Disentangling a dynamical Higgs

TL;DR

The paper develops a model-independent comparison between linear and non-linear realizations of electroweak symmetry breaking in the presence of a light Higgs, using an effective Lagrangian framework that includes CP-even gauge and gauge–Higgs operators up to four derivatives in the non-linear case and dimension-six operators in the linear case. It shows that decorrelations of couplings and a larger set of leading interactions arise in the non-linear (chiral) realization, and it identifies new signals that would appear at leading order only in the non-linear framework (e.g., $\xi^n$ with $n\ge2$ and anomalous $ZWW$/$\gamma ZWW$ couplings). The authors provide a complete renormalization procedure, derive Feynman rules for the non-linear basis, and compare to the HISZ linear basis, establishing both commonalities and distinctive predictions for LHC phenomenology, EWPD constraints, and Higgs observables. They quantify present bounds on the $\xi$-weighted operators from Higgs and electroweak data and project the potential reach of the LHC (including $g_5^Z$ and quartic couplings) to discriminate between linear and non-linear EWSB dynamics. Collectively, this work offers a practical framework to test the Higgs’s nature and the underlying EWSB mechanism through precise measurements of HVV/TGV and multi-boson interactions at the LHC and future colliders.

Abstract

The pattern of deviations from Standard Model predictions and couplings is different for theories of new physics based on a non-linear realization of the $SU(2)_L\times U(1)_Y$ gauge symmetry breaking and those assuming a linear realization. We clarify this issue in a model-independent way via its effective Lagrangian formulation in the presence of a light Higgs particle, up to first order in the expansions: dimension-six operators for the linear expansion and four derivatives for the non-linear one. Complete sets of pure gauge and gauge-Higgs operators are considered, implementing the renormalization procedure and deriving the Feynman rules for the non-linear expansion. We establish the theoretical relation and the differences in physics impact between the two expansions. Promising discriminating signals include the decorrelation in the non-linear case of signals correlated in the linear one: some pure gauge versus gauge-Higgs couplings and also between couplings with the same number of Higgs legs. Furthermore, anomalous signals expected at first order in the non-linear realization may appear only at higher orders of the linear one, and vice versa. We analyze in detail the impact of both type of discriminating signals on LHC physics.

Figures (3)

• Figure 1: $\Delta\chi^2_{\rm Higgs}$ dependence on the coefficients of the seven bosonic operators in Eq. (\ref{['eq:Hbase']}) from the analysis of all Higgs collider (ATLAS, CMS and Tevatron) data. In each panel, we marginalized over the five undisplayed variables. The six upper (lower) panels corresponds to analysis with set A ( B). In each panel the red solid (blue dotted) line stands for the analysis with the discrete parameter $s_Y=+(-)$.
• Figure 2: Left:A BSM sensor irrespective of the type of expansion: constraints from TGV and Higgs data on the combinations $\Sigma_B=4(2c_2+a_4)$ and $\Sigma_W=2(2c_3-a_5)$, which converge to $f_B$ and $f_W$ in the linear $d=6$ limit. The dot at $(0,0)$ signals the SM expectation. Right:A non-linear versus linear discriminator: constraints on the combinations $\Delta_B=4(2c_2-a_4)$ and $\Delta_W=2(2c_3+a_5)$, which would take zero values in the linear (order $d=6$) limit (as well as in the SM), indicated by the dot at $(0,0)$. For both figures the lower left panels shows the 2-dimensional allowed regions at 68%, 90%, 95%, and 99% CL after marginalization with respect to the other six parameters ($a_G$, $a_W$, $a_B$, $c_H$, $\Delta_B$, and $\Delta_W$) and ($a_G$, $a_W$, $a_B$, $c_H$, $\Sigma_B$, and $\Sigma_W$) respectively. The star corresponds to the best fit point of the analysis. The upper left and lower right panels give the corresponding 1-dimensional projections over each of the two combinations.
• Figure 3: The left (right) panel displays the number of expected events as a function of the $Z$ transverse momentum for a center--of--mass energy of 7 (14) TeV, assuming an integrated luminosity of $4.64$ ($300$) fb$^{-1}$. The black histogram corresponds to the sum of all background sources except for the SM electroweak $pp\rightarrow W^\pm Z$ process, while the red histogram corresponds to the sum of all SM backgrounds, and the dashed distribution corresponds to the addition of the anomalous signal for $g_5^Z=0.2$ ($g_5^Z=0.1$). The last bin contains all the events with $p_T^Z>180$ GeV.