High Energy Asymptotics Research Articles

Total Born cross section of e+e−-pair production by an electron in the Coulomb field of a nucleus

We calculate the total Born cross section of the e+e−-pair production by an electron in the field of a nucleus (trident process) using the modern multiloop methods. For general energies we obtain the cross section in terms of converging power series. The threshold asymptotics and the high-energy asymptotics are obtained analytically. In particular, we obtain an additional contribution to the Racah formula due to the identity of the final electrons. Besides, our result for the leading term of the high-energy asymptotics reveals a typo in an old Racah paper.

The local Borg-Marchenko uniqueness theorem for matrix-valued Schrödinger operators with locally smooth at the right endpoint potentials

We present a new expression for the Weyl-Titchmarsh matrix-valued function of a self-adjoint matrix-valued Schrödinger operator defined on the interval [ 0 , b ) , where 0 < b ≤ ∞ . Let H j = − d 2 d x 2 I m + Q j , j=1,2, be two self-adjoint Schrödinger operators in L 2 ( ( 0 , b ) ) m × m and Q 1 = Q 2 a.e. on the interval [ 0 , a ] , where a ∈ ( 0 , b ) . It is assumed that the potentials Q 1 and Q 2 are sufficiently smooth in the right neighborhood of the point a, where the right-hand derivatives of Q 1 = Q 2 at a coincide up to a certain order. Let M j ( z ) be the Weyl-Titchmarsh functions of H j = − d 2 d x 2 I m + Q j , j=1,2. As a specific application of this expression, we establish a high-energy asymptotic for the difference between M 1 ( z ) and M 2 ( z ) . Besides, new proofs are given for the local Borg-Marchenko uniqueness theorem and the high-energy asymptotics of the Weyl-Titchmarsh functions.

Yangian symmetry applied to quantum chromodynamics

We review applications of Yangian symmetry to high-energy Quantum chromodynamics (QCD) phenomenology. Some basic facts about high-energy QCD are recalled, in particular the spinor-helicity form of scattering amplitudes, the scale evolution equations of deep-inelastic scattering structure functions and the high-energy asymptotics of scattering. As the working tool the Yangian symmetric correlators are introduced and constructed in the framework of the Yangian algebra of [Formula: see text] type. We present the application to the tree scattering amplitudes and their iterative relation, to the parton splitting amplitudes and the kernels of the scale evolution equations of structure functions and to the equations describing the high-energy asymptotics of scattering.

Charge asymmetry in the spectra of bremsstrahlung and pair production

We calculate the first Coulomb correction to the spectra of two processes: the electron bremsstrahlung and electron-positron photoproduction in the Coulomb field. We show that, in contrast to the results obtained in the Born approximation and in the high-energy limit, the obtained corrections for these two process are not related by the crossing symmetry substitutions. The found corrections determine the leading contribution to the charge asymmetry in these processes. We use modern multiloop methods based on the IBP reduction and on the differential equations for master integrals. The results are presented in terms of classical polylogarithms. We provide both the threshold and the high-energy asymptotics of the obtained expressions and compare them with available results.

Charge asymmetry in electron/positron energy loss in nuclear Bremsstrahlung

We calculate the leading Coulomb correction to the Bremsstrahlung energy loss in the electron-nucleus collisions for arbitrary energy of the incoming particle. This correction determines the charge asymmetry, i.e., the difference of electron and positron energy loss. The result is presented in terms of the classical polylogarithms Li2 and Li3. We use modern multiloop methods based on the IBP reduction and on the differential equations for master integrals. We provide both the threshold and the high-energy asymptotics of the found asymmetry and compare them with the available results.

On factorizable S-matrices, generalized TTbar, and the Hagedorn transition

We study solutions of the Thermodynamic Bethe Ansatz equations for relativistic theories defined by the factorizable S-matrix of an integrable QFT deformed by CDD factors. Such S-matrices appear under generalized TTbar deformations of integrable QFT by special irrelevant operators. The TBA equations, of course, determine the ground state energy E(R) of the finite-size system, with the spatial coordinate compactified on a circle of circumference R. We limit attention to theories involving just one kind of stable particles, and consider deformations of the trivial (free fermion or boson) S-matrix by CDD factors with two elementary poles and regular high energy asymptotics — the “2CDD model”. We find that for all values of the parameters (positions of the CDD poles) the TBA equations exhibit two real solutions at R greater than a certain parameter-dependent value R*, which we refer to as the primary and secondary branches. The primary branch is identified with the standard iterative solution, while the secondary one is unstable against iterations and needs to be accessed through an alternative numerical method known as pseudo-arc-length continuation. The two branches merge at the “turning point” R* (a square-root branching point). The singularity signals a Hagedorn behavior of the density of high energy states of the deformed theories, a feature incompatible with the Wilsonian notion of a local QFT originating from a UV fixed point, but typical for string theories. This behavior of E(R) is qualitatively the same as the one for standard TTbar deformations of local QFT.

Master integrals for bipartite cuts of three-loop photon self energy

We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the 4m cut (the cut of 4 massive lines), reduce to Goncharov’s polylogarithms. The master integrals for 4m cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for 4m cut.

Optimized single-step (OSS) chemistry for auto-ignition of heterogeneous mixtures

With the objective of recovering the values of ignition delays of reactive heterogeneous mixtures a single-step chemistry model has been developed. The corresponding model extends a recent optimization procedure introduced to describe flame propagation in heterogeneous media featuring composition variations (equivalence ratio and temperature) in the fresh reactants or containing residual burned gases (RBG). It is based on the use of an optimized virtual species and a tabulation of the pre-exponential coefficient of an Arrhenius law. The main results of high activation energy asymptotics (AEA) are first recalled to put in evidence the key parameters and the dependence of the ignition delay on the corresponding quantities. The optimization procedure is then applied to these parameters, namely, the pre-exponential factor K and the activation energy E a of the associated single-step Arrhenius law. An efficient tabulation method benefiting from both rapid access and low storage is proposed for the composition variable (the mixture fraction, in the present case). Finally, the restitution of both ignition and propagation features is ensured through the consideration of the cross-over temperature. The performance of the resulting model is then assessed through comparisons with data obtained from detailed chemistry computations used as reference in several conditions of increasing complexity.

Total cross sections of e\u03b3 \u2192 eXoverline{X} processes with X = \u03bc, \u03b3, e via multiloop methods

Using modern multiloop calculation methods, we derive the analytical expressions for the total cross sections of the processes e−γ → {e}^{-}Xoverline{X} with X = μ, γ or e at arbitrary energies. For the first two processes our results are expressed via classical polylogarithms. The cross section of e−γ → e−e−e+ is represented as a one-fold integral of complete elliptic integral K and logarithms. Using our results, we calculate the threshold and high-energy asymptotics and compare them with available results.

Towards reconciling the holographic and lattice descriptions of radially excited hadrons

Within the framework of AdS/QCD models, the spectra of radially excited hadrons are identified with towers of Kaluza–Klein (KK) states in a putative dual theory. The infinite number of KK states is indispensable to provide correct high energy asymptotics of correlation functions in QCD. It is known, however, that the KK modes of dual theory must be qualitatively different from real hadrons. And what is more important, the radially excited states appear in lattice calculations not as ”excitations” of some ground state, but rather as independent states coupled to higher dimensional QCD operators – the larger is a basis of interpolating operators, the larger set of states can be resolved. A question arises whether is it possible to reconcile the holographic and lattice descriptions of radially excited hadrons? We propose a new phenomenological ”consistency test” for bottom-up holographic models: If the KK spectrum of massive 5D fields dual to higher dimensional operators in QCD coincides with the conventional radial KK spectrum, then the holographic KK states can be identified with real excited mesons in the large-N_c limit of QCD. We demonstrate that the Soft Wall holographic model passes this test while the Hard Wall model does not.

Screening properties of quark-gluon plasma obtained from distribution and correlation functions of the constituent quasiparticle model

Based on the constituent quasiparticle model of quark-gluon plasma (QGP), the matrix elements of the density operator and the Wigner function in the color phase space are presented in form of color path integrals over Wiener and SU(3) group Haar measures. Monte Carlo calculations of quark and gluon momentum distributions and spatial pair distribution functions have been carried out for the strongly coupled QGP plasma in thermal equilibrium at zero baryon chemical potential. The Debye screening mass and the running coupling constant have been obtained from the spatial pair distribution function and are in agreement with the available lattice QCD data. At densities related to the average interparticle distance more than 0.4 fm the gluon bound states in the form of glueballs have been found. Comparison with the Maxwell Boltzmann distribution shows significant influence of interparticle interaction on high energy asymptotics of the momentum distribution functions, resulting in appearance of quantum tails. The new color pair correlation function has been introduced, and related new color screening mass has been discussed.

MILD Combustion Limit Phenomena

This work contains an analysis of the existence of critical phenomena in MILD combustion systems through an exploration of classical results from high-energy asymptotics theory for extinction conditions of non-premixed flames and well-stirred reactors. Through the derivation of an expression linking burning rate to Damkohler number, the criteria for a folded S-Shaped Curve, representative of a combustion system with sudden extinction and ignition behaviour, was derived. This theory is discussed in detail, with particular focus on the limitations of the global chemistry it presents. The conditions reported by various previously-published numerical and experimental investigations are then discussed in the context of this theory. Of these investigations, those with the highest level of preheat and dilution had monotonic rather than folded S-Shaped Curves, indicating a lack of sudden extinction phenomena. It suggests that MILD combustion systems are those which lack sudden ignition and extinction behaviour, therefore exhibiting a smooth, stretched S-Shaped Curve rather than a folded one with inflection points. The results suggest that the delineation between folded versus monotonic S-Shaped Curves may provide a useful alternative definition of MILD combustion.

High energy photoionization of bound systems

We demonstrate how the nonrelativistic high energy asymptotics for the photoionization cross sections of systems bound by a central field can be obtained without solving the wave equations. The earlier analysis carried out for s bound states is extended for p states. We show that the physically expected asymptotics for ionization of fullerenes is not reproduced by the model potentials employed nowadays.

Spectral asymptotics of the Laplacian on Platonic solids graphs

We investigate the high-energy eigenvalue asymptotics of quantum graphs consisting of the vertices and edges of the five Platonic solids considering two different types of the vertex coupling. One is the standard δ-condition and the other is the preferred-orientation one introduced in the work by Exner and Tater [Phys. Lett. A 382, 283–287 (2018)]. The aim is to provide another illustration of the fact that the asymptotic properties of the latter coupling are determined by the vertex parity by showing that the octahedron graph differs in this respect from the other four for which the edges at high energies effectively disconnect and the spectrum approaches the one of the Dirichlet Laplacian on an interval.

Perturbations of Gibbs semigroups and the non-selfadjoint harmonic oscillator

Let T be the generator of a C0-semigroup e−Tt which is of trace class for all t>0 (a Gibbs semigroup). Let A be another closed operator, T-bounded with T-bound equal to zero. In general T+A might not be the generator of a Gibbs semigroup. In the first half of this paper we give sufficient conditions on A so that T+A is the generator of a Gibbs semigroup. We determine these conditions in terms of the convergence of the Dyson-Phillips expansion in suitable Schatten-von Neumann norms.In the second half of the paper we consider T=Hϑ=−e−iϑ∂x2+eiϑx2, the non-selfadjoint harmonic oscillator, on L2(R) and A=V, a locally integrable potential growing like |x|α at infinity for 0≤α<2. We establish that the Dyson-Phillips expansion converges in r Schatten-von Neumann norm in this case for r large enough and show that Hϑ+V is the generator of a Gibbs semigroup e−(Hϑ+V)τ for |arg⁡τ|≤π2−|ϑ|≠π2. From this we determine high energy asymptotics for the eigenvalues and the resolvent norm of Hϑ+V.

Double-logarithms in mathcal{N} = 8 supergravity: impact parameter description & mapping to 1-rooted ribbon graphs

The set of double-logarithmic (DL) contributions (α t ln2s)n to the 4-graviton amplitude in mathcal{N} = 8 supergravity (SUGRA), with α being the gravitational coupling and (s, t) the Mandelstam invariants, is studied in impact parameter (ρ) representation. This sector of the amplitude shows interesting properties which shed light on the nature of quantum corrections in gravity. Besides having a convergent behaviour as s increases, which is not present in mathcal{N} < 4 SUGRA theories, there exists a critical line ρc(s) above which the Born amplitude prevails. The short distance region ρ < ρc(s) is dominated by the DL terms. As a consequence, when studied in terms of an eikonal approach in the forward limit, the scattering angle linked to the bending of the semiclassical trajectory of the graviton shows a transition from attractive gravity at large distances to a region at small ρ characterized by a repulsive DL contribution to the gravitational potential due to the gravitino content of the theory. In the complex angular momentum plane, this DL high energy asymptotics is driven by the rightmost pole singularity of a parabolic cylinder function. The resummation of DL quantum corrections in mathcal{N} = 8 SUGRA can be understood in terms of the counting of 1-rooted maps on orientable surfaces.

Momentum Distribution Functions in Quark-Gluon Plasma

Based on the constituent quasiparticle model of the quark-gluon plasma (QGP), the Wigner function is presented in the form of a color path integral. The Monte Carlo calculations of the quark and gluon densities, pair correlation functions and the momentum distribution functions for strongly coupled QGP plasma in thermal equilibrium at barion chemical potential equal to zero have been carried out. Analysis of the pair correlation functions points out on arising glueballs and related gluon bound states. Comparison results between the momentum distribution functions and Maxwell-Boltzmann distributions show the significant influence of the interparticle interaction on the high energy asymptotics of the momentum distribution functions resulting in the appearance of quantum “tails”.

Quantum Dynamics of Charged Fermions in the Wigner Formulation of Quantum Mechanics

To study the kinetic properties of dense quantum plasma, a new quantum dynamics method in the Wigner representation of quantum mechanics has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. This method combines the Feynman and Wigner formulation of quantum mechanics and uses for calculation the path integral Monte-Carlo (WPIMC) in phase space and quantum generalization of the classical molecular dynamics methods (WMD) allowing to solve the quantum Wigner–Liouville-like equation. The Fermi–Dirac statistical effects are accounted for by the effective pair pseudopotential depending on coordinates and momenta and allowing to avoid the famous “sign problem” due to realization of the Pauli blocking of fermions. Significant influence of the interparticle interaction on the high energy asymptotics of the momentum distribution functions have been observed. According to the quantum Kubo formula, we also study the electron conductivity of dense plasma media.

Quench dynamics of the Ising field theory in a magnetic field

We numerically simulate the time evolution of the Ising field theory after quenches starting from the $E_8$ integrable model using the Truncated Conformal Space Approach. The results are compared with two different analytic predictions based on form factor expansions in the pre-quench and post-quench basis, respectively. Our results clarify the domain of validity of these expansions and suggest directions for further improvement. We show for quenches in the $E_8$ model that the initial state is not of the integrable pair state form. We also construct quench overlap functions and show that their high-energy asymptotics are markedly different from those constructed before in the sinh/sine-Gordon theory, and argue that this is related to properties of the ultraviolet fixed point.

Light-by-light scattering in double-logarithmic approximation

In the present paper we consider the elastic 2 rightarrow 2 -scattering of virtual photons at high energies in the forward kinematics at zero and non-zero values of t. Accounting for both gluon and quark double-logarithmic (DL) contributions to all orders in the QCD coupling, we obtain explicit expressions for amplitudes of this process in double-logarithmic approximation (DLA). First we keep the QCD coupling fixed and then account for running coupling effects. Applying the saddle-point method to the obtained expressions for the scattering amplitude, we calculate the high-energy asymptotics of the amplitude, which proved to be of the Regge form. The Reggeon bears the vacuum quantum numbers and therefore it is a new, DL contribution to Pomeron. Comparison of the DL Pomeron to the BFKL Pomeron shows that contribution of the DL Pomeron to the high-energy asymptotics is of the same order as contribution of the BFKL Pomeron, so the DL Pomeron should be taken into account together with the BFKL Pomeron. We estimate the applicability region for the asymptotics of the light-by-light scattering amplitude, where the the DL Pomeron can reliably represent the parent amplitude.