Higgs VEV Research Articles

Primordial black holes from conformal Higgs

Scale-invariant extensions of the electroweak theory are not only attractive because they can dynamically generate the weak scale, but also due to their role in facilitating supercooled first-order phase transitions. We study the minimal scale-invariant U(1)D extension of the standard model and show that Primordial Black Holes (PBHs) can be abundantly produced. The mass of these PBHs is bounded from above by that of the moon due to QCD catalysis limiting the amount of supercooling. Lunar-mass PBHs, which are produced for dark Higgs vev vϕ≃20TeV, correspond to the best likelihood to explain the HSC lensing anomaly. For vϕ≳400TeV, the model can explain hundred per cent of dark matter. At even larger hierarchy of scales, it can contribute to the 511keV line. While the gravitational wave (GW) signal produced by the HSC anomaly interpretation is large and detectable by LISA above astrophysical foreground, the dark matter interpretation in terms of PBHs can not be entirely probed by future GW detection. This is due to the dilution of the signal by the entropy injected during the decay of the long-lived U(1)D scalar. This extended lifetime is a natural consequence of the large hierarchy of scales.

Cosmological phase transitions and the swampland

I consider the Festina Lente Swampland bound and argue taking thermal effects, as for instance occur during reheating, into account significantly strengthens the implications of this bound. I argue that the confinement scale should be higher than a scale proportional to the vacuum energy, while Festina Lente without thermal effects only bounds the confinement scale to be above the Hubble scale. For Higgsing of nonabelian gauge fields, I find that the magnitude of the Higgs mass should be heavier than a bound proportional to the Electroweak scale (or generally the scale set by the Higgs VEV). The measured values of the Higgs in the SM satisfy the bound. A way to avoid the bound being violated during inflation is to have a large number of species becoming light. If one wants the inflationary scale to lie below the species scale in this case, this bounds the inflationary scale to be ≪ 105 GeV. These bounds have phenomenological implications for BSM physics such as GUTs, suggesting for example a weak or absent gravitational wave signature from the GUT Higgsing phase transition.

The dark dimension and the Swampland

Motivated by principles from the Swampland program, which characterize requirements for a consistent UV completion of quantum gravity, combined with observational data, we are led to a unique corner of the quantum gravity landscape. In particular, using the Distance/Duality conjecture and the smallness of dark energy, we predict the existence of a light tower of states and a unique extra mesoscopic dimension of length lsim {Lambda}^{-frac{1}{4}}sim {10}^{-6}m , with extra massless fermions propagating on it. This automatically leads to a candidate for a tower of sterile neutrinos, and an associated active neutrino mass scale {m}_{nu}sim {leftlangle Hrightrangle}^2{Lambda}^{-frac{1}{12}}{M}_{textrm{pl}}^{-frac{2}{3}} . Moreover, assuming the mechanism for stabilization of this dark dimension leads to similar masses for active and sterile neutrinos we are led to the prediction of a Higgs vev leftlangle Hrightrangle sim {Lambda}^{frac{1}{6}}{M}_{textrm{pl}}^{frac{1}{3}} . Another prediction of the scenario is a species scale hat{M}sim {Lambda}^{frac{1}{12}}{M}_{textrm{pl}}^{frac{2}{3}}sim {10}^9hbox{--} {10}^{10} GeV, corresponding to the higher-dimensional Planck scale. This energy scale may be related to the resolution of the instability of the Higgs effective potential present at a scale of ~1011 GeV. We also speculate about the interplay between this energy scale and the GZK limit on ultra-high energy cosmic rays.

The electroweak horizon problem

Spontaneously broken symmetries in particle physics may have produced several phase transitions in cosmology, e.g., at the GUT energy scale (~10^15 GeV), resulting in a quasi-de Sitter inflationary expansion, solving the background temperature horizon problem. This transition would have occurred at t~10^-36 to 10^-33 seconds, leading to a separation of the strong and electroweak forces. The discovery of the Higgs boson confirms that the Universe must have undergone another phase transition at the electroweak (EWPT) scale 159.5+/-1.5 GeV, about 10^-11 seconds later, when fermions and the W^+/- and Z^0 bosons gained mass, leading to the separation of the electric and weak forces. But today the vacuum expectation value (vev) of the Higgs field appears to be uniform throughout the visible Universe, a region much larger than causally-connected volumes at the EWPT. The discovery of the Higgs boson thus creates another serious horizon problem for LCDM, for which there is currently no established theoretical resolution. The EWPT was a smooth crossover, however, so previously disconnected electroweak vacuua might have homogenized as they gradually came into causal contact. But using the known Higgs potential and vev, we estimate that this process would have taken longer than the age of the Universe, so it probably could not have mitigated the emergence of different standard model parameters across the sky. The EWPT horizon problem thus argues against the expansion history of the early Universe predicted by standard cosmology.

Natural TeV cutoff of the Higgs field from a multiplicative Lagrangian

The various types of the non-standard Lagrangian can be added to the standard Lagrangian with the invariant of the equation of motion in the low energy limit. In this paper, we construct the multiplicative Lagrangian of a complex scalar field giving the approximated Klein-Gordon equation from the inverse problem of the calculus of variation. Then, this multiplicative Lagrangian with arbitrary high cutoff is applied to the toy model of the Higgs mechanism in U(1)-gauge symmetry in order to study the simple effects in the Higgs physics. We show that, after spontaneous symmetry breaking happens, the Higgs vev is free from the Fermi-coupling constant and the Higgs field gets the natural cutoff in TeV scale. The other relevant coupling constants, the UV-sensitivity of Higgs mass due to the loop correction, some applications on the strong CP problem as well as anomalous small fermion mass, and the cosmological constant problem are also discussed.

Extra W-boson mass from a D3-brane

Motivated by the recent CDF measurement of the W-boson mass, we study string-based particle physics models which can accommodate this deviation from the Standard Model. We consider an F-theory GUT in which the visible sector is realized on intersecting 7-branes, and extra sector states arise from a probe D3-brane near an E-type Yukawa point. The D3-brane worldvolume naturally realizes a strongly coupled sector which mixes with the Higgs. In the limit where some extra sector states get their mass solely from Higgs vevs, this leads to a contribution to the ρ parameter which is too large, but as the D3-brane is separated from the 7-brane stack, this effect is suppressed, leading to O(1) - O(10) TeV scale extra sector states and a correction to ρ which would be in accord with the CDF result. We also estimate the contribution to the oblique electroweak parameter S, and find that it is compatible with existing constraints. This also leads to additional signatures, including diphoton resonances (as well as other diboson final states) in the O(1) - O(10) TeV range.

Beyond the standard model effective field theory with b→cτ−ν¯

Electroweak interactions assign a central role to the gauge group $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}U(1{)}_{Y}$, which is either realized linearly (SMEFT) or nonlinearly (e.g., HEFT) in the effective theory obtained when new physics above the electroweak scale is integrated out. Although the discovery of the Higgs boson has made SMEFT the default assumption, nonlinear realization remains possible. The two can be distinguished through their predictions for the size of certain low-energy dimension-6 four-fermion operators: for these, HEFT predicts $O(1)$ couplings, while in SMEFT they are suppressed by a factor ${v}^{2}/{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{NP}}^{2}$, where $v$ is the Higgs vev. One such operator, ${O}_{V}^{LR}\ensuremath{\equiv}(\overline{\ensuremath{\tau}}{\ensuremath{\gamma}}^{\ensuremath{\mu}}{P}_{L}\ensuremath{\nu})(\overline{c}{\ensuremath{\gamma}}_{\ensuremath{\mu}}{P}_{R}b)$, contributes to $b\ensuremath{\rightarrow}c{\ensuremath{\tau}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$. We show that present constraints permit its non-SMEFT coefficient to have a HEFTy size. We also note that the angular distribution in $\overline{B}\ensuremath{\rightarrow}{D}^{*}(\ensuremath{\rightarrow}D{\ensuremath{\pi}}^{\ensuremath{'}}){\ensuremath{\tau}}^{\ensuremath{-}}(\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}){\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$ contains enough information to extract the coefficients of all new-physics operators. Future measurements of this angular distribution can therefore tell us if non-SMEFT new physics is really necessary.

Elliptic quantum curves of 6d SO(N) theories

We discuss supersymmetric defects in 6d mathcal{N} = (1, 0) SCFTs with SO(Nc) gauge group and Nc− 8 fundamental flavors. The codimension 2 and 4 defects are engineered by coupling the 6d gauge fields to charged free fields in four and two dimensions, respectively. We find that the partition function in the presence of the codimension 2 defect on ℝ4× \U0001d54b2 in the Nekrasov-Shatashvili limit satisfies an elliptic difference equation which quantizes the Seiberg-Witten curve of the 6d theory. The expectation value of the codimension 4 defect appearing in the difference equation is an even (under reflection) degree Nc section over the elliptic curve when Nc is even, and an odd section when Nc is odd. We also find that RG-flows of the defects and the associated difference equations in the 6d SO(2N + 1) gauge theories triggered by Higgs VEVs of KK-momentum states provide quantum Seiberg-Witten curves for ℤ2 twisted compactifications of the 6d SO(2N) gauge theories.

UV completed composite Higgs model with heavy composite partners

We study electroweak symmetry breaking in minimal composite Higgs models $SU(4)/Sp(4)$ with purely fermionic UV completions based on a confining Hypercolor gauge group and find that the extra Higgs potential from the underlying preon mass can destruct the correlation between the mass of Higgs and composite partners. Thus the composite partners can be very heavy for successful electroweak symmetry breaking without enhancing the separation between the new physical scale and Higgs VEV. So this kind of model can be easily realized by ordinary strong dynamics theories without artificial assumptions and more likely consistent with lattice simulations. The UV completion of partial compositeness predicts a light singlet Goldstone boson which interacts with QCD and electroweak gauge bosons through Wess-Zumino-Witten terms. It can be produced through gluon fusion at LHC and decay into gauge boson pairs. We briefly discuss its phenomenology and derive its bounds from LHC searches.

Crunching Dilaton, Hidden Naturalness.

We introduce a new approach to the Higgs naturalness problem. The Higgs mixes with the dilaton of a conformal field theory (CFT) sector whose true ground state has a large negative vacuum energy. If the Higgs vacuum expectation value is nonzero and below O(TeV), the CFT admits a second metastable vacuum, where the expansion history of the Universe is conventional. As a result, only Hubble patches with unnaturally small values of the Higgs mass do not immediately crunch. The main experimental prediction of this mechanism is a dilaton in the 0.1-10GeV range that mixes with the Higgs and can be detected at future colliders and experiments searching for weakly coupled particles.

Dark Energy and the Time Dependence of Fundamental Particle Constants

AbstractThe cosmic time dependencies of G, α, ℏ and of Standard Model parameters like the Higgs vev and elementary particle masses are studied in the framework of a new dark energy interpretation. Due to the associated time variation of rulers, many effects turn out to be invisible. However, a rather large time dependence is claimed to arise in association with dark energy measurements, and smaller ones in connection with the Standard Model.

Sphalerons, baryogenesis, and helical magnetogenesis in the electroweak transition of the minimal standard model

We start by considering the production rates of sphalerons with different size $\rho$ in the symmetric phase, $T>T_{EW}$. At small $\rho$, the distribution is cut off by the growing mass $M\sim 1/\rho$, and at large $\rho$ by the magnetic screening mass. In the broken phase, $T<T_{EW}$ the scale is set by the Higgs VEV $v(T)$. We introduce the concept of "Sphaleron freezeout" whereby the sphaleron production rate matches the Hubble Universe expansion rate. At freezeout the sphalerons are out of equilibrium. Sphaleron explosions generate sound and even gravity waves, when nonzero Weinberg angle make them non-spherical. We revisit CP violation during the sphaleron explosions. We assess its magnitude using the Standard Model CKM quark matrix, first for nonzero and then zero Dirac eigenstates. We find that its magnitude is maximal at the sphaleron freezeout condition with $T\approx 130\, GeV$. We proceed to estimate the amount of CP violation needed to generate the observed magnitude of baryon asymmetry of Universe. The result is about an order of magnitude below our CKM-based estimates. We also relate the baryon asymmetry to the generation of $U(1)$ magnetic chirality, which is expected to be conserved and perhaps visible in polarized intergalactic magnetic fields.

Higgsing and twisting of 6d DN gauge theories

We propose Type IIB 5-brane configurations that engineer the 6d mathcal{N} = (1, 0) SCFTs with SO(N) gauge symmetry coupled to a single tensor multiplet on a circle, by considering RG flows on Higgs branches of D-type conformal matter theories. We test the brane systems against known Calabi-Yau threefolds for the 6d SCFTs on a circle. In addition we study a new RG flow involving Higgs vevs of scalar operators with Kaluza-Klein momentum along the circle. The new RG flow results in the 5-brane webs for the 6d SCFTs of DN gauge symmetry compactified on a circle with Z2 outer-automorphism twist.

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.

A Goldilocks Higgs

The Higgs may couple to a topological 4-form sector which yields a complex vacuum structure. In many of the resulting Higgs vacua electroweak symmetry is unbroken. In just as many it breaks when the 4-form flux is large enough. For a fixed value of flux, the symmetry breaking vacua have a smaller vacuum energy than the symmetric ones, where the difference is quantized because it is set by the 4-form flux. This leads to the possibility that there is a value of the 4-form flux for any UV contributions to the Higgs vev that automatically cancels it down to the right value, ∼ TeV, if the 4-form charges are quantized in the units of the electroweak scale. This would still leave the cosmological constant which could be selected anthropically. In addition, the 4-form couplings could lead to direct CP violation in a non-minimal Higgs sector.

Neutrino masses from outer space

Neutrinos can gain mass from coupling to an ultralight field in slow roll. When such a field is displaced from its minimum, its vev acts just like the Higgs vev in spontaneous symmetry breaking. Although these masses may eventually vanish, they do it over a very long time. The theory is technically natural, with the ultralight field-dependent part being the right-handed Majorana mass. The mass variation induced by the field correlates with the cosmological evolution. The change of the mass term changes the mixing matrix, and therefore suppresses the fraction of sterile neutrinos at earlier times and increases it at later times. Since the issue of quantum gravity corrections to field theories with large field variations remains open, this framework may give an observational handle on the Weak Gravity Conjecture.

The fundamental need for a SM Higgs and the weak gravity conjecture

Compactifying the SM down to 3D or 2D one may obtain AdS vacua depending on the neutrino mass spectrum. It has been recently shown that, by insisting in the absence of these vacua, as suggested by Weak Gravity Conjecture (WGC) arguments, intriguing constraints on the value of the lightest neutrino mass and the 4D cosmological constant are obtained. For fixed Yukawa coupling one also obtains an upper bound on the EW scale 〈H〉≲Λ41/4/Yνi, where Λ4 is the 4D cosmological constant and Yνi the Yukawa coupling of the lightest (Dirac) neutrino. This bound may lead to a reassessment of the gauge hierarchy problem. In this letter, following the same line of arguments, we point out that the SM without a Higgs field would give rise to new AdS lower dimensional vacua. Absence of latter would require the very existence of the SM Higgs. Furthermore one can derive a lower bound on the Higgs vev 〈H〉≳ΛQCD which is required by the absence of AdS vacua in lower dimensions. The lowest number of quark/lepton generations in which this need for a Higgs applies is three, giving a justification for family replication. We also reassess the connection between the EW scale, neutrino masses and the c.c. in this approach. The EW fine-tuning is here related to the proximity between the c.c. scale Λ41/4 and the lightest neutrino mass mνi by the expression ΔHH≲(aΛ41/4−mνi)mνi. We emphasize that all the above results rely on the assumption of the stability of the AdS SM vacua found.

The Higgs boson can delay reheating after inflation

The Standard Model Higgs boson, which has previously been shown to develop an effective vacuum expectation value during inflation, can give rise to large particle masses during inflation and reheating, leading to temporary blocking of the reheating process and a lower reheat temperature after inflation. We study the effects on the multiple stages of reheating: resonant particle production (preheating) as well as perturbative decays from coherent oscillations of the inflaton field. Specifically, we study both the cases of the inflaton coupling to Standard Model fermions through Yukawa interactions as well as to Abelian gauge fields through a Chern-Simons term. We find that, in the case of perturbative inflaton decay to SM fermions, reheating can be delayed due to Higgs blocking and the reheat temperature can decrease by up to an order of magnitude. In the case of gauge-reheating, Higgs-generated masses of the gauge fields can suppress preheating even for large inflaton-gauge couplings. In extreme cases, preheating can be shut down completely and must be substituted by perturbative decay as the dominant reheating channel. Finally, we discuss the distribution of reheat temperatures in different Hubble patches, arising from the stochastic nature of the Higgs VEV during inflation and its implications for the generation of both adiabatic and isocurvature fluctuations.

Spiked monopoles

We introduce the spiked monopole, which is a ’t Hooft-Polyakov monopole with two charged scalar Higgs fields, of which one enjoys a quartic self-interaction. The free Higgs field behaves as in a BPS monopole, reducing the inter-monopole repulsion. The other Higgs has a spiked profile similar to a non-BPS monopole. Using the methods from numerical relativity recently adapted to the Yang-Mills-Higgs theory by Vachaspati, we simulate the interactions of such monopoles. During the long lifetime of these simulations the individual monopoles are stable. We find that they are always repulsive, with a small repulsion only when the interaction Higgs VEV is proportionately small. We briefly comment on implications for giant monopole dark matter models and on supermassive black hole seeding by the spikes.

Fundamental constant observational bounds on the variability of the QCD scale

Many physical theories beyond the Standard Model predict time variations of basic physics parameters. Direct measurement of the time variations of these parameters is very difficult or impossible to achieve. By contrast, measurements of fundamental constants are relatively easy to achieve, both in the laboratory and by astronomical spectra of atoms and molecules in the early universe. In this work measurements of the proton to electron mass ratio $\mu$ and the fine structure constant $\alpha$ are combined to place mildly model dependent limits on the fractional variation of the Quantum Chromodynamic Scale and the sum of the fractional variations of the Higgs Vacuum Expectation Value and the Yukawa couplings on time scales of more than half the age of the universe. The addition of another model parameter allows the fractional variation of the Higgs VEV and the Yukawa couplings to be computed separately. Limits on their variation are found at the level of less than $5 \times 10^{-5}$ over the past seven gigayears. A model dependent relation between the expected fractional variation of $\alpha$ relative to $\mu$ tightens the limits to $10^{-7}$ over the same time span. Limits on the present day rate of change of the constants and parameters are then calculated using slow roll quintessence. A primary result of this work is that studies of the dimensionless fundamental constants such as $\alpha$ and $\mu$, whose values depend on the values of the physics parameters, are excellent monitors of the limits on the time variation of these parameters.