We discuss the vacuum structure of a version of the Georgi-Machecek model with an exact $\mathbb{Z}_2$ symmetry acting on the triplet fields. Besides the usual custodial-symmetric model, with $ρ=1$ at tree-level, a model with a dark matter candidate is also viable. The other phases of the model lead to electric charge breaking, a wrong pattern of electroweak symmetry breaking or to $ρ\neq 1$ at tree-level. We derive conditions to have an absolute minimum in each of the two viable phases, the custodial and the dark matter phases.
The Georgi-Machacek model extends the standard model Higgs sector by adding two isospin triplet scalar fields and imposing global SU(2)$_R$ symmetry on them. A feature of the model is that the triplets can acquire a large vacuum expectation value without conflicting with the current experimental bound on the $ρ$ parameter. We investigate the electroweak phase transition in the Georgi-Machacek model by evaluating the finite-temperature effective potential of the Higgs sector. The electroweak phase transition can be sufficiently strong in a large parameter space when the triplets acquire a vacuu…
We study consequences of custodial symmetry in the Higgs sector of the Georgi-Machacek (GM) model. We discuss how the 5-plet and 3-plet Higgs bosons classified under the custodial SU(2) symmetry are produced and decay at the CERN Large Hadron Collider. By determining their masses through proposed channels, we can test the mass degeneracy in each Higgs multiplet.
We update the indirect constraints on the Georgi-Machacek model from $B$-physics and electroweak precision observables, including new constraints from $b \to s γ$ and $B^0_s \to μ^+ μ^-$. We illustrate the effect of these constraints on the couplings of the Standard Model-like Higgs boson by performing scans using the most general scalar potential, subject to vacuum stability and perturbativity constraints. We find that simultaneous enhancements of all the Higgs production cross sections by up to 39\% are still allowed after imposing these constraints. LHC rate measurements on the Higgs pole c…
The Georgi-Machacek model predicts the existence of four neutral Higgs bosons, one of which can be identified as the 125-GeV Higgs boson. The latest Higgs data favor the parameter space of small mixing angle alpha between the two custodial singlets of the model. The other two neutral Higgs bosons belong respectively to the custodial triplet and quintet. We study the general decay and production properties of these particles in the small-alpha scenario. Constraints on the SU(2)_L triplet vacuum expectation value are obtained as a function of the exotic Higgs boson masses using latest ATLAS data…
We show that in the absence of trilinear terms in the scalar potential of Georgi-Machacek model, heavy charged scalars do not necessarily decouple from the $h \to γγ$ decay amplitude. In such scenarios, measurement of the Higgs to diphoton signal strength can place stringent constraints in the parameter space. Using the projected precisions at the High Luminosity LHC (HL-LHC) and the ILC, we find that the upper bound on the triplet vacuum expectation value can be as low as 10 GeV. We also found that when combined with the theoretical constraints from perturbative unitarity and stability, such …
In this talk I discuss extended Higgs sectors in which the 125 GeV Higgs boson couplings to W and Z bosons can be larger than in the Standard Model. Constraints from perturbative unitarity and the electroweak rho parameter limit the number of possible models to a tractable few. Focusing on generalizations of the Georgi-Machacek model and taking advantage of the custodial symmetry, I show that existing experimental and theoretical constraints can be combined to set an upper limit on the enhancement of the Higgs couplings to W and Z bosons. This talk is based mostly on arXiv:1502.01275.
The Georgi-Machacek model adds two SU(2)_L-triplet scalars to the Standard Model in such a way as to preserve custodial SU(2) symmetry. We study the generalizations of the Georgi-Machacek model to SU(2)_L representations larger than triplets. Perturbative unitarity considerations limit the possibilities to models containing only SU(2)_L quartets, quintets, or sextets. These models are phenomenologically interesting because they allow the couplings of the 125 GeV Higgs boson to WW and ZZ to be larger than their values in the Standard Model. We write down the most general custodial SU(2)-preserv…
The Georgi-Machacek model is used to motivate and interpret LHC searches for doubly- and singly-charged Higgs bosons decaying into vector boson pairs. In this paper we study the constraints on and phenomenology of the "H5plane" benchmark scenario in the Georgi-Machacek model, which has been proposed for use in these searches. We show that the entire H5plane benchmark is compatible with the LHC measurements of the 125 GeV Higgs boson couplings. We also point out that, over much of the H5plane benchmark, the lineshapes of the two CP-even neutral heavy Higgs bosons $H$ and $H_5^0$ will overlap an…
We study a model that extends the Georgi-Machacek model by the addition of an inert doublet, $Φ_2$. This allows for the model to contain a natural dark matter candidate, $H^0$. For a number of benchmark points at two DM candidate masses ($m_{H^0} \in \{70,\,250\}$ GeV), we determine the relic abundance, direct detection cross section, and collider constraints. We find that the collider studies used do not constrain the model. For the parameter region chosen, the points are ruled out by direct detection experimental results. At the lower mass point, we do not find a viable parameter point, whil…
The Georgi-Machacek model is one of many beyond Standard Model scenarios with an extended scalar sector which can group under the custodial $\rm SU(2)_C$ symmetry. There are 5-plet, 3-plet and singlet Higgs bosons under the classification of such symmetry in addition to the Standard Model Higgs boson. In this paper, we study the prospects for detecting the doubly-charged Higgs boson ($\rm H_5^{\pm\pm}$) through the vector boson fusion production at the electron-proton (ep) colliders. We concentrate on our analysis through $μ$-lepton pair production via pair of same-sign W bosons decay. The $\r…
The recent CDF-II measurement of the mass of the $W$ boson shows a significant tension with the Standard Model (SM) expectation, even when averaged with earlier measurements. The tension can be explained in the framework of any beyond-SM dynamics that contributes substantially to the oblique $S$ and $T$ parameters. As a typical example of such beyond-SM physics, we try to explain the tension in the framework of the Georgi-Machacek model that keeps $ρ=1$ at the tree-level, and explore the parameter space that can accommodate the $W$ mass shift. We find that a sizeable split between the custodia…
We explore the phenomenology of the Georgi-Machacek model extended with two Higgs doublets and vector fermion doublets invariant under $SU(2)_L \times U(1)_Y\times \mathcal {Z}_4 \times \mathcal {Z}_2$. The $\mathcal {Z}_4$ symmetry is broken spontaneously while the imposed $\mathcal {Z}_2$ symmetry forbids triplet fields to generate any vacuum expectation value and leading to an inert dark sector providing a viable candidate for dark matter and generate neutrino mass radiatively. Another interesting feature of the model is leptogenesis arising from decay of vector-like fermions. A detailed st…
We compute renormalized vertices of the 125 GeV Higgs boson $h$ with the weak gauge bosons ($hVV$), fermions ($hf\bar{f}$) and itself ($hhh$) in the Georgi-Machacek model at one-loop level. The renormalization is performed based on the on-shell scheme with the use of the minimal subtraction scheme only for the $hhh$ vertex. We explicitly show the gauge dependence in the counterterms of the scalar mixing parameters in the general $R_ξ$ gauge, and that the dependence can be removed by using the pinch technique in physical scattering processes. We then discuss the possible allowed deviations in t…
We study the phenomenology of the exotic Higgs bosons in the Georgi-Machacek model at future electron-positron colliders such as the International Linear Collider (ILC), assuming the collision energies of 500 GeV and 1 TeV. We show that the existence of the neutral and singly-charged Higgs bosons in the 5-plet representation under the custodial $SU(2)_V$ symmetry can be readily identified by studying various energy and invariant mass distributions of the $W^+W^-Z$ final state. Moreover, their masses can be determined with sufficiently high precision to test the mass degeneracy, a feature due t…
In this work, we perform the electroweak phase transition study with the Georgi-Machacek model. We investigate both the one-step and two-step strong first order electroweak phase transition (SFOEWPT). The SFOEWPT viable parameter spaces could be tested by the future 14 TeV LHC, HL-LHC, and ILC. The LHC Higgs signal strength measurements severely bound the SFOEWPT valid parameter spaces, a tinny region of the mixing angle between the neutral fields of the isospin-doublet and isospin-triplet scalars around $α\sim 0$ can allow the two-step SFOEWPT to occur. The triplet vacuum expectation value (V…
The Georgi-Machacek model is one of many beyond Standard Model scenarios with an extended scalar sector which can group under the custodial $\rm SU(2)_C$ symmetry. There are 5-plet, 3-plet and singlet Higgs bosons under the classification of such symmetry in addition to the Standard Model Higgs boson. Here we study the prospects for detecting the doubly-charged Higgs boson ($\rm H_5^{\pm\pm}$) through the vector boson fusion production at the electron-proton colliders. Typically, we concentrate on our analysis through $μ$-lepton pair production via pair of same-sign W bosons decay. The discove…
The $H\to ZZ$ decay mode is usually considered as one of the most promising ways to discover new heavy neutral scalar $H$. We show that in the Georgi-Machacek model it is possible to get large enhancement of double SM-like Higgs boson production due to $H$ decays while $ZZ$ and $WW$ decay channels could be highly suppressed.
Higgs bosons pair production is well known for its sensitivity to probing the sign and size of Higgs boson self coupling, providing a way to determine whether there is an extended Higgs sector. The Georgi-Machacek (GM) model extends the Standard Model (SM) with an $SU(2)_L$ triplet scalar field that has one real and one complex components. The Higgs self coupling now has a wider range than that in the SM, with even the possibility of a sign flip. The new heavy singlet Higgs boson $H^{0}_{1}$ can contribute to s-channel production of the $hh$ pairs. In this work, we study non-resonant/resonant …
We compute the decay widths for the neutral and singly-charged Higgs bosons in the Georgi-Machacek model into the final states $γγ$, $Zγ$, and $Wγ$. These decays are most phenomenologically interesting for the fermiophobic custodial fiveplet states $H_5^0$ and $H_5^{\pm}$ when their masses are below threshold for decays into $WW$, $ZZ$, or $WZ$. We study the allowed branching ratios into these final states using scans over the allowed parameter space, and show how the model can be constrained by LEP searches for a fermiophobic Higgs boson decaying to two photons. The calculation involves evalu…
In an SU(2) gauge theory, if the gauge bosons turn out to be degenerate after spontaneous symmetry breaking, obviously these mass terms are invariant under a global SU(2) symmetry that is unbroken. The pure gauge terms are also invariant under this symmetry. This symmetry is called the {\em custodial symmetry} (CS). In $\rm SU(2)\times U(1)$ gauge theories, CS implies a mass relation between the $W$ and the $Z$ bosons. The Standard Model (SM), as well as various extensions of it in the scalar sector, possess such a symmetry. In this paper, we critically examine the notion of CS and show that t…
The same-sign diboson process $pp\to W^\pm W^\pm jj$ has been measured at the LHC using leptonic decay channels of the $W$ bosons, with production cross sections of two fiducial regions reported to be consistent with the standard model expectations within 1 sigma. These results constrain new physics models with a modified $W^+W^+W^-W^-$ vertex. We consider in particular the Georgi-Machacek model in which the quartic $W$ boson vertex is effectively modified due to mediations of new Higgs bosons in the model. The relevant gauge-gauge-scalar couplings are all proportional to the vacuum expectatio…
We derive the most general sets of viable mass spectra of the exotic Higgs bosons in the Georgi-Machacek model that are consistent with the theoretical constraints of vacuum stability and perturbative unitarity and the experimental constraints of electroweak precision observables, $Zb \bar b$ coupling and Higgs boson signal strengths. Branching ratios of various cascade decay channels of the doubly-charged Higgs boson in the ${\bf 5}$ representation, the singly-charged Higgs boson in ${\bf 3}$, and the singlet Higgs boson are further computed. As one of the most promising channels for discover…
The Georgi-Machacek Model allows for a large triplet vacuum expectation value (vev) with a custodial symmetric scalar potential. This manifestly leads to large charged Higgs coupling to SM fermions thus enhancing the detection probability of the model at the Large hadron collider. We show that the latest bound from LHC searches on singly charged Higgs scalar decaying to top and bottom quark restricts the triplet vev from above. We demonstrate that the combined limit from theoretical constraints and the latest Higgs data together with this charged Higgs bound can already curb the model paramete…
The double Higgs production in the models with isospin-triplet scalars is studied. It is shown that in the see-saw type II model the mode with an intermediate heavy scalar, $pp\to H+X\to 2h+X$, may have the cross section which is compatible with that in the Standard Model. In the Georgi-Machacek model this cross section could be much larger than in SM since the vacuum expectation value of the triplet can be large.
The Georgi-Machacek (GM) model is one of many Beyond Standard Model scenarios with an extended scalar sector which can group under the custodial $\rm SU(2)_C$ symmetry into a fiveplet, a triplet, and two singlets. The heavy charged custodial fiveplet Higgs $\rm H_5^{\pm}$ are typical particles in GM model which couple to the electroweak gauge bosons, therefore provide a good testing ground for the detection of the $\rm H^\pm W^\mp Z$ vertex. The neutral custodial fiveplet Higgs $\rm H_5^{0}$ in the GM model has the same mass with $\rm H_5^{\pm}$ and couples to the electroweak gauge bosons $\rm…
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 $ρ$ 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 $β$-functions for all the model parameters. Assuming the $δ…
We study the effects of including Yukawa-like dimension-5 operators in the Georgi-Machacek model where the Standard Model is augmented with triplet scalars. We focus only on the charged Higgs sector and investigate the constraints arising from radiative B-meson decays, neutral B-meson mixing and precision measurement of Zbb vertex. We observe that the inclusion of the dimension-5 operators causes substantial alteration of the limits on the charged Higgs masses and the vacuum expectation value of the triplets, derived otherwise using only the dimension-4 operators.
We study the most general scalar potential of the Georgi-Machacek model, which adds isospin-triplet scalars to the Standard Model (SM) in a way that preserves custodial SU(2) symmetry. We show that this model possesses a decoupling limit, in which the predominantly-triplet states become heavy and degenerate while the couplings of the remaining light neutral scalar approach those of the SM Higgs boson. We find that the SM-like Higgs boson couplings to fermion pairs and gauge boson pairs can deviate from their SM values by corrections as large as $\mathcal{O}(v^2/M_{\rm new}^2)$, where $v$ is th…
We study the effects of custodial symmetry violation in the Georgi-Machacek (GM) model. The GM model adds isospin-triplet scalars to the Standard Model in a way that preserves custodial symmetry at tree level; however, this custodial symmetry has long been known to be violated at the one-loop level by hypercharge interactions. We consider the custodial-symmetric GM model to arise at some high scale as a result of an unspecified ultraviolet completion, and quantify the custodial symmetry violation induced as the model is run down to the weak scale. The measured value of the eletroweak rho param…
We study how the dominant single and double SM-like Higgs ($h$) production at future $e^+e^-$ colliders is modified in the Georgi-Machacek (GM) model. On imposing theoretical, indirect and direct constraints, significant deviations of $h$-couplings from their SM values are still possible; for instance, the Higgs-gauge coupling coupling can be corrected by a factor $κ_{hVV}\in[0.93,1.15]$ in the allowed parameter space. For the Higgs-strahlung $e^+e^-\to hZ$ and vector boson fusion processes $e^+e^-\to hν\barν,~he^+e^-$, the cross section could increase by $32\%$ or decrease by $13\%$. In the c…
Interpreting the 95 GeV di-photon and di-tau Excesses in the Georgi-Machacek Model
Institute of Physics, Henan Academy of Sciences（河南科学院物理研究所）；Centre for Theoretical Physics, Henan Normal University（河南师范大学理论物理中心）；Center for High Energy Physics, Henan Academy of Sciences（河南科学院高能物理中心）；ARC Centre of Excellence for Dark Matter Particle Physics & CSSM, Department of Physics, Adelaide University（阿德莱德大学物理系暗物质粒子物理学卓越研究中心及CSSM）
We study how the custodial symmetry in the Higgs sector of the Georgi-Machacek (GM) model can be tested at the LHC. As the minimal extension of the Higgs triplet model, in which tiny neutrino masses are generated via the Type-II Seesaw Mechanism, the GM model keeps the electroweak $ρ$ parameter at unity at tree level. In the GM model, there are 5-plet ($H_5$), 3-plet ($H_3$) and singlet ($H_1$) Higgs bosons under the classification of the custodial $SU(2)_V$ symmetry, in addition to the standard model-like Higgs boson ($h$). These new Higgs bosons have the following characteristic features at …
The Georgi-Machacek model adds scalar triplets to the Standard Model Higgs sector in such a way as to preserve custodial SU(2) symmetry in the scalar potential. This allows the triplets to have a non-negligible vacuum expectation value while satisfying constraints from the rho parameter. Depending on the parameters, the 125~GeV neutral Higgs particle can have couplings to WW and ZZ larger than in the Standard Model due to mixing with the triplets. The model also contains singly- and doubly-charged Higgs particles that couple to vector boson pairs at tree level (WZ and like-sign WW, respectivel…
The Georgi-Machacek model, introducing a complex and a real scalar triplet as additional components of the electroweak symmetry breaking sector, enables substantial triplet contributions to the weak gauge boson masses, subject to the equality of the complex and the real triplet vacuum expectation values (vev) via a custodial SU(2) symmetry. We present an updated set of constraints on this scenario, from collider data (including those from 137/139~fb$^{-1}$ of luminosity at the Large Hadron Collider), available data on the 125-GeV scalar, indirect limits and also theoretical restrictions from v…
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 M…
Many researches from both the theoretical and experimental sides have been performed to search for a new Higgs Boson lighter than the 125 $GeV$ Higgs boson which was discovered at the LHC in 2012. In this paper we explore the possibility of constraining a lighter neutral custodial fiveplet scalar $H_{5}^{0}$ in the Georgi-Machacek (GM) model by the latest results of the search for a lighter Higgs boson decaying into two photons from LHC data. The custodial-singlet mass eigenstate $h$ or $H$ is considered to be the LHC observed 125 $GeV$ Higgs boson. A new set of constrained parameters that is …
We show that the well known Georgi-Machacek (GM) model can be realized as a limit of the recently constructed Supersymmetric Custodial Higgs Triplet Model (SCTM) which in general contains a significantly more complex scalar spectrum. We dub this limit of the SCTM, which gives a weakly coupled origin for the GM model at the electroweak scale, the Supersymmetric GM (SGM) model. We derive a mapping between the SGM and GM models using it to show how a supersymmetric origin implies constraints on the Higgs potential in conventional GM model constructions which would generically not be present. We t…
The CP-even static form factors $Δκ'_V$ and $ΔQ_V$ ($V=γ,\, Z$) associated with the $WWV$ vertex are studied in the context of the Georgi-Machacek model (GMM), which predicts nine new scalar bosons accommodated in a singlet, a triplet and a fiveplet. General expressions for the one-loop contributions to $Δκ'_V$ and $ΔQ_V$ arising from neutral, singly and doubly charged scalar bosons are obtained in terms of both parametric integrals and Passarino-Veltman scalar functions, which can be numerically evaluated. It is found that the GMM yields 15 (28) distinct contributions to $Δκ'_γ$ and $ΔQ_γ$ ($…
We study the phenomenology of the Georgi-Machacek model at next-to-leading order (NLO) in QCD matched to parton shower, using a fully-automated tool chain based on MadGraph5_aMC@NLO and FeynRules. We focus on the production of the fermiophobic custodial fiveplet scalars H_5^0, H_5^+/-, and H_5^++/-- through vector boson fusion (VBF), associated production with a vector boson (V H_5), and scalar pair production (H_5 H_5). For these production mechanisms we compute NLO corrections to production rates as well as to differential distributions. Our results demonstrate that the Standard Model (SM) o…
The $Z_{2}$-symmetric version of the Georgi-Machacek model does not possess a decoupling limit in which all the new particles can be made arbitrarily heavy, opening the possibility that the model can be entirely excluded if experiments reveal no deviations from the Standard Model. We explore this model, focusing on the part of parameter space in which the vacuum expectation value of the triplets, $ν_χ$, is small. In the small-$ν_χ$ limit, the second custodial-singlet scalar field $S$ necessarily becomes very light and can contribute to the total width of the 125 GeV Higgs boson $h$ via $h \to …
The Georgi-Machacek (GM) model is a distinctive TeV-scale extension of the Standard Model (SM) due to the introduction of two (one real and one complex) scalar triplets to the Higgs sector. It predicts the existence of doubly charged Higgs bosons $H_5^{\pm\pm}$ and the vacuum expectation value of Higgs triplets $v_Δ$ can reach a few tens of GeV. In this paper, we perform a parameter scan of the GM model within the H5plane benchmark scenario and investigate in detail the single production of a doubly charged Higgs boson in association with a SM-like Higgs boson via vector-boson fusion at the $1…
The CDF II experiment has recently determined the mass of the $W$ boson to be $m_W(\text{CDF II}) = 80.4335 \pm 0.0094~$GeV, which deviates from the standard model prediction at $7σ$ level. Although this new result is in tension with other experiments such as those at LHC and LEP, it is worth discussing possible implications on new physics by this anomaly. We show that this large discrepancy can be explained by non-aligned vacuum expectation values of isospin triplet scalar fields in the Georgi-Machacek model extended with custodial symmetry breaking terms in the potential. The latter is requi…
In the Georgi-Machacek model with a custodial symmetry in the Higgs potential and vacuum alignment, the triplet vacuum expectation value is allowed to be of ${\cal O}(10)$ GeV, which leads to the possibility of significant modifications in the couplings of the SM-like Higgs bosons $h$ with other SM particles. In this talk given at the HPNP2015 conference held at Toyama University, we review constraints on the model based on the latest LHC data of the SM-like Higgs boson, like-sign $W$ boson events, and searches for additional neutral Higgs bosons. In particular, we concentrate on the parameter…
Following various LHC indications for new scalars, an interpretation of these is given in terms of the Georgi-Machacek (GM) model. On top of the confirmed SM Higgs boson, there are indications for a light Higgs at 96 GeV, for a CP-odd boson at 400 GeV, A(400), and for a heavy Higgs boson at 660 GeV. An extension of the GM is needed to interpret the fermion couplings of A(400). Potentially interesting deviations are also observed in the ttW cross-section measurement, which naturally fit into this picture. None of them crosses the fatidic five s.d. evidence but the addition of these effects, con…
Off the beaten track of scalar singlet and doublet extensions of the Standard Model, triplets combine an interesting LHC phenomenology with an explanation for neutrino masses. The Georgi-Machacek model falls into this category, but it has never been fully explored in a global fit. We use the {\texttt{HEPfit}} package to combine recent experimental Higgs data with theoretical constraints and obtain strong limits on the mixing angles and mass differences between the heavy new scalars as well as their decay widths. We also find that the current signal strength measurements allow for a Higgs to ve…
