arXiv subjects

Lawrence J. Hall

Publications and source records attributed to Lawrence J. Hall.

At least 19 recordsLinked to original sources

arXiv2026

The Very Nearly Right Theory of Flavor

A striking empirical observation about the CKM matrix is that the angles of the unitarity triangle $(\alpha, \beta, \gamma)$ are very close to $(\pi/2, \pi/8, 3 \pi/8) $, simple fractions of $\pi$ that are suggestive of an underlying theory linking flavor and spontaneous CP violation. However, relating this empirical observation to an underlying theory of flavor is challenging, since the unitarity triangle is a complicated function of the Yukawa matrices. In this letter we present a simple picture for the Yukawas where this direct link is possible. We begin by parametrizing the ten-dimensional space of flavor data via "nine-link textures", full-rank $Y_{u,d}$ matrices with a total of nine non-zero entries, with a single CP violating phase. Fitting the ten parameters of all such textures to the flavor data reveals a wonderful surprise: the CP phases cluster tightly around multiples of $\pi/8$! This happens because the entries of $Y_{u,d}$ naturally define a "Yukawa triangle", in most cases identical to the unitarity triangle at leading order in small flavor parameters. Most interestingly, these two triangles are not the same beyond leading order, yielding precise predictions for $(\alpha, \beta, \gamma)$ with calculable deviation from $(\pi/2, \pi/8, 3 \pi/8)$, which can be decisively excluded or strongly confirmed by the next generation of experimental measurements of the angles. The 9-link textures are sparse and their determinants are naturally real, which taken together with spontaneous CP violation can resolve the strong CP problem.

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arXiv2026

Maximal Abelian Flavor Symmetries

A framework, MAFS, is introduced that provides an approximate description of the hierarchies of quark and lepton masses and mixing angles in terms of a set of small parameters, $\epsilon_a$, one for each fermion multiplet. MAFS is an alternative to the Froggatt-Nielsen mechanism and has a unique application in any theory, as there are no fermion charges to choose. It becomes more powerful as the number of multiplets is reduced. In $SU(5)$ unified theories, 15 observed mass ratios and mixing angles are described, at the factor of two level, by five small $\epsilon_a$ parameters. Even though quarks and leptons are unified, the observed hierarchical pattern of quark masses and mixings {\it requires} large neutrino mixing angles and small neutrino mass hierarchies. In an $SO(10)$ unified theory, MAFS successfully describes the 15 observed flavor hierarchies with just three small $\epsilon_a$, taking values of $0.01, 0.02$ and $0.002$. The observed cosmological baryon asymmetry results approximately from leptogenesis using MAFS in $SU(5)$, without the need for any additional small parameter; while in $SO(10)$, a further small parameter of about 0.2 appears necessary.

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arXiv2026

Generating the fermion mass hierarchy at the TeV scale

We propose a class of theories to generate quark and lepton mass matrices where the scale of new physics is at the TeV scale, without inducing the large flavor and CP violating processes that are often thought to relegate the origin of flavor to energies above $\sim 100$ TeV. The models have new vector-like leptons and quarks, with mass mixings to each other and Yukawa couplings to light Standard Model fields encoded in "chains" reminiscent of dimensional deconstruction. Locality in the chains both generates the hierarchical Standard Model Yukawa matrices, and ensures that CP and flavor violating effects are small, even with the vector-like particles at the TeV scale. A simple extension also generates neutrino masses, whose tiny size is parametrically related to the square of the electron Yukawa coupling. We outline the essential features of these models, explain how fermion mass hierarchies and mixing angles emerge, and explore their phenomenological implications. This framework can be tested both in the final run of the LHC as well as at possible future colliders operating at the 10 TeV scale, and we identify some of the distinctive experimental signatures associated with the production and decay of the new vector-like fermions.

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arXiv2025

A Flavor of SO(10) Unification with a Spinor Higgs

We investigate Higgs Parity Unification-a realization of $SO(10)$ grand unification based on the Higgs Parity mechanism in which the Standard Model (SM) Higgs resides in a spinor representation. The theory has an intermediate left-right symmetric stage where the $SU(2)_R$ symmetry breaking scale is fixed by the vanishing of the SM Higgs quartic coupling. The strong $CP$ problem is solved by parity. Gauge coupling unification successfully predicts $α_s(M_Z)$ to within 1%. The spinor Higgs naturally leads to a seesaw origin for SM flavor observables. We identify a novel mechanism where large mixing of third generation fermions with additional heavy vector-like fermions accounts for the anarchical nature of the PMNS matrix and the lack of hierarchy in the neutrino mass spectrum, relative to the up-quarks. A fit to quark and lepton masses and mixings, with a minimal parameter set, predicts 1) A testable relation between the top quark mass and $α_s(M_Z)$ which is about $(1-2)σ$ from current best fit values, 2) The order of magnitude of the baryon asymmetry of the universe, via leptogenesis from second-generation right-handed neutrino decays. 3) The proton decay and the neutron EDM are likely observable in next generation experiments, and 4) A normal ordered neutrino mass spectrum where $0νββ$ decay and the mass of the lightest neutrino are out of reach of next generation experiments.

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arXiv2025

Two Higgs Doublet Solutions to the Strong CP Problem

We solve the strong CP problem in a broad class of two Higgs doublet theories that will be probed at the Large Hadron Collider and at future colliders. These theories feature CP and Abelian flavor symmetries, both broken softly in the scalar potential, that yield realistic quark masses and mixings. The flavor symmetry charges are chosen so that $\barθ=0$ at tree level for all values of the Yukawa and quartic couplings of the theory. We prove that in all such theories the 1-loop contribution to $\barθ$ also vanishes, independently of the mass scale of the second Higgs doublet. We study two illustrative models with flavor group $\mathbb{Z}_3$. The direct contributions to the neutron electric dipole moment are negligible in both models. While the 2-loop contribution to $\barθ$ is less than $10^{-12}$ in one model, it can be as large as $10^{-10}$ in the other, yielding the prospect of a signal in planned experiments. Even with Abelian flavor symmetries, CP violation in neutral kaon mixing is generally expected to yield naturalness bounds on the masses of additional Higgs doublets of order 20 TeV. We prove that for all models in our class, where the flavor symmetry forces $\barθ$ to vanish at tree-level, the flavor-changing neutral currents are CP-conserving, yielding model-dependent bounds from neutral meson mixing near 1 TeV. Mixing of the two CP-even scalars gives corrections to the couplings of the 125 GeV Higgs state to $\bar{t}t, \bar{b}b, \bar{c}c, \barττ$ and $\barμ μ$, giving possible signals at high luminosity runs at LHC and at future colliders. Furthermore, distinctive correlations between corrections in the various channels can probe the underlying flavor symmetry.

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arXiv2024

Gravitational Wave and CMB Probes of Axion Kination

Rotations of an axion field in field space provide a natural origin for an era of kination domination, where the energy density is dominated by the kinetic term of the axion field, preceded by an early era of matter domination. Remarkably, no entropy is produced at the end of matter domination and hence these eras of matter and kination domination may occur even after Big Bang Nucleosynthesis. We derive constraints on these eras from both the cosmic microwave background and Big Bang Nucleosynthesis. We investigate how this cosmological scenario affects the spectrum of possible primordial gravitational waves and find that the spectrum features a triangular peak. We discuss how future observations of gravitational waves can probe the viable parameter space, including regions that produce axion dark matter by the kinetic misalignment mechanism or the baryon asymmetry by axiogenesis. For QCD axion dark matter produced by the kinetic misalignment mechanism, a modification to the inflationary gravitational wave spectrum occurs above 0.01 Hz and, for high values of the energy scale of inflation, the prospects for discovery are good. We briefly comment on implications for structure formation of the universe.

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arXiv2023

Radiative Majorana Neutrino Masses in a Parity Solution to the Strong CP Problem

The strong CP problem can be solved in Parity symmetric theories with electroweak gauge group containing $SU(2)_L \times SU(2)_R$ broken by the minimal Higgs content. Neutrino masses may be explained by adding the same number of gauge singlet fermions as the number of generations. The neutrino masses vanish at tree-level and are only radiatively generated, leading to larger couplings of right-handed neutrinos to Standard Model particles than with the tree-level seesaw mechanism. We compute these radiative corrections and the mixing angles between left- and right-handed neutrinos. We discuss sensitivities to these right-handed neutrinos from a variety of future experiments that search for heavy neutral leptons with masses from tens of MeV to the multi-TeV scale.

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arXiv2023

Leptogenesis in Parity Solutions to the Strong CP Problem and Standard Model Parameters

We study the simplest theories with exact spacetime parity that solve the strong CP problem and successfully generate the cosmological baryon asymmetry via decays of right-handed neutrinos. Lower bounds are derived for the masses of the right-handed neutrinos and for the scale of spontaneous parity breaking, $v_R$. For generic thermal leptogenesis, $v_R \gtrsim 10^{12}$ GeV, unless the small observed neutrino masses arise from fine-tuning. We compute $v_R$ in terms of the top quark mass, the QCD coupling, and the Higgs boson mass and find this bound is consistent with current data at $1 σ$. Future precision measurements of these parameters may provide support for the theory or, if $v_R$ is determined to be below $10^{12}$ GeV, force modifications. However, modified cosmologies do not easily allow reductions in $v_R$ -- no reduction is possible if leptogenesis occurs in the collisions of domain walls formed at parity breaking, and at most a factor 10 reduction is possible with non-thermal leptogenesis. Standard Model parameters that yield low values for $v_R$ can only be accommodated by having a high degree of degeneracy among the right-handed neutrinos involved in leptogenesis. If future precision measurements determine $v_R$ to be above $10^{12}$ GeV, it is likely that higher-dimensional operators of the theory will yield a neutron electric dipole moment accessible to ongoing experiments. This is especially true in a simple UV completion of the neutrino sector, involving gauge singlet fermions, where the bound from successful leptogenesis is strengthened to $v_R \gtrsim 10^{13}$ GeV.

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arXiv2023

A Heavy QCD Axion and the Mirror World

We study the mirror world with dark matter arising from the thermal freeze-out of the lightest, stable mirror particle -- the mirror electron. The dark matter abundance is achieved for mirror electrons of mass 225 GeV, fixing the mirror electroweak scale near $10^8$ GeV. This highly predictive scenario is realized by an axion that acts as a portal between the two sectors through its coupling to the QCD and mirror QCD sectors. The axion is more massive than the standard QCD axion due to additional contributions from mirror strong dynamics. Still, the strong CP problem is solved by this "heavy" axion due to the alignment of the QCD and mirror QCD potentials. Mirror entropy is transferred into the Standard Model sector via the axion portal, which alleviates overproduction of dark radiation from mirror glueball decays. This mirror scenario has a variety of signals: (1) primordial gravitational waves from the first-order mirror QCD phase transition occurring at a temperature near 35 GeV, (2) effects on large-scale structure from dark matter self-interactions from mirror QED, (3) dark radiation affecting the cosmic microwave background, and (4) the rare kaon decay, $K^+ \rightarrow (π^+ + \rm{axion})$. The first two signals do not depend on any fundamental free parameters of the theory while the latter two depend on a single free parameter, the axion decay constant.

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arXiv2022

Dark Radiation Constraints on Heavy QCD Axions

The naturalness problem of PQ symmetry motivates study of the heavy QCD axion, with masses $m_a >$ 1 MeV generated at scales above the QCD scale, and low values of the PQ symmetry breaking scale, $f_a$. We compute the abundance of such axions in a model-independent way, assuming only that they freeze-out after reheating from inflation, and are not subsequently diluted by new physics. If these axions decay between neutrino decoupling and the last scatter era of the Cosmic Microwave Background (CMB), they dilute the neutrinos and their abundance is constrained by CMB measurements of the energy density in dark radiation, $N_{\rm eff}$. We accurately compute this bound using a numerical code to evolve the axion momentum distribution, including many key processes and effects previously ignored. We assume that the only relevant axion decays are to final states involving Standard Model particles. We determine regions of $(m_a, f_a)$ that will give a signal in $N_{\rm eff}$ at CMB Stage 4 experiments. We similarly compute the $N_{\rm eff}$ bound and CMB Stage 4 signal for heavy axions that can decay to light mirror photons. Finally, we compute the bounds on heavy axions with mass below 1 MeV that decay after the era of CMB last scatter, from their contribution to cold or hot dark matter or $N_{\rm eff}$ at this era.

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arXiv2021

Lepto-Axiogenesis

We propose a baryogenenesis mechanism that uses a rotating condensate of a Peccei-Quinn (PQ) symmetry breaking field and the dimension-five operator that gives Majorana neutrino masses. The rotation induces charge asymmetries for the Higgs boson and for lepton chirality through sphaleron processes and Yukawa interactions. The dimension-five interaction transfers these asymmetries to the lepton asymmetry, which in turn is transferred into the baryon asymmetry through the electroweak sphaleron process. QCD axion dark matter can be simultaneously produced by dynamics of the same PQ field via kinetic misalignment or parametric resonance, favoring an axion decay constant $f_a \lesssim 10^{10}$ GeV, or by conventional misalignment and contributions from strings and domain walls with $f_a \sim 10^{11}$ GeV. The size of the baryon asymmetry is tied to the mass of the PQ field. In simple supersymmetric theories, it is independent of UV parameters and predicts the supersymmtry breaking mass scale to be $\mathcal{O}(10-10^4)$ TeV, depending on the masses of the neutrinos and whether the condensate is thermalized during a radiation or matter dominated era. We also construct a theory where TeV scale supersymmetry is possible. Parametric resonance may give warm axions, and the radial component of the PQ field may give signals in rare kaon decays from mixing with the Higgs and in dark radiation.

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arXiv2021

Sterile Neutrino Dark Matter and Leptogenesis in Left-Right Symmetric Theories

Left-Right symmetric theories solve the strong CP problem and explain the small Higgs quartic coupling at high energy scales via the Higgs Parity mechanism, which forces the Higgs quartic coupling to vanish at the Left-Right symmetry breaking scale. They also predict three right-handed neutrinos; one may be stable and provide dark matter, and another may decay and explain the baryon asymmetry of the universe through leptogenesis. For the dark matter abundance to arise from freeze-out, the required range of the Left-Right symmetry breaking scale is $10^{10}$-$10^{13}$ GeV, in remarkable agreement with the energy scale at which the Higgs quartic coupling vanishes. The allowed parameter space can be probed by the warmness of dark matter, precise measurements of the top quark mass and QCD coupling constant by future colliders and lattice computations, and measurement of the neutrino mass hierarchy.

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arXiv2020

Dark Matter Detection, Standard Model Parameters, and Intermediate Scale Supersymmetry

The vanishing of the Higgs quartic coupling at a high energy scale may be explained by Intermediate Scale Supersymmetry, where supersymmetry breaks at $(10^9$-$10^{12})$ GeV. The possible range of supersymmetry breaking scales can be narrowed down by precise measurements of the top quark mass and the strong coupling constant. On the other hand, nuclear recoil experiments can probe Higgsino or sneutrino dark matter up to a mass of $10^{12}$ GeV. We derive the correlation between the dark matter mass and precision measurements of standard model parameters, including supersymmetric threshold corrections. The dark matter mass is bounded from above as a function of the top quark mass and the strong coupling constant. The top quark mass and the strong coupling constant are bounded from above and below respectively for a given dark matter mass. We also discuss how the observed dark matter abundance can be explained by freeze-out or freeze-in during a matter-dominated era after inflation, with the inflaton condensate being dissipated by thermal effects.

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arXiv2020

Sterile Neutrino Dark Matter in Left-Right Theories

$SU(2)_L \times SU(2)_R$ gauge symmetry requires three right-handed neutrinos ($ N _i $), one of which, $N_1$, can be sufficiently stable to be dark matter. In the early universe, $ W _R $ exchange with the Standard Model thermal bath keeps the right-handed neutrinos in thermal equilibrium at high temperatures. $N_1$ can make up all of dark matter if they freeze-out while relativistic and are mildly diluted by subsequent decays of a long-lived and heavier right-handed neutrino, $N_2$. We systematically study this parameter space, constraining the symmetry breaking scale of $SU(2)_R$ and the mass of $N_1$ to a triangle in the $(v_R,M_1)$ plane, with $v_R = (10^6 - 3 \times 10^{12})$ GeV and $M_1 = (2\, {\rm keV} - 1 \, {\rm MeV)}$. Much of this triangle can be probed by signals of warm dark matter, especially if leptogenesis from $N_2$ decay yields the observed baryon asymmetry. The minimal value of $v_R$ is increased to $10^8 \, {\rm GeV}$ for doublet breaking of $SU(2)_R$, and further to $10^9 \, {\rm GeV}$ if leptogenesis occurs via $N_2$ decay, while the upper bound on $M_1$ is reduced to 100 keV. In addition, there is a component of hot $N_1$ dark matter resulting from the late decay of $N_2 \rightarrow N_1 \ell^+ \ell^-$ that can be probed by future cosmic microwave background observations. Interestingly, the range of $v_R$ allows both precision gauge coupling unification and the Higgs Parity understanding of the vanishing of the Standard Model Higgs quartic at scale $v_R$. Finally, we study freeze-in production of $N_1$ dark matter via the $W_R$ interaction, which allows a much wider range of $(v_R,M_1)$.

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arXiv2020

Sterile Neutrino Dark Matter and Leptogenesis in Left-Right Higgs Parity

The standard model Higgs quartic coupling vanishes at $(10^{9}-10^{13})$ GeV. We study $SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ theories that incorporate the Higgs Parity mechanism, where this becomes the scale of Left-Right symmetry breaking, $v_R$. Furthermore, these theories solve the strong CP problem and predict three right-handed neutrinos. We introduce cosmologies where $SU(2)_R \times U(1)_{B-L}$ gauge interactions produce right-handed neutrinos via the freeze-out or freeze-in mechanisms. In both cases, we find the parameter space where the lightest right-handed neutrino is dark matter and the decay of a heavier one creates the baryon asymmetry of the universe via leptogenesis. A theory of flavor is constructed that naturally accounts for the lightness and stability of the right-handed neutrino dark matter, while maintaining sufficient baryon asymmetry. The dark matter abundance and successful natural leptogenesis require $v_R$ to be in the range $(10^{10}-10^{13})$ GeV for freeze-out, in remarkable agreement with the scale where the Higgs quartic coupling vanishes, whereas freeze-in requires $v_R \gtrsim 10^9$ GeV. The allowed parameter space can be probed by the warmness of dark matter, precise determinations of the top quark mass and QCD coupling by future colliders and lattice computations, and measurement of the neutrino mass hierarchy.

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arXiv2020

Axion Kinetic Misalignment Mechanism

In the conventional misalignment mechanism, the axion field has a constant initial field value in the early universe and later begins to oscillate. We present an alternative scenario where the axion field has a nonzero initial velocity, allowing an axion decay constant much below the conventional prediction from axion dark matter. This axion velocity can be generated from explicit breaking of the axion shift symmetry in the early universe, which may occur as this symmetry is approximate.

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arXiv2020

Predictions for Axion Couplings from ALP Cogenesis

Adding an axion-like particle (ALP) to the Standard Model, with a field velocity in the early universe, simultaneously explains the observed baryon and dark matter densities. This requires one or more couplings between the ALP and photons, nucleons, and/or electrons that are predicted as functions of the ALP mass. These predictions arise because the ratio of dark matter to baryon densities is independent of the ALP field velocity, allowing a correlation between the ALP mass, $m_a$, and decay constant, $f_a$. The predicted couplings are orders of magnitude larger than those for the QCD axion and for dark matter from the conventional ALP misalignment mechanism. As a result, this scheme, ALP cogenesis, is within reach of future experimental ALP searches from the lab and stellar objects, and for dark matter.

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arXiv2020

Axion Kinetic Misalignment and Parametric Resonance from Inflation

Axion cold dark matter from standard misalignment typically requires a decay constant $f_a~\gtrsim~10^{11}$ GeV. Kinetic misalignment and parametric resonance easily allow lower values of $f_a$ when the radial Peccei-Quinn (PQ) symmetry breaking field takes large initial values. Here, we consider the effects of inflation on kinetic misalignment and parametric resonance. We assume that the initial PQ field value is determined by quantum fluctuations, and is set by the Hubble parameter during inflation, $H_I$, and the PQ field mass. PQ field oscillations begin before or after the completion of reheating after inflation at a temperature $T_R$. We determine the range of $f_a$ and the inflationary parameters $(H_I, T_R)$ consistent with axion dark matter for a quartic potential for the PQ field. We find that $4\times 10^8$ GeV $< f_a < 10^{11}$ GeV can consistently produce axion dark matter. A significant portion of the allowed parameter space predicts rare kaon decays, $K_L \rightarrow (π^0 + \rm{missing \; energy})$, and/or suppression of structure formation on small scales.

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