Quartic Interaction Research Articles

Nonperturbative RG for the weak interaction corrections to the magnetic moment

We analyze, by rigorous renormalization group methods, a Fermi model for weak forces with a single family of leptons, one massless and the other with mass m=Me−β, with M the gauge boson mass, a quartic nonlocal interaction with coupling λ2, and a momentum cutoff Λ. The magnetic moment is written as a series in λ2, with n-th coefficients bounded by Cn(m2M2)β2n(Λ2M2)(1+0+)(n−1) if C is a constant; this implies convergence and provides nonperturbative bounds on the higher order contributions. The fact that the magnetic moment is associated with a dimensionally irrelevant quantity requires the implementation of cancellations in the multiscale analysis. Published by the American Physical Society 2024

Addressing the non-perturbative regime of the quantum anharmonic oscillator by physics-informed neural networks

Abstract The use of deep learning in physical sciences has recently boosted the ability of researchers to tackle physical systems where little or no analytical insight is available. Recently, the Physics−Informed Neural Networks (PINNs) have been introduced as one of the most promising tools to solve systems of differential equations guided by some physically grounded constraints. In the quantum realm, such an approach paves the way to a novel approach to solve the Schrödinger equation for non-integrable systems. By following an unsupervised learning approach, we apply the PINNs to the anharmonic oscillator in which an interaction term proportional to the fourth power of the position coordinate is present. We compute the eigenenergies and the corresponding eigenfunctions while varying the weight of the quartic interaction. We bridge our solutions to the regime where both the perturbative and the strong coupling theory work, including the pure quartic oscillator. We investigate systems with real and imaginary frequency, laying the foundation for novel numerical methods to tackle problems emerging in quantum field theory.

From higher-spin gauge interactions to Compton amplitudes for root-Kerr

We develop massive higher-spin theory as a framework for describing dynamics of rotating compact objects, such as Kerr black holes. In this paper, we explore gauge interactions up to quartic order and corresponding Compton amplitudes of higher-spin massive objects coupled to electromagnetism and Yang-Mills theory. Their classical counterparts are known as root-Kerr gauge-theory solutions, whose amplitudes are closely related to those of Kerr black holes. We use three distinct approaches: (i) massive higher-spin gauge symmetry to introduce cubic interactions for all spins and the quartic interactions up to spin 3, which is implemented both off shell and via Ward identities; (ii) a chiral higher-spin approach to construct quartic Lagrangians with correct degrees of freedom to all spins; (iii) on-shell functional patterns before and after taking the classical limit to constrain the Compton amplitudes. As final results, we arrive at simple local formulae for the candidate root-Kerr Compton amplitudes both in the quantum regime and classical limit, to all orders in spin. This is a precursor to the gravitational Kerr case, which is presented in a follow-up paper.

Two types of series expansions valid at strong coupling

It is known that perturbative expansions in powers of the coupling in quantum mechanics (QM) and quantum field theory (QFT) are asymptotic series. This can be useful at weak coupling but fails at strong coupling. In this work, we present two types of series expansions valid at strong coupling. We apply the series to a basic integral as well as a QM path integral containing a quadratic and quartic term with coupling constant λ. The first series is the usual asymptotic one, where the quartic interaction is expanded in powers of λ. The second series is an expansion of the quadratic part where the interaction is left alone. This yields an absolutely convergent series in inverse powers of λ valid at strong coupling. For the basic integral, we revisit the first series and identify what makes it diverge even though the original integral is finite. We fix the problem and obtain, remarkably, a series in powers of the coupling which is absolutely convergent and valid at strong coupling. We explain how this series avoids Dyson’s argument on convergence. We then consider the QM path integral (discretized with time interval divided into N equal segments). As before, the second series is absolutely convergent and we obtain analytical expressions in inverse powers of λ for the nth order terms by taking functional derivatives of generalized hypergeometric functions. The expressions are functions of N and we work them out explicitly up to third order. The general procedure has been implemented in a Mathematica program that generates the expressions at any order n. We present numerical results at strong coupling for different values of N starting at N = 2. The series matches the exact numerical value for a given N (up to a certain accuracy). The continuum is formally reached when N → ∞ but in practice this can be reached at small N.

Q-balls in the presence of attractive force

Q-balls are non-topological solitons in field theories whose stability is typically guaranteed by the existence of a global conserved charge. A classic realization is the Friedberg-Lee-Sirlin (FLS) Q-ball in a two-scalar system where a real scalar χ triggers symmetry breaking and confines a complex scalar Φ with a global U(1) symmetry. A quartic interaction κχ2|Φ|2 with κ > 0 is usually considered to produce a nontrivial Q-ball configuration, and this repulsive force contributes to its stability. On the other hand, the attractive cubic interaction Λχ|Φ|2 is generally allowed in a renormalizable theory and could induce an instability. In this paper, we study the behavior of the Q-ball under the influence of this attractive force which has been overlooked. We find approximate Q-ball solutions in the limit of weak and moderate force couplings using the thin-wall and thick-wall approximations respectively. Our analytical results are consistent with numerical simulations and predict the parameter dependencies of the maximum charge. A crucial difference with the ordinary FLS Q-ball is the existence of the maximum charge beyond which the Q-ball solution is classically unstable. Such a limitation of the charge fundamentally affects Q-ball formation in the early Universe and could plausibly lead to the formation of primordial black holes.

No time to derive: unraveling total time derivatives in in-in perturbation theory

The in-in formalism provides a way to systematically organize the calculation of primordial correlation functions. Although its theoretical foundations are now firmly settled, the treatment of total time derivative interactions, incorrectly trivialized as “boundary terms”, has been the subject of intense discussions and conceptual mistakes. In this work, we demystify the use of total time derivatives — as well as terms proportional to the linear equations of motion — and show that they can lead to artificially large contributions cancelling at different orders of the in-in operator formalism. We discuss the treatment of total time derivative interactions in the Lagrangian path integral formulation of the in-in perturbation theory, and we showcase the importance of interaction terms proportional to linear equations of motion. We then provide a new route to the calculation of primordial correlation functions, which avoids the generation of total time derivatives, by working directly at the level of the full Hamiltonian in terms of phase-space variables. Instead of integrating by parts, we perform canonical transformations to simplify interactions. We explain how to retrieve correlation functions of the initial phase-space variables from the knowledge of the ones after canonical transformations. As an important first application, we find the explicit sizes of Hamiltonian cubic interactions in single-field inflation with canonical kinetic terms and for any background evolution, straight in terms of the primordial curvature perturbation and its canonical conjugate momentum, as well as the corresponding ones in the tensor sector, and the ones mixing scalars and tensors. We also briefly comment on quartic interactions. Our results are important for performing complete calculations of exchange diagrams in inflation, such as the (scalar and tensor) exchange trispectrum and the one-loop power spectrum. Being already written in a form amenable to characterize quantum properties of primordial fluctuations, they also promise to shed light on the non-linear dynamics of quantum states during inflation.

Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization

The paper studies the quantum action for the four-dimensional real ϕ4-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The absence of non-local singular contributions and the correctness of the renormalization R-operation on the example of separate three-loop diagrams are also discussed. The explicit forms of the first three coefficients for the renormalization constants and for the β-function are presented. Consistency with previously known results is shown.

One-loop power spectrum in ultra slow-roll inflation and implications for primordial black hole dark matter

We apply the in-in formalism to address the question of whether the size of the one-loop spectrum of curvature fluctuations in ultra-slow-roll inflation models designed for producing a large population of primordial black holes implies a breakdown of perturbation theory. We consider a simplified piece-wise description of inflation, in which the ultra-slow-roll phase is preceded and followed by slow-roll phases linked by transitional periods. We work in the δϕ-gauge, including all relevant cubic and quartic interactions and the necessary counterterms to renormalize the ultraviolet divergences, regularized by a cutoff. The ratio of the one-loop to the tree-level contributions to the spectrum of curvature perturbations is controlled by the duration of the ultra-slow-roll phase and of the transitions. Our results indicate that perturbation theory does not necessarily break in well-known models proposed to account for all the dark matter in the form of primordial black holes.

All-optical quantum computing using cubic phase gates

If suitable quantum optical interactions were available, transforming the field mode operators in a nonlinear fashion, the all-photonics platform could be one of the strongest contenders for realizing a quantum computer. While single-photon qubits may be processed directly, “brighter” logical qubits may be embedded in individual oscillator modes, using so-called bosonic codes, for an in-principle fault-tolerant processing. In this paper, we show how elements of all-optical, universal, and fault-tolerant quantum computation can be implemented using only beam splitters together with single-mode cubic phase gates in reasonable numbers, and possibly off-line squeezed-state or single-photon resources. Our approach is based on a decomposition technique combining exact gate decompositions and approximate Trotterization. This allows for efficient decompositions of certain nonlinear continuous-variable multimode gates into the elementary gates, where the few cubic gates needed may even be weak or all identical, thus facilitating potential experiments. The final gate operations include two-mode controlled phase rotation and three-mode Rabi-type Hamiltonian gates, which are shown to be employable for realizing high-fidelity single-photon two-qubit entangling gates or creating high-quality Gottesman-Kitaev-Preskill states. We expect our method to be of general use with various applications, including those that rely on quartic Kerr-type interactions. Published by the American Physical Society 2024

Simulating a numerical UV completion of quartic Galileons

The Galileon theory is a prototypical effective field theory that incorporates the Vainshtein screening mechanism—a feature that arises in some extensions of general relativity, such as massive gravity. The Vainshtein effect requires that the theory contain higher order derivative interactions, which results in Galileons, and theories like them, failing to be technically well posed. While this is not a fundamental issue when the theory is correctly treated as an effective field theory, it nevertheless poses significant practical problems when numerically simulating this model. These problems can be tamed using a number of different approaches: introducing an active low-pass filter and/or constructing a UV completion at the level of the equations of motion, which controls the high momentum modes. These methods have been tested on cubic Galileon interactions, and have been shown to reproduce the correct low-energy behavior. Here we show how the numerical UV-completion method can be applied to quartic Galileon interactions, and present the first simulations of the quartic Galileon model using this technique. We demonstrate that our approach can probe physics in the regime of the effective field theory in which the quartic term dominates, while successfully reproducing the known results for cubic interactions. Published by the American Physical Society 2024

Effect of squared, cubic and quartic on-site potentials on heat conduction in a nonlinear silicon lattice

This paper explains the process of heat conduction in a nonlinear silicon lattice governed by squared, cubic and quartic on-site potentials along with squared and quartic interaction potentials. The tanh method is employed to construct solutions to the resulting nonlinear equations. The results show the transfer of heat in the form of solitary waves which are presented graphically.

Scalar radiation with a quartic Galileon

The class of Galileon scalar fields theories encapsulate the Vainshtein screening mechanism, which is characteristic of a large range of infrared modified theories of gravity. Such theories can lead to testable departures from general relativity through fifth forces and new scalar modes of gravitational radiation. However, the inherent nonlinearity of the Vainshtein mechanism has limited analytic attempts to describe Galileon theories with both cubic and quartic interactions. To improve on this, we perform direct numerical simulations of the quartic Galileon model for a rotating binary source and infer the power spectrum of given multipoles. To tame numerical instabilities we utilize a low-pass filter, extending previous work on the cubic Galileon. Our findings show that the multipole expansion is well defined and under control. Moreover, our results confirm that despite being a nonlinear scalar, the dominant Galileon radiation is quadrupole, and we find a new scaling behavior deep inside the Vainshtein region. Published by the American Physical Society 2024

Phi4tools: compilation of Feynman diagrams for Landau-Ginzburg-Wilson theories

Scalar field theories with quartic interactions are of central interest in the study of second-order phase transitions. For three-dimensional theories, numerous studies make use of the fixed-dimensional perturbative computation of [B. Nickel, D. Meiron, and G. Baker Jr, Compilation of 2-pt and 4-pt graphs for continuous spin model, University of Guelph report (1977)], unfortunately left unpublished. We independently verify the results of Nickel et al., and we extend the computation to the eighth order in the coupling constant. The results of our calculations, together with the tools developed, are made available in Phi4tools, a user-friendly package that allows displaying the information about the individual Feynman diagrams, including the numerical values for the diagrams for zero, two, and four-point functions. We also provide the perturbative series up to order eight for the renormalization-group functions for the O(N) and cubic anisotropic models.

Double Higgs production at the HL-LHC: probing a loop-enhanced model with kinematical distributions

We study di-Higgs production via gluon fusion at the high luminosity LHC in the presence of new physics, focusing on the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b\\overline{b }\\gamma \\gamma $$\\end{document} final states. Taking a minimal set of three scalar leptoquarks (LQs) with cubic and quartic interactions with the Higgs and choosing four benchmark points with a light LQ, we perform a detailed analysis of differential distributions of the di-Higgs production cross section, studying the imprints of the new physics states running in the loops. Simulating the signal and main backgrounds, we study the influence of the new physics in differential distributions such as the invariant mass of the subsystems of final particles, the transverse momentum, and angular variables, finding in particular a resonance peak associated with the light LQ. It turns out that the angular separation of the photons, which is correlated with the resonance LQ peak, is a very sensitive observable that helps in discriminating the new physics signal from the Standard Model background. We find that for two of our benchmarks discovery could be reached with 3 ab−1, whereas exclusion limits at 95% C.L. could be claimed with 0.60–0.75 ab−1. For the other two benchmarks that have heavier LQ masses significances of order 2σ are possible for 3 ab−1. A similar analysis could be applied to other loop-enhanced models.

S-matrix positivity without Lorentz invariance: a case study

We investigate the analytic structure of scattering amplitudes in theories in which Lorentz invariance is spontaneously broken. We do so by computing and studying the S-matrix for a simple example: a superfluid described by a complex scalar with quartic interactions. The computation is confined to tree-level, for there are no absolutely stable single-particle states, though the lifetime can be made long by lowering the chemical potential. For the 2 → 2 amplitude in center-of-mass configurations, not only is crossing symmetry violated, there appears a tree level branch cut for unphysical kinematics. Its appearance is a consequence of non-analyticity in the dispersion relation. The branch point defines a new scale in the problem, which scales inversely with the chemical potential. In this example, even derivatives of the forward amplitude are positive while odd derivatives are negative. This pattern can be understood in a general way in the limit of a small chemical potential, or weak Lorentz breaking.

Gravitational wave turbulence: A multiple time scale approach for quartic wave interactions

Gravitational wave turbulence: A multiple time scale approach for quartic wave interactions

Weakly constrained double field theory as the double copy of Yang-Mills theory

The weakly constrained double field theory, in the sense of Hull and Zwiebach, captures the subsector of string theory on toroidal backgrounds that includes gravity, B-field, and dilaton together with all of their massive Kaluza-Klein and winding modes, which are encoded in doubled coordinates subject to the “weak constraint.” Due to the complications of the weak constraint, this theory was only known to cubic order. Here we construct the quartic interactions for the case that all dimensions are toroidal and doubled. Starting from the kinematic C∞ algebra K of pure Yang-Mills theory and its hidden Lie-type algebra, we construct the L∞ algebra of weakly constrained double field theory on a subspace of the “double copied” tensor product space K⊗K¯, by doing homotopy transfer to the weakly constrained subspace and performing a nonlocal shift that is well-defined on the torus. We test the resulting three-brackets and establish their uniqueness up to cohomologically trivial terms, by verifying the Jacobi identities up to homotopy for the gauge sector. Published by the American Physical Society 2024

Abnormally large radiational S2 tides in the Gulf of Tonkin and implications for other diurnal resonant seas

Radiational tides derived from solar radiation are important components of ocean tides. Understanding dynamical features of radiational tides can be beneficial for further promoting the accuracy of water level prediction. Generally, radiational S2 amplitudes are only 10%–30% of gravitational S2 amplitudes, which has been verified by numerous studies. However, a previous study indicated that radidational S2 amplitudes can reach 60% of gravitational S2 amplitudes in the Gulf of Tonkin and related physical processes are unknown. In this paper, we revisit this abnormal phenomenon and find that such large radiational S2 amplitudes are not real, but artifacts induced by the inadaptation of the method based on the credo of smoothness. Specifically, observed semi-diurnal tidal admittances in the Gulf of Tonkin are not smooth due to strong nonlinear interactions between large main diurnal tides. We quantitatively estimate and remove the contributions of quadratic and quartic nonlinear interactions to main semi-diurnal tides and find that the real ratio of radiational S2 amplitude to astronomical S2 amplitude is only 0.17 at Beihai, which is basically consistent with previous model results. Our study highlights the importance of eliminating the interference of nonlinear interactions to semi-diurnal tidal admittances in all diurnal resonant sea areas like the Gulf of Tonkin and the Gulf of Thailand when extracting radiational S2 tides from sea level observations.

Phonon Thermal Transport in UO_{2} via Self-Consistent Perturbation Theory.

Computing thermal transport from first-principles in UO_{2} is complicated due to the challenges associated with Mott physics. Here, we use irreducible derivative approaches to compute the cubic and quartic phonon interactions in UO_{2} from first principles, and we perform enhanced thermal transport computations by evaluating the phonon Green's function via self-consistent diagrammatic perturbation theory. Our predicted phonon lifetimes at T=600 K agree well with our inelastic neutron scattering measurements across the entire Brillouin zone, and our thermal conductivity predictions agree well with previous measurements. Both the changes due to thermal expansion and self-consistent contributions are nontrivial at high temperatures, though the effects tend to cancel, and interband transitions yield a substantial contribution.

Soft Factors and Interaction Vertices from Light‐Cone Actions

AbstractUniversal factors associated with the emission of a soft boson in gauge theories and gravity, formulated in the light‐cone gauge, are presented. The inverse‐soft method, for constructing higher‐point amplitudes from lower‐point ones, using these factors is reviewed. These ideas are then examined in (light‐cone) superspace and applied to both the super Yang–Mills and supergravity theories. One highlight is a compact result for the quartic interaction vertex in supergravity, a crucial ingredient for finiteness analyses.