$WW$ scattering in a radiative electroweak symmetry breaking scenario

A classically scale invariant (CSI) extension of the standard model (SM) induces radiative electroweak symmetry breaking and predicts anomalously large Higgs self-interactions. Hence, $W_L{W}_L$ scattering processes can be a good probe of the symmetry breaking mechanism. We develop a theoretical framework for perturbative computation and calculate $WW$ scattering amplitudes in a CSI model. We show that $W_L{W}_L$ scattering amplitudes satisfy the equivalence theorem and that a large deviation of $W_L{W}_L$ differential cross sections from the SM predictions is predicted depending on the c.m. energy and scattering angle. The results are more accurate than those based on the effective-potential approach. A prescription to implement predictions of the CSI model to Monte Carlo event generators is also presented.

Figure 1

Higgs tadpole diagrams in the CSI model and the SM. A blob in the CSI model represents the tree-level vertex, while a vertex with cross represents the counterterms. (The counterterms in the CSI model and the SM are different. See text).

Figure 2

Higgs self-energy diagrams in the CSI model and the SM. Similar to Fig. 1, a blob and a vertex with a cross represent the tree-level vertex and counterterm, respectively.

Figure 3

Singlet self-energy diagrams contributing to the lowest-order radiative corrections to the singlet mass $m_s$. (Note that ${\lambda }_S$ is omitted throughout the paper).

Figure 4

Diagrams for $W^{+}{W}^{-}\to W^{+}{W}^{-}$ scattering. Time flows upwards.

Figure 5

Diagrams for $W^{+}{W}^{+}\to W^{+}{W}^{+}$ scattering. (Time flows upwards, which is similar to Fig. 4).

Figure 6

Differential cross sections for the $W_L^{+}{W}_L^{-}\to W_L^{+}{W}_L^{-}$ process for the c.m. energies $\sqrt{s}=0.2$, 1, and 2 TeV. We set $N=1$. $\theta$ represents the angle between the initial $W^{+}$ and final $W^{+}$ momenta in the c.m. frame. See text for the input parameters. Dot-dashed (green) line represents the Born SM cross section, dashed (blue) line the SM cross section, and solid (red) line the CSI model cross section.

Figure 7

Ratio of the $W_L^{+}{W}_L^{-}$ scattering differential cross sections for the CSI model and SM vs $\cos \theta$, at $\sqrt{s}=0.2\mathrm{TeV}$ (green dot dashed), 1 TeV (blue dashed), and 2 TeV (red solid).

Figure 8

Same as Fig. 6 but for the $W_L^{+}{W}_L^{+}\to W_L^{+}{W}_L^{+}$ process.

Figure 9

Same as Fig. 7 but for the $W_L^{+}{W}_L^{+}$ scattering.

Figure 10

Insertion of the ${\lambda }_{\mathrm{HS}}{v}^2{s}_i{s}_i$ vertex to a 1PI diagram, and insertion of the ${\lambda }_{\mathrm{H}}{v}^{2}hh$ vertex to a 1PI diagram, respectively. These manipulations do not increase the number of loops.

Figure 11

Diagrams for $G^{+}{G}^{-}\to G^{+}{G}^{-}$ scattering. (Time flows upwards.) The last two diagrams are the new contributions in the CSI model.

Figure 12

Same as Fig. 11 but for $G^{+}{G}^{+}\to G^{+}{G}^{+}$ scattering.