Higgs Vacuum Expectation Value Research Articles

Effective field theory of the two Higgs doublet model

We revisit the effective field theory of the two Higgs doublet model at tree level. The introduction of a novel basis in the UV theory allows us to derive matching coefficients in the effective description that resum important contributions from the Higgs vacuum expectation value. The new basis typically provides a significantly better approximation of the full theory prediction than the traditional approach that utilizes the Higgs basis, particularly for alignment away from the decoupling limit.

Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly

The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing Nature. The origin of scales, such as the Higgs vacuum expectation value (vev), may result from the spontaneous breakdown of the conformal symmetry by the dilaton field. In this work, we study whether this classical setup can be implemented in quantum theory and be phenomenologically viable by presenting an explicit construction where the exact conformal symmetry can be preserved and is anomaly free while being spontaneously broken. Not only the Higgs mass but also the genuine quantum scales like the QCD confinement radius are generated by the dilaton vev. We also discuss the extension of these ideas to the theories with dynamical gravity and show that the only finite subgroup of the local Weyl transformations which is anomaly free corresponds to the global scale symmetry. This means that the conformal invariance of the flat space theory is explicitly broken down to the scale symmetry by gravitational effects related to the Weyl anomaly.

Axion-Higgs cosmology: Cosmic microwave background and cosmological tensions

Non-canonical cosmology with an uplifted Higgs vacuum expectation value (Higgs-VEV) in the early universe is believed to provide the solution for existing tensions within the $\Lambda$CDM regime. We recently proposed a theoretical model called axi-Higgs to explore this framework. The axi-Higgs model features an ultralight axion with mass $m_a \sim 10^{-29}$ eV, which couples to the Higgs field such that the Higgs-VEV is driven by the axion background evolution. Phenomenologically, the axi-Higgs model is equivalent to $\Lambda$CDM+$m_e$+$\omega_a$ which is defined as $\Lambda$CDM with electron mass variation and the presence of an ultralight axion. In this paper, we perform Markov Chain Monte Carlo analyses to investigate the parameter space of axi-Higgs and compare it with $\Lambda$CDM, $\Lambda$CDM+$m_e$ where only electron mass variation is allowed, and $\Lambda$CDM+$\omega_a$ where only an ultralight axion is present. Combining observational data from Cosmic Microwave Background, Baryon Acoustic Oscillations, weak-lensing cosmic shear survey we found $H_0 = 69.4 \pm 1.3$ km/s/Mpc, which reduces the Hubble tension to approximately $2.4\sigma$. Including data from supernovae Type IA and local Hubble measurement from SH0ES we found $H_0 = 71.34 \pm 0.96$ km/s/Mpc. The presence of this Higgs-VEV-driving axion may be tested by atomic clock and quasar spectral measurements in the near future.

Sensitivity and constraints to the 2HDM soft-breaking Z2 parameter m12

In this letter we study the specific sensitivity and constraints to the soft breaking Z2 parameter m12 of the Two Higgs Doublet Model (2HDM). m12 is considered here as an input parameter of the model together with the masses of the Higgs bosons, mh, mH, mA, mH±, the ratio of the two Higgs vacuum expectation values, tan⁡β, and cos⁡(β−α), with α and β the mixing angles of the CP-even and CP-odd Higgs sector, respectively. We explore in particular the sensitivity to m12 in the decays of the lightest Higgs boson h to two photons, assuming: 1) that h is the state observed at the LHC at ∼125GeV, and 2) the h couplings to the SM particles are SM-like, by going to the alignment limit, cos⁡(β−α)=0. The aim of this work is to demonstrate possible constraints on m12 from the present measurement of the di-photon signal strength, μγγ. These constraints are relevant in the region of the 2HDM parameter space that is allowed by all the other constraints, specifically, theoretical constraints as well as experimental constraints from LHC Higgs rate measurements, Higgs boson searches, flavor physics and precision observables. The exploration is performed in the four different Yukawa types of 2HDM, where the allowed region by all the other constraints depends on the model type. We also analyze the case that the Higgs-boson mass spectrum accommodates a possible new world average of mW including the recent CDF measurement.

Sensitivity to dark sector scales from gravitational wave signatures

We consider gravitational sound wave signals produced by a first-order phase transition in a theory with a generic renormalizable thermal effective potential of power law form. We find the frequency and amplitude of the gravitational wave signal can be related in a straightforward manner to the parameters of the thermal effective potential. This leads to a general conclusion; if the mass of the dark Higgs is less than 1% of the dark Higgs vacuum expectation value, then the gravitational wave signal will be unobservable at all upcoming and planned gravitational wave observatories. Although the understanding of gravitational wave production at cosmological phase transitions is still evolving, we expect this result to be robust.

Hubble selection of the weak scale from QCD quantum critical point

There is growing evidence that the small weak scale may be related to self-organized criticality. In this regard, we note that if the strange quark were lighter, the QCD phase transition could have been first order, possibly exhibiting quantum critical points at zero temperature as a function of the Higgs vacuum expectation value $v_h$ smaller than (but near) the weak scale. We show that these quantum critical points allow a dynamical selection of the observed weak scale, via quantum-dominated stochastic evolutions of the value of $v_h$ during eternal inflation. Although the values of $v_h$ in different Hubble patches are described by a probability distribution in the multiverse, inflationary quantum dynamics ensures that the peak of the distribution evolves toward critical points (self-organized criticality), driven mainly by the largest Hubble expansion rate there -- the Hubble selection of the universe. To this end, we first explore the quantum critical points of the three-flavor QCD linear sigma model, parametrized by $v_h$ at zero temperature, and we present a relaxion model for the weak scale. Among the patches that have reached reheating, it results in a sharp probability distribution of $v_h$ near the observed weak scale, which is critical not to the crossover at $v_h=0$ but to the sharp transition at ${\sim}\Lambda_{\rm QCD}$.

Toward a realistic model of dark atoms to resolve the Hubble tension

It has recently been shown that a subdominant hidden sector of atomic dark matter in the early universe provides a novel avenue towards resolving the Hubble ($H_0$) tension while maintaining good agreement with Cosmic Microwave Background era observables. However, such a mechanism requires a hidden sector whose energy density ratios are the same as in our sector and whose recombination also takes place at redshift $z \approx 1100$, which presents an apparent fine tuning. We introduce a realistic model of this scenario that dynamically enforces these coincidences without fine tuning. In our setup, the hidden sector contains an identical copy of Standard Model (SM) fields, but has a smaller Higgs vacuum expectation value (VEV) and a lower temperature. The baryon asymmetries and reheating temperatures in both sectors arise from the decays of an Affleck-Dine scalar field, whose branching ratios automatically ensure that the reheating temperature in each sector is proportional to the corresponding Higgs VEV. The same setup also naturally ensures that the Hydrogen binding energy in each sector is proportional to the corresponding VEV, so the ratios of binding energy to temperature are approximately equal in the two sectors. Furthermore, our scenario predicts a correlation between the SM/hidden temperature ratio and the atomic dark matter abundance and automatically yields values for these quantities favored by concordant early- and late-universe measurements of $H_0$.

Festina-Lente bound on Higgs vacuum structure and inflation

The recently suggested Festina-Lente (FL) bound provides a lower bound on the masses of U(1) charged particles in terms of the positive vacuum energy. Since the charged particle masses in the Standard Model (SM) are generated by the Higgs mechanism, the FL bound provides a testbed of consistent Higgs potentials in the current dark energy-dominated universe as well as during inflation. We study the implications of the FL bound on the UV behavior of the Higgs potential for a miniscule vacuum energy, as in the current universe. We also present values of the Hubble parameter and the Higgs vacuum expectation value allowed by the FL bound during inflation, which implies that the Higgs cannot stay at the electroweak scale during this epoch.

On the Conformal Frames in f(R) Gravity

We discuss gravitational physics in the Jordan and Einstein frames of f(R) gravity coupled to the Standard Model. We elucidate the way in which the observed gravitational coupling arises in the Einstein frame for generic f(R). We point out that the effect of “running units” in the Einstein frame is related to the fact that the explicit and implicit quantum parameters of the Standard Model, such as the Higgs vacuum expectation value and the parameter ΛQCD, are modified by the conformal transformation of the metric and matter fields and become scalaron-dependent. Considering the scalaron of f(R) gravity describing dark matter, we show that the effect of running units in this case is extremely weak, making two frames practically equivalent.

Sliding Naturalness: New Solution to the Strong-CP and Electroweak-Hierarchy Problems.

We present a novel framework to solve simultaneously the electroweak-hierarchy problem and the strong-CP problem. A small but finite Higgs vacuum expectation value and a small θ angle are selected after the QCD phase transition, without relying on the Peccei-Quinn mechanism or other traditional solutions. We predict a distinctive pattern of correlated signals at hadronic EDM, fuzzy dark matter, and axion experiments.

Addendum to “Invisible Higgs decay width versus dark matter direct detection cross section in Higgs portal dark matter models”

This article is an addendum to Ref.~\cite{Baek:2014jga}. Here, we discuss the invisible Higgs decay width $\Gamma_{h}^{\rm inv}$ in the Higgs portal vector dark matter (VDM) model in the limit $m_V \rightarrow 0^+$. In the effective field theory (EFT) approach where the VDM mass is attributed to the St\"{u}ckelberg mechanism, $( \Gamma_{h}^{\rm inv} )_{\rm EFT}$ is divergent, which is unphysical and puzzling. On the other hand $( \Gamma_{h}^{\rm inv} )_{\rm UV}$ becomes finite in a UV completion, where the VDM mass is generated by the dark Higgs mechanism. Then we can take the limit $m_V \rightarrow 0^+$ by taking either {\it (i)} the dark gauge coupling $g_X \rightarrow 0^+$ with a fixed dark Higgs vacuum expectation value $v_\Phi$, or {\it (ii)} $v_\Phi \to 0^+$ with a fixed $g_X$. Such a difference in the behavior of $\Gamma_{h}^{\rm inv}$ in the massless VDM limit demonstrates another limitation of EFT for the Higgs portal VDM, and the importance of gauge-invariant and renormalizable models for the Higgs portal VDM.

Confronting the magnetically-induced holographic composite inflation with observation

We study the observational predictions of the phenomenological anti-de Sitter (AdS)/QCD inspired model, in which the inflaton field emerges in a four-dimensional strongly coupled gauge theory, in which the chiral symmetry breaking occurs through the formation of the quark condensate. Based on a top-down approach of AdS/QCD, using a D7-brane in the background of ${N}_{c}$ D3-branes, it has already been shown that chiral symmetry breaking in a magnetic field through the generation of the Higgs vacuum expectation value could be a second-order phase transition, although it was doubted that this scenario could lead to enough inflation. Using an iterative method, we consistently solve for the time-dependent parameters, including the embedding function of the D7-brane and the Hubble parameter of the expanding background. We show that with ${N}_{c}\ensuremath{\sim}{10}^{7}$ and ${g}_{\mathrm{UV}}\ensuremath{\sim}\mathrm{few}\ifmmode\times\else\texttimes\fi{}0.1$, the predictions of the inflationary model are consistent with the most stringent constraints placed on the inflationary models by Planck 2018. Although the model is capable of producing a large amount of gravitational waves, $r\ensuremath{\simeq}0.01$, the displacement of the canonical mass dimension-1 scalar field remains below the Planck mass, in violation of the Lyth bound.

Axi-Higgs cosmology

If the electroweak Higgs vacuum expectation value v in early universe is ∼ 1 % higher than its present value v0=246 GeV, the 7Li puzzle in BBN and the CMB/ΛCDM tension with late-universe measurements on Hubble parameter are mitigated. We propose a model of an axion coupled to the Higgs field, named “axi-Higgs”, with its mass ma ∼ 10-30 - 10-29 eV and decay constant fa ∼ 1017 - 1018 GeV, to achieve this goal. The axion initial value aini yields an initial Δ vini/v0 ∼ 0.01 throughout the BBN-recombination epoch and a percent level contribution to the total matter density today. Because of its very large de Broglie wavelength, this axion matter density ωa suppresses the matter power spectrum, alleviating the CMB/ΛCDM S8/σ8 tension with the weak-lensing data. It also explains the recently reported isotropic cosmic birefringence by its coupling with photons. Adding the axion (m ∼ 10-22eV) in the fuzzy dark matter model to the axi-Higgs model allows bigger Δ vrec and ωa to address the Hubble and S8/σ8 tensions simultaneously. The model predicts that Δ v may be detected by the spectral measurements of quasars, while its oscillation may be observed in the atomic clock measurements.

Cosmic variation of proton-to-electron mass ratio with an interacting Higgs scalar field

ABSTRACT We discuss that it is quite possible to realize the smooth transition of the universe between a matter/radiation-dominated deceleration and a dark-energy-dominated acceleration, even with a variation of proton-to-electron mass ratio μ. The variation is incorporated into the theory of gravity using a cosmological Higgs scalar field with a non-trivial and self-interaction potential, leading to a varying Higgs vacuum expectation value (VEV). This matches well with the data from molecular absorption spectra of a series of Quasars. In comparison with late-time cosmology, an observational consistency is reached using a Markov chain Monte Carlo simulation and JLA + OHD + BAO data sets. We find that the the pattern of variation is embedded within the evolving equation of state (EOS) of the scalar Dark Energy/Matter components, but leaves negligible trace on the effective EOS of the system. We discuss three cases of scalar extended theory of gravity, (a) a minimally coupled scalar, (b) a non-minimally coupled scalar, and (c) a generalized Brans–Dicke set-up. We also give a toy model of a unified cosmic history from inflation to the present era and discuss how the Higg VEV might have changed as a function of look-back time.

Vacuum expectation value renormalization in the standard model and beyond

We show how the renormalization constant of the Higgs vacuum expectation value, fixed by a tadpole condition, is responsible for gauge dependences in various definitions of parameters in the $R_{\xi}$-gauge. Then we show the relationship of this renormalization constant to the Fleischer-Jegerlehner (FJ) scheme, which is used to avoid these gauge dependences. In this way, we also present a viewpoint on the FJ-scheme complementary to the ones already existing in the literature. Additionally, we compare and discuss different approaches to the renormalization of tadpoles by identifying the similarities and relations between them. The relationship to the Higgs background field renormalization is also discussed.

Electroweak restoration at the LHC and beyond: The Vh channel

The LHC is exploring electroweak (EW) physics at the scale EW symmetry is broken. As the LHC and new high energy colliders push our understanding of the Standard Model to ever-higher energies, it will be possible to probe not only the breaking of but also the restoration of EW symmetry. We propose to observe EW restoration in double EW boson production via the convergence of the Goldstone boson equivalence theorem. This convergence is most easily measured in the vector boson plus Higgs production, $Vh$, which is dominated by the longitudinal polarizations. We define EW restoration by carefully taking the limit of zero Higgs vacuum expectation value (vev). EW restoration is then measured through the ratio of the $p_T^h$ distributions between $Vh$ production in the Standard Model and Goldstone boson plus Higgs production in the zero vev theory, where $p_T^h$ is the Higgs transverse momentum. As EW symmetry is restored, this ratio converges to one at high energy. We present a method to extract this ratio from collider data. With a full signal and background analysis, we demonstrate that the 14 TeV HL-LHC can confirm that this ratio converges to one to 40% precision while at the 27 TeV HE-LHC the precision will be 6%. We also investigate statistical tests to quantify the convergence at high energies. Our analysis provides a roadmap for how to stress test the Goldstone boson equivalence theorem and our understanding of spontaneously broken symmetries, in addition to confirming the restoration of EW symmetry.

Nucleon and dinucleon decays to leptonic final states in a left-right symmetric model with large extra dimensions

We consider baryon-number-violating nucleon and dinucleon decays to leptonic final states in the context of a left-right symmetric (LRS) model with large extra dimensions. Specifically, we study (a) nucleon to trilepton decays with varDelta B=-1 and varDelta L=-3, and (b) dinucleon to dilepton decays with varDelta B=-2 and varDelta L=-2. In the LRS model, B-L is gauged and is spontaneously broken by a Higgs vacuum expectation value v_R, which characterizes the scale at which processes violating B-L occur. We show that together with the lower bound on v_R from experimental limits on n-{bar{n}} oscillations, constraints from searches for other nucleon decay modes imply sufficient suppression of these nucleon to trilepton and dinucleon to dilepton decay modes in this model to agree with experimental bounds.

Improving fermion mass hierarchy in grand gauge\u2013Higgs unification with localized gauge kinetic terms

Grand gauge–Higgs unification of five dimensional SU(6) gauge theory on an orbifold S^1/Z_2 with localized gauge kinetic terms is discussed. The Standard model (SM) fermions on one of the boundaries and some massive bulk fermions coupling to the SM fermions on the boundary are introduced, so that they respect an SU(5) symmetry structure. The SM fermion masses including top quark are reproduced by mild tuning the bulk masses and parameters of the localized gauge kinetic terms. Gauge coupling universality is not guaranteed by the presence of the localized gauge kinetic terms and it severely constrains the Higgs vacuum expectation value. Higgs potential analysis shows that the electroweak symmetry breaking occurs by introducing additional bulk fermions in simplified representations. The localized gauge kinetic terms enhance the magnitude of the compactification scale, which helps Higgs boson mass large. Indeed the observed Higgs boson mass 125 GeV is obtained.

High-temperature electroweak symmetry non-restoration from new fermions and implications for baryogenesis

The strength of electroweak symmetry breaking may substantially differ in the early Universe compared to the present day value. In the Standard Model, the Higgs vacuum expectation value (vev ) vanishes and electroweak symmetry gets restored at temperatures above ∼ 160 GeV due to the Higgs field interactions with the high-temperature plasma. It was however shown that new light singlet scalar fields may change this behaviour. The key feature is the non-standard dependence on the Higgs vev of the new particles mass which can vanish at large Higgs vev, inducing a negative correction to the Higgs thermal mass, leading to electroweak symmetry non-restoration at high temperature. We show that such an effect can also be induced by new singlet fermions which on the other hand have the advantage of not producing unstable directions in the scalar potential at tree level, nor bringing additional severe hierarchy problems. As temperature drops, such a high-temperature breaking phase may continuously evolve into the zero-temperature breaking phase or the two phases can be separated by a temporary phase of restored symmetry. We discuss how our construction can naturally arise in motivated models of new physics, such as Composite Higgs. This is particularly relevant for baryogenesis, as it opens a whole class of possibilities in which the baryon asymmetry can be produced during a high temperature phase transition, while not being erased later by sphalerons.

Muon and electron g − 2 and the origin of the fermion mass hierarchy

Abstract We present a model that gives a natural explanation to the charged lepton mass hierarchy and study the contributions to the electron and the muon $g-2$. In the model, we introduce lepton-flavor-dependent $U(1)_F$ symmetry and three additional Higgs doublets with $U(1)_F$ charges, to realize that each generation of charged leptons couples to one of the three additional Higgs doublets. The $U(1)_F$ symmetry is softly broken by $+1$ charges, and the smallness of the soft breaking naturally gives rise to the hierarchy of the Higgs vacuum expectation values, which then accounts for the charged lepton mass hierarchy. Since electron and muon couple to different scalar particles, each scalar contributes to the electron and the muon $g-2$ differently. We survey the space of parameters of the Higgs sector and find that there are sets of parameters that explain the muon $g-2$ discrepancy. On the other hand, we cannot find parameter sets that can explain the $g-2$ discrepancy within 2 $\sigma$. Here, the $U(1)_F$ symmetry suppresses charged lepton flavor violation.