Electroweak Breaking Research Articles

Composite topological structures in SO(10)

We explore a variety of composite topological structures that arise from the spontaneous breaking of SO(10) to SU(3)c× U(1)em via one of its maximal subgroups SU(5) × U(1)χ, SU(4)c× SU(2)L× SU(2)R, and SU(5) × U(1)X (also known as flipped SU(5)). They include i) a network of ℤ strings which develop monopoles and turn into necklaces with the structure of ℤ2 strings, ii) dumbbells connecting two different types of monopoles, or monopoles and antimonpoles, iii) starfish-like configurations, iv) polypole configurations, and v) walls bounded by a necklace. We display these structures both before and after the electroweak breaking. The appearance of these composite structures in the early universe and their astrophysical implications including gravitational wave emission would depend on the symmetry breaking patterns and scales, and the nature of the associated phase transitions.

Effects of the axion through the Higgs portal on primordial gravitational waves during the electroweak breaking

We investigate the effects of short axion kination eras on the energy spectrum of the primordial gravitational waves corresponding to modes that reenter the Hubble horizon at the postelectroweak symmetry breaking epoch well within the radiation domination era. Our main assumption is the existence of an extremely weakly coupled hidden sector between the Higgs and the axion, materialized by higher order nonrenormalizable dimension six and dimension eight operators, active at a scale $M$ of the order 20--100 TeV. This new physics scale $M$, which is way higher than the electroweak scale, is motivated by the lack of new particle observations in the large hadron collider to date beyond the electroweak scale. Once the electroweak symmetry breaking occurs at $T\ensuremath{\sim}100\text{ }\text{ }\mathrm{GeV}$, the axion potential acquires a new minimum due to the new terms generated by the electroweak breaking, and the axion oscillations at the origin are destabilized. In effect after some considerable amount of time, the axion rolls swiftly to its new minimum, experiencing a short kination epoch, where its energy density redshifts as ${\ensuremath{\rho}}_{a}\ensuremath{\sim}{a}^{\ensuremath{-}6}$. After it reaches the new minimum, since the latter is energetically less favorable that the Higgs minimum, it decays to the Higgs minimum and the Universe is described again by the Higgs minimum. The axion returns to the origin and commences again oscillations initiated by quantum fluctuations, redshifts as dark matter, and the same procedure is repeated perpetually. These short axion kination eras may disturb the background total equation of state parameter during the radiation domination era, changing it from that of radiation $w=1/3$ to some value closer to the kination value $w=1$. We examined the effect of a value $w=1/2$ on the energy density of the primordial gravitational waves. As we show, the energy spectrum of the gravitational waves mainly depends on how many times the short axion kination epochs occur, on the inflationary theory, on the actual value of the background equation of state parameter during the short kination eras, and finally on the reheating temperature. Our findings indicate a characteristic shape in the energy spectrum that can be observed in future gravitational wave experiments. We however disregarded the contribution of the electroweak phase transition on the gravitational waves for simplicity and transparency of our results.

Fine-tuning in the 2HDM

The Two-Higgs Doublet Model (2HDM) is one of the most popular and natural extensions of the Higgs sector; but it has two potential fine-tuning problems, related to the electroweak (EW) breaking and the requirement of alignment with the SM Higgs boson. We have quantified the fine-tunings obtaining analytical expressions, both in terms of the initial 2HDM parameters and the physical ones (masses, mixing angles, etc.). We also provide simple approximate expressions. We have taken into account that the fine-tunings are not independent and removed the “double counting” by projecting the variations of the alignment onto the constant-v^2 hypersurface. The EW and the alignment fine-tunings become severe in different, even opposite, regions of the parameter space, namely in the regimes of large and small extra-Higgs masses, respectively; emerging an intermediate region, 500~{textrm{GeV}} {mathop {{}_sim }limits ^{<}}{m_H, m_A, m_{H^pm }} {mathop {{}_sim }limits ^{<}}700~{textrm{GeV}}, where both are acceptably small. We also discuss a remarkable trend that is not obvious at first glance. Namely, for large tan beta both the EW and the alignment fine-tunings become mitigated. In consequence, the 2HDM becomes quite natural for tan beta ge {mathcal {O}} (10), even if m_H, m_A, m_{H^pm } are as large as 1500 GeV. We explain why this is not the case for the 2HDM stemming from supersymmetry. We have illustrated all these trends by numerically analyzing several representative scenarios.

BRST view of spontaneous symmetry breaking

After the phase transition of a Grand Unified Theory (GUT), its single coupling splits into the couplings of the basic interactions. On the other side, the measurement of the Weinberg mixing angle in the eletroweak theory determines that the couplings associated to the SU(2) and U(1) symmetries were already distinct in its symmetric phase, before the electroweak breaking. This picture is consistent as we understand that such couplings evolve independently with the energy scale, meeting a common point together with the strong interaction coupling at the GUT scale. From a BRST symmetry point of view, this implies that each independent coupling should be associated to independent cocycles defined on a cohomological basis. The problem is that, before the GUT symmetry breaking, the BRST operator associated to this symmetric phase predicts a single Yang-Mills coupling. This sets the question of what should be the BRST operator of the asymmetric phase, that would allow for the splitting of this coupling but at the same time remain compatible with the BRST operator of the symmetric phase. In this work we proceed to answer this question.

The Scoto-seesaw model: Dark matter and Stability

We analyze the consistency of electroweak breaking, neutrino and dark matter phenomenology within the simplest scoto-seesaw model. The scoto-seesaw model can be obtained by adding the minimal dark sector to the simplest “missing partner” type-I seesaw. This way one has a physical picture for the neutrino oscillation lengths: the “atmospheric” mass scale arises from the tree-level seesaw, while the “solar” scale is induced radiatively, mediated by the dark sector. One also has a lower bound for the neutrinoless double beta decay amplitude 1.

Scalar and gauge sectors in the 3-Higgs Doublet Model under the S_3 symmetry

We analyse the Higgs sector of an S_3 model with three Higgs doublets and no CP violation. After electroweak breaking there are nine physical Higgs bosons, one of which corresponds to the Standard Model one. We study the scalar and gauge sectors of this model, taking into account the conditions set by the minimisation and stability of the potential. We calculate the masses, trilinear and quartic Higgs-Higgs, and Higgs-gauge couplings. We consider two possible alignment scenarios, where only one of the three neutral scalars has couplings to the gauge bosons and corresponds to the SM Higgs, and whose trilinear and quartic couplings reduce exactly to the SM ones. We also obtain numerically the allowed parameter space for the scalar masses in each of the alignment scenarios. We use the calculated trilinear and quartic couplings to find the analytical structure of the one-loop neutral scalar mass matrix, without fermionic contributions. We show that it is possible to have a compact mass spectrum where the contribution to the oblique parameters might be small. We explore some scenarios for the loop contributions to the neutral scalar masses.

Vector Boson scattering from the compact muon solenoid (CMS) experiment at the large hadron collider

Triggered by the electroweak symmetry spontaneous breaking, the Higgs Boson provides mass to fundamental particles and ensures the unitarity safety of the vector Boson scattering. This scattering is crucial for testing the Higgs mechanism, and it can also be used to probe new physics beyond the standard model. In this paper, after a brief introduction of the standard model Higgs theory, we present a detailed review of the research on the vector Boson scattering. This review includes an early study on the two same-charged W Boson based on Monte Carlo samples, the searches for vector Boson scattering and studies on beyond standard model physics using data collected by the compact muon solenoid (CMS) experiment during Run I in 2012 and Run II in 2016–2018 as well as the recently achieved first measurement of polarized vector Boson scattering.

Dynamical inverse seesaw mechanism as a simple benchmark for electroweak breaking and Higgs boson studies

The Standard Model (SM) vacuum is unstable for the measured values of the top Yukawa coupling and Higgs mass. Here we study the issue of vacuum stability when neutrino masses are generated through spontaneous low-scale lepton number violation. In the simplest dynamical inverse seesaw, the SM Higgs has two siblings: a massive CP-even scalar plus a massless Nambu-Goldstone boson, called majoron. For TeV scale breaking of lepton number, Higgs bosons can have a sizeable decay into the invisible majorons. We examine the interplay and complementarity of vacuum stability and perturbativity restrictions, with collider constraints on visible and invisible Higgs boson decay channels. This simple framework may help guiding further studies, for example, at the proposed FCC facility.

The simplest scoto-seesaw model: WIMP dark matter phenomenology and Higgs vacuum stability

We analyze the consistency of electroweak breaking, neutrino and dark matter phenomenology within the simplest scoto-seesaw model. By adding the minimal dark sector to the simplest “missing partner” type-I seesaw one has a physical picture for the neutrino oscillation lengths: the “atmospheric” mass scale arises from the tree-level seesaw, while the “solar” scale is induced radiatively, mediated by the dark sector. We identify parameter regions consistent with theoretical constraints, as well as dark matter relic abundance and direct detection searches. Using two-loop renormalization group equations we explore the stability of the vacuum and the consistency of the underlying dark parity symmetry. One also has a lower bound for the neutrinoless double beta decay amplitude.

A more natural composite Higgs model

Composite Higgs models provide an attractive solution to the hierarchy problem. However, many realistic models suffer from tuning problems in the Higgs potential. There are often large contributions from the UV dynamics of the composite resonances to the Higgs potential, and tuning between the quadratic term and the quartic term is required to separate the electroweak breaking scale and the compositeness scale. We consider a composite Higgs model based on the SU(6)/Sp(6) coset, where an enhanced symmetry on the fermion resonances can minimize the Higgs quadratic term. Moreover, a Higgs quartic term from the collective symmetry breaking of the little Higgs mechanism can be realized by the partial compositeness couplings between elementary Standard Model fermions and the composite operators, without introducing new elementary fields beyond the Standard Model and the composite sector. The model contains two Higgs doublets, as well as several additional pseudo-Nambu-Goldstone bosons. To avoid tuning, the extra Higgs bosons are expected to be relatively light and may be probed in the future LHC runs. The deviations of the Higgs couplings and the weak gauge boson couplings also provide important tests as they are expected to be close to the current limits in this model.

Consistency of the dynamical high-scale type-I seesaw mechanism

We analyze the consistency of electroweak breaking within the simplest high-scale Standard Model type-I seesaw mechanism. We derive the full two-loop RGEs of the relevant parameters, including the quartic Higgs self-coupling of the Standard Model. For the simplest case of bare "right-handed" neutrino mass terms we find that, with large Yukawa couplings, the Higgs quartic self-coupling becomes negative much below the seesaw scale, so that the model may be inconsistent even as an effective theory. We show, however, that the "dynamical" type-I high-scale seesaw with spontaneous lepton number violation has better stability properties.

Electroweak breaking and Higgs boson profile in the simplest linear seesaw model

We examine the simplest realization of the linear seesaw mechanism within the Standard Model gauge structure. Besides the standard scalar doublet, there are two lepton-number-carrying scalars, a nearly inert SU(2)L doublet and a singlet. Neutrino masses result from the spontaneous violation of lepton number, implying the existence of a Nambu-Goldstone boson. Such “majoron” would be copiously produced in stars, leading to stringent astrophysical constraints. We study the profile of the Higgs bosons in this model, including their effective couplings to the vector bosons and their invisible decay branching ratios. A consistent electroweak symmetry breaking pattern emerges with a compressed spectrum of scalars in which the “Standard Model” Higgs boson can have a sizeable invisible decay into the invisible majorons.

Naturalness versus stringy naturalness with implications for collider and dark matter searches

The notion of stringy naturalness-- that an observable O_2 is more natural than O_1 if more (phenomenologically acceptable) vacua solutions lead to O_2 rather than O_1-- is examined within the context of the Standard Model (SM) and various SUSY extensions: CMSSM/mSUGRA, high-scale SUSY and radiatively-driven natural SUSY (RNS). Rather general arguments from string theory suggest a (possibly mild) statistical draw towards vacua with large soft SUSY breaking terms. These vacua must be tempered by an anthropic veto of non-standard vacua or vacua with too large a value of the weak scale m(weak). We argue that the SM, the CMSSM and the various high-scale SUSY models are all expected to be relatively rare occurances within the string theory landscape of vacua. In contrast, models with TeV-scale soft terms but with m(weak)~100 GeV and consequent light higgsinos (SUSY with radiatively-driven naturalness) should be much more common on the landscape. These latter models have a statistical preference for m_h~ 125 GeV and strongly interacting sparticles beyond current LHC reach. Thus, while conventional naturalness favors sparticles close to the weak scale, stringy naturalness favors sparticles so heavy that electroweak symmetry is barely broken and one is living dangerously close to vacua with charge-or-color breaking minima, no electroweak breaking or pocket universe weak scale values too far from our measured value. Expectations for how landscape SUSY would manifest itself at collider and dark matter search experiments are then modified compared to usual notions.

Non-standard neutrino interactions and low energy experiments

We formulate an Effective Field Theory (EFT) for Non Standard neutrino Interactions (NSI) in elastic scattering with light quarks, leptons, gluons and photons, including all possible operators of dimension 5, 6 and 7. We provide the expressions for the cross sections in coherent neutrino-nucleus scattering and in deep inelastic scattering. Assuming single operator dominance we constrain the respective Wilson coefficient using the measurements by the COHERENT and CHARM collaborations. We also point out the constraining power of future elastic neutrino-nucleus scattering experiments. Finally, we explore the implications of the bounds for SMEFT operators above the electroweak breaking scale.

Gapped continuum Kaluza-Klein spectrum

We consider a warped five-dimensional model with an ultraviolet (UV) brane and, on top of the Standard Model isolated modes, continua of KK modes with different mass gaps for all particles: gauge bosons, fermions, graviton, radion and Higgs boson. The model can be considered as a modelization in five dimensions of gapped unparticles. The five dimensional metric has a singularity, at a finite (infinite) value of the proper (conformal) coordinate, which is admissible as it supports finite temperature in the form of a black hole horizon. An infrared (IR) brane, with particular jumping conditions, is introduced to trigger correct electroweak breaking. The gravitational metric is AdS5 near the UV brane, to solve the hierarchy problem with a fundamental Planck scale, and linear, in conformal coordinates, near the IR, as in the linear dilaton and five-dimensional clockwork models. The branes, and singularity, distances are fixed, à la Goldberger-Wise, by a bulk scalar field with brane potentials explicitly breaking the conformal symmetry. The bosonic continuum of KK modes with the smallest mass gap are those of gauge bosons, and so they are the most likely produced at the LHC. Mass gaps of the continuum of KK fermions do depend on their localization in the extra dimension. We have computed the spectral functions, and arbitrary Green’s functions, and shown how they can modify some Standard Model processes.

Higgsino dark matter in an economical Scherk-Schwarz setup

We consider a minimal natural supersymmetric model based on an extra dimension with supersymmetry breaking provided by the Scherk-Schwarz mechanism. The lightest supersymmetric particle is a neutral, quasi-Dirac Higgsino and, unlike in previous studies, we assume that all Standard Model fields are propagating in the bulk. The resulting setup is minimal, as neither extra matter, effective operators, nor extra $U(1)$ groups are needed in order to be viable. The model has three free parameters which are fixed by the Higgsino mass -- set to the range 1.1-1.2 TeV so it can play the role of Dark Matter, and by the requirements of correct electroweak breaking and the mass of the Higgs. After imposing the previous conditions we find a benchmark scenario that passes all experimental constrains with an allowed range for the supersymmetric parameters. In particular we have found gluinos in the range 2.0-2.1 TeV mass, electroweakinos and sleptons almost degenerate in the range 1.7-1.9 TeV and squarks degenerate in the range 1.9-2.0 TeV. The best discovery prospects are: i.) gluino detection at the high luminosity LHC ($\gtrsim 3\, \text{ab}^{-1}$), and ii.) Higgsino detection at next-generation dark matter direct detection experiments. The model is natural, as the fine-tuning for the fixed values of the parameters is moderate mainly because supersymmetry breaking parameters contribute linearly to the Higgs mass parameter, rather than quadratically as in most models.

TeV‐ and MeV‐Physics Out of an Model

AbstractThe standard electroweak interaction is here re‐assessed to accommodate two different situations in Particle Physics. The first one is a ‐model at the TeV‐scale physics. The second one tackles the recent discussion of a possible fifth force mediated by a 17‐MeV X‐boson associated with an electron‐positron emission in the transition of an excited 8‐Beryllium to its ground state. The anomaly‐free model that provides these two scenarios is based on an ‐symmetry. It yields a new massive neutral boson, an exotic massive neutral fermion, right‐neutrinos and an additional neutral Higgs particle, which stems from a supplementary Higgs field, introduced along with the usual Higgs doublet responsible for the electroweak breaking and the masses of and Z0. Yukawa interactions of the two scalars generate the masses of the Standard Model leptons, neutrinos and a new exotic fermion of the model. The vacuum expectation values of the Higgses fix up two independent energy scales. One of them is the well‐confirmed electroweak scale, 246 GeV, whereas the other one is set up by adopting an experimental estimate for the ‐mass.

Correction to Neutrino Mass Square Difference in the Co-Bimaximal Mixings due to Quantum Gravity

We consider non-renormalizable interaction term as a perturbation of the neutrino mass matrix. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck scale and the electroweak breaking scale. We also assume that, just above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is Co-bimaximal mixing by assumming mixing angle $\theta _{13}\neq 0=10^{\circ },\theta _{23}=\frac {\pi }{4},\,\,\, tan\theta _{12}^{2}=\frac {1-3sin\theta _{13}^{2}}{2}=34^{\circ }$ and Dirac phase $\delta =\pm \frac {\pi }{2}$ . . Quantum gravity (Planck scale effects) lead to an effective S U(2) L × U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields. On symmetry breaking, this operator gives rise to correction to the above masses and mixing. The gravitational interaction M X = M p l , we find that for degenerate neutrino mass spectrum, the considered perturbation term change the ${\Delta }_{21}^{\prime }$ by 12% and ${\Delta }_{31}^{\prime }$ mass square difference is unchanged above GUT scale. The nature of gravitational interaction demands that the element of this perturbation matrix should be independent of flavor indices. In this paper, we study the quantum gravity effects on neutrino mass square difference, namely modified dispersion relation for neutrino mass square differences.

Inverse amplitude method for the perturbative electroweak symmetry breaking sector: The singlet Higgs portal as a study case

We explore the use of the Inverse Amplitude Method for unitarization of scattering amplitudes to derive the existence and properties of possible new heavy states associated with perturbative extensions of the electroweak breaking sector of the Standard Model starting from the low energy effective theory. We use a toy effective theory generated by integrating out a heavy singlet scalar and compare the pole mass and width of the unitarized amplitudes with those of the original model. Our results show that the Inverse Amplitude Method reproduces correctly the singlet mass up to factors of O(1-3), but its width is overestimated.

Status and implications of neutrino masses: A brief panorama

With the historic discovery of the Higgs boson our picture of particle physics would have been complete were it not for the neutrino sector and cosmology. I briefly discuss the role of neutrino masses and mixing upon gauge coupling unification, electroweak breaking and the flavor sector. Time is ripe for new discoveries such as leptonic CP violation, charged lepton flavor violation and neutrinoless double beta decay. Neutrinos could also play a role in elucidating the nature of dark matter and cosmic inflation.