (blue shaded area), $K>100\%$ (brown area), and $K<-50\%$ (green area).

Figure 2

Absolute value of partial wave amplitude $a_{B1}^{\mathrm{IAM}}(s)$ shown together with $a_{B1}^{\mathrm{NLO}}(s)$ and $a_{B1}^{\mathrm{LO}}(s)$ for $\sin \theta =0.2$ and $\sin \theta =0.15$.

Figure 3

Absolute value of partial wave amplitude $a_{A0}^{\mathrm{IAM}}(s)$ shown together with $a_{A0}^{\mathrm{NLO}}(s)$ and $a_{A0}^{\mathrm{LO}}(s)$.

Figure 4

Value of ${\upsilon }_C$ as a function of ${\upsilon }_A$ for fixed value of ${\upsilon }_B=3.2$.

Figure 5

Absolute value of partial wave amplitude $a_{B1}^0(s)+a_{B1}^v(s)$ together with LO, NLO and IAM equivalents, for three values of $a_V=0.8$, 1, 1.2 and $\sin \theta =0.2$.

Figure 6

(Left) Absolute value of partial wave amplitudes $a_{A0}^0(s)+a_{A0}^{\sigma }(s)+a_{A0}^v(s)$ together with LO, NLO and IAM equivalents. (Right) Equivalent amplitudes for $B1$ channel, $a_{B1}^0(s)+a_{B1}^{\sigma }(s)+a_{B1}^v(s)$. Parameters are ${\upsilon }_A=1$, $\sin \theta =0.2$, $g_{\sigma }=0.63$. The effect of inelastic channels in the unitarity bound is depicted by the dotted black curve and explained in the text.

Figure 7

Absolute value of partial wave amplitudes $a_{A0}^0(s)+a_{A0}^{\sigma }(s)$ for ${\upsilon }_A=0.5$, 1, 1.5, using the IAM unitarization model (solid curve), a fixed width $\sigma$ resonance (dashed line) and a running width (dotted line).

Figure 8

Absolute value of partial wave amplitudes $a_{A0}^0(s)+a_{A0}^{\sigma }(s)$ for $g_{\sigma }=0.4$, 0.63, 0.8, using a fixed width (solid curve) and a running width (dashed line) compared to the IAM (cyan line).

Figure 9

The 95% C.L. exclusion regions in the $(\tilde{g},r)$ plane for $\sin \theta =0.2$ (left) and $\sin \theta =0.15$ (right) in the $\rho \to WZ$ (blue contour, hashed) and $\rho \to {\ell }^{+}{\ell }^{-}$ (red, shaded) channels. $L=1{\mathrm{ab}}^{-1}$ (solid contour) and $L=10{\mathrm{ab}}^{-1}$.

Figure 10

(a) The $ZZ$ system reconstructed invariant mass distribution for $\sin \theta =0.1$, 0.15, 0.2 in the nonresonant excess scenario and the SM backgrounds (EW $ZZjj$ and QCD $ZZ+\text{jets}$). (b) The corresponding $1-\beta$.

Figure 11

(a) The $ZZ$ system reconstructed invariant mass distribution in the $\sigma$ resonant excess scenarios (Table 2). (b) The corresponding $1-\beta$.

Figure 12

$ZZ$ invariant mass at the LHC for the composite scenario devised for LHC ($g_{\sigma }=0.8$, $M_{\sigma }=4\mathrm{TeV}$) and the SM backgrounds (EW $ZZjj$ and QCD $ZZ+\text{jets}$).