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Precision Tests and Fine Tuning in Twin Higgs Models

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Precision Tests and Fine Tuning in Twin Higgs Models PHYSICAL REVIEW D 96, 095036 (2017) Precision tests and fine tuning in twin Higgs models † ‡ ∥ Roberto Contino,1,* Davide Greco,2, Rakhi Mahbubani,3, Riccardo Rattazzi,2,§ and Riccardo Torre2, 1Scuola Normale Superiore and INFN, Pisa IT-56125, Italy 2Theoretical Particle Physics Laboratory, Institute of Physics, EPFL, Lausanne CH-1015, Switzerland 3Theoretical Physics Department, CERN, Geneva CH-1211, Switzerland (Received 27 February 2017; revised manuscript received 7 November 2017; published 29 November 2017) We analyze the parametric structure of twin Higgs (TH) theories and assess the gain in fine tuning which they enable compared to extensions of the standard model with colored top partners. Estimates show that, at least in the simplest realizations of the TH idea, the separation between the mass of new colored particles and the electroweak scale is controlled by the coupling strength of the underlying UV theory, and that a parametric gain is achieved only for strongly-coupled dynamics. Motivated by this consideration we focus on one of these simple realizations, namely composite TH theories, and study how well such constructions can reproduce electroweak precision data. The most important effect of the twin states is found to be the infrared contribution to the Higgs quartic coupling, while direct corrections to electroweak observables are subleading and negligible. We perform a careful fit to the electroweak data including the leading- logarithmic corrections to the Higgs quartic up to three loops. Our analysis shows that agreement with electroweak precision tests can be achieved with only a moderate amount of tuning, in the range 5%–10%, in theories where colored states have mass of order 3–5 TeVand are thus out of reach of the LHC. For these levels of tuning, larger masses are excluded by a perturbativity bound, which makes these theories possibly discoverable, hence falsifiable, at a future 100 TeV collider. DOI: 10.1103/PhysRevD.96.095036 I. INTRODUCTION where each Λ represents the physical cutoff scale in a different sector of the theory. The above equation is simply The principle of naturalness offers arguably the main dictated by symmetry: dilatations (dimensional analysis) motivation for exploring physics at around the weak scale. determine the scale dependence and the broken shift According to naturalness, the plausibility of specific symmetry of the Higgs field sets the coupling dependence. parameter choices in quantum field theory must be assessed Unsurprisingly, these contributions arise in any explicit UV using symmetries and selection rules. When viewing the completion of the SM, although in some cases there may be standard model (SM) as an effective field theory valid other larger ones. According to Eq. (1.1), any given (large) below a physical cutoff scale and considering only the value of the scale of new physics can be associated with a known interactions of the Higgs boson, we expect the (small) number ϵ, which characterizes the accuracy at following corrections to its mass.1 which the different contributions to the mass must cancel 2 2 2 among themselves, in order to reproduce the observed 3y 9g2 3g1 3λ δm2 ¼ t Λ2 − Λ2 − Λ2 − h Λ2 þÁÁÁ; ≃ 125 h 4π2 t 32π2 g2 32π2 g1 8π2 h value mh GeV. As the largest loop factor is due to the top Yukawa coupling, according to Eq. (1.1) the scale ð1:1Þ Λ 2 NP where new states must first appear is related to mh and ϵ via *[email protected] rffiffiffi † 4π2 2 1 [email protected] Λ2 ∼ mh ⇒ Λ ∼ 0 45 ‡ NP 2 × ϵ NP . ϵTeV: ð1:2Þ [email protected] 3yt §[email protected] ∥ [email protected] pffiffiffi The dimensionless quantity ϵ measures how finely-tuned 1 2 2 2 λ 2 2 2 174 2 We take mh ¼ mH ¼ hv = with hHi¼v= ¼ GeV, Λ mh is, given NP, and can therefore be regarded as a which corresponds to a potential 2 measure of the tuning. Notice that the contributions fromffiffiffi g2 λ λ Λ 1 1 pϵ − 2 2 h 4 and h in Eq. (1.1) ffiffifficorrespond to NP ¼ . TeV= and V ¼ mHjHj þ 4 jHj : p ΛNP ¼ 1.3 TeV= ϵ, respectively. Although not signifi- cantly different from the relation in the top sector, these Published by the American Physical Society under the terms of scales would still be large enough to push new states out of the Creative Commons Attribution 4.0 International license. ϵ ∼ 0 1 Further distribution of this work must maintain attribution to direct reach of the LHC for . the author(s) and the published article’s title, journal citation, Indeed, for a given ϵ, Eq. (1.2) only provides an upper and DOI. bound for ΛNP; in the more fundamental UV theory there 2470-0010=2017=96(9)=095036(31) 095036-1 Published by the American Physical Society ROBERTO CONTINO et al. PHYSICAL REVIEW D 96, 095036 (2017) 2 can in principle exist larger corrections to mh which are not coupling. As discussed in the next section, depending on captured by Eq. (1.1). In particular, in the minimal super- the structure of the model, gSM can be either the top Yukawa symmetric SM (MSSM) with high-scale mediation of the or the square root of the Higgs quartic. As a result, given the δ 2 tuning ϵ, the squared mass of the new colored and charged soft terms, mh in Eq. (1.1) is logarithmically enhanced by RG evolution above the weak scale. In that case, Eq. (1.2) is states is roughly given by modified as follows: 4π2 m2 g 2 m2 ∼ h à : : 2π2 1 2 à 3 2 × ϵ × ð1 4Þ Λ2 ∼ mh yt gSM NP 2 × Λ Λ × ϵ ; ð1:3Þ 3yt ln UV= NP For gà >gSM, we could define these model as effectively where ΛNP corresponds to the overall mass of the stops and hypersoft, in that, for fixed fine tuning, the gap between the Λ ≫ Λ UV NP is the scale of mediation of the soft terms. SM-charged states and the weak scale is even larger than However, for generic composite Higgs (CH) models, as that in supersoft models. In practice the above equation well as for supersymmetric models with low-scale media- implies that, for strong gÃ, the new states are out of reach of tion, Eq. (1.2) provides a fair estimate of the relation the LHC even for mild tuning (see Sec. II A for a more between the scale of new physics and the amount of tuning, precise statement). Equation (1.4) synthesizes the potential the Higgs mass being fully generated by quantum correc- relevance of the TH mechanism, and makes it clear that the tions at around the weak scale. If the origin of mh is new dynamics must be rather strong for the mechanism to Λ normally termed soft in the MSMM with large UV work. Given the hierarchy problem, it then seems almost [Eq. (1.3)], it should then be termed supersoft in models inevitable to make the TH a composite TH (although it respecting Eq. (1.2). As is well known, and shown by could also be a supersymmetric composite TH). Realizations Λ ≳ Eq. (1.3), the natural expectation in the MSSM for UV of the TH mechanism within the paradigm of CH models 100 TeV is ΛNP ∼ mZ ∼ mh. In view of this, soft scenarios with fermion partial compositeness [23] have already been were already somewhat constrained by direct searches at proposed, both in the holographic and effective theory LEP and Tevatron, whereas the natural range of the scale of setups [6,9,13,14]. supersoft models is only now being probed at the LHC. It is important to recognize that the factor that boosts the Equation (1.2) sets an absolute upper bound on ΛNP for a mass of the states with SM gauge quantum numbers in given fine tuning ϵ, but does not give any information on its Eq. (1.4) is the coupling gà itself. Because of this, strong- nature. In particular it does not specify the quantum dynamics effects in the Higgs sector, which are described numbers of the new states that enter the theory at or below in the low-energy theory by nonrenormalizable operators this scale. Indeed, the most relevant states associated with with coefficients proportional to powers of gÃ=mÃ, do not the top sector, the so-called top partners, are bosonic in “decouple” when these states are made heavier, at fixed fine ϵ standard supersymmetric models and fermionic in CH tuning . In the standard parametrics of the CH, mÃ=gà is of models. Nonetheless, one common feature of these stan- the order of f, the decay constant of the σ-model within dard scenarios is that the top partners carry SM quantum which the Higgs doublet emerges as a pseudo-Nambu- 2 2 numbers, color in particular. They are thus copiously Goldstone boson (pNGB). Then ξ ≡ v =f , as well as produced in hadronic collisions, making the LHC a good being a measure of the fine tuning through ϵ ¼ 2ξ, also probe of these scenarios. Yet there remains the logical measures the relative deviation of the Higgs couplings from 2 possibility that the states that are primarily responsible for the SM ones, in the TH like in any CH model. Recent ξ ≲ the origin of the Higgs mass at or below ΛNP are not Higgs coupling measurements roughly constrain charged under the SM, and thus much harder to produce 10–20% [24], and a sensitivity of order 5% is expected and detect at the LHC. The twin Higgs (TH) is probably the in the high-luminosity phase of the LHC [25].
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