Electroweak Scale Research Articles

Uncovering the root of LEFT in SMEFT

At energies below the electroweak scale, baryon number B and lepton number L violating processes are of significant importance in identifying the nature of UV extensions of the Standard Model. The imprint of UV theories on low-energy measurements can be calculated to a high accuracy using the theoretical framework of the Low-Energy Effective Theory (LEFT). Using and the operators' dimensions as classifying characteristics, we construct a network connecting operator classes of the LEFT with the Standard Model Effective Theory (SMEFT). Following the links of this network, the contact interactions described by the effective operators of LEFT can be unambiguously embedded into those of SMEFT, which enables us to constrain the possible realisations of UV theories. In turn, this can help to prioritise low-energy measurements with the aim of comprehensively testing all classes of LEFT and SMEFT operators.

Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I

We compute the one-loop renormalisation group running of the bosonic Standard Model effective operators to order v^4/\Lambda^4v4/Λ4, with v\sim 246v∼246 GeV being the electroweak scale and \LambdaΛ the unknown new physics threshold. We concentrate on the effects triggered by pairs of the leading dimension-six interactions, namely those that can arise at tree level in weakly-coupled ultraviolet completions of the Standard Model. We highlight some interesting consequences, including the interplay between positivity bounds and the form of the anomalous dimensions; the non-renormalisation of the SS and UU parameters; or the importance of radiative corrections to the Higgs potential for the electroweak phase transition. As a byproduct of this work, we provide a complete Green basis of operators involving only the Higgs and derivatives at dimension-eight, comprising 13 redundant interactions.

New approach to electroweak symmetry nonrestoration

Electroweak symmetry non-restoration up to high temperatures well above the electroweak scale offers new alternatives for baryogenesis. We propose a new approach for electroweak symmetry non-restoration via an inert Higgs sector that couples to the Standard Model Higgs as well as an extended scalar singlet sector. We implement renormalization group improvements and thermal resummation, necessary to evaluate the effective potential spanning over a broad range of energy scales and temperatures. We present examples of benchmark scenarios that allow for electroweak symmetry non-restoration all the way up to hundreds of TeV temperatures, and also feature suppressed sphaleron washout factors down to the electroweak scale. Our method for transmitting the Standard Model broken electroweak symmetry to an inert Higgs sector has several intriguing implications for (electroweak) baryogenesis, early universe thermal histories, and can be scrutinized through Higgs physics phenomenology and electroweak precision measurements at the HL-LHC.

Vacuum stability vs. positivity in real singlet scalar extension of the standard model

We assume a generic real singlet scalar extension of the Standard Model living in the vacuum (v,w) at the electroweak scale with v=246 GeV and w being respectively the Higgs and the singlet scalar vacuum expectation values. By requiring absolute vacuum stability for the vacuum (v,w), the positivity condition and the perturbativity up to the Planck scale, we show that the viable space of parameters in the model is strongly constrained for various singlet scalar vacuum expectation values w=0.1,1,10,100 TeV. Also, it turns out that the singlet scalar mass can be from a few GeV up to less than TeV.

Weak scale right-handed neutrino as pseudo-Goldstone fermion of spontaneously broken mathrm{U}{(1)}_{L_{mu }-{L}_{tau }}

Possibility of a Right-Handed (RH) neutrino being a Goldstone fermion of a spontaneously broken global U(1) symmetry in a supersymmetric theory is considered. This fermion obtains mass from the supergravity effects leading to a RH neutrino at the electroweak scale with a mass similar to the gravitino mass. A prototype model realizing this scenario contains just three gauge singlet superfields needed for the type I seesaw mechanism. Masses of the other two neutrinos are determined by the U(1) breaking scale which too can be around the electroweak scale. Light neutrinos obtain their masses in this scenario through (a) mixing with the RH neutrinos (type I seesaw), (b) mixing with neutralinos (R-parity breaking), (c) indirectly through mixing of the RH neutrinos with neutralinos, and (d) radiative corrections. All these contributions are described by the same set of a small number of underlying parameters and provide a very constrained and predictive framework for the neutrino masses which is investigated in detail for various choices of U(1) symmetries. It is found that flavour independent U(1) symmetries cannot describe neutrino masses if the soft supersymmetry breaking terms are flavour universal and one needs to consider flavour dependent symmetries. Considering a particular example of Lμ− Lτ symmetry, it is shown that viable neutrino masses and mixing can be obtained without introducing any flavour violation in the soft sector. The leptonic couplings of Majoron are worked out in the model and shown to be consistent with various laboratory, astrophysical and cosmological constraints. The neutrino data allows sizeable couplings between the RH neutrinos and Higgsinos which can be used to probe the pseudo-Goldstone fermion at colliders through its displaced decay vertex.

Portal Effective Theories. A framework for the model independent description of light hidden sector interactions

We present a framework for the construction of portal effective theory (PETs) that couple effective field theories of the Standard Model (SM) to light hidden messenger fields. Using this framework we construct electroweak and strong scale PETs that couple the SM to messengers carrying spin zero, one half, or one. The electroweak scale PETs encompass all portal operators up to dimension five, while the strong scale PETs additionally contain all portal operators of dimension six and seven that contribute at leading order to quark-flavour violating transitions. Using the strong scale PETs, we define a set of portal currents that couple hidden sectors to QCD, and construct portal chiral perturbation theory (χPTs) that relate these currents to the light pseudoscalar mesons. We estimate the coefficients of the portal χPT Lagrangian that are not fixed by SM observations using non-perturbative matching techniques and give a complete list of the resulting one- and two-meson portal interactions. From those, we compute transition amplitudes for three golden channels that are used in hidden sector searches at fixed target experiments: i) charged kaon decay into a charged pion and a spin zero messenger, ii) charged kaon decay into a charged lepton and a spin one half messenger, and iii) neutral pion decay into a photon and a spin one messenger. Finally, we compare these amplitudes to specific expressions for models featuring light scalar particles, axion-like particles, heavy neutral leptons, and dark photons.

Heavy neutral leptons in effective field theory and the high-luminosity LHC

Heavy neutral leptons (HNLs) with masses around the electroweak scale are expected to be rather long-lived particles, as a result of the observed smallness of the active neutrino masses. In this work, we study long-lived HNLs in NRSMEFT, a Standard Model (SM) extension with singlet fermions to which we add non-renormalizable operators up to dimension-6. Operators which contain two HNLs can lead to a sizable enhancement of the production cross sections, compared to the minimal case where HNLs are produced only via their mixing with the SM neutrinos. We calculate the expected sensitivities for the ATLAS detector and the future far-detector experiments: AL3X, ANUBIS, CODEX-b, FASER, MATHUSLA, and MoEDAL-MAPP in this setup. The sensitive ranges of the HNL mass and of the active-heavy mixing angle are much larger than those in the minimal case. We study both, Dirac and Majorana, HNLs and discuss how the two cases actually differ phenomenologically, for HNL masses above roughly 100 GeV.

Gravitational waves from a dark U(1)D phase transition in light of NANOGrav 12.5 yr data

We study a possibility of a strong first-order phase transition (FOPT) taking place below the electroweak scale in the context of $U(1)_D$ gauge extension of the standard model. As pointed out recently by the NANOGrav collaboration, gravitational waves from such a phase transition with appropriate strength and nucleation temperature can explain their 12.5 yr data. We first find the parameter space of this minimal model consistent with NANOGrav findings considering only a complex singlet scalar and $U(1)_D$ vector boson. Existence of a singlet fermion charged under $U(1)_D$ can give rise to dark matter in this model, preferably of non-thermal type, while incorporating additional fields can also generate light neutrino masses through typical low scale seesaw mechanisms like radiative or inverse seesaw.

Flavor symmetries in the Yukawa sector of non-supersymmetric SO(10): numerical fits using renormalization group running

We consider a class of SO(10) models with flavor symmetries in the Yukawa sector and investigate their viability by performing numerical fits to the fermion masses and mixing parameters. The fitting procedure involves a top-down approach in which we solve the renormalization group equations from the scale of grand unification down to the electroweak scale. This allows the intermediate scale right-handed neutrinos and scalar triplet, involved in the type I and II seesaw mechanisms, to be integrated out at their corresponding mass scales, leading to a correct renormalization group running. The result is that, of the 14 models considered, only two are able to fit the known data well. Both these two models correspond to ℤ2 symmetries. In addition to being able to fit the fermion masses and mixing parameters, they provide predictions for the sum of light neutrino masses and the effective neutrinoless double beta decay mass parameter, which are both within current observational bounds.

Inflation based on a classically scale invariant extended standard model

We extend a classically scale invariant model where the electroweak symmetry breaking is triggered by the dynamical chiral symmetry breaking in a hidden QCD sector, and a real singlet scalar [Formula: see text] mediates these two sectors. Our model can explain cosmic inflation without unitarity violation in addition. Slow-roll inflation occurs along a valley in scalar potential. In the original model, the coupling [Formula: see text] between the Higgs field [Formula: see text] and [Formula: see text] is always negative and therefore, the potential has its valleys in [Formula: see text]-[Formula: see text] mixed directions. For large value of the top Yukawa coupling [Formula: see text], the potential along the valley becomes negative since the Higgs quartic coupling [Formula: see text] becomes negative at inflationary scale. Then slow-roll inflation cannot occur. For inflation to definitely occur, we render the coupling [Formula: see text] positive at inflationary scale and consider the [Formula: see text]-inflation case. This is achieved by introducing a new singlet scalar [Formula: see text] with the large coupling [Formula: see text] to [Formula: see text]. By this extension, [Formula: see text] can also always be positive, and we consider this case as the simplest case. We consider inflation with the nonminimal coupling [Formula: see text] between [Formula: see text] and gravity. Although [Formula: see text] is large such as [Formula: see text], unitarity is not violated since couplings between [Formula: see text] and other fields are sufficiently small. [Formula: see text] is odd under a new symmetry [Formula: see text] not to mix with [Formula: see text] regardless of largeness of [Formula: see text]. Because of this symmetry, [Formula: see text] may have its relic abundance [Formula: see text] comparable with the observational value [Formula: see text] of the dark matter relic abundance. However, the spin-independent elastic cross-section [Formula: see text] of [Formula: see text] exceeds the observational bound [Formula: see text] cm2. Hence, we impose the resonance condition [Formula: see text] and reduce [Formula: see text] to much smaller than [Formula: see text]. Constraints from the electroweak scale physics and inflationary scale physics are much strong, and the allowed parameter space is very narrow.

Fake doublet solution to the muon anomalous magnetic moment

Extensions to the Standard Model that use strictly off-shell degrees of freedom---the fakeons---allow for new measurable interactions at energy scales usually precluded by the constraints that target the on-shell propagation of new particles. Here we employ the interactions between a new fake scalar doublet and the muon to explain the recent Fermilab measurement of its anomalous magnetic moment. Remarkably, unlike in the case of usual particles, the experimental result can be matched for fakeon masses below the electroweak scale without contradicting the stringent precision data and collider bounds on new light degrees of freedom. Our analysis, therefore, demonstrates that the fakeon approach offers unexpected viable possibilities to model new physics naturally at low scales.

The Swampland Conjectures: A Bridge from Quantum Gravity to Particle Physics

The swampland is the set of seemingly consistent low-energy effective field theories that cannot be consistently coupled to quantum gravity. In this review we cover some of the conjectural properties that effective theories should possess in order not to fall in the swampland, and we give an overview of their main applications to particle physics. The latter include predictions on neutrino masses, bounds on the cosmological constant, the electroweak and QCD scales, the photon mass, the Higgs potential and some insights about supersymmetry.

Confronting spin-3/2 and other new fermions with the muon g-2 measurement

The new measurement of the muon's anomalous magnetic moment released by the Muon g-2 experiment at Fermilab sets strong constraints on the properties of many new particles. Using an effective field theory approach to the interactions of higher-spin fields, we evaluate the contribution of an electrically neutral and colour singlet spin-3/2 fermion to (g−2)μ and derive the corresponding constraints on its mass and couplings. These constraints are then compared with the ones on spin-1/2 fermions, such as the vector-like leptons that are predicted by various extensions of the Standard Model, the excited leptons which appear in composite models, as well as the charginos and neutralinos of supersymmetric theories. Unlike these new spin-1/2 fermions, the spin-3/2 particles generate only small contributions to the muon anomalous magnetic moment unless the effective new physics scale is very close to the electroweak scale.

Gravitational tests of electroweak relaxation

We consider a scenario in which the electroweak scale is stabilized via the relaxion mechanism during inflation, focussing on the case in which the back-reaction potential is generated by the confinement of new strongly interacting vector-like fermions. If the reheating temperature is sufficiently high to cause the deconfinement of the new strong interactions, the back-reaction barrier then disappears and the Universe undergoes a second relaxation phase. This phase stops when the temperature drops sufficiently for the back-reaction to form again. We identify the regions of parameter space in which the second relaxation phase does not spoil the successful stabilization of the electroweak scale. In addition, the generation of the back-reaction potential that ends the second relaxation phase can be associated to a strong first order phase transition. We then study when such transition can generate a gravitational wave signal in the range of detectability of future interferometer experiments.

Consequences of chirally enhanced explanations of (g − 2)μ for h → μμ and Z → μμ

With the long-standing tension between experiment and Standard-Model (SM) prediction in the anomalous magnetic moment of the muon aμ recently reaffirmed by the Fermilab experiment, the crucial question becomes which other observables could be sensitive to the underlying physics beyond the SM to which aμ may be pointing. While from the effective field theory (EFT) point of view no direct correlations exist, this changes in specific new physics models. In particular, in the case of explanations involving heavy new particles above the electroweak (EW) scale with chiral enhancement, which are preferred to evade exclusion limits from direct searches, correlations with other observables sensitive to EW symmetry breaking are expected. Such scenarios can be classified according to the SU(2)L representations and the hypercharges of the new particles. We match the resulting class of models with heavy new scalars and fermions onto SMEFT and study the resulting correlations with h → μμ and Z → μμ decays, where, via SU(2)L symmetry, the latter process is related to Z → νν and modified W-μ-ν couplings.

Leading logs in QCD axion effective field theory

The axion is much lighter than all other degrees of freedom introduced by the Peccei-Quinn mechanism to solve the strong CP problem. It is therefore natural to use an effective field theory (EFT) to describe its interactions. Loop processes calculated in the EFT may however explicitly depend on the ultraviolet cutoff. In general, the UV cutoff is not uniquely defined, but the dimensionful couplings suggest to identify it with the Peccei-Quinn symmetry-breaking scale. An example are K+ → π+ + a decays that will soon be tested to improved precision in NA62 and KOTO and whose amplitude is dominated by the term logarithmically dependent on the cutoff. In this paper, we critically examine the adequacy of using such a naive EFT approach to study loop processes by comparing EFT calculations with ones performed in complete QCD axion models. In DFSZ models, for example, the cutoff is found to be set by additional Higgs degrees of freedom and to therefore be much closer to the electroweak scale than to the Peccei-Quinn scale. In fact, there are non-trivial requirements on axion models where the cutoff scale of loop processes is close to the Peccei-Quinn scale, such that the naive EFT result is reproduced. This suggests that the existence of a suitable UV embedding may impose restrictions on axion EFTs. We provide an explicit construction of a model with suitable fermion couplings and find promising prospects for NA62 and IAXO.

Electroweak-like baryogenesis with new chiral matter

We propose a framework where a phase transition associated with a gauge symmetry breaking that occurs (not far) above the electroweak scale sets a stage for baryogenesis similar to the electroweak baryogenesis in the Standard Model. A concrete realization utilizes the breaking of SU(2)R× U(1)X→ U(1)Y. New chiral fermions charged under the extended gauge symmetry have nonzero lepton numbers, which makes the B − L symmetry anomalous. The new lepton sector contains a large flavor-dependent CP violation, similar to the Cabibbo-Kobayashi-Maskawa phase, without inducing sizable electric dipole moments of the Standard Model particles. A bubble wall dynamics associated with the first-order phase transition and SU(2)R sphaleron processes generate a lepton asymmetry, which is transferred into a baryon asymmetry via the ordinary electroweak sphaleron process. Unlike the Standard Model electroweak baryogenesis, the new phase transition can be of the strong first order and the new CP violation is not significantly suppressed by Yukawa couplings, so that the observed asymmetry can be produced. The model can be probed by collider searches for new particles and the observation of gravitational waves. One of the new leptons becomes a dark matter candidate. The model can be also embedded into a left-right symmetric theory to solve the strong CP problem.

NANOGrav results and dark first order phase transitions

The recent NANOGrav evidence of a common-source stochastic background provides a hint to Gravitational Waves (GW) radiation from the Early Universe. We show that this result can be interpreted as a GW spectrum produced from First Order Phase Transitions (FOPTs) around a temperature in the KeV-MeV window. Such a class of FOPTs at temperatures much below the electroweak scale can be naturally envisaged in several Warm Dark Matter models such as Majoron Dark Matter.

Top–Bottom Condensation Model: Symmetries and Spectrum of the Induced 2HDM

Here, we use the Schwinger–DeWitt approach to address the four-fermion composite Higgs effective model proposed by Miransky, Tanabashi and Yamawaki (MTY). The surprising benefit of such an approach is that it is possible to ascribe to a SM-type Higgs a quark–antiquark structure of predominantly a b¯b nature with a small t¯t admixture, which in turn yields a Higgs mass compatible with the observed value of 125 GeV. We discuss this result in a detailed and pedagogical way, as it goes against the common belief that this model and akin composite descriptions should predict a Higgs mass-of-order of twice the top quark mass, contrary to empirical evidence. A further aspect of this approach is that it highlights the link of the SU(2)L×U(1)R symmetric four-fermion MTY model interactions of the heavy quark family to a specific two-Higgs-doublet model (2HDM), and the necessity to go beyond the one Higgs doublet to obtain the empirical Higgs mass within composite models. By appropriately fixing the symmetry-defining interaction parameters, we show that the resulting CP-preserving spectrum harbors the following collective states at the electroweak scale ΛEW=246 GeV: a light scalar to which the standard Higgs is associated; a heavier neutral state preconized as the Nambu partner of the standard Higgs within the Nambu sum rule; the expected triplet of Goldstone bosons associated with the longitudinal polarizations of the electroweak massive bosons; and a neutral pseudoscalar state that in the limit of a global U(1)A symmetry would be a Goldstone mode. The anomalous breaking of this axial symmetry is a subleading effect in a large Nc counting scheme, and we discuss how it modifies the leading-order Nambu sum rule result and its relevance for the qualitative description of the spectrum.

Impact of a midband gravitational wave experiment on detectability of cosmological stochastic gravitational wave backgrounds

We make forecasts for the impact a future "midband" space-based gravitational wave experiment, most sensitive to $10^{-2}- 10$ Hz, could have on potential detections of cosmological stochastic gravitational wave backgrounds (SGWBs). Specific proposed midband experiments considered are TianGo, B-DECIGO and AEDGE. We propose a combined power-law integrated sensitivity (CPLS) curve combining GW experiments over different frequency bands, which shows the midband improves sensitivity to SGWBs by up to two orders of magnitude at $10^{-2} - 10$ Hz. We consider GW emission from cosmic strings and phase transitions as benchmark examples of cosmological SGWBs. We explicitly model various astrophysical SGWB sources, most importantly from unresolved black hole mergers. Using Markov Chain Monte Carlo, we demonstrated that midband experiments can, when combined with LIGO A+ and LISA, significantly improve sensitivities to cosmological SGWBs and better separate them from astrophysical SGWBs. In particular, we forecast that a midband experiment improves sensitivity to cosmic string tension $G\mu$ by up to a factor of $10$, driven by improved component separation from astrophysical sources. For phase transitions, a midband experiment can detect signals peaking at $0.1 - 1$ Hz, which for our fiducial model corresponds to early Universe temperatures of $T_*\sim 10^4 - 10^6$ GeV, generally beyond the reach of LIGO and LISA. The midband closes an energy gap and better captures characteristic spectral shape information. It thus substantially improves measurement of the properties of phase transitions at lower energies of $T_* \sim O(10^3)$ GeV, potentially relevant to new physics at the electroweak scale, whereas in this energy range LISA alone will detect an excess but not effectively measure the phase transition parameters. Our modelling code and chains are publicly available.