High-energy Behavior Research Articles

BFKL Equation: Status and Problems

The BFKL equation was derived for description of high energy behaviour of scattering amplitudes in non-Abelian gauge theories. Now it is widely known and used in quantum chromodynamics in the leading and next-to-leading logarithmic approximations. Its derivation is based on the pole Regge form of amplitudes with gluon exchanges in cross channels. In higher approximations this form is violated by contributions of Regge cuts, which complicates the derivation of the equation in the BFKL approach.

An improved hadronic model for pion electroproduction

Current measurements of the high energy behavior of the pion form factor are obtained from pion electroproduction data. These values are model dependent, utilizing the Vanderhaeghen, Guidal and Laget Regge (VGL) Model for their extraction. Recent work which examined the implementation of gauge invariance in that model suggested that it might lead to extracted pion form factors larger than the true values. Here we introduce a new model which preserves the successes of the VGL Model but implements gauge invariance in a new way. To demonstrate the validity of this new approach, we first use it to extract the pion form factor in a simple toy model. When compared with the previous extraction method, the improved model leads to a more reliable extraction. The success in this simple model leads us to reanalyze the electroproduction cross section data, where we obtain comparable values for the pion form factor to those obtained using the VGL procedure.

Electron collisions with BeH2 below 20 eV

We present calculations of electron scattering from ${\mathrm{BeH}}_{2}$ using the $R$-matrix method. Integral and differential elastic and inelastic cross sections for energies up to 20 eV have been determined and the position and width (when possible) of shape and core-excited resonances is reported. The use of Gaussian, $B$-spline, and mixed bases has been investigated. Results are compared with earlier calculations: it is shown that inclusion of both more target states and higher partial waves affects both the resonant behavior at lower energies and the high-energy behavior of the inelastic cross sections.

High-Energy Impact Behaviors of Concrete Structures Strengthened with Multi-Walled Carbon Nanotube Composites

This study analyzed high-energy impact behaviors of concrete structures strengthened with multi-walled carbon nanotube (MWCNT) composites. The proposed multi-walled carbon nanotubes demonstrated excellent mechanical properties such as high stiffness, high strength, and improved elongation. These distinctive properties allow the use of the product in several high-performance applications. Using a multi-scale analysis, we investigated the impact mechanism of an MWCNT-reinforced concrete structure using various parameters. The parametric studies focused on the various impact effects on structural performance. In addition, a three-dimensional simulation was carried out for the verification of our experimental results.

Model of diffractive excitation in pp collisions at high energies

A phenomenological model for the description of the single and double diffractive excitation in $pp$ collisions at high energies is presented. Considering the Good -- Walker approach, we propose a model for the eigenstates of the scattering operator and for the treatment of the interaction between them, with the high energy behavior of the cross section driven by perturbative QCD. The behavior of the total, elastic, single and double diffractive cross sections are analyzed and predictions for the energies of Run 3 of the LHC and those of the Cosmic Rays experiments are derived. We demonstrate that the model describes the current data for the energy dependence of the cross sections. A comparison with the recent data for the $\rho$ parameter and the differential elastic cross section are also presented and shortcomings of the current model are discussed.

Ring chains with vertex coupling of a preferred orientation

We consider a family of Schrödinger operators supported by a periodic chain of loops connected either tightly or loosely through connecting links of the length [Formula: see text] with the vertex coupling which is non-invariant with respect to the time reversal. The spectral behavior of the model illustrates that the high-energy behavior of such vertices is determined by the vertex parity. The positive spectrum of the tightly connected chain covers the entire halfline while the one of the loose chain is dominated by gaps. In addition, there is a negative spectrum consisting of an infinitely degenerate eigenvalue in the former case, and of one or two absolutely continuous bands in the latter. Furthermore, we discuss the limit [Formula: see text] and show that while the spectrum converges as a set to that of the tight chain, as it should in view of a result by Berkolaiko, Latushkin, and Sukhtaiev, this limit is rather non-uniform.

A broadband X-ray view of the NLSy1 1E 0754.6+3928

Context. The soft X-ray band of many active galactic nuclei (AGNs) is affected by obscuration due to partially ionised matter crossing our line of sight. In this context, two past XMM-Newton observations that were six months apart and a simultaneous NuSTAR-Swift exposure of the Narrow Line Seyfert 1 galaxy 1E 0754.6+3928, which was approximately eight years later, revealed an intense and variable warm absorber (WA) and hints of additional absorbers in the Fe Kα band. Aims. We aim to provide the first X-ray characterisation of this AGN by discussing its broadband (0.3–79 keV) spectrum and temporal properties. Methods. We conduct a temporal and spectroscopic analysis on two ∼10 ks (net exposure) XMM-Newton snapshots performed in April and October 2006. We also study the high energy behaviour of 1E 0754.6+3928 and model its broadband spectrum by using simultaneous Swift-NuSTAR data. Both phenomenological and physically motivated models are tested. Results. We find the presence of flux variability of ∼150% and 30% for 0.3–2 and 2–10 keV bands, respectively, and spectral changes at months timescales of ΔΓ ∼ 0.4. A reflection component that is consistent with being constant over years and arising from relatively cold material that is far from the central super massive black hole is detected. The main spectral feature shaping the 1E 0754.6+3928 spectrum is a WA. Such a component is persistent over the years and the variability of its ionisation and column density is observed down on months in the ranges 3 × 1022cm−2 ≲ NH ≲ 7.2 × 1022cm−2 and 1.5 ≲ log (ξ/erg s−1 cm) ≲ 2.1. Despite the short exposures, we find possible evidence of two additional high-ionisation and high-velocity outflow components in absorption. Conclusions. Our analysis suggests the existence of a complex system of absorbers in 1E 0754.6+3928. Longer exposures are required in order to characterise, on more solid grounds, the absorbers in this AGN.

Investigation of high energy behaviour of HERA data

We analyse the high precision HERA F2 data in the low-x, x<0,01, and very-low-x, x<0.001, regions using λ-fits. λ is a measure of the rate of rise of F2 defined by F2∝(1/x)λ. We show that λ determined in these two regions, at various Q2 values, is systematically smaller in the very-low-x region as compared to the low-x region. We discuss some possible physical interpretations of this effect.

OPE of Green Functions of Chiral Currents

A study of high-energy behavior of the three-point Green functions of chiral currents within the framework of the operator product expansion (OPE) is presented. In detail, we introduce an expansion of such correlators in terms of the QCD condensates up to dimension six. Next, we discuss some specifics of matching the OPE with calculations of the correlators within the chiral perturbation theory and resonance chiral theory, which can lead to important constraints of the coupling constants of the chiral/resonance Lagrangian.

Unitarization from geometry

We study the perturbative unitarity of scattering amplitudes in general dimensional reductions of Yang-Mills theories and general relativity on closed internal manifolds. For the tree amplitudes of the dimensionally reduced theory to have the expected high-energy behavior of the higher-dimensional theory, the masses and cubic couplings of the Kaluza-Klein states must satisfy certain sum rules that ensure there are nontrivial cancellations between Feynman diagrams. These sum rules give constraints on the spectra and triple overlap integrals of eigenfunctions of Laplacian operators on the internal manifold and can be proven directly using Hodge and eigenfunction decompositions. One consequence of these constraints is that there is an upper bound on the ratio of consecutive eigenvalues of the scalar Laplacian on closed Ricci-flat manifolds with special holonomy. This gives a sharp bound on the allowed gaps between Kaluza-Klein excitations of the graviton that also applies to Calabi-Yau compactifications of string theory.

Forward elastic scattering: dynamical gluon mass and semihard interactions

The role of low-x parton dynamics in dictating the high-energy behavior of forward scattering observables at LHC energies is investigated using a QCD-based model with even-under-crossing amplitude dominance at high-energies. We explore the effects of different sets of pre- and post-LHC fine-tuned parton distributions on the forward quantities sigma _{tot} and rho , from pp and {bar{p}}p scattering in the interval 10 GeV–13 TeV. We also investigate the role of the leading soft contribution, the low-energy cuttoff, and the energy dependence of the semihard form factor on these observables. We show that in all cases investigated the highly restrictive data on rho parameter at sqrt{s}=13 TeV indicate that a crossing-odd component may play a crucial role in forward elastic scattering at the highest energies, namely the Odderon contribution.

The warped dark sector

Five-dimensional braneworld constructions in anti-de Sitter space naturally lead to dark sector scenarios in which parts of the dark sector vanish at high 4d momentum or temperature. In the language of modified gravity, such feature implies a new mechanism for hiding light scalars, as well as the possibility of UV-completing chameleon-like effective theories. In the language of dark matter phenomenology, the high-energy behavior of the mediator sector changes dark matter observational complementarity. A multitude of signatures—including exotic ones—are present from laboratory to cosmological scales, including long-range forces with non-integer behavior, periodic signals at colliders, “soft bombs” events well-known from conformal theories, as well as a dark phase transition and a typically small amount of dark radiation.

Constraints on a gravitational Higgs mechanism

We show that it is impossible to improve the high-energy behavior of the tree-level four-point amplitude of a massive spin-2 particle by including the exchange of any number of scalars and vectors in four spacetime dimensions. This constrains possible weakly coupled ultraviolet extensions of massive gravity, ruling out gravitational analogues of the Higgs mechanism based on particles with spins less than two. Any tree-level ultraviolet extension that is Lorentz invariant and unitary must involve additional massive particles with spins greater than or equal to two, as in Kaluza-Klein theories and string theory.

Top-quark electroweak interactions at high energy

Modified interactions in the electroweak sector may lead to scattering amplitudes that grow with energy compared to their Standard Model (SM) counterparts. We present a detailed study of all 2 → 2 scattering amplitudes involving at least one top quark and a pair of EW bosons. We analyse the high energy behaviour of the amplitudes using the Standard Model Effective Field Theory (SMEFT) to parametrise the departures from the SM. We discuss the origin of the energy growth that arise from effective contact interactions by appealing to the Goldstone equivalence theorem and find that the amplitudes obey expected patterns of (non-)interference. The results are connected to unitary-violating behaviour in the framework of anomalous SM interactions. Therein, we identify the appearance of additional growth due to the violation of SU(2) gauge symmetry that leads to substantial differences between the SMEFT and the anomalous couplings approaches. We also discuss the embeddings of the scattering amplitudes into physical collider processes, presenting the parametric SMEFT sensitivity to relevant top quark operators and paying special attention to the extent to which the high energy behaviour of the 2 → 2 amplitude is retained in the actual processes accessible at colliders. The effective W approximation is exploited to gain analytical insight into the embeddings of the 2 → 2 helicity amplitudes. Finally, we provide a compendium of processes detailing numerous directions in which the SMEFT parameter space can be accessed through high energy top quark processes in current and future colliders.

RG equations and high energy behaviour in non-renormalizable theories

We suggest a novel view on non-renormalizable interactions. It is based on the usual BPHZ R-operation which is equally applicable to any local QFT independently of whether it is renormalizable or not. As a playground we take the ϕD4 theory in D dimensions for D=4,6,8,10 and consider the four-point scattering amplitude on shell. We derive the generalized RG equation and find the solution valid for any D that sums up the leading logarithms in all orders of PT in full analogy with the renormalizable case. It is found that the scattering amplitude in the ϕD4 theory possesses the Landau pole at high energy for any D. We discuss the application of the proposed procedure to other non-renormalizable theories.

Four-gauge-particle scattering amplitudes and Polyakov string path integral in the proper-time gauge

We evaluate four-gauge-particle tree level scattering amplitudes using the Polyakov string path integral in the proper-time gauge, where the string path integral can be cast into the Feynman-Schwinger proper-time representation. We compare the resultant scattering amplitudes, which include α′-corrections, with the conventional ones that may be obtained by substituting local vertex operators for the external string states. In the zero-slope limit, both amplitudes are reduced to the four-gauge-particle scattering amplitude of non-Abelian Yang-Mills gauge theory. However, when the string corrections become relevant with finite α′, the scattering amplitude in the proper-time gauge differs from the conventional one: The Polyakov string path integral in the proper-time gauge, equivalent to the deformed cubic string field theory, systematically provides the alpha prime corrections. In addition, we find that the scattering amplitude in the proper-time gauge contains tachyon poles in a manner consistent with three-particle-scattering amplitudes. The scattering amplitudes evaluated using the Polyakov string path integral in the proper-time gauge may be more suitable than conventional ones for exploring string corrections to the quantum field theories and high energy behaviors of open string.

High-energy behavior of strong-field QED in an intense plane wave

Analytical calculations of radiative corrections in strong-field QED have hinted that in the presence of an intense plane wave the effective coupling of the theory in the high-energy sector may increase as the $(2/3)$-power of the energy scale. These findings have raised the question of their compatibility with the corresponding logarithmic increase of radiative corrections in QED in vacuum. However, all these analytical results in strong-field QED have been obtained within the limiting case of a background constant crossed field. Starting from the polarization operator and the mass operator in a general plane wave, we show that the constant-crossed-field limit and the high-energy limit do not commute with each other and identify the physical parameter discriminating between the two alternative limits orders. As a result, we find that the power-law scaling at asymptotically large energy scales pertains strictly speaking only to the case of a constant crossed background field, whereas high-energy radiative corrections in a general plane wave depend logarithmically on the energy scale as in vacuum. However, we also confirm the possibility of testing the ``power-law'' regime experimentally by means of realistic setups involving, e.g., high-power lasers or high-density electron-positron bunches.

Gauge-independent approach to resonant dark matter annihilation

In spontaneously broken gauge theories, transition amplitudes describing dark-matter (DM) annihilation processes through a resonance may become highly inaccurate close to a production threshold, if a Breit-Wigner (BW) ansatz with a constant width is used. To partially overcome this problem, the BW propagator needs to be modified by including a momentum dependent decay width. However, such an approach to resonant transition amplitudes generically suffers from gauge artefacts that may also give rise to a bad or ambiguous high-energy behaviour for such amplitudes. We address the two problems of gauge dependence and high-energy unitarity within a gauge-independent framework of resummation implemented by the so-called Pinch Technique. We study DM annihilation via scalar resonances in a gauged U(1)X complex-scalar extension of the Standard Model that features a massive stable gauge field which can play the role of the DM. We find that the predictions for the DM abundance may vary significantly from previous studies based on the naive BW ansatz and propose an alternative simple approximation which leads to the correct DM phenomenology. In particular, our results do not depend on the gauge-fixing parameter and are consistent with considerations from high-energy unitarity.

High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions

Maximally supersymmetric field theories in various dimensions are believed to possess special properties due to extended supersymmetry. In four dimensions, they are free from UV divergences but are IR divergent on shell; in higher dimensions, on the contrary, they are IR finite but UV divergent. In what follows, we consider the four-point on-shell scattering amplitudes in D = 6 , 8 , 10 supersymmetric Yang–Mills theory in the planar limit within the spinor-helicity and on-shell supersymmetric formalism. We study the UV divergences and demonstrate how one can sum them over all orders of PT. Analyzing the R -operation, we obtain the recursive relations and derive differential equations that sum all leading, subleading, etc., divergences in all loops generalizing the standard RG formalism for the case of nonrenormalizable interactions. We then perform the renormalization procedure, which differs from the ordinary one in that the renormalization constant becomes the operator depending on kinematics. Solving the obtained RG equations for particular sets of diagrams analytically and for the general case numerically, we analyze their high energy behavior and find that, while each term of PT increases as a power of energy, the total sum behaves differently: in D = 6 two partial amplitudes decrease with energy and the third one increases exponentially, while in D = 8 and 10 the amplitudes possess an infinite number of periodic poles at finite energy.

Contribution of QCD condensates to the OPE of Green functions of chiral currents

A framework of operator product expansion (OPE) allows us to study high-energy behaviour of Green functions. A calculation of such Green functions within chiral perturbation theory (χPT) or resonance chiral theory (RχT) and subsequent matching of the result to the OPE enables us to determine constraints for unknown parameters of the effective theories. We present such procedure for Green functions in the odd-intrinsic parity sector of QCD.