Electroweak Symmetry Breaking Scale Research Articles

ALP-LEFT Interference and the Muon (g − 2)

The low-energy effective field theory (LEFT) provides the appropriate framework to describe particle interactions below the scale of electroweak symmetry breaking, μw ~ v. By matching the Standard Model onto the LEFT, non-zero Wilson coefficients of higher-dimensional operators are generated, suppressed by the corresponding power of 1/v. An axion or axion-like particle (ALP) with mass ma ≪ μw that interacts with the Standard Model via classically shift-invariant dimension-five operators would also contribute to the LEFT Wilson coefficients, since it can appear as a virtual particle in divergent Green’s functions and thus has an impact on the renormalization of the LEFT operators. We present the full set of one-loop ALP-induced source terms modifying the renormalization-group evolution equations of the LEFT Wilson coefficients up to dimension-six order. Our framework allows for model-independent ALP searches at low energies from current bounds on LEFT Wilson coefficients. As a concrete application, we present an improved prediction for ALP effects on the anomalous magnetic moment of the muon.

Inflation and electroweak symmetry breaking

We present a model of Cosmological Electroweak Symmetry Breaking (CEWSB), where a Higgs-like field and a cosmological background of weak boson gauge fields interact with gravity to realize the epoch of cosmic inflation, which is then followed by a Higgs resonance preheating. As a result, the scale of electroweak symmetry breaking is linked with the end of inflation. The theory is equipped with a shift symmetry that can protect the Higgs mass, and it has close semblance to natural inflation and its variants. As the Higgs field's amplitude decays at the end of inflation, its mass emerges. The model has a built in Higgs self-resonance preheating mechanism which leads to the possible emergence of the cosmic microwave background (CMB) due to resonant Higgs, quark and lepton production after inflation. We provide a pathway to implement a similar mechanism with the realistic Higgs-doublet of the standard electroweak theory and discuss phenomenological considerations.

Complete NNLO operator bases in Higgs effective field theory

For the first time, we list the complete and independent set of operators at the next-to-next-to-leading order (NNLO) in the Higgs effective field theory (HEFT). The Young tensor technique utilized in this work guarantees the completeness and independence of the on-shell amplitude basis while the Adler zero condition imposes non-linear symmetry on the Nambu-Goldstone bosons that play the central role in the chiral Lagrangian. The spurion fields are incorporated into the gauge structure of operators following the Littlewood-Richardson rule to accommodate custodial symmetry breaking. We construct 11506 (1927574) NNLO operators for one (three) flavor of fermions for the electroweak chiral Lagrangian with the light Higgs, and enumerate 8065(1179181) operators for one (three) flavor of fermions when the right-handed neutrino is absent by Hilbert series technique. Below the electroweak symmetry breaking scale, the dimension-8 standard model effective field theory (SMEFT) operators could be matched to these HEFT operators at both the NLO and NNLO orders.

W-Boson Mass Anomaly as a Manifestation of Spontaneously Broken Additional SU(2) Global Symmetry on a New Fundamental Scale

Recently, the CDF Collaboration has announced a new precise measurement of the W-boson mass MW that deviates from the Standard Model (SM) prediction by 7σ. The discrepancy in MW is about ΔW ≃ 70 MeV and is probably caused by a beyond the SM physics. Within a certain scenario of extension of the SM, we obtain the relation ΔW ≃ 3α8πMW ≃ 70 MeV, where α is the electromagnetic fine structure constant. The main conjecture is the appearance of longitudinal components of the W-bosons as the Goldstone bosons of a spontaneously broken additional SU(2) global symmetry at distances much smaller than the electroweak symmetry breaking scale rEWSB. We argue that within this scenario, the masses of charged Higgs scalars can obtain an electromagnetic radiative contribution which enhances the observed value of MW± with respect to the usual SM prediction. Our relation for ΔW follows from the known one-loop result for the corresponding effective Coleman–Weinberg potential in combination with the Weinberg sum rules.

Massive Gravitons as Feebly Interacting Dark Matter Candidates.

We detail our discovery of a chiral enhancement in the production cross sections of massive spin-2 gravitons, below the electroweak symmetry breaking scale, that makes them ideal dark matter candidates for the freeze-in mechanism. The result is independent of the physics at high scales and points toward masses in the keV-MeV range. The graviton is, therefore, a sub-MeV dark matter particle, as favored by the small scale galaxy structures. We apply the novel calculation to a Randall-Sundrum model with multiple branes, showing a significant parameter space where the first two massive gravitons saturate the dark matter relic density.

Natural inflation after Planck 2018

We calculate high-precision constraints on Natural Inflation relative to current observational constraints from Planck 2018 + BICEP/Keck(BK15) Polarization + BAO on r and n S, including post-inflationary history of the universe. We find that, for conventional post-inflationary dynamics, Natural Inflation with a cosine potential is disfavored at greater than 95% confidence out by current data. If we assume protracted reheating characterized by w̅>1/3, Natural Inflation can be brought into agreement with current observational constraints. However, bringing unmodified Natural Inflation into the 68% confidence region requires values of T re below the scale of electroweak symmetry breaking. The addition of a SHOES prior on the Hubble Constant H 0 only worsens the fit.

Unified emergence of energy scales and cosmic inflation

In the quest for unification of the Standard Model with gravity, classical scale invariance can be utilized to dynamically generate the Planck mass MPl. However, the relation of Planck scale physics to the scale of electroweak symmetry breaking μH requires further explanation. In this paper, we propose a model that uses the spontaneous breaking of scale invariance in the scalar sector as a unified origin for dynamical generation of both scales. Using the Gildener-Weinberg approximation, only one scalar acquires a vacuum expectation value of υS ∼ (1016−17) GeV, thus radiatively generating {M}_{mathrm{P}1}approx {beta}_S^{1/2}{upsilon}_S and μH via the neutrino option with right handed neutrino masses mN = yMυS ∼ 107 GeV. Consequently, active SM neutrinos are given a mass with the inclusion of a type-I seesaw mechanism. Furthermore, we adopt an unbroken Z2 symmetry and a Z2-odd set of right-handed Majorana neutrinos χ that do not take part in the neutrino option and are able to produce the correct dark matter relic abundance (dominantly) via inflaton decay. The model also describes cosmic inflation and the inflationary CMB observables are predicted to interpolate between those of R2 and linear chaotic inflationary model and are thus well within the strongest experimental constraints.

ALP \u2014 SMEFT interference

The Standard Model Effective Field Theory (SMEFT) offers a powerful theoretical framework for parameterizing the low-energy effects of heavy new particles with masses far above the scale of electroweak symmetry breaking. Additional light degrees of freedom extend the effective theory. We show that light new particles that are weakly coupled to the SM via non-renormalizable interactions induce non-zero Wilson coefficients in the SMEFT Lagrangian via renormalization-group evolution. For the well-motivated example of axions and axion-like particles (ALPs) interacting with the SM via classically shift-invariant dimension-5 interactions, we calculate how these interactions contribute to the one-loop renormalization of the dimension-6 SMEFT operators, and how this running sources additional contributions to the Wilson coefficients on top of those expected from heavy new states. As an application, we study the ALP contributions to the magnetic dipole moment of the top quark and comment on implications of electroweak precision constraints on ALP couplings.

Dark matter spectra from the electroweak to the Planck scale

We compute the decay spectrum for dark matter (DM) with masses above the scale of electroweak symmetry breaking, all the way to the Planck scale. For an arbitrary hard process involving a decay to the unbroken standard model, we determine the prompt distribution of stable states including photons, neutrinos, positrons, and antiprotons. These spectra are a crucial ingredient in the search for DM via indirect detection at the highest energies as being probed in current and upcoming experiments including IceCube, HAWC, CTA, and LHAASO. Our approach improves considerably on existing methods, for instance, we include all relevant electroweak interactions.

Interplay of New Physics effects in (g \u2212 2)\u2113 and h \u2192 \u2113+\u2113\u2212 \u2014 lessons from SMEFT

We explore the interplay of New Physics (NP) effects in (g− 2)ℓ and h→ℓ+ℓ− within the Standard Model Effective Field Theory (SMEFT) framework, including one-loop Renormalization Group (RG) evolution of the Wilson coefficients as well as matching to the observables below the electroweak symmetry breaking scale. We include both the leading dimension six chirality flipping operators including a Higgs and SU(2)L gauge bosons as well as four-fermion scalar and tensor operators, forming a closed operator set under the SMEFT RG equations. We compare present and future experimental sensitivity to different representative benchmark scenarios. We also consider two simple UV completions, a Two Higgs Doublet Model and a single scalar LeptoQuark extension of the SM, and show how tree level matching to SMEFT followed by the one-loop RG evolution down to the electroweak scale can reproduce with high accuracy the (g−2)ℓ and h→ℓ+ℓ− contributions obtained by the complete one- and even two-loop calculations in the full models.

The low-energy effective theory of axions and ALPs

Axions and axion-like particles (ALPs) are well-motivated low-energy relics of high-energy extensions of the Standard Model, which interact with the known particles through higher-dimensional operators suppressed by the mass scale Λ of the new-physics sector. Starting from the most general dimension-5 interactions, we discuss in detail the evolution of the ALP couplings from the new-physics scale to energies at and below the scale of electroweak symmetry breaking. We derive the relevant anomalous dimensions at two-loop order in gauge couplings and one-loop order in Yukawa interactions, carefully considering the treatment of a redundant operator involving an ALP coupling to the Higgs current. We account for one-loop (and partially two-loop) matching contributions at the weak scale, including in particular flavor-changing effects. The relations between different equivalent forms of the effective Lagrangian are discussed in detail. We also construct the effective chiral Lagrangian for an ALP interacting with photons and light pseudoscalar mesons, pointing out important differences with the corresponding Lagrangian for the QCD axion.

Implications of dark sector mixing on leptophilic scalar dark matter

We propose a new viable outlook to the mixing between a singlet and a doublet leptonic dark sector fields. This choice relaxes the dark matter (DM) search constraints on the quintessential scalar singlet DM as well as presents new opportunities for its detection in the lab. The mixing produces an arbitrary mass difference between the two components of the extra doublet in a gauge-invariant way, without introducing any new scale of electroweak symmetry breaking in the theory. It also provides a useful handle to distinguish between the dark sector particles of different isospins, which is a challenging task other-wise. As the dark leptons coannihilate non-trivially, the mixing effectively enhances the viable parameter space for the relic density constraint. In low DM mass regime, our analysis shows that with a non-zero mixing, it is possible to relax the existing indirect search bounds on the upper limit of the DM-Standard Model coupling. From the analysis of the 3tau +{E}_T^{mathrm{miss}} and mathrm{ell}tau +{E}_T^{mathrm{miss}} channels for LHC at sqrt{s} = 13 TeV, we show that one ensures the presence of the mixing parameter between the dark sector particles of the theory by looking at the peak and tail positions of the kinematic distributions. Even with a tweak in the values of other free parameters within the viable parameter region, the distinct peak and tail positions of the kinematic distributions remains a constant feature of the model. While both the channels present us the opportunity to detect the mixing signature at the LHC/HL-LHC, the former gives better results in terms of a larger region of mixing parameter. From the fiducial cross section, the projected statistical significance for the integrated luminosity, mathcal{L} = 3 ab−1, are shown for a combined parameter region obeying all the existing constraints, where there is the best possibility to detect such a signature.

Nuclear EDM from SMEFT flavor-changing operator

We study nuclear electric dipole moments induced by ∆F = 1 effective operators in the Standard Model Effective Field Theory. Such contributions arise through renormalization group evolutions and matching conditions at the electroweak symmetry breaking scale. We provide one-loop formulae for the matching conditions. We also discuss correlations of these effects with ∆F = 2 observables such as ϵK and Delta {M}_{B_d} .

Dark energy without fine tuning

We present a two-field model that realises inflation and the observed density of dark energy today, whilst solving the fine-tuning problems inherent in quintessence models. One field acts as the inflaton, generically driving the other to a saddle-point of the potential, from which it acts as a quintessence field following electroweak symmetry breaking. The model exhibits essentially no sensitivity to the initial value of the quintessence field, naturally suppresses its interactions with other fields, and automatically endows it with a small effective mass in the late Universe. The magnitude of dark energy today is fixed by the height of the saddle point in the potential, which is dictated entirely by the scale of electroweak symmetry breaking.

Effective theory analysis for vector-like quark model

We study a model with a down-type SU(2) singlet vector-like quark (VLQ) as a minimal extension of the standard model (SM). In this model, flavor changing neutral currents (FCNCs) arise at tree level and the unitarity of the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM) matrix does not hold. In this paper, we constrain the FCNC coupling from $b\rightarrow s$ transitions, especially $B_s\rightarrow \mu^+\mu^-$ and $\bar{B}\rightarrow X_s\gamma$ processes. In order to analyze these processes, we derive an effective Lagrangian which is valid below the electroweak symmetry breaking scale. For this purpose, we first integrate out the VLQ field and derive an effective theory by matching Wilson coefficients up to one-loop level. Using the effective theory, we construct the effective Lagrangian for $b\rightarrow s\gamma^{(*)}$. It includes the effects of the SM quarks and the violation of the CKM unitarity. We show the constraints on the magnitude of the FCNC coupling and its phase by taking account of the current experimental data on $\Delta M_{B_s}$, $\mathrm{Br}[B_s\rightarrow\mu^+\mu^-]$, $\mathrm{Br}[\bar{B}\rightarrow X_s\gamma]$ and CKM matrix elements as well as theoretical uncertainties. We find that the constraint from the $\mathrm{Br}[B_s\rightarrow\mu^+\mu^-]$ is more stringent than that from the $\mathrm{Br}[\bar{B}\rightarrow X_s\gamma$]. We also obtain the bound for the mass of the VLQ and the strength of the Yukawa couplings related to the FCNC coupling of $b\rightarrow s$ transition. Using the CKM elements which satisfy above constraints, we show how the unitarity is violated on the complex plane.

Neutrino mass generation at TeV scale and new physics signatures from charged Higgs at the LHC for photon initiated processes

We consider the collider phenomenology of a simple extension of the Standard Model (SM), which consists of an EW isospin 3/2 scalar, Δ and a pair of EW isospin 1 vector like fermions, Σ and overline{varSigma} , responsible for generating tiny neutrino mass via the effective dimension seven operator. This scalar quadruplet with hypercharge Y = 3 has a plethora of implications at the collider experiments. Its signatures at TeV scale colliders are expected to be seen, if the quadruplet masses are not too far above the electroweak symmetry breaking scale. In this article, we study the phenomenology of multi-charged quadruplet scalars. In particular, we study the multi-lepton signatures at the Large Hadron Collider (LHC) experiment, arising from the production and decays of triply and doubly charged scalars. We studied Drell-Yan (DY) pair production as well as pair production of the charged scalars via photon-photon fusion. For doubly and triply charged scalars, photon fusion contributes significantly for large scalar masses. We also studied LHC constraints on the masses of doubly charged scalars in this model. We derive a lower mass limit of 725 GeV on doubly charged quadruplet scalar.

A supersymmetric electroweak scale seesaw model

In this paper we propose a novel supersymmetric inverse seesaw model which has only one additional Z6 symmetry. The field content is minimal to get a viable neutrino spectrum at tree-level. Interestingly, the inverse seesaw scale in our model is related to the scale of electroweak symmetry breaking. Due to that origin we are less biased about hierarchies and discuss three different types of the inverse seesaw mechanism with different phenomenologies. We can successfully reproduce neutrino masses and mixing and our model is consistent with current bounds on neutrinoless double beta decay, non-unitarity of the PMNS matrix and charged lepton flavor violation.

Renormalisation-group improved analysis of \u03bc \u2192 e processes in a systematic effective-field-theory approach

In this article, a complete analysis of the three muonic lepton-flavour violating processes μ → eγ, μ → 3e and coherent nuclear μ → e conversion is performed in the framework of an effective theory with dimension six operators defined below the electroweak symmetry breaking scale mW . The renormalisation-group evolution of the Wilson coefficients between mW and the experimental scale is fully taken into account at the leading order in QCD and QED, and explicit analytic and numerical evolution matrices are given. As a result, muonic decay and conversion rates are interpreted as functions of the Wilson coefficients at any scale up to mW . Taking the experimental limits on these processes as input, the phenomenology of the mixing effects is investigated. It is found that a considerable set of Wilson coefficients unbounded in the simplistic tree-level approach are instead severely constrained. In addition, correlations among operators are studied both in the light of current data and future experimental prospects.

Are supersymmetric models with minimal particle content under tension for testing at LHC?

Abstract In supersymmetric models with minimal particle content and without large left-right squarks mixing, the conventional knowledge is that the Higgs Boson mass around 125 GeV leads to top squark masses O ( 10 ) TeV , far beyond the reach of colliders. Here, we pointed out that this conclusion is subject to several theoretical uncertainties. We find that electroweak symmetry breaking and evaluation of Higgs mass at a scale far away from the true electroweak symmetry breaking scale introduce a large uncertainty in Higgs mass calculation. We show that the electroweak symmetry breaking at the scale near the true vacuum expectation value of Higgs field can increase the Higgs Boson mass about 4–5 GeV and can lower the bounds on squarks and slepton masses to 1 TeV. Here we pointed out that the Higgs mass even with inclusion of radiative corrections can vary with electroweak symmetry breaking scale. We calculate it at two loop level and show that it varies substantially. We argue that Higgs mass like other coupling parameters can vary with energy scale and the Higgs potential with all orders loop corrections is scale invariant. This uncertainty to the Higgs mass calculation due to electroweak symmetry breaking around the supersymmetry breaking scale, normally taken as m t ˜ L m t ˜ R , to minimize the 1-loop radiative corrections can be removed if one considers all significant radiative contributions to make Higgs potential renormalization group evolution scale invariant and evaluates electroweak symmetry breaking at the scale near the electroweak symmetry breaking scale. A large parameter space becomes allowed when one considers electroweak symmetry breaking at its true scale not only for producing correct values of the Higgs masses, but also for providing successful breaking of this symmetry in more parameter spaces.

The Standard Model: how far can it go and how can we tell?

The Standard Model of particle physics encapsulates our current best understanding of physics at the smallest distances and highest energies. It incorporates quantum electrodynamics (the quantized version of Maxwell's electromagnetism) and the weak and strong interactions, and has survived unmodified for decades, save for the inclusion of non-zero neutrino masses after the observation of neutrino oscillations in the late 1990s. It describes a vast array of data over a wide range of energy scales. I review a selection of these successes, including the remarkably successful prediction of a new scalar boson, a qualitatively new kind of object observed in 2012 at the Large Hadron Collider. New calculational techniques and experimental advances challenge the Standard Model across an ever-wider range of phenomena, now extending significantly above the electroweak symmetry breaking scale. I will outline some of the consequences of these new challenges, and briefly discuss what is still to be found.This article is part of the themed issue 'Unifying physics and technology in light of Maxwell's equations'.