We use the effective field theory approach to systematically study the dynamics of classical and quantum systems in an oscillating magnetic field. We find that the fast field oscillations give rise to an effective interaction which is able to confine charged particles as well as neutral particles with a spin magnetic moment. The effect is reminiscent of the renown dynamical stabilization of charges by the oscillating electric field and provides a foundation for a new class of magnetic traps. The properties characteristic to the dynamical magnetic confinement are reviewed.

We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in inverse powers of the oscillation frequency ω. The explicit expression for the effective Lagrangian is derived up to O(1/ω^6) next-to-next-to-leading approximation. The general structure of the high-frequency expansion reveals a broad class of nonlinear systems whose transition curves are identical to those of the linear Mathieu equation, which enables a fully nonperturbative stability analysis in the case of strong driving and nonlinearity. The method is generalized to velocity-dependent forces and configuration space with curvature, characteristic to systems with constraints. Several applications are discussed in detail, including the dynamical magnetic trapping of electric charges.

We study the large-scale dynamics of charged particles in a rapidly oscillating field and formulate its classical and quantum effective theory description. The high-order perturbative results for the effective action are presented. Remarkably, the action models the effects of post-Newtonian general relativity on the motion of nonrelativistic particles, with the values of the emergent curvature and speed of light determined by the field spatial distribution and frequency. Our results can be applied to a wide range of physical problems including the high-precision analysis and design of the charged particle traps and Floquet quantum materials.

This corrects the article DOI: 10.1103/PhysRevLett.112.151801.

Abstract We study the light quark effect on the Higgs boson production in association with a jet at the LHC in the intermediate transverse momentum region between the quark and the Higgs boson mass scales. Though the effect is suppressed by the small Yukawa coupling, it is enhanced by large logarithms of the quark mass ratio to the Higgs boson mass or transverse momentum. Following a remarkable success of the logarithmic expansion [40] for the prediction of the next-to-next-to-leading bottom quark contribution to the total cross section of the Higgs boson production we extend the analysis to its kinematical distributions. A new factorization formula is derived for the light quark mediated gg → Hg amplitudes and the differential cross section of the process is computed in the logarithmic approximation, which is used for an estimate of the bottom quark effect at the next-to-next-to-leading order.

We study the large-scale dynamics of charged particles in a rapidly oscillating field and formulate its classical and quantum effective theory description. The high-order perturbative results for the effective action are presented. Remarkably, the action models the effects of general relativity on the motion of nonrelativistic particles, with the values of the emergent curvature and speed of light determined by the field spatial distribution and frequency. Our results can be applied to a wide range of physical problems including the high-precision analysis and design of the charged particle traps and Floquet quantum materials.

Zero-energy solutions of the Dirac equation for the fermions bound to giant vortices of large winding number n are studied in the abelian Higgs and Chern-Simons Higgs models. The case of Jackiw-Rossi theory of the Majorana states in topological superconductors is discussed in detail. By expanding in inverse powers of n we find an analytic result for asymptotically all n solutions required by the index theorem. In the abelian Higgs model the zero modes fill the vortex core and reveal a universal structure independent of fine details of the gauge and scalar field interactions which, in particular, determines the general properties of the large-n superconducting cosmic strings. On the contrary, for the Chern-Simons Higgs vortices the zero modes are localized on the core boundary and the explicit solution is obtained for the supersymmetric couplings in a self-dual background.

We study Majorana zero modes bound to giant vortices in topological superconductors or topological insulator/normal superconductor heterostructures. By expanding in inverse powers of a large winding number $n$, we find an analytic solution for asymptotically all $n$ zero modes required by the index theorem. Contrary to the existing estimates, the solution is not pinned to the vortex boundary and is composed of the warped lowest Landau level states. While the dynamics which shapes the zero modes is a subtle interference of the magnetic effects and Andreev reflection, the solution is very robust and is determined by a single parameter, the vortex radius. The resulting local density of states has a number of features which give remarkable signatures for an experimental observation of the Majorana fermions in two dimensions.

Resummation techniques are essential for high-precision phenomenology at current and future high-energy collider experiments. Perturbative computations of cross sections often suffer from large logarithmic corrections, which must be resummed to all orders to restore the reliability of predictions from first principles. The precise understanding of the all-order structure of field theories allows for fundamental tests of the Standard Model and new physics searches. In this white paper, we review recent progress in modern resummation techniques and outline future directions. In particular, we focus on the resummation beyond leading power, the joint resummation of different classes of logarithms relevant for jets and their substructure, small-x resummation in the high-energy regime and the QCD fragmentation process in the small-zh limit.

We study the amplitudes of the quark scattering by an external electromagnetic field and of the light quark mediated Higgs boson production via gluon fusion in the high-energy limit. The asymptotic behavior of the quark form factors is obtained in the double-logarithmic approximation to all orders in strong coupling constant through O(m(q)(3)) in the small quark mass expansion and the asymptotic formula is given in a closed analytic form. In the case of the two-gluon Higgs boson form factor we obtain a complete analytic result for the three-loop O(m(q)(3)) double-logarithmic term while the all-order analysis is performed in the large-N-c limit of QCD and for the abelian gauge group. An estimate of the high-order high-power light quark mass effect in the Higgs boson production and decay is given.

In the paper a NLL contribution of the gluon vertex correction figure 4(c) has been omitted.

We elaborate a theory of giant vortices [1] based on an asymptotic expansion in inverse powers of their winding number $n$. The theory is applied to the analysis of vortex solutions in the abelian Higgs (Ginzburg-Landau) model. Specific properties of the giant vortices for charged and neutral scalar fields as well as different integrable limits of the scalar self-coupling are discussed. Asymptotic results and the finite-$n$ corrections to the vortex solutions are derived in analytic form and the convergence region of the expansion is determined.

We discuss vortex solutions of the Abelian Higgs model in the limit of large winding number n. We suggest a framework where a topological quantum number n is associated with a ratio of dynamical scales and a systematic expansion in inverse powers of n is then derived in the spirit of effective field theory. The general asymptotic form of giant vortices is obtained. For critical coupling the axially symmetric vortices become integrable in the large-n limit and we present the corresponding analytic solution. The method provides simple asymptotic formulas for the vortex shape and parameters with accuracy that can be systematically improved, and can be applied to topological solitons of other models. After including the next-to-leading terms the approximation works remarkably well down to n=1.

We discuss vortex solutions of the abelian Higgs model in the limit of large winding number n. We suggest a framework where a topological quantum number n is associated with a ratio of dynamical scales and a systematic expansion in inverse powers of n is then derived in the spirit of effective field theory. The general asymptotic form of giant vortices is obtained. For critical coupling the axially symmetric vortices become integrable in the large-n limit and we present the corresponding analytic solution. The method provides simple asymptotic formulae for the vortex shape and parameters with accuracy that can be systematically improved, and can be applied to topological solitons of other models. After including the next-to-leading terms the approximation works remarkably well down to n=1.

We discuss nonfactorizable QCD corrections to Higgs boson production in vector boson fusion at the Large Hadron Collider. We point out that these corrections can be computed in the eikonal approximation retaining all the terms that are not suppressed by the ratio of the transverse momenta of the tagging jets to the total center-of-mass energy. Our analysis shows that in certain kinematic distributions the nonfactorizable corrections can be as large as a percent making them quite comparable to their factorizable counter-parts.

We present a detailed analysis of the factorization and all-order resummation of the double-logarithmic radiative corrections which determine the asymptotic behavior of the gauge theory amplitudes suppressed by the leading power of the fermion mass in the limit of high-energy fixed-angle scattering. The result is applied to estimate the bottom quark mediated contribution to the Higgs boson production in gluon fusion.

We compute the leading mass corrections to the high-energy behavior of the massive quark vector form factor to three loops in QCD in the double-logarithmic approximation.

We study the high-energy fixed-angle Sudakov limit of the scattering amplitudes suppressed by the leading power of the quark mass in perturbative quantum chromodynamics. We prove the factorization and perform all-order resummation of the double-logarithmic radiative corrections which determine the asymptotic behavior of the amplitudes. In contrast to the Sudakov logarithms, the mass-suppressed double-logarithmic corrections are induced by soft quark exchange. The structure of the corrections and the asymptotic behavior of the amplitudes in this case crucially depend on the color flow in a given process and are determined by the eikonal color charge nonconservation. We present explicit results for the Higgs boson production in gluon fusion mediated by a light-quark loop and for the leading power-suppressed contributions to the quark form factors, which reveal "magical" universality. Nontrivial relations between the asymptotic behavior of different amplitudes and the amplitudes in different gauge theories are found.

By studying an explicit analytical solution of the Schrödinger equation with the Coulomb potential on the lattice we demonstrate a breakdown of perturbative matching for the description of the Coulomb artifacts in lattice NRQCD, which leads to a large systematic error in the predictions for the heavy quarkonium spectrum. The breakdown is a result of a fine interplay between the short and long distance effects specific to the lattice regularization of NRQCD. We show how the problem can be solved by matching the lattice and continuum results for the solution of the full Schrödinger equation without the expansion in the Coulomb interaction.