Low-energy Effective Theory Research Articles

Flavor structures of quarks and leptons from flipped SU(5) GUT with A4 modular flavor symmetry

We propose to generate the flavor structures of the Standard Model plus neutrinos from flipped SU(5) GUT with A4 modular flavor symmetry. Possible way to assign different moduli values for quarks and leptons in modular GUT scheme is discussed. We propose to reduce the multiple modular symmetries to a single modular symmetry in the low energy effective theory with proper boundary conditions. We classify all possible scenarios in this scheme according to the assignments of the modular A4 representations for matter superfields and give the expressions of the quark and lepton mass matrices predicted by our scheme at the GUT scale. After properly selecting the modular weights for various superfields that can lead to better fitting, we can obtain the best-fit points with the corresponding χ2 values for the sample subscenarios. We find that the flavor structures of the Standard Model plus neutrinos can be fitted perfectly in such a A4 modular flavor GUT scheme with single or two modulus fields. Especially, the {chi}_{textrm{total}}^2 of our fitting can be as low as 1.558 for sample IX′ of scenario III even if only a single common modulus field for both quark and lepton sectors is adopted. The most predictive scenario III, in which all superfields transform as triplets of A4, can be fitted much better with two independent moduli fields τq, τl for quark sector and lepton sector ( {chi}_{textrm{total}}^2 ≈ 95) than that with the single modulus case ( {chi}_{textrm{total}}^2 ≈ 282.4).

Partition functions and fibering operators on the Coulomb branch of 5d SCFTs

We study 5d mathcal{N} = 1 supersymmetric field theories on closed five-manifolds mathcal{M} 5 which are principal circle bundles over simply-connected Kähler four-manifolds, mathcal{M} 4, equipped with the Donaldson-Witten twist. We propose a new approach to compute the supersymmetric partition function on mathcal{M} 5 through the insertion of a fibering operator, which introduces a non-trivial fibration over mathcal{M} 4, in the 4d topologically twisted field theory. We determine the so-called Coulomb branch partition function on any such mathcal{M} 5, which is conjectured to be the holomorphic ‘integrand’ of the full partition function. We precisely match the low-energy effective field theory approach to explicit one-loop computations, and we discuss the effect of non-perturbative 5d BPS particles in this context. When mathcal{M} 4 is toric, we also reconstruct our Coulomb branch partition function by appropriately gluing Nekrasov partition functions. As a by-product of our analysis, we provide strong new evidence for the validity of the Lockhart-Vafa formula for the five-sphere partition function.

Long-lived heavy neutral leptons from mesons in effective field theory

In the framework of the low-energy effective field theory of the Standard Model extended with heavy neutral leptons (HNLs), we calculate the production rates of HNLs from meson decays triggered by dimension-six operators. We consider both lepton-number-conserving and lepton-number-violating four-fermion operators involving either a pair of HNLs or a single HNL. Assuming that HNLs are long-lived, we perform simulations and investigate the reach of the proposed far detectors at the high-luminosity LHC to (i) active-heavy neutrino mixing and (ii) the Wilson coefficients associated with the effective operators, for HNL masses below the mass of the B-meson. We further convert the latter to the associated new-physics scales. Our results show that scales in excess of hundreds of TeV and the active-heavy mixing squared as small as 10−15 can be probed by these experiments.

Analytical model of the energy spectrum and Landau levels of a twisted double bilayer graphene

Motivated by recent experiments Adak et al. (2020) and Szentpéter et al. (2021), in this work we have considered a twisted double bilayer graphene system. Within the low energy effective theory, the bandwidth expression of the moire flatbands (with weak dispersion and diverging effective mass) and Landau level spectrum of the Bernal stacked twisted double bilayer graphene are obtained analytically. We analyze the dependence of the bandwidth, effective mass, and Landau level spectrum on twist angle, inter layer tunneling, and interlayer potential difference. Also, we have investigated the phase diagram of the effective mass as a function of the twist angle and interlayer tunneling strength to seek the parameter space with diverging effective mass. We find that the magic angle at which the flat bands exist is increasing with increasing inter layer tunneling strength. • In this work, in this work we have considered a twisted double bilayer graphene system. • Within the low energy effective theory, the bandwidth expression of the moiré flatbands (with weak dispersion and diverging effective mass) and Landau level spectrum of the Bernal stacked twisted double bilayer graphene are obtained analytically. • We analyze the dependence of the bandwidth, effective mass, and Landau level spectrum on twist angle, inter layer tunneling, and interlayer potential difference. • Also, we have investigated the phase diagram of the effective mass as a function of the twist angle and interlayer tunneling strength to seek the parameter space with diverging effective mass. • We find that the magic angle at which the flat bands exist is increasing with increasing inter layer tunneling strength. • The results presented in this work will be useful for the experimental investigation of the tDBG system.

SU(5) grand unification and W-boson mass

A realistic extension of the minimal SU(5) theory consisting of the addition of an adjoint fermion is known to predict light real fermion and scalar weak triplets, potentially accessible at the LHC. These particles, in addition to playing a key role in gauge coupling unification, have profound phenomenological implications. The fermion triplet, that through the seesaw mechanism offers a testable origin of neutrino mass, has been already extensively discussed. The scalar triplet develops a vacuum expectation value that modifies the W-boson mass. We show that its low-energy effective theory is remarkably predictive: in the leading approximation, all the relevant physical processes involving the scalar triplet depend only on its mass and the deviation from the Standard Model W-mass value.

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers. II. Zero-field topological superconductivity

It has been proposed that band-inverted electron-hole bilayers support a phase transition from an insulating phase with spontaneously broken time-reversal symmetry to a quantum spin Hall insulator phase as a function of increasing electron and hole densities. Here we show that in the presence of proximity-induced superconductivity, it is possible to realize Majorana zero modes in the time-reversal symmetry broken phase in the absence of magnetic field. We develop an effective low-energy theory for the system in the presence of a time-reversal symmetry-breaking order parameter to obtain analytically the Majorana zero modes and we find good agreement between the numerical and analytical results in the limit of weakly broken time-reversal symmetry. We show that the Majorana zero modes can be detected in superconductor/time-reversal symmetry broken insulator/superconductor Josephson junctions through the measurement of a $4\ensuremath{\pi}$ Josephson current. Finally, we demonstrate that the Majorana fusion-rule detection is feasible by utilizing the gate voltage dependence of the spontaneous time-reversal symmetry breaking order parameter.

Finite-temperature dynamics in gapped one-dimensional models in the sine-Gordon family

The sine-Gordon model appears as the low-energy effective field theory of various one-dimensional gapped quantum systems. Here we investigate the dynamics of generic, nonintegrable systems belonging to the sine-Gordon family at finite temperature within the semiclassical approach. Focusing on timescales where the effect of nontrivial quasiparticle scatterings becomes relevant, we obtain universal results for the long-time behavior of dynamical correlation functions. We find that correlation functions of vertex operators behave neither ballistically nor diffusively but follow a stretched exponential decay in time. We also study the full counting statistics of the topological current and find that distribution of the transferred charge is non-Gaussian with its cumulants scaling nonuniformly in time.

Super-resonant dark matter

We introduce Super-Resonant Dark Matter, a model of self-interacting dark matter based on the low energy effective theory of supersymmetric QCD. The structure of the theory ensures a resonant enhancement of the self-interactions of the low energy mesons, since their mass ratio is set by the number of colors and flavors. The velocity dependence of the resonantly enhanced self-interactions allows such theories to accommodate puzzles in small scale structure that arise from dark matter halos of different sizes. The dark matter mass is then predicted to be around 3–4 MeV, with its abundance set by freeze-in via a kinetically mixed dark photon.

Generalized symmetry breaking scales and weak gravity conjectures

We explore the notion of approximate global symmetries in quantum field theory and quantum gravity. We show that a variety of conjectures about quantum gravity, including the weak gravity conjecture, the distance conjecture, and the magnetic and axion versions of the weak gravity conjecture can be motivated by the assumption that generalized global symmetries should be strongly broken within the context of low-energy effective field theory, i.e. at a characteristic scale less than the Planck scale where quantum gravity effects become important. For example, the assumption that the electric one-form symmetry of Maxwell theory should be strongly broken below the Planck scale implies the weak gravity conjecture. Similarly, the violation of generalized non-invertible symmetries is closely tied to analogs of this conjecture for non-abelian gauge theory. This reasoning enables us to unify these conjectures with the absence of global symmetries in quantum gravity.

Effective Field Theory Description of Horizon-Fluid Determines the Scrambling Time

Black hole horizons interact with external fields when matter or energy falls through them. Such non-stationary black hole horizons can be described using viscous fluid equations. This work attempts to describe this process using effective field theory methods. Such a description can provide important insights beyond classical black hole physics. In this work, we construct a low-energy effective field theory description for the horizon-fluid of a 4-dimensional, asymptotically flat, Einstein black hole. The effective field theory of the dynamical horizon has two ingredients: degrees of freedom involved in the interaction with external fields and symmetry. The dual requirements of incorporating near-horizon symmetries (S1 diffeomorphism) and possessing length scales due to external perturbations are naturally satisfied if the theory on the non-stationary black hole horizon is a deformed Conformal Field Theory (CFT). For the homogeneous external perturbations, at the lowest order, this leads to a (2+1)-dimensional massive scalar field where the mass is related to the extent of the deformation of the CFT. We determine the mass by obtaining the correlation function corresponding to the effective field and relating it to the bulk viscosity of the horizon-fluid. Additionally, we show that the coefficient of bulk viscosity of the horizon-fluid determines the time required for black holes to scramble. Furthermore, we argue that matter-field modes with energy less than meff falling into the horizon thermalize more slowly. Finally, we construct a microscopic toy model for the horizon-fluid that reduces to the effective field theory with a single scalar degree of freedom. We then discuss the usefulness of the effective field model in understanding how information escapes from a black hole at late times.

Scaling solution for field-dependent gauge couplings in quantum gravity

Quantum gravity can determine the dependence of gauge couplings in a scalar field, which is related to possible fifth forces and time varying fundamental “constants”. This prediction is based on the scaling solution of functional flow equations. For momenta below the field-dependent Planck mass the quantum scale invariant standard model emerges as an effective low energy theory. For a small non-zero value of the infrared cutoff scale the time-variation of couplings or apparent violations of the equivalence principle turn out to be negligibly small for the present cosmological epoch, unless some further quantum scale symmetry violation beyond the standard model comes into play. More sizable effects of quantum scale symmetry violation are expected during nucleosynthesis or before. Scaling solutions relate field dependence and dependence on the renormalization scale. We find asymptotically free gauge couplings for the standard model coupled to gravity, while for grand unified models the gauge couplings are asymptotically safe with non-zero values at the ultraviolet fixed point. The scaling solution of asymptotically safe metric quantum gravity yields restrictions for model building, as limiting the number of scalars in grand unified theories.

From Skyrmions to One Flavored Baryons and Beyond

While the identification of skyrmions as the low energy description of baryons in Nf≥2 QCD is known for decades, a parallel construction for the case of Nf=1 is more mysterious. In the case of one fermionic flavor, there is no chiral symmetry breaking, no non-linear sigma model, and the conventional construction of skyrmions fails to work. In this article, I will review developments from the last couple of years trying to identify baryons as certain singular configurations in the large Nc limit of Nf=1 QCD. We will give various arguments supporting this identification, and discuss some of its applications. Unlike skyrmions, the new baryons are not contained completely inside the low energy effective theory. They give rise to a singular ring on which the chiral condensate must vanish, with new degrees of freedom living on this ring. These configurations may serve as a bridge between the UV and the IR, and hopefully shed some light on the connection between different phases of QCD.

Nonperturbative effects in neutrino magnetic moments

In this paper, we calculate the QCD nonperturbative contributions of the neutrino-quark tensor operators to the neutrino magnetic moments by matching onto the chiral perturbation theory at low energies. These nonperturbative contributions can be compared to the perturbative ones, which are induced from one-loop mixing when performing the renormalization group evolutions from $\mu=m_W$ down to $\mu=2~\mathrm{GeV}$. We then constrain the dipole and tensor Wilson coefficients of the low-energy neutrino effective field theory (LNEFT) separately from the neutrino-electron scattering with Borexino data and coherent elastic neutrino-nucleus scattering (CE$\nu$NS) with COHERENT data to show the competition between these two contributions, at the renormalization scales $\mu=2~\mathrm{GeV}$ and $\mu=m_W$ in the $\bar{\mathrm{MS}}$ scheme. In the neutrino-electron scattering, it is found that the nonperturbative contributions dominate for the coefficients involving up and down quarks, while they are expected to be of the same order of magnitude as the perturbative contributions for the coefficients involving strange quark. As for constraints in the CE$\nu$NS, the tensor operators can contribute to the process through either direct or indirect way. As a result, the indirect contributions including nonperturbative and perturbative parts for all couplings become negligible in comparison with the direct ones. As the nonperturbative contributions crucially depend on the value of $c_T$, its inputs will affect the extraction of limits on the tensor LNEFT Wilson coefficients. We compute the upper bounds on these coefficients with $c_T$ quoting from the model and lattice estimates.

Topological superconductor from the quantum Hall phase: Effective field theory description

We derive low-energy effective field theories for the quantum anomalous Hall and topological superconducting phases. The quantum Hall phase is realized in terms of free fermions with nonrelativistic dispersion relation, possessing a global $U(1)$ symmetry. We couple this symmetry with a background gauge field and compute the effective action by integrating out the gapped fermions. In spite of the fact that the corresponding Dirac operator governing the dynamics of the original fermions is nonrelativistic, the leading contribution in the effective action is a usual Abelian $U(1)$ Chern-Simons term. The proximity to a conventional superconductor induces a pairing potential in the quantum Hall state, favoring the formation of Cooper pairs. When the pairing is strong enough, it drives the system to a topological superconducting phase, hosting Majorana fermions. Even though the continuum $U(1)$ symmetry is broken down to a $\mathbb{Z}_2$ one, we can forge fictitious $U(1)$ symmetries that enable us to derive the effective action for the topological superconducting phase, also given by a Chern-Simons theory. To eliminate spurious states coming from the artificial symmetry enlargement, we demand that the fields in the effective action are $O(2)$ instead of $U(1)$ gauge fields. In the $O(2)$ case we have to sum over the $\mathbb{Z}_2$ bundles in the partition function, which projects out the states that are not $\mathbb{Z}_2$ invariants. The corresponding edge theory is the $U(1)/\mathbb{Z}_2$ orbifold, which contains Majorana fermions in its operator content.

Unitarity and dilaton effective theory

From the low-energy effective theory of dilatons, consistent with the scale anomaly, we calculate the $2\to2$ scattering amplitudes of dilatons. We find that the one-loop amplitude violates the unitarity bound as the scattering energy approaches the cutoff of the effective theory, $\sqrt{s}=\sqrt{4\pi} f_D$. We then show that the inclusion of the next-to-lightest state, namely the spin-2 state, of mass around the cutoff improves the unitarity. The unitarity argument suggests that the mass ratio of the dilaton and the spin-2 state is proportional to the square of the Miransky-BKT scaling of the near conformal dynamics.

Surface waves and bulk Ruderman mode of a bosonic superfluid vortex crystal in the lowest Landau level

We determine and analyze collective normal modes of a finite disk-shaped two-dimensional vortex crystal formed in a compressible bosonic superfluid in an artificial magnetic field. Using the microscopic Gross-Pitaevskii theory in the lowest Landau level approximation, we generate vortex crystal ground states and solve the Bogoliubov-de Gennes equations for small amplitude collective oscillations. We find chiral surface waves that propagate at frequencies larger than those of the bulk Tkachenko modes. Furthermore, we study low frequency bulk excitations and identify a torsional Ruderman mode, which we find is well-described by a previously developed low-energy effective field theory.

Spacetime instability and quantum gravity as low energy effective field theory

We discuss spacetime instability for effective field theories of quantum gravity. The effective action of gravity introduces infinite higher derivative curvature terms $R^{2}, { R }_{ \mu \nu }{ R }^{ \mu \nu }, R_{\mu\nu\kappa\lambda} R^{\mu\nu\kappa\lambda}\dots$. Although these higher derivative curvature terms are indispensable to construct the self-consistent renormalizable theory of quantum gravity, they lead to several pathologies. We clearly show that even if they are written as the Planck-suppressed operators they lead to serious consequences and and de Sitter or radiation-dominated Universe is highly unstable. We show that the couplings of these higher derivative curvatures must satisfy $\left|a_{1,2,3}\right|\gtrsim 10^{118}$ to be consistent with the cosmological observations. Thus, the standard effective field theories of quantum gravity fail to describe the observed Universe unless introducing a specific technique dealing with the higher derivative curvature terms.

Emergent non-Abelian gauge theory in coupled spin-electron dynamics

A clear separation of the time scales governing the dynamics of "slow" and "fast" degrees of freedom often serves as a prerequisite for the emergence of an independent low-energy theory. Here, we consider (slow) classical spins exchange coupled to a tight-binding system of (fast) conduction electrons. The effective equations of motion are derived under the constraint that the quantum state of the electron system at any instant of time $t$ lies in the $n$-dimensional low-energy subspace for the corresponding spin configuration at $t$. The effective low-energy theory unfolds itself straightforwardly and takes the form of a non-abelian gauge theory with the gauge freedom given by the arbitrariness of the basis spanning the instantaneous low-energy sector. The holonomic constraint generates a gauge covariant spin-Berry curvature tensor in the equations of motion for the classical spins. In the non-abelian theory for $n>1$, opposed to the $n=1$ adiabatic spin dynamics theory, the spin-Berry curvature is generically nonzero, even for time-reversal symmetric systems. Its expectation value with the representation of the electron state is gauge invariant and gives rise to an additional {\em geometrical} spin torque. Besides anomalous precession, the $n\ge 2$ theory also captures the spin nutational motion, which is usually considered as a retardation effect. This is demonstrated by proof-of-principle numerical calculations for a minimal model with a single classical spin. Already for $n=2$ and in parameter regimes where the $n=1$ adiabatic theory breaks down, we find good agreement with results obtained from the full (unconstrained) theory.

Pion-Induced Radiative Corrections to Neutron β Decay.

We compute the electromagnetic corrections to neutron β decay using a low-energy hadronic effective field theory. We identify new radiative corrections arising from virtual pions that were missed in previous studies. The largest correction is a percent-level shift in the axial charge of the nucleon proportional to the electromagnetic part of the pion-mass splitting. Smaller corrections, comparable to anticipated experimental precision, impact the β-ν angular correlations and the β asymmetry. We comment on implications of our results for the comparison of the experimentally measured nucleon axial charge with first-principles computations using lattice QCD and on the potential of β decay experiments to constrain beyond-the-standard-model interactions.

Variational Adiabatic Gauge Transformation on Real Quantum Hardware for Effective Low-Energy Hamiltonians and Accurate Diagonalization

Effective low-energy theories represent powerful theoretical tools to reduce the complexity in modeling interacting quantum many-particle systems. However, common theoretical methods rely on perturbation theory, which limits their applicability to weak interactions. Here we introduce the Variational Adiabatic Gauge Transformation (VAGT), a nonperturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit that brings the Hamiltonian to either its block-diagonal or full-diagonal form. If a Hamiltonian can be diagonalized via a shallow quantum circuit, then VAGT can learn the optimal parameters using a polynomial number of runs. The accuracy of VAGT is tested through numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.