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Christopher T. Hill

Publications and source records attributed to Christopher T. Hill.

At least 37 records · Page 2Linked to original sources
arXiv2019

Scale independent $R^2$ inflation

Weyl (scale) invariant theories of scalars and gravity can generate all mass scales spontaneously. In this paper we study a particularly simple version -- scale invariant $R^2$ gravity -- and show that, during an inflationary period, it leads to fluctuations which, for a particular parameter choice, are almost indistinguishable from normal $R^2$ inflation. Current observations place tight constraints on the primary coupling constant of this theory and predict a tensor to scalar ratio, $0.0033 > r > 0.0026$, which is testable with the next generation of cosmic microwave background experiments.

gr-qc↗
arXiv2019

Where are the Next Higgs Bosons?

Simple symmetry arguments applied to the third generation lead to a prediction: there exist new sequential Higgs doublets with masses of order $\lesssim 5 $ TeV, with approximately universal Higgs-Yukawa coupling constants, $g\sim 1$. This is calibrated by the known Higgs boson mass, the top quark Higgs-Yukawa coupling, and the $b$-quark mass. A new massive weak-isodoublet, $H_b$, coupled to the $b$-quark with $g\sim 1$ is predicted, and may be accessible to the LHC at $13$ TeV, and definitively at the energy upgraded LHC of $26$ TeV. The extension to leptons generates a new $H_τ$ and a possible $H_{ν_τ}$ doublet. The accessibility of the latter depends upon whether the mass of the $τ$-neutrino is Dirac or Majorana.

hep-ph↗
arXiv2019

Scalar Democracy

We conjecture that there exists a scalar bound state for every pair of fundamental fermions at a UV (`composite') scale, $Λ\gg v_{\text{weak}}$. This implies a large number of universally coupled, sub-critical Higgs doublets. All but the Standard Model Higgs are `dormant,' with large positive squared masses and each receives a small vacuum expectation values via mixing with the Standard Model Higgs. Universal couplings, modulo renormalization group running effects, flips the flavor problem into the masses and mixings of the Higgs system. Doublets associated with heavy fermion masses, $b,c, τ$ likely lie in the multi-TeV range, but may be observable at the current LHC, or a high-luminosity and/or an energy-upgraded LHC. In the lepton sector we are lead to a Higgs seesaw for neutrino masses, and corollary processes of observable flavor violation. The observation of the first sequential doublet coupled to $\bar{b}b$ with masses $\lesssim 3.5$ TeV would lend credence to the hypothesis.

hep-ph↗
arXiv2018

Inertial Spontaneous Symmetry Breaking and Quantum Scale Invariance

Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of "inertial spontaneous symmetry breaking" that does not involve a potential. This is dictated by the structure of the Weyl current, $K_μ$, and a cosmological phase during which the universe expands and the Einstein-Hilbert effective action is formed. Maintaining exact Weyl invariance in the renormalised quantum theory is straightforward when renormalisation conditions are referred back to the VEV's of fields in the action of the theory, which implies a conserved Weyl current. We do not require scale invariant regulators. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential.

hep-th↗
arXiv2018

Inflation in a scale invariant universe

A scale-invariant universe can have a period of accelerated expansion at early times: inflation. We use a frame-invariant approach to calculate inflationary observables in a scale invariant theory of gravity involving two scalar fields - the spectral indices, the tensor to scalar ratio, the level of isocurvature modes and non-Gaussianity. We show that scale symmetry leads to an exact cancellation of isocurvature modes and that, in the scale-symmetry broken phase, this theory is well described by a single scalar field theory. We find the predictions of this theory strongly compatible with current observations.

astro-ph.CO↗
arXiv2018

Inertial Symmetry Breaking

We review and expand upon recent work demonstrating that Weyl invariant theories can be broken "inertially," which does not depend upon a potential. This can be understood in a general way by the "current algebra" of these theories, independently of specific Lagrangians. Maintaining the exact Weyl invariance in a renormalized quantum theory can be accomplished by renormalization conditions that refer back to the VEV's of fields in the action. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential that breaks a U(1) symmetry together,with scale invariance.

hep-th↗
arXiv2017

Reply to "Comment on `Axion induced oscillating electric dipole moments' " [1]

We respond to a paper of Flambaum, et.al. [Phys. Rev. D95, no. 5, 058701 (2017)], claiming there is no effective induced oscillating electric dipole moment, e.g., for the electron, arising from interaction with an oscillating cosmic axion background via the anomaly. The relevant Feynman amplitude, Fig.(1), as computed by Flambaum et.al., becomes a total divergence, and vanishes. Contrary to this result, we obtained a nonvanishing amplitude, that yields physical electric dipole radiation for an electron (or any magnetic dipole moment) immersed in a cosmic axion field. We argue that the Flambaum et.al. counter-claim is incorrect, and is based upon a misunderstanding of a physics choice vs. gauge choice, and an assumption that electric dipoles be defined only by coupling to static (constant in time) electric fields.

hep-ph↗
arXiv2016

Weyl Current, Scale-Invariant Inflation and Planck Scale Generation

Scalar fields, $ϕ_i$ can be coupled non-minimally to curvature and satisfy the general criteria: (i) the theory has no mass input parameters, including the Planck mass; (ii) the $ϕ_i$ have arbitrary values and gradients, but undergo a general expansion and relaxation to constant values that satisfy a nontrivial constraint, $K(ϕ_i) =$ constant; (iii) this constraint breaks scale symmetry spontaneously, and the Planck mass is dynamically generated; (iv) there can be adequate inflation associated with slow roll in a scale invariant potential subject to the constraint; (v) the final vacuum can have a small to vanishing cosmological constant (vi) large hierarchies in vacuum expectation values can naturally form; (vii) there is a harmless dilaton which naturally eludes the usual constraints on massless scalars. These models are governed by a global Weyl scale symmetry and its conserved current, $K_μ$ . At the quantum level the Weyl scale symmetry can be maintained by an invariant specification of renormalized quantities.

hep-th↗
arXiv2016

No fifth force in a scale invariant universe

We revisit the possibility that the Planck mass is spontaneously generated in scale invariant scalar-tensor theories of gravity, typically leading to a "dilaton." The fifth force, arising from the dilaton, is severely constrained by astrophysical measurements. We explore the possibility that nature is fundamentally Weyl-scale invariant and argue that, as a consequence, the fifth force effects are dramatically suppressed and such models are viable. We discuss possible obstructions to maintaining scale invariance and how these might be resolved.

gr-qc↗
arXiv2016

Scale-Independent Inflation and Hierarchy Generation

We discuss models involving two scalar fields coupled to classical gravity that satisfy the general criteria: (i) the theory has no mass input parameters, (ii) classical scale symmetry is broken only through $-\frac{1}{12}ςϕ^2 R$ couplings where $ς$ departs from the special conformal value of $1$; (iii) the Planck mass is dynamically generated by the vacuum expectations values (VEVs) of the scalars (iv) there is a stage of viable inflation associated with slow roll in the two--scalar potential; (v) the final vacuum has a small to vanishing cosmological constant and an hierarchically small ratio of the VEVs and the ratio of the scalar masses to the Planck scale. This assumes the paradigm of classical scale symmetry as a custodial symmetry of large hierarchies.

hep-th↗
arXiv2016

Axion Induced Oscillating Electric Dipole Moment of the Electron

A cosmic axion, via the electromagnetic anomaly, induces an oscillating electric dipole for the electron of frequency $m_a$ and strength $\sim$(few)$\times 10^{-32}$ e-cm, two orders of magnitude above the nucleon, and within a few orders of magnitude of the present standard model constant limit. We give a detailed study of this phenomenon via the interaction of the cosmic axion, through the electromagnetic anomaly, with particular emphasis on the decoupling limit of the axion, $\partial_t a(t)\propto m_a \rightarrow 0$. The analysis is subtle, and we find the general form of the action involves a local contact interaction and a nonlocal contribution, analogous to the "transverse current" in QED, that enforces the decoupling limit. We carefully derive the effective action in the Pauli-Schroedinger non-relativistic formalism, and in Georgi's heavy quark formalism adapted to the "heavy electron" ($m_e>>m_a$). We compute the electric dipole radiation emitted by free electrons, magnets and currents, immersed in the cosmic axion field, and discuss experimental configurations that may yield a detectable signal.

hep-ph↗
arXiv2015

Axion Induced Oscillating Electric Dipole Moments

The axion electromagnetic anomaly induces an oscillating electric dipole for {\em any} static magnetic dipole. Static electric dipoles do not produce oscillating magnetic moments. This is a low energy theorem which is a consequence of the space-time dependent cosmic background field of the axion in the limit that it is only locally time dependent $(\overrightarrowβ=0)$. The electron will acquire an oscillating electric dipole of frequency $m_a$ and strength $\sim 10^{-32}$ e-cm, three orders of magnitude above the nucleon, and within four orders of magnitude of the present standard model DC limit. This may suggest sensitive new experimental venues for the axion dark matter search.

hep-ph↗
arXiv2014

An ultra-weak sector, the strong CP problem and the pseudo-Goldstone dilaton

In the context of a Coleman-Weinberg mechanism for the Higgs boson mass, we address the strong CP problem. We show that a DFSZ-like invisible axion model with a gauge-singlet complex scalar field S, whose couplings to the Standard Model are naturally ultra-weak, can solve the strong CP problem and simultaneously generate acceptable electroweak symmetry breaking. The ultra-weak couplings of the singlet S are associated with underlying approximate shift symmetries that act as custodial symmetries and maintain technical naturalness. The model also contains a very light pseudo-Goldstone dilaton that is consistent with cosmological Polonyi bounds, and the axion can be the dark matter of the universe. We further outline how a SUSY version of this model, which may be required in the context of Grand Unification, can avoid introducing a hierarchy problem.

hep-ph↗
arXiv2014

Composite Vectorlike Fermions

We study a dynamical mechanism that generates a composite vectorlike fermion, formed by the binding of an $N$-tuplet of elementary chiral fermions to an $N$-tuplet of scalars. Deriving the properties of the composite fermion in the large $N$ limit, we show that its mass is much smaller than the compositeness scale when the binding coupling is near a critical value. We compute the contact interactions involving four composite fermions, and find that their coefficients scale as $1/N$. Physics beyond the Standard Model may include composite vectorlike fermions arising from this mechanism.

hep-ph↗
arXiv2014

Ultra-weak sector, Higgs boson mass, and the dilaton

The Higgs boson mass may arise from a portal coupling to a singlet field $σ$ which has a very large VEV $f \gg m_\text{Higgs}$. This requires a sector of "ultra-weak" couplings $ζ_i$, where $ζ_i \lesssim m_\text{Higgs}^2 / f^2$. Ultra-weak couplings are technically naturally small due to a custodial shift symmetry of $σ$ in the $ζ_i \rightarrow 0$ limit. The singlet field $σ$ has properties similar to a pseudo-dilaton. We engineer explicit breaking of scale invariance in the ultra-weak sector via a Coleman-Weinberg potential, which requires hierarchies amongst the ultra-weak couplings.

hep-ph↗
arXiv2014

Is the Higgs Boson Associated with Coleman-Weinberg Dynamical Symmetry Breaking?

The Higgs mechanism may be a quantum phenomenon, i.e., a Coleman-Weinberg potential generated by the explicit breaking of scale symmetry in Feynman loops. We review the relationship of scale symmetry, trace anomalies, and emphasize the role of the renormalization group in determining Coleman- Weinberg potentials. We propose a simple phenomenological model with "maximal visibility" at the LHC containing a "dormant" Higgs doublet (no VEV, coupled to standard model gauge interactions $SU(2)\times U(1)$) with a mass of $\sim 380$ GeV. We discuss the LHC phenomenology and UV challenges of such a model. We also give a schematic model in which new heavy fermions, with masses $\sim 230$ GeV, can drive a Coleman-Weinberg potential at two-loops. The role of the "improved stress tensor" is emphasized, and we propose a non-gravitational term, analogous to the $θ$-term in QCD, which generates it from a scalar action.

hep-ph↗