Abstract
In this chapter we focus on the phenomenology of the composite resonances. Due to their ubiquitous presence and their tight connection with the Higgs and Electro-Weak (EW) dynamics, these states are one of the primary targets to directly test the composite Higgs scenarios in collider experiments.
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Notes
- 1.
In order to avoid confusion with the notation used for the composite states, we denote the embedding of the elementary fields in the fundamental SO(5) representation by \(q_{L}^{\mathbf{5}}\) and \(t_{R}^{\mathbf{5}}\), and not by Q L and T R as in the previous chapters. Later on we will adopt an analogous notation for the embedding in the 14.
- 2.
The X 2∕3 can be the lightest resonance inside the fourplet due to level-repulsion effects if the singlet and fourplet are close in mass. In this case, however, the lightest charge 2∕3 state is not purely the X 2∕3, but contains a large admixture of the \(\tilde{T}\).
- 3.
For simplicity in the following we will drop the prime in front of the T ′ and \(X_{2/3}^{{\prime}}\) resonances and we will denote them simply by T and X 2∕3.
- 4.
For shortness we denote by Z 2∕3 the combination of states that mixes with the top and by Y 2∕3 and U 2∕3 the orthogonal ones.
- 5.
The cross sections for pair and single production of top partners at the 8 and 13 TeV LHC can be found in [5].
- 6.
- 7.
Other corrections can arise from finite-mass effects due to the Z boson. These effects however are suppressed by \(m_{Z}^{2}/m_{\rho }^{2}\) and are negligible.
- 8.
For shortness we do not report the explicit couplings of the resonances in the 9 multiplet. The explicit expressions for the leading couplings of these states can be found in [4].
- 9.
Significant deviations from this estimate can appear if a light singlet is present or if the t R mixing is much larger than the t L one (\(y_{R} \gg y_{L}\)). In these cases the coupling follows the general estimate in Eq. (6.43).
- 10.
One free parameter, namaly y L4 in the 5 + 5 model and y Lt in the 14 + 1, has been fixed by requiring the correct value of the top mass.
- 11.
The interested reader can find a more detailed discussion in [4].
- 12.
Notice that the assumption that \(\rho _{\mu }^{X}\) transforms as a gauge field does not imply any real constraint on its properties. In full generality one can define a shifted version of the \(\rho _{\mu }^{X}\) field, namely \(\rho _{\mu }^{{\prime}X} \equiv \rho _{\mu }^{X} - g_{0}^{{\prime}}B_{\mu }\), that is invariant under U(1) X and rewrite the effective Lagrangian in terms of the new field.
- 13.
This situation is not uncommon in explicit models. For instance in the minimal scenarios all the top partners are charged under the U(1) X subgroup, thus we expect them to be coupled to vector fields with the quantum numbers of the \(\rho _{\mu }^{X}\) resonance.
- 14.
See for instance [39] for a collider study of heavy gluons decaying to top partners.
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Panico, G., Wulzer, A. (2016). Collider Phenomenology. In: The Composite Nambu-Goldstone Higgs. Lecture Notes in Physics, vol 913. Springer, Cham. https://doi.org/10.1007/978-3-319-22617-0_6
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