Quartic Interaction Research Articles

Polynomial modeling of emergency department arrivals: An analysis of local and national utilization patterns

Emergency department (ED) overcrowding is a national problem that is associated with ambulance diversion, decreased patient and provider satisfaction and poor patient outcomes. This study presents a novel approach to modeling the relationship between time of day, day of week, and ED arrivals using a hierarchical polynomial regression model. A series of hierarchical regression models were created to determine polynomial effects and capture the covariability (defined as R2) of the relationships from the 2009 to 2017 National Hospital Ambulatory Medical Care Survey (NHAMCS) Emergency Department Public Use Data File and institutional data from a regional medical center from 2018 to 2019. The following hierarchical regression models were constructed: cubic main effects, cubic interaction effects, quartic main effects, quartic interaction effects, quintic main effects, and quintic interaction effects. Based on maximal improvement in R2 and significance of each of the four effects in both the national and institutional data sets, the quartic main effects model was determined to be optimal for describing ED arrival patterns. In alignment with prior studies, significantly higher ED arrival volumes were observed on Mondays in comparison to all other weekdays.

Trifundamental quartic model

We consider a multi-scalar field theory with either short-range or long-range free action and with quartic interactions that are invariant under $O(N_1)\times O(N_2) \times O(N_3)$ transformations, of which the scalar fields form a tri-fundamental representation. We study the renormalization group fixed points at two loops at finite $N$ and in various large-$N$ scaling limits for small $\epsilon$, the latter being either the deviation from the critical dimension or from the critical scaling of the free propagator. In particular, for the homogeneous case $N_i = N$ for $i=1,2,3$, we study the subleading corrections to previously known fixed points. In the short-range model, for $\epsilon N^2\gg 1$, we find complex fixed points with non-zero tetrahedral coupling, that at leading order reproduce the results of arXiv:1707.03866 ; the main novelty at next-to-leading order is that the critical exponents acquire a real part, thus allowing a correct identification of some fixed points as IR stable. In the long-range model, for $\epsilon N \ll 1 $, we find again complex fixed points with non-zero tetrahedral coupling, that at leading order reproduce the line of stable fixed points of arXiv:1903.03578; at next-to-leading order, this is reduced to a discrete set of stable fixed points. One difference between the short-range and long-range cases is that, in the former the critical exponents are purely imaginary at leading-order and gain a real part at next-to-leading order, while for the latter the situation is reversed.

Recursive construction of the operator product expansion in curved space

I derive a formula for the coupling-constant derivative of the coefficients of the operator product expansion (Wilson OPE coefficients) in an arbitrary curved space, as the natural extension of the quantum action principle. Expanding the coefficients themselves in powers of the coupling constants, this formula allows to compute them recursively to arbitrary order. As input, only the OPE coefficients in the free theory are needed, which are easily obtained using Wick’s theorem. I illustrate the method by computing the OPE of two scalars ϕ in hyperbolic space (Euclidean Anti-de Sitter space) up to terms vanishing faster than the square of their separation to first order in the quartic interaction gϕ4, as well as the OPE coefficient at second order in g.

Role of Anharmonic Interactions for Vibration Density of States in α-Cristobalite.

The vibrational density of states (VDOS) of solids in the low-energy regime controls the thermal and transport properties of materials, such as heat capacity, heat conduction, free energy and entropy. In α-Cristobalite, the low-frequency part of vibration density of states (VDOS) has many common features with the Boson peak in silica glass of matched densities. Recent theoretical work reported that anharmonic phonon–phonon interactions were critical for the low-frequency part of VDOS in α-Cristobalite. Therefore, it is urgent to identify the role of different anharmonic interactions from first principles. In this paper, we focus on the main peak of the low-frequency part of VDOS in α-Cristobalite. Calculated by our own developed codes and first principles, we find that the quartic anharmonic interaction can increase the frequency of the peak, while the cubic anharmonic can reduce the frequency and change the shape of the peak. Meanwhile, the anharmonic interactions are critical for the temperature effect. Therefore, we calculated the temperature-dependent property of the peak. We find that the frequency of the peak is directly proportional to the temperature. The atomic displacement patterns of different temperatures also confirm the above conclusion. All our calculations converged well. Moreover, our basic results agree well with other published results. Finally, we highlight that our codes offer a general and reliable way to calculate the VDOS with temperature.

Gentle introduction to rigorous Renormalization Group: a worked fermionic example

Much of our understanding of critical phenomena is based on the notion of Renormalization Group (RG), but the actual determination of its fixed points is usually based on approximations and truncations, and predictions of physical quantities are often of limited accuracy. The RG fixed points can be however given a fully rigorous and non- perturbative characterization, and this is what is presented here in a model of symplectic fermions with a nonlocal (“long-range”) kinetic term depending on a parameter ε and a quartic interaction. We identify the Banach space of interactions, which the fixed point belongs to, and we determine it via a convergent approximation scheme. The Banach space is not limited to relevant interactions, but it contains all possible irrelevant terms with short-ranged kernels, decaying like a stretched exponential at large distances. As the model shares a number of features in common with ϕ4 or Ising models, the result can be used as a benchmark to test the validity of truncations and approximations in RG studies. The analysis is based on results coming from Constructive RG to which we provide a tutorial and self-contained introduction. In addition, we prove that the fixed point is analytic in ε, a somewhat surprising fact relying on the fermionic nature of the problem.

Corrections to Yukawa couplings from higher dimensional operators in a natural SUSY SO(10) and HL-LHC implications

We consider a class of unified models based on the gauge group SO(10) which with appropriate choice of Higgs representations generate in a natural way a pair of light Higgs doublets needed to accomplish electroweak symmetry breaking. In this class of models higher dimensional operators of the form matter-matter-Higgs-Higgs in the superpotential after spontaneous breaking of the GUT symmetry generate contributions to Yukawa couplings which are comparable to the ones from cubic interactions. Specifically we consider an SO(10) model with a sector consisting of 126 + overline{126} + 210 of heavy Higgs which breaks the GUT symmetry down to the standard model gauge group and a sector consisting of 2 × 10 + 120 of light Higgs fields. In this model we compute the corrections from the quartic interactions to the Yukawa couplings for the top and the bottom quarks and for the tau lepton. It is then shown that inclusion of these corrections to the GUT scale Yukawas allows for consistency of the top, bottom and tau masses with experiment for low tan β with a value as low as tan β of 5–10. We compute the sparticle spectrum for a set of benchmarks and find that satisfaction of the relic density is achieved via a compressed spectrum and coannihilation and three sets of coannihilations appear: chargino-neutralino, stop-neutralino and stau-neutralino. We investigate the chargino-neutralino coannihilation in detail for the possibility of observation of the light chargino at the high luminosity LHC (HL-LHC) and at the high energy LHC (HE-LHC) which is a possible future 27 TeV hadron collider. It is shown that all benchmark models but one can be discovered at HL-LHC and all would be discoverable at HE-LHC. The ones discoverable at both machines require a much shorter time scale and a lower integrated luminosity at HE-LHC.

Phonon soft modes and para- to ferro-electric phase transitions

In this special issue of Physica A in memory of Professor Dietrich Stauffer, I first recall my impression on him while being his postdoc for a year at HLRZ. In the following scientific part, I discuss the theory of soft phonons with quartic nonlinear interactions. This is applied to the cubic crystal BaTiO3 for phase transition from para- to ferro-electric phase.

Heavy light inflaton and dark matter production

We study the minimal extension of the SM by a scalar with quartic interaction serving as an inflaton. For the model where scale symmetry is broken only in the inflaton sector, the mass of the inflaton is constrained to be relatively low. Here, we analysed the previously omitted situation of the inflaton masses $m_{\chi}\gtrsim 250\text{ GeV}$. Therefore, we provide a window of inflaton masses with viable inflationary properties that evade direct observational constraints, due to their small mixing with the Higgs sector. The addition of heavy neutral leptons with Majorana masses induced by the interaction with the inflaton allow for Cold Dark Matter in the model with masses $O(1-10)\text{ MeV}$.

General scalar renormalisation group equations at three-loop order

For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the overline{mathrm{MS}} scheme. Utilising pre-existing literature expressions for a specific model, loop integrals are avoided and templates for general theories are obtained. We reiterate known four-loop expressions, and from those derive β functions for scalar masses and cubic interactions. As an example, the results are applied to compute all renormalisation group equations in U(n) × U(n) scalar theories.

Central exclusive production of W boson pairs in pp collisions at the LHC in hadronic and semi-leptonic final states

We present a phenomenology study on central exclusive production of W+W− boson pairs in proton-proton collisions at the Large Hadron Collider at 14 TeV using the forward proton detectors, such as the ATLAS Forward Proton or the CMS-TOTEM Precision Proton Spectrometer detectors. Final states where at least one of the W bosons decay hadronically in a large-radius jet are considered. The latter extends previous efforts that consider solely leptonic final states. A measurement of exclusive W+W− also allows us to further constrain anomalous quartic gauge boson interactions between photons and W bosons. Expected limits on anomalous quartic gauge couplings {a}_{0,C}^W associated to dimension-six effective operators are derived for the hadronic, semi-leptonic, and leptonic final states. It is found that the couplings can be probed down to one-dimensional values of {a}_0^W=3.7times {10}^{-7}{mathrm{GeV}}^{-2} and {a}_C^W=9.2times {10}^{-7}{mathrm{GeV}}^{-7} at 95% CL at an integrated luminosity of 300 fb−1 by combining all final states, compared to values of about {a}_0^W=4times {10}^{-6}{mathrm{GeV}}^{-2} and {a}_C^W=1times {10}^{-5}{mathrm{GeV}}^{-2} at 95% CL expected for the leptonic channel alone.

Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation

Here, we analyse two Dirac fermion species in two spatial dimensions in the presence of general quartic contact interactions. By employing functional bosonisation techniques, we demonstrate that depending on the couplings of the fermion interactions the system can be effectively described by a rich variety of topologically massive gauge theories. Among these effective theories, we obtain an extended Chern–Simons theory with higher order derivatives as well as two coupled Chern–Simons theories. Our formalism allows for a general description of interacting fermions emerging, for example, at the gapped boundary of three-dimensional topological crystalline insulators.

Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs

Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge CT, we clarify the properties of stress tensor composite primary operators of minimal twist, [Tm], using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling leftlangle {mathcal{O}}_L{mathcal{O}}_Lleft[{T}^mright]rightrangle , where {mathcal{O}}_L is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling leftlangle TT{mathcal{O}}_Lrightrangle , the three-point coupling leftlangle {mathcal{O}}_L{mathcal{O}}_Lleft[{T}^2right]rightrangle is modified at large CT if leftlangle TT{mathcal{O}}_Lrightrangle sim sqrt{C_T} . This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to {mathcal{O}}_L can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin-ℓ ≥ 2 bulk field at tree level, or any spin ℓ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.

Long-range multi-scalar models at three loops

We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power 0 < ζ < 1, rendering the computation of Feynman diagrams much harder than in the usual short-range case (ζ = 1). As a consequence, previous results stopped at two loops, while seven-loop results are available for short-range models. We push the renormalization group analysis to three loops, in an ϵ = 4ζ − d expansion at fixed dimension d < 4, extensively using the Mellin–Barnes representation of Feynman amplitudes in the Schwinger parametrization. We then specialize the beta functions to various models with different symmetry groups: O(N), , and O(N) × O(M). For such models, we compute the fixed points and critical exponents.

Dynamical tunneling of a nanomechanical oscillator

The study of the quantum to classical transition is of fundamental as well as technological importance, and focusses on mesoscopic devices, with a size for which either classical physics or quantum physics can be brought to dominate. A particularly diverse selection of such devices is available in cavity quantum-optomechanics. We show that these can be leveraged for the study of dynamical-tunnelling in a quantum chaotic system. This effect probes the quantum to classical transition deeply, since tunnelling rates sensitively depend on the ability of the quantum system to resolve the underlying classical phase space. We show that the effective Planck's constant, which determines this phase space resolution, can be varied over orders of magnitude as a function of tunable parameters in an opto-mechanical experiment. Specifically, we consider a membrane-in-the-middle configuration of a mechanical oscillator within an optical cavity, where the intracavity field is modulated periodically by the external laser source. We demonstrate that a mixed regular and chaotic phase space can be engineered in one spatial dimension, through a significant quartic opto-mechanical interaction. For that case, we explore the expected dynamical tunnelling rates using Floquet theory and map out values of the effective Planck's constant that should be within practical reach.

Gravitational-wave detectors as particle-physics laboratories: Constraining scalar interactions with a coherent inspiral model of boson-star binaries

Gravitational-wave (GW) detections of binary neutron star coalescences play a crucial role to constrain the microscopic interaction of matter at ultrahigh density. Similarly, if boson stars exist in the universe their coalescence can be used to constrain the fundamental coupling constants of a scalar field theory. We develop the first coherent waveform model for the inspiral of boson stars with quartic interactions. The waveform includes coherently spin-induced quadrupolar and tidal-deformability contributions in terms of the masses and spins of the binary and of a single coupling constant of the theory. We show that future instruments such as the Einstein Telescope and the Laser Interferometer Space Antenna can provide strong complementary bounds on bosonic self-interactions, while the constraining power of current detectors is marginal.

Anomalous dimensions from thermal AdS partition functions

We develop an efficient method for computing thermal partition functions of weakly coupled scalar fields in AdS. We consider quartic contact interactions and show how to evaluate the relevant two-loop vacuum diagrams without performing any explicit AdS integration, the key step being the use of Källén-Lehmann type identities. This leads to a simple method for extracting double-trace anomalous dimensions in any spacetime dimension, recovering known first-order results in a streamlined fashion.

Covert symmetry breaking

Reduction from a higher-dimensional to a lower-dimensional field theory can display special features when the zero-level ground state has nontrivial dependence on the reduction coordinates. In particular, a delayed ‘covert’ form of spontaneous symmetry breaking can occur, revealing itself only at fourth order in the lower-dimensional effective field theory action. This phenomenon is explored in a simple model of (d + 1)-dimensional scalar QED with one dimension restricted to an interval with Dirichlet/Robin boundary conditions on opposing ends. This produces an effective d-dimensional theory with Maxwellian dynamics at the free theory level, but with unusual symmetry breaking appearing in the quartic vector-scalar interaction terms. This simple model is chosen to illuminate the mechanism of effects which are also noted in gravitational braneworld scenarios.

Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) type

The Langmann–Szabo–Zarembo (LSZ) matrix model is a complex matrix model with a quartic interaction and two external matrices. The model appears in the study of a scalar field theory on the non-commutative plane. We prove that the LSZ matrix model computes the probability of atypically large fluctuations in the Stieltjes–Wigert matrix model, which is a q-ensemble describing U(N) Chern–Simons theory on the three-sphere. The correspondence holds in a generalized sense: depending on the spectra of the two external matrices, the LSZ matrix model either describes probabilities of large fluctuations in the Chern–Simons partition function, in the unknot invariant or in the two-unknot invariant. We extend the result to supermatrix models, and show that a generalized LSZ supermatrix model describes the probability of atypically large fluctuations in the ABJ(M) matrix model.

New features in the JHU generator framework: Constraining Higgs boson properties from on-shell and off-shell production

We present an extension of the JHUGen and MELA framework, which includes an event generator and library for the matrix element analysis. It enables simulation, optimal discrimination, reweighting techniques, and analysis of a bosonic resonance and the triple and quartic gauge boson interactions with the most general anomalous couplings. The new features, which become especially relevant at the current stage of LHC data taking, are the simulation of gluon fusion and vector boson fusion in the off-shell region, associated $ZH$ production at NLO QCD including the $gg$ initial state, and the simulation of a second spin-zero resonance. We also quote translations of the anomalous coupling measurements into constraints on dimension-six operators of an effective field theory. Some of the new features are illustrated with projections for experimental measurements with the full LHC and HL-LHC datasets.

Critical models with N≤4 scalars in d=4−ε

We adopt a combination of analytical and numerical methods to study the renormalization group flow of the most general field theory with quartic interaction in $d=4-\epsilon$ with $N=3$ and $N=4$ scalars. For $N=3$, we find that it admits only three nondecomposable critical points: the Wilson-Fisher with $O(3)$ symmetry, the cubic with $H_3=(\mathbb{Z}_2)^3\rtimes S_3$ symmetry, and the biconical with $O(2)\times \mathbb{Z}_2$. For $N=4$, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions.