Nonperturbative Model Research Articles

Combining nonperturbative transverse momentum dependence with TMD evolution

Central to understanding the nonperturbative, intrinsic partonic nature of hadron structure are the concepts of transverse momentum dependent (TMD) parton distribution and fragmentation functions. A TMD factorization approach to the phenomenology of semi-inclusive processes that includes evolution, higher orders, and matching to larger transverse momentum is ultimately necessary for reliably connecting with phenomenologically extracted nonperturbative structures, especially when widely different scales are involved. In this paper, we will address some of the difficulties that arise when phenomenological techniques that were originally designed for very high energy applications are extended to studies of hadron structures, and we will solidify the connection between standard high energy TMD implementations and the more intuitive, parton model based approaches to phenomenology that emphasize nonperturbative hadron structure. In the process, we will elaborate on differences between forward and backward TMD evolution, which in the context of this paper, we call ``bottom-up'' and ``top-down'' approaches, and we will explain the advantages of a bottom-up strategy. We will also emphasize and clarify the role of the integral relations that connect TMD and collinear correlation functions. We will show explicitly how they constrain the nonperturbative ``$g$-functions'' of standard Collins-Soper-Sterman implementations of TMD factorization. This paper is especially targeted toward phenomenologists and model builders who are interested in merging specific nonperturbative models and calculations (including lattice QCD) with TMD factorization at large $Q$. Our main result is a recipe for incorporating nonperturbative models into TMD factorization and for constraining their parameters in a way that matches perturbative QCD and evolution.

Toroidal modeling of energetic passing particle drift kinetic effects on tearing mode stability

Drift kinetic effects of the neutral beam injection induced passing energetic particles (EPs) on the linear stability of the n = 1 tearing mode (TM) (with the dominant poloidal harmonic of m = 2) are numerically investigated utilizing the MARS-K code (Liu et al 2008 Phys. Plasmas 15 112503), in a tokamak plasma with finite equilibrium pressure and anisotropic thermal transport. In the low plasma pressure regime, it is found that co- (counter-) passing EPs stabilize (destabilize) the TM, agreeing with previous studies. However, as the plasma pressure increases beyond a critical value, it is found that co-passing EPs also destabilize the mode. An in-depth analysis reveals that the net effect of co-passing EPs is a result of competition between the stabilizing contribution from the non-adiabatic drift kinetic terms and the destabilizing contribution associated with adiabatic terms, with the latter becoming more dominant at higher equilibrium pressure. Non-perturbative magnetohydrodynamic-kinetic hybrid modeling also finds that co- and counter-passing EPs modify the TM eigenfunction differently, with the counter-passing EPs enhancing the sideband harmonics. Furthermore, effects of the plasma resistivity and toroidal rotation, as well as that of the equilibrium distribution of EPs in the particle pitch angle space, are also investigated, showing asymmetric results on the TM stability between the co- and counter-passing EPs. The first order finite orbit width correction is found to be stabilizing with co-passing EPs and destabilizing with counter-passing particles. Finally, drift resonances between passing EPs and the TM induce finite frequency to the mode and generate finite net torques inside the plasma, due to the neoclassical toroidal viscosity and the Reynolds stress associated with 3D perturbations.

Plasma solitons in gated two-dimensional electron systems: Exactly solvable analytical model for the regime beyond weak nonlinearity

We analytically study plasma solitary waves, or solitons, in a two-dimensional electron system placed in close proximity to and between two ideal metallic gates. As a rule, solitons are described using a perturbative approach applicable only in the weak nonlinearity regime. In contrast, we analyze solitons considering a nonperturbative model. This framework enables an exact analytical description of the soliton shape. Moreover, it can be achieved in the regime beyond weak nonlinearity---when the concentration deviation due to the soliton is of the order of the equilibrium concentration. We determine the conditions required for a soliton to exist and derive the relationship between its amplitude, width, and velocity. We believe that our results obtained for the given model can provide valuable insight into the physics of nonlinear waves.

Residual mean field model of valence quarks in the nucleon

We develop a non-perturbative model for valence parton distribution functions (PDFs) based on the mean field interactions of valence quarks in the nucleonic interior. The main motivation for the model is to obtain a mean field description of the valence quarks as a baseline to study the short range quark–quark interactions that generate the high x tail of PDFs. The model is based on the separation of the valence three-quark cluster and residual system in the nucleon. Then the nucleon structure function is calculated within the effective light-front diagrammatic approach introducing nonperturbative light-front valence quark and residual wave functions. Within the model a new relation is obtained between the position, x_p, of the peak of xq_V(x) distribution of the valence quark and the effective mass of the residual system, m_R, in the form: x_{p} approx {1over 4} (1-{m_Rover m_N}) at starting Q^2. This relation explains the difference in the peak positions for d- and u-quarks through the expected difference of residual masses for valence d- and u-quark distributions. The parameters of the model are fixed by fitting the calculated valence quark distributions to the phenomenological PDFs. This allowed us to estimate the overall mean field contribution in baryonic and momentum sum rules for valence d- and u-quarks. Finally, the evaluated parameters of the non-perturbative wave functions of valence 3q-cluster and residual system can be used in calculation of other quantities such as nucleon form factors, generalized partonic and transverse momentum distributions.

Dynamical effective field model for interacting ferrofluids: I. Derivations for homogeneous, inhomogeneous, and polydisperse cases

Quite recently I have proposed a nonperturbative dynamical effective field model (DEFM) to quantitatively describe the dynamics of interacting ferrofluids. Its predictions compare very well with the results from Brownian dynamics simulations. In this paper I put the DEFM on firm theoretical ground by deriving it within the framework of dynamical density functional theory, taking into account nonadiabatic effects. The DEFM is generalized to inhomogeneous finite-size samples for which the macroscopic and mesoscopic scale separation is nontrivial due to the presence of long-range dipole–dipole interactions. The demagnetizing field naturally emerges from microscopic considerations and is consistently accounted for. The resulting mesoscopic dynamics only involves macroscopically local quantities such as local magnetization and Maxwell field. Nevertheless, the local demagnetizing field essentially couples to magnetization at distant macroscopic locations. Thus, a two-scale parallel algorithm, involving information transfer between different macroscopic locations, can be applied to fully solve the dynamics in an inhomogeneous sample. I also derive the DEFM for polydisperse ferrofluids, in which different species can be strongly coupled to each other dynamically. I discuss the underlying assumptions in obtaining a thermodynamically consistent polydisperse magnetization relaxation equation, which is of the same generic form as that for monodisperse ferrofluids. The theoretical advances presented in this paper are important for both qualitative understanding and quantitative modeling of the dynamics of ferrofluids and other dipolar systems.

Cone-Size Dependence of Jet Suppression in Heavy-Ion Collisions.

The strong suppression of high-p_{T} jets in heavy-ion collisions is a result of elastic and inelastic energy loss suffered by the jet multiprong collection of color charges that are resolved by medium interactions. Hence, quenching effects depend on the fluctuations of the jet substructure that are probed by the cone-size dependence of the spectrum. In this Letter, we present the first complete, analytic calculation of the inclusive R-dependent jet spectrum in PbPb collisions at LHC energies, including resummation of energy loss effects from hard, vacuumlike emissions occurring in the medium and modeling of soft energy flow and recovery at the jet cone. Both the geometry of the collision and the local medium properties, such as the temperature and fluid velocity, are given by a hydrodynamic evolution of the medium, leaving only the coupling constant in the medium as a free parameter. The calculation yields a good description of the centrality and p_{T} dependence of jet suppression for R=0.4 together with a mild cone-size dependence, which is in agreement with recent experimental results. Gauging the theoretical uncertainties, we find that the largest sensitivity resides in the leading logarithmic approximation of the phase space of resolved splittings, which can be improved systematically, while nonperturbative modeling of the soft-gluon sector is of relatively minor importance up to large cone sizes.

Role of Equilibrium Fluctuations in Light-Induced Order.

Engineering novel states of matter with light is at the forefront of materials research. An intensely studied direction is to realize broken-symmetry phases that are "hidden" under equilibrium conditions but can be unleashed by an ultrashort laser pulse. Despite a plethora of experimental discoveries, the nature of these orders and how they transiently appear remain unclear. To this end, we investigate a nonequilibrium charge density wave (CDW) in rare-earth tritellurides, which is suppressed in equilibrium but emerges after photoexcitation. Using a pump-pump-probe protocol implemented in ultrafast electron diffraction, we demonstrate that the light-induced CDW consists solely of order parameter fluctuations, which bear striking similarities to critical fluctuations in equilibrium despite differences in the length scale. By calculating the dynamics of CDW fluctuations in a nonperturbative model, we further show that the strength of the light-induced order is governed by the amplitude of equilibrium fluctuations. These findings highlight photoinduced fluctuations as an important ingredient for the emergence of transient orders out of equilibrium. Our results further suggest that materials with strong fluctuations in equilibrium are promising platforms to host hidden orders after laser excitation.

K0 and K+ -meson electromagnetic form factors: A nonperturbative relativistic quark model versus experimental, perturbative, and lattice quantum-chromodynamics results

It has been previously shown that a particular nonperturbative constituent-quark model of hadrons describes experimental measurements of electromagnetic form factors of light charged mesons through a small number of common phenomenological parameters, matching at the same time the Quantum-Chromodynamics (QCD) asymptotics for the pi-meson form factor at large momentum transfer. Here we start with the determination of the K0 electromagnetic form factor in this approach. Precise measurement of the K0 charge radius makes it possible to constrain model parameters with high accuracy. Then, with all parameters fixed, we revisit the K+ form factor and find that it matches experimental measurements in the infrared, lattice results at moderate momentum transfer and the perturbative QCD asymptotics in the ultraviolet. In this way we obtain a narrow constraint on the K+ charge radius, <r_K+^2> = 0.403 +0.007 -0.006 fm^2, and extend the successful infrared-ultraviolet connection from pi to K mesons.

Soft-drop grooming for hadronic event shapes

Soft-drop grooming of hadron-collision final states has the potential to significantly reduce the impact of non-perturbative corrections, and in particular the underlying-event contribution. This eventually will enable a more direct comparison of accurate perturbative predictions with experimental measurements. In this study we consider soft-drop groomed dijet event shapes. We derive general results needed to perform the resummation of suitable event-shape variables to next-to-leading logarithmic (NLL) accuracy matched to exact next-to-leading order (NLO) QCD matrix elements. We compile predictions for the transverse-thrust shape accurate to NLO + NLL′ using the implementation of the Caesar formalism in the Sherpa event generator framework. We complement this by state-of-the-art parton- and hadron-level predictions based on NLO QCD matrix elements matched with parton showers. We explore the potential to mitigate non-perturbative corrections for particle-level and track-based measurements of transverse thrust by considering a wide range of soft-drop parameters. We find that soft-drop grooming indeed is very efficient in removing the underlying event. This motivates future experimental measurements to be compared to precise QCD predictions and employed to constrain non-perturbative models in Monte-Carlo simulations.

Effect of deuteron breakup on the deuteron- Ξ correlation function

The hadron-deuteron correlation function has attracted many interests as a potential method to access the three-hadron interactions. However, the weakly-bound nature of deuteron has not been considered in the preceding studies. In this study, the breakup effect of deuteron on the deuteron-$\Xi^-$ ($d$-$\Xi^-$) correlation function $C_{d\Xi^-}$ is investigated. The $d$-$\Xi^-$ scattering is described by a nucleon-nucleon-$\Xi$ three-body reaction model. The continuum-discretized coupled-channels method, which is a fully quantum-mechanical and non-perturbative reaction model, is adopted. $C_{d\Xi^-}$ turns out to be sensitive to the strong interaction and enhanced by the deuteron breakup effect by 6--8 % for the $d$-$\Xi^-$ relative momentum below about 70 MeV/$c$. Low-lying neutron-neutron continuum states are responsible for this enhancement. Within the adopted model, the deuteron breakup effect on $C_{d\Xi^-}$ is found to be appreciable but not very significant. Except for the enhancement by several percent, studies on $C_{d\Xi^-}$ without the deuteron breakup effect can be justified.

A comparative study of internal kink stability in EU DEMO designs with negative and positive triangularity

Internal kink (IK) instability is investigated for European demonstration fusion reactor (EU DEMO) plasmas in both negative triangularity (NT) and positive triangularity (PT) configurations. For NT plasmas, the IK becomes more unstable as an ideal conformal wall moves away from the plasma boundary, with the mode growth rate saturating at the wall radial location of about , where a is the plasma minor radius and b the wall radial location. The plasma resistivity destabilizes the IK mode. The effect of sub-sonic toroidal plasma flow is sufficiently weak and can thus be ignored for these EU DEMO equilibria. These results are consistent with those for PT plasmas, albeit with larger mode growth rate in the NT configuration. Both perturbative and self-consistent magneto-hydrodynamic (MHD)-kinetic hybrid calculations predict (partial) stabilization of the IK modes in both NT and PT configurations, with inclusion of various kinetic contributions. Precessional drift motion of trapped fusion-born alphas in EU DEMO produces weak stabilization to the IK mode. Stronger stabilization occurs with the toroidal precession of trapped thermal particles (ions and electrons) and the bounce-transit motion of thermal ions. The stabilization is similar between the NT and PT configurations, due to the similarity of the mode eigenfunction (occupying a nearly circular region in the plasma core) despite the sign difference in the triangularity. The non-perturbative MHD-kinetic hybrid model predicts much less stabilization of the mode than the perturbative model, primarily due to the self-consistent determination of the mode eigenvalue in the former. Generally, no significant difference in the IK mode stability is found between the NT and PT plasmas in EU DEMO.

Second-harmonic generation in nonlinear plasmonic lattices enhanced by quantum emitter gain medium.

We report on a theoretical study of second-harmonic generation (SHG) in plasmonic nanostructures interacting with two-level quantum emitters (QEs) under incoherent energy pump. We generalize the driven-dissipative Tavis-Cummings model by introducing the anharmonic surface plasmon-polariton (SPP) mode coupled to QEs and examine physical properties of corresponding SPP-QE polariton states. Our calculations of the SHG efficiency for strong QE-SPP coupling demonstrate orders of magnitude enhancement facilitated by the polariton gain. We further discuss time-domain numerical simulations of SHG in a square lattice comprising Ag nanopillars coupled to QEs utilizing a fully vectorial nonperturbative nonlinear hydrodynamic model for conduction electrons coupled to Maxwell-Bloch equations for QEs. The simulations support the idea of gain enhanced SHG and show orders of magnitude increase in the SHG efficiency as the QEs are tuned in resonance with the lattice plasmon mode and brought above the population inversion threshold by incoherent pumping. By varying pump frequency and tuning QEs to a localized plasmon mode, we demonstrate further enhancement of the SHG efficiency facilitated by strong local electric fields. The incident light polarization dependence of the SHG is examined and related to the symmetries of participating plasmon modes.

Second Harmonic Generation from a Single Plasmonic Nanorod Strongly Coupled to a WSe2 Monolayer.

Monolayer transition metal dichalcogenides, coupled to metal plasmonic nanocavities, have recently emerged as new platforms for strong light-matter interactions. These systems are expected to have nonlinear-optical properties that will enable them to be used as entangled photon sources, compact wave-mixing devices, and other elements for classical and quantum photonic technologies. Here, we report the first experimental investigation of the nonlinear properties of these strongly coupled systems, by observing second harmonic generation from a WSe2 monolayer strongly coupled to a single gold nanorod. The pump-frequency dependence of the second-harmonic signal displays a pronounced splitting that can be explained by a coupled-oscillator model with second-order nonlinearities. Rigorous numerical simulations utilizing a nonperturbative nonlinear hydrodynamic model of conduction electrons support this interpretation and reproduce experimental results. Our study thus lays the groundwork for understanding the nonlinear properties of strongly coupled nanoscale systems.

Aspects of nonperturbative GUP models

We review on further new developments of Generalized Uncertainty Principle (GUP) and implications for the cosmological vacuum energy. First, we introduce basic aspects of GUP as well as several possible different and viable formulation of it. Second, we move on discussing two recent new types of higher D-dimensional nonperturbative GUP models; which we dub D-Type-I and D-Type-II GUPs. The D-Type-I and D-Type-II GUPs are both related to the existence of a critical conspiracy between a minimal uncertainty length and a maximal observable momentum. Finally, we show direct implications of D-Type-I and D-Type-II on the cosmological vacuum energy obtained in quantum mechanical systems such as the typical quantum harmonic oscillator. Such a computation goes through investigations of the density of states for D-dimensional coordinate systems in the momentum space. We will also comment on several possible connections with fundamental issues of quantum gravity such as black hole physics and gravitational radiative aspects.

Generating multi-partite entanglement from the quantum vacuum with a finite-lifetime mirror

Observers following special classes of finite-lifetime trajectories have been shown to experience an effective temperature, a generalisation of the Unruh temperature for uniformly accelerated observers. We consider a mirror following such a trajectory—and is hence localised to a strictly bounded causal diamond—that perfectly reflects incoming field modes. We find that inertial observers in the Minkowski vacuum detect particles along the half null-rays at the beginning and end of the mirror’s lifetime. These particle distributions exhibit multi-partite entanglement, which reveals novel structure within the vacuum correlations. The interaction is modelled using a non-perturbative circuit model and does not suffer from energy divergences.

The Nelson-Seiberg Theorem Generalized with Nonpolynomial Superpotentials

The Nelson-Seiberg theorem relates R-symmetries to F-term supersymmetry breaking and provides a guiding rule for new physics model building beyond the Standard Model. A revision of the theorem gives a necessary and sufficient condition to supersymmetry breaking in models with polynomial superpotentials. This work revisits the theorem to include models with nonpolynomial superpotentials. With a generic R-symmetric superpotential, a singularity at the origin of the field space implies both R-symmetry breaking and supersymmetry breaking. We give a generalized necessary and sufficient condition for supersymmetry breaking which applies to both perturbative and nonperturbative models.

Self-similar dynamics of order parameter fluctuations in pump-probe experiments

Upon excitation by a laser pulse, broken-symmetry phases of a wide variety of solids demonstrate similar order parameter dynamics characterized by a dramatic slowing down of relaxation for stronger pump fluences. Motivated by this recurrent phenomenology, we develop a simple non-perturbative effective model of dynamics of collective bosonic excitations in pump-probe experiments. We find that as the system recovers after photoexcitation, it shows universal prethermalized dynamics manifesting a power-law, as opposed to exponential, relaxation, explaining the slowing down of the recovery process. For strong quenches, long-wavelength over-populated transverse modes dominate the long-time dynamics; their distribution function exhibits universal scaling in time and space, whose universal exponents can be computed analytically. Our model offers a unifying description of order parameter fluctuations in a regime far from equilibrium, and our predictions can be tested with available time-resolved techniques.

Continuous-variable quantum teleportation with vacuum-entangled Rindler modes

We consider a continuous-variable quantum teleportation protocol between a uniformly accelerated sender in the right Rindler wedge, a conformal receiver restricted to the future light cone, and an inertial observer in the Minkowski vacuum. Using a nonperturbative quantum circuit model, the accelerated observer interacts unitarily with the Rindler modes of the field, thereby accessing entanglement of the vacuum as a resource. We find that a Rindler-displaced Minkowski vacuum state prepared and teleported by the accelerated observer appears mixed according to the inertial observer, despite a reduction of the quadrature variances below classical limits. This is a surprising result, since the same state transmitted directly from the accelerated observer appears as a pure coherent state to the inertial observer. The decoherence of the state is caused by an interplay of opposing effects as the acceleration increases: the reduction of vacuum noise in the output state for a stronger entanglement resource, constrained by the amplification of thermal noise due to the presence of Unruh radiation.

Effects of the non-perturbative mode structure on energetic particle transport

Energetic particles (EPs) are known to change the properties of shear Alfvén waves in tokamaks, and for this reason non-perturbative models have to be used to describe their linear and non-linear evolution. In this work, mode structures distortion with symmetry breaking properties featured by a finite radial wave phase velocity due to EP effects are considered. A mode structure of the form with complex parameters σ and s0 is used, to describe not only the width () and the mean location (Re{s0}) of the bell-shaped radial structure, but also the radial phase variations (Im{σ}, Im{s0}), where s is the normalized radial coordinate. The values of (σ, s0) are fitted from the results given by the gyrokinetic eigenvalue code LIGKA. The impact on EP transport is investigated using the drift-kinetic code HAGIS. The effects of the mode structure symmetry breaking on the mode saturation level and the EP transport are analysed. In the presence of mode structure symmetry breaking which is relevant to the simulation and experimental observations, the growth rate as well as the particle and energy transport level can vary by ∼10%. The velocity-space averaged parallel velocity of EPs in the inner region s = 0.2 ∼ 0.5 can change its sign for different mode structures, demonstrating the importance of the mode structure symmetry breaking on EP toroidal velocity reversal. This large effect (∼100%) on the mean parallel flow could have implications for EP current drive and the transport in the burning plasmas.

The Kerr–Newman Black Hole Solution as Strong Gravity for Elementary Particles

Analyzing the model of a spinning particle based on the over-rotating Kerr–Newman solution regularized by a supersymmetric bag model, we arrive at the conclusion that a unification of gravity with quantum theory is achieved in this model due to a strong topological influence of the Kerr spinning gravity which occurs on the Compton scale. We obtain that the correct formation of the nonperturbative bag model requires the use of the supersymmetric Landau–Ginzburg field model. We obtain that one of the most important gravitational phenomena in particle physics is the appearance of the quantum Wilson loop caused by the effect of frame-dragging related to the spin. Being located on the sharp border of the bag, the Wilson loop has a strong influence on the circular D-string structure located there.