The Higgs Trilinear Coupling and the Scale of New Physics
TL;DR: In this paper, modifications of the Higgs trilinear coupling were considered and the violation of tree-level unitarity was used as an estimate of the scale where the theory breaks down.
Abstract: We consider modifications of the Higgs potential due to new physics at high energy scales. These upset delicate cancellations predicted by the Standard Model for processes involving Higgs bosons and longitudinal gauge bosons, and lead to a breakdown of the theory at high energies. We focus on modifications of the Higgs trilinear coupling and use the violation of tree-level unitarity as an estimate of the scale where the theory breaks down. We obtain a completely model-independent bound of ~ 13 TeV for an order-1 modification of the trilinear. We argue that this bound can be saturated only in fine-tuned models, and the scale of new physics is likely to be much lower. The most stringent bounds are obtained from amplitudes involving multiparticle states that are not conventional scattering states. Our results show that a future determination of the Higgs cubic coupling can point to a well-defined scale of new physics that can be targeted and explored at future colliders.
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TL;DR: In this paper, indirect constraints on the quartic Higgs self-coupling arising from double-Higgs production at future hadron colliders were studied and the reach of a $pp$ collider operating at $27 \, {\rm TeV}$ and $100 \, Ω( √ TeV) center-of-mass energy was estimated.
Abstract: We study the indirect constraints on the quartic Higgs self-coupling that arise from double-Higgs production at future hadron colliders. To this purpose, we calculate the two-loop contributions to the $gg \to hh$ amplitudes that involve a modified $h^4$ vertex. Based on our results, we estimate the reach of a $pp$ collider operating at $27 \, {\rm TeV}$ and $100 \, {\rm TeV}$ centre-of-mass energy in constraining the cubic and quartic Higgs self-couplings by measurements of double-Higgs and triple-Higgs production in gluon-fusion.
2 citations
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TL;DR: In this article, the authors derived compact expressions for the bounds on the Yukawa couplings for the cases where the fields transform under trivial, fundamental or adjoint representation of the various $SU(N) factors.
Abstract: We study perturbative unitarity constraints on generic Yukawa interactions where the involved fields have arbitrary quantum numbers under an $\prod_i SU(N_i) \otimes U(1)$ group. We derive compact expressions for the bounds on the Yukawa couplings for the cases where the fields transform under the trivial, fundamental or adjoint representation of the various $SU(N)$ factors. We apply our results to specific models formulated to explain the anomalous measurements of $(g-2)_\mu$ and of the charged- and neutral-current decays of the $B$ mesons. We show that, while these models can generally still explain the observed experimental values, the required Yukawa couplings are pushed at the edge of the perturbative regime.
2 citations
TL;DR: Generalized Effective Field Theory (GEFT) as mentioned in this paper is a non-renormalizable extension of an effective field theory where the Wilson coefficients are endowed by their own independent scale dependence, and can be constructed by quantizing a Lagrangian in the presence of all internal symmetry respecting operators of any mass dimension.
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TL;DR: In this paper, the authors considered the Standard Model as an effective low-energy theory, higher dimensional interaction terms appear in the Lagrangian and performed their classification once again from the outset.
Abstract: When the Standard Model is considered as an effective low-energy theory, higher dimensional interaction terms appear in the Lagrangian. Dimension-six terms have been enumerated in the classical article by Buchmuller and Wyler [3]. Although redundance of some of those operators has been already noted in the literature, no updated complete list has been published to date. Here we perform their classification once again from the outset. Assuming baryon number conservation, we find 15 + 19 + 25 = 59 independent operators (barring flavour structure and Hermitian conjugations), as compared to 16 + 35 + 29 = 80 in ref. [3]. The three summed numbers refer to operators containing 0, 2 and 4 fermion fields. If the assumption of baryon number conservation is relaxed, 5 new operators arise in the four-fermion sector.
2,090 citations
"The Higgs Trilinear Coupling and th..." refers background in this paper
...First, we do not assume that the leading deviations from the Standard Model arise from the leading terms in an effective field theory framework such as SMEFT [33,34] or HEFT [35] (as reviewed in [36,37])....
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TL;DR: In this paper, the first two terms of the effective lagrangian were constructed in an expansion in powers of 1/Λ and studied systematically possible effects of new interactions such as anomalous magnetic moments, deviations from universality in weak interactions and rare processes.
2,023 citations
"The Higgs Trilinear Coupling and th..." refers background in this paper
...First, we do not assume that the leading deviations from the Standard Model arise from the leading terms in an effective field theory framework such as SMEFT [33,34] or HEFT [35] (as reviewed in [36,37])....
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TL;DR: In this paper, the consequences of an effective lagrangian for quarks, gluons and goldstone bosons in the region between the chiral symmetry breaking and confinement scales were studied.
1,582 citations
"The Higgs Trilinear Coupling and th..." refers methods in this paper
...f the SILH power counting to the case where the Higgs is not a pseudo-Nambu-Goldstone boson [38, 47]. For g ˘4ˇ= p N Eq. (3.1) reproduces \nave dimensional analysis" (NDA) for large-N theories [52,53], which works reasonably well in estimating the size of terms in the eective chiral Lagrangian of QCD, as well as in calculable strongly-coupled SUSY theories [54{56]. The second line in Eq. (3.1) sh...
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TL;DR: In this paper, it was shown that the parital wave unitarity is not respected by the tree diagrams for two-body scattering of gauge bosons, and the weak interactions must become strong at high energies.
Abstract: We give an $S$-matrix-theoretic demonstration that if the Higgs-boson mass exceeds ${M}_{c}={(8\ensuremath{\pi}\frac{\sqrt{2}}{3}{G}_{F})}^{\frac{1}{2}}$, parital-wave unitarity is not respected by the tree diagrams for two-body scattering of gauge bosons, and the weak interactions must become strong at high energies. We exhibit the relation of this bound to the structure of the Higgs-Goldstone Lagrangian, and speculate on the consequences of strongly coupled Higgs-Goldstone systems. Prospects for the observation of massive Higgs scalars are noted.
1,206 citations
"The Higgs Trilinear Coupling and th..." refers background in this paper
...e interpret it as an upper bound on the scale of new physics. This is a variation on a classic success story in particle physics. Long before the discovery of the Higgs boson, Lee, Quigg, and Thacker [27,28] observed that in a theory without a Higgs sector, the scattering of longitudinally polarized Wand Zbosons violates tree-level unitarity in the UV, and used this to give a model-independent upper boun...
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TL;DR: In this paper, the authors developed a simple description of models where electroweak symmetry breaking is triggered by a light composite Higgs, which emerges from a strongly-interacting sector as a pseudo-Goldstone boson.
Abstract: We develop a simple description of models where electroweak symmetry breaking is triggered by a light composite Higgs, which emerges from a strongly-interacting sector as a pseudo-Goldstone boson. Two parameters broadly characterize these models: mρ, the mass scale of the new resonances and gρ, their coupling. An effective low-energy Lagrangian approach proves to be useful for LHC and ILC phenomenology below the scale mρ. We identify two classes of operators: those that are genuinely sensitive to the new strong force and those that are sensitive to the spectrum of the resonances only. Phenomenological prospects for the LHC and the ILC include the study of high-energy longitudinal vector boson scattering, strong double-Higgs production and anomalous Higgs couplings. We finally discuss the possibility that the top quark could also be a composite object of the strong sector.
1,015 citations
"The Higgs Trilinear Coupling and th..." refers background or methods in this paper
...There is no universally correct expansion; various types of new physics have effective theories with different low-energy expansions (see for example [36])....
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...This is a modification of the SILH power counting to the case where the Higgs is not a pseudo-Nambu-Goldstone boson [36, 37]....
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...As shown in [36], a nonlinear field transformation h→ h− v 2 Λ2 ( h+ h(2) v + h(3) 3v2 ) (2....
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