Custodial Symmetry Research Articles

The bulk Higgs in the deformed RS model

Electroweak precision tests allow for lighter Kaluza–Klein (KK) Higgs modes in the deformed Randall–Sundrum (RS) model than in models with custodial symmetry. The first KK mode of the Higgs (h1) in such a model could have a mass as low as 900 GeV. In this paper, we study the production of h1 and its subsequent decay to a tt¯ pair at the Large Hadron Collider (LHC), in the context of the deformed RS model. We have performed a hadron-level Monte Carlo simulation of the signal and the relevant Standard Model background. We present strategies to effectively suppress the huge SM background and provide a signal that is tractable at the future runs of the LHC.

Non-Abelian strings and domain walls in two Higgs doublet models

Contrary to the standard model that does not admit topologically nontrivial solitons, two Higgs doublet models admit topologically stable vortex strings and domain walls. We numerically confirm the existence of a topological Z-string confining fractional Z-flux inside. We show that topological strings at sin θW = 0 limit reduce to non-Abelian strings which possess non-Abelian moduli S2 associated with spontaneous breakdown of the SU(2) custodial symmetry. We numerically solve the equations of motion for various parameter choices. It is found that a gauging U(1)Y always lowers the tension of the Z-string while it keeps that of the W-string. On the other hand, a deformation of the Higgs potential is either raising or lowering the tensions of the Z-string and W-string. We numerically obtain an effective potential for the non-Abelian moduli S2 for various parameter deformations under the restriction tan β = 1. It is the first time to show that there exists a certain parameter region where the topological W-string can be the most stable topological excitation, contrary to conventional wisdom of electroweak theories. We also obtain numerical solutions of composites of the string and domain walls in a certain condition.

Topological defects in the Georgi-Machacek model

We study topological defects in the Georgi-Machacek model in a hierarchical symmetry breaking in which extra triplets acquire vacuum expectation values before the doublet. We find a possibility of topologically stable non-Abelian domain walls and non-Abelian flux tubes (vortices) in this model. In the limit of the vanishing $U(1)_{\rm Y}$ gauge coupling in which the custodial symmetry becomes exact, the presence of a vortex spontaneously breaks the custodial symmetry, giving rise to $S^2$ Nambu-Goldstone (NG) modes localized around the vortex corresponding to non-Abelian fluxes. Vortices are continuously degenerated by these degrees of freedom, thereby called non-Abelian. By taking into account the $U(1)_{\rm Y}$ gauge coupling, the custodial symmetry is explicitly broken, the NG modes are lifted, and all non-Abelian vortices fall into a topologically stable $Z$-string. This is in contrast to the SM in which $Z$-strings are non-topological and are unstable in the realistic parameter region.Non-Abelian domain walls also break the custodial symmetry and are accompanied by localized $S^2$ NG modes. Finally, we discuss the existence of domain wall solutions bounded by flux tubes, where their $S^2$ NG modes match. The domain walls may quantum mechanically decay by creating a hole bounded by a flux tube loop, and would be cosmologically safe. Gravitational waves produced from unstable domain walls could be detected by future experiments

Light (and darkness) from a light hidden Higgs

We examine light diphoton signals from extended Higgs sectors possessing (approximate) fermiophobia with Standard Model (SM) fermions as well as custodial symmetry. This class of Higgs sectors can be realized in various beyond the SM scenarios and is able to evade many experimental limits, even at light masses, which are otherwise strongly constraining. Below the WW threshold, the most robust probes of the neutral component are di and multi-photon searches. Utilizing the dominant Drell-Yan Higgs pair production mechanism and combining it with updated LHC diphoton data, we derive robust upper bounds on the allowed branching ratio for masses between 45 − 160 GeV. Furthermore, masses ≲ 110 GeV are ruled out if the coupling to photons is dominated by W boson loops. We then examine two simple ways to evade these bounds via cancellations between different loop contributions or by introducing decays into an invisible sector. This also opens up the possibility of future LHC diphoton signals from a light hidden Higgs sector. As explicit realizations, we consider the Georgi-Machacek (GM) and Supersymmetric GM (SGM) models which contain custodial (degenerate) Higgs bosons with suppressed couplings to SM fermions and, in the SGM model, a (neutralino) LSP. We also breifly examine the recent ∼ 3σ CMS diphoton excess at ∼ 95 GeV.

Conditions for the custodial symmetry in multi-Higgs-doublet models

We derive basis-independent, necessary and sufficient conditions for the custodial symmetry in N-Higgs-doublet models (NHDM) for N ≥ 3, and apply them on some 3HDM examples.

Low scale composite Higgs model and 1.8 ∼2 TeV diboson excess

We consider a simple solution to explain the recent diboson excess observed by ATLAS and CMS Collaborations in models with custodial symmetry [Formula: see text]. The [Formula: see text] triplet vector boson [Formula: see text] with mass range of [Formula: see text] TeV would be produced through the Drell–Yan process with sizable diboson decay branching to account for the excess. The other [Formula: see text] bidoublet axial vector boson [Formula: see text] would cancel all deviations of electroweak obervables induced by [Formula: see text] even if the SM fermions mix with some heavy vector-like (composite) fermions which couple to [Formula: see text] (“nonuniversally partially composite”), therefore allows arbitrary couplings between each SM fermion and [Formula: see text]. We present our model in the “General Composite Higgs” framework with [Formula: see text] breaking at scale [Formula: see text] and demand the first Weinberg sum rule and positive gauge boson form factors as the theoretical constraints. We find that our model can fit the diboson excess very well if the left-handed SM light quarks, charged leptons and tops have zero, zero/moderately small and moderate/large composite components for reasonable values of [Formula: see text] and [Formula: see text]. The correlation between tree level [Formula: see text] parameter and the [Formula: see text] suggest a large [Formula: see text] contribution to [Formula: see text] and it is indeed a [Formula: see text] effect in our parameter space which provides a strong hint for our scenario if this diboson excess is confirmed by the [Formula: see text] TeV LHC Run II.

Perturbativity constraints in BSM models

Phenomenological studies performed for non-supersymmetric extensions of the Standard Model usually use tree-level parameters as input to define the scalar sector of the model. This implicitly assumes that a full on-shell calculation of the scalar sector is possible – and meaningful. However, this doesn’t have to be the case as we show explicitly at the example of the Georgi-Machacek model. This model comes with an appealing custodial symmetry to explain the smallness of the rho parameter. However, the model cannot be renormalised on-shell without breaking the custodial symmetry. Moreover, we find that it can often happen that the radiative corrections are so large that any consideration based on a perturbative expansion appears to be meaningless: counter-terms to quartic couplings can become much larger than 4pi and/or two-loop mass corrections can become larger than the one-loop ones. Therefore, conditions are necessary to single out parameter regions which cannot be treated perturbatively. We propose and discuss different sets of such perturbativity conditions and show their impact on the parameter space of the Georgi-Machacek model. Moreover, the proposed conditions are general enough that they can be applied to other models as well. We also point out that the vacuum stability constraints in the Georgi-Machacek model, which have so far only been applied at the tree level, receive crucial radiative corrections. We show that large regions of the parameter space which feature a stable electroweak vacuum at the loop level would have been – wrongly – ruled out by the tree-level conditions.

Leptogenesis as an origin of hot dark matter and baryon asymmetry in the E6 inspired SUSY models

We explore leptogenesis within the E6 inspired U(1) extension of the MSSM in which exact custodial symmetry forbids tree-level flavour-changing transitions and the most dangerous baryon and lepton number violating operators. This supersymmetric (SUSY) model involves extra exotic matter beyond the MSSM. In the simplest phenomenologically viable scenarios the lightest exotic fermions are neutral and stable. These states should be substantially lighter than 1eV forming hot dark matter in the Universe. The low-energy effective Lagrangian of the SUSY model under consideration possesses an approximate global U(1)E symmetry associated with the exotic states. The U(1)E symmetry is explicitly broken because of the interactions between the right-handed neutrino superfields and exotic matter supermultiplets. As a consequence the decays of the lightest right-handed neutrino/sneutrino give rise to both U(1)E and U(1)B−L asymmetries. When all right-handed neutrino/sneutrino are relatively light ∼106–107GeV the appropriate amount of the baryon asymmetry can be induced via these decays if the Yukawa couplings of the lightest right-handed neutrino superfields to the exotic matter supermultiplets vary between ∼10−4–10−3.

Neutrino mass with large SU(2)L multiplet fields

We propose an extension of the standard model introducing large $SU(2)_L$ multiplet fields which are quartet and septet scalars and quintet Majorana fermions. These multiplets can induce the neutrino masses via interactions with the $SU(2)$ doublet leptons. We then find the neutrino masses are suppressed by small vacuum expectation value of the quartet/septet and an inverse of quintet fermion mass relaxing the Yukawa hierarchies among the standard model fermions. We also discuss collider physics at the Large Hadron Collider considering production of charged particles in these multiplets, and due to effects of violating custodial symmetry, some specific signatures can be found. Then we discuss the detectability of these signals.

Vector SIMP dark matter

Strongly Interacting Massive Particles (SIMPs) have recently been proposed as light thermal dark matter relics. Here we consider an explicit realization of the SIMP mechanism in the form of vector SIMPs arising from an SU(2)X hidden gauge theory, where the accidental custodial symmetry protects the stability of the dark matter. We propose several ways of equilibrating the dark and visible sectors in this setup. In particular, we show that a light dark Higgs portal can maintain thermal equilibrium between the two sectors, as can a massive dark vector portal with its generalized Chern-Simons couplings to the vector SIMPs, all while remaining consistent with experimental constraints.

Exploring the warped bulk

A review of the class of models that go under the name bulk Randall–Sundrum models is presented here. The issue of localization of quantum fields in the five-dimensional bulk and the profiles of the zero modes and the Kaluza–Klein excitations are discussed. The zero modes of these bulk fields are, in general, partially composite. The degree of compositeness of the different fields is discussed and this provides the basis for realizing a Standard Model in the bulk, albeit partially composite. The viability of this model and its extensions when confronted with electroweak precision measurements is also discussed. Two such extensions are: (1) models with a bulk custodial symmetry and (2) models with a deformed metric. The signatures of these models that we expect at collider experiments are discussed and also the search for the Kaluza–Klein excitation of the gluon as the most important of these signatures.

Effects of custodial symmetry breaking in the Georgi-Machacek model at high energies

The model proposed by Georgi and Machacek enables the Higgs sector to involve isospin triplet scalar fields while retaining a custodial $SU(2)_V$ symmetry in the potential and thus ensuring the electroweak $\rho$ parameter to be one at tree level. This custodial symmetry, however, is explicitly broken by loop effects of the $U(1)_Y$ hypercharge gauge interaction. In order to make the model consistent at high energies, we construct the most general form of the Higgs potential without the custodial symmetry, and then we derive the one-loop $\beta$-functions for all the model parameters. Assuming the $\delta_i$ quantities describing the custodial symmetry breaking to be zero at low energy, we find that $|\delta_i|$ are typically smaller than the magnitude of the $U(1)_Y$ gauge coupling and the other running parameters in the potential also at high energy without spoiling perturbativity and vacuum stability. We also clarify that the mass degeneracy among the $SU(2)_V$ 5-plet and 3-plet Higgs bosons is smoothly broken by $\sim 0.1\%$ corrections. These results show that the amount of the custodial symmetry breaking is well kept under control up to energies close to the theory cutoff.

CEPC precision of electroweak oblique parameters and weakly interacting dark matter: The fermionic case

Future electroweak precision measurements in the Circular Electron Positron Collider (CEPC) project would significantly improve the precision of electroweak oblique parameters. We evaluate the expected precision through global fits, and study the corresponding sensitivity to weakly interacting fermionic dark matter. Three models with electroweak multiplets in the dark sector are investigated as illuminating examples. We find that the CEPC data can probe up to TeV scales and explore some regions where direct detection cannot reach, especially when the models respect the custodial symmetry.

Constraining the scalar septet model through vector boson scattering

The scalar septet model extends the Standard Model Higgs sector by an isospin septet with hypercharge chosen to preserve $\rho \equiv M_W^2/M_Z^2 \cos^2\theta_W = 1$. In this paper we constrain the model at high septet masses using perturbative unitarity of longitudinal vector boson scattering amplitudes. We also apply the constraints from LHC searches for doubly-charged Higgs bosons produced in vector boson fusion, which constrain the model at lower septet masses. We point out some important differences between the septet model and extended Higgs models that preserve custodial symmetry in the scalar spectrum.

Real singlet scalar dark matter extension of the Georgi-Machacek model

The Georgi-Machacek model extends the Standard Model Higgs sector with the addition of isospin-triplet scalar fields in such a way as to preserve the custodial symmetry. The presence of higher-isospin scalars contributing to electroweak symmetry breaking offers the interesting possibility that the couplings of the 125 GeV Higgs boson to both gluons and vector boson pairs could be larger than those of the Standard Model Higgs boson. Constraining this possibility using measurements of Higgs production and decay at the CERN Large Hadron Collider is notoriously problematic if a new, non--Standard Model decay mode of the 125 GeV Higgs boson is present. We study an implementation of this scenario in which the Georgi-Machacek model is extended by a real singlet scalar dark matter candidate, and require that the singlet scalar account for all the dark matter in the Universe. The combination of the observed dark matter relic density and direct-detection constraints exclude singlet scalar masses below about 57 GeV. Higgs measurements are not yet precise enough to be very sensitive to $h\ensuremath{\rightarrow}SS$ in the remaining allowed kinematic region, so that constraints from Higgs measurements are so far the same as in the GM model without a singlet scalar. We also find that, above the Higgs pole, a substantial region of parameter space yielding the correct dark matter relic density can escape the near-future direct-detection experiments DEAP and XENON 1T for dark matter masses as low as 120 GeV and even have a direct-detection cross section below the neutrino floor for ${m}_{S}\ensuremath{\gtrsim}150\text{ }\text{ }\mathrm{GeV}$. This is in contrast to the singlet scalar dark matter extension of the Standard Model, for which these future experiments are expected to exclude dark matter masses above the Higgs pole up to the multi-TeV range.

Golden Probe of Electroweak Symmetry Breaking.

The ratio of the Higgs couplings to WW and ZZ pairs, λ_{WZ}, is a fundamental parameter in electroweak symmetry breaking as well as a measure of the (approximate) custodial symmetry possessed by the gauge boson mass matrix. We show that Higgs decays to four leptons are sensitive, via tree level or one-loop interference effects, to both the magnitude and, in particular, overall sign of λ_{WZ}. Determining this sign requires interference effects, as it is nearly impossible to measure with rate information. Furthermore, simply determining the sign effectively establishes the custodial representation of the Higgs boson. We find that h→4ℓ (4ℓ≡2e2μ, 4e, 4μ) decays have excellent prospects of directly establishing the overall sign at a high luminosity 13TeV LHC. We also examine the ultimate LHC sensitivity in h→4ℓ to the magnitude of λ_{WZ}. Our results are independent of other measurements of the Higgs boson couplings and, in particular, largely free of assumptions about the top quark Yukawa couplings which also enter at one loop. This makes h→4ℓ a unique and independent probe of electroweak symmetry breaking and custodial symmetry.

Dark matter in a constrained E 6 inspired SUSY model

We investigate dark matter in a constrained $E_6$ inspired supersymmetric model with an exact custodial symmetry and compare with the CMSSM. The breakdown of $E_6$ leads to an additional $U(1)_N$ symmetry and a discrete matter parity. The custodial and matter symmetries imply there are two stable dark matter candidates, though one may be extremely light and contribute negligibly to the relic density. We demonstrate that a predominantly Higgsino, or mixed bino-Higgsino, neutralino can account for all of the relic abundance of dark matter, while fitting a 125 GeV SM-like Higgs and evading LHC limits on new states. However we show that the recent LUX 2016 limit on direct detection places severe constraints on the mixed bino-Higgsino scenarios that explain all of the dark matter. Nonetheless we still reveal interesting scenarios where the gluino, neutralino and chargino are light and discoverable at the LHC, but the full relic abundance is not accounted for. At the same time we also show that there is a huge volume of parameter space, with a predominantly Higgsino dark matter candidate that explains all the relic abundance, that will be discoverable with XENON1T. Finally we demonstrate that for the $E_6$ inspired model the exotic leptoquarks could still be light and within range of future LHC searches.

A Higgs in the warped bulk and LHC signals

Warped models with the Higgs in the bulk can generate light Kaluza-Klein (KK) Higgs modes consistent with the electroweak precision analysis. The first KK mode of the Higgs (h_{1}) could lie in the 1-2 TeV range in the models with a bulk custodial symmetry. We find that the h_{1} is gaugephobic and decays dominantly into a t\bar{t} pair. We also discuss the search strategy for h_{1} decaying to t\bar{t} at the Large Hadron Collider. We used substructure tools to suppress the large QCD background associated with this channel. We find that h_{1} can be probed at the LHC run-2 with an integrated luminosity of 300 fb^{-1}.

Scale-independent inflation and hierarchy generation

We discuss models involving two scalar fields coupled to classical gravity that satisfy the general criteria: (i) the theory has no mass input parameters, (ii) classical scale symmetry is broken only through $-\frac{1}{12}\varsigma \phi^2 R$ couplings where $\varsigma$ departs from the special conformal value of $1$; (iii) the Planck mass is dynamically generated by the vacuum expectations values (VEVs) of the scalars (iv) there is a stage of viable inflation associated with slow roll in the two--scalar potential; (v) the final vacuum has a small to vanishing cosmological constant and an hierarchically small ratio of the VEVs and the ratio of the scalar masses to the Planck scale. This assumes the paradigm of classical scale symmetry as a custodial symmetry of large hierarchies.

Probing Higgs-radion mixing in warped models through complementary searches at the LHC and the ILC

We consider the Higgs-radion mixing in the context of warped space extra dimensional models with custodial symmetry and investigate the prospects of detecting the mixed radion. Custodial symmetries allow the Kaluza-Klein excitations to be lighter, and protect Zbb to be in agreement with experimental constraints. We perform a complementary study of discovery reaches of the Higgs-radion mixed state at the 13 and 14 TeV LHC and at the 500 and 1000 GeV ILC. We carry out a comprehensive analysis of the most significant production and decay modes of the mixed radion in the 80 GeV - 1 TeV mass range, and indicate the parameter space that can be probed at the LHC and the ILC. There exists a region of the parameter space which can be probed, at the LHC, through the diphoton channel even for a relatively low luminosity of 50 fb^{-1}. The reach of the 4-lepton final state, in probing the parameter space is also studied in the context of 14 TeV LHC, for a luminosity of 1000 fb^{-1}. At the ILC, with an integrated luminosity of 500 fb^{-1}, we analyze the Z-radion associated production and the WW fusion production, followed by the radion decay into bb and W+W-. The WW fusion production is favored over the Z-radion associated channel in probing regions of the parameter space beyond the LHC reach. The complementary study at the LHC and the ILC is useful both for the discovery of the radion and the understanding of its mixing sector.