Effects of the transverse coherence length in relativistic collisions

Abstract

Effects of the quantum interference in collisions of particles have a twofold nature: they arise because of the auto-correlation of a complex scattering amplitude and due to spatial coherence of the incoming wave packets. Both these effects are neglected in a conventional scattering theory dealing with the delocalized plane waves, although they sometimes must be taken into account in particle and atomic physics. Here, we study the role of a transverse coherence length of the packets, putting special emphasis on the case in which one of the particles is twisted, that is, it carries an orbital angular momentum ℓ . In ee, ep, and pp collisions the interference results in corrections to the plane-wave cross sections, usually negligible at the energies √ s ≫ 1 GeV but noticeable for smaller ones, especially if there is a twisted hadron with |ℓ| > 10 3 in initial state. Beyond the perturbative QCD, these corrections become only moderately attenuated allowing one to probe a phase of the hadronic amplitude as a function of s and t. In this regime, the coherence effects can compete with the loop corrections in QED and facilitate testing the phenomenological models of the strong interaction at intermediate and low energies.

Quantum mechanical formulation of the Busch theorem

“…Thus, the particle packet acquires a quantized orbital angular momentum when leaving the solenoid field. Equations (6) and 7represent a quantum counterpart of the classical Busch theorem. Due to similarities of the fringe fields of the solenoid and those of a tip of a magnetic needle, the effect is somewhat analogous to that arising from the interaction with an effective magnetic monopole [16]-the particle's wave function gets an Aharonov-Bohm phase,…”

“…The generation of vortex beams as twisted photons [1], vortex neutrons [2], or vortex electrons has inspired versatile theoretical studies and interesting experiments or proposals to unveil the basic properties of such beams and of effects of quantum interference and coherence in particle collisions, inaccessible with ordinary beams [3][4][5][6][7][8][9]. Quantized vortex electrons-i.e., electron beams carrying a quantized orbital angular momentum (OAM)-generated in electron microscopes [10][11][12] can be applied as probes for the study of chiral [13] or magnetic structures [14] and enable magnetic mapping with atomic resolution [15].…”

“…[5]), e.g., by means of spiral phase plates [10], holographic diffraction gratings [11], or the interaction with a magnetic needle, which mimics an approximate magnetic monopole [16]. The low efficiency and the limited flexibility of these methods hampers, however, the broad application of vortex beams for explorations of the atomic structure of matter and of fundamental interactions beyond a plane-wave approximation [3][4][5][6][7][8][9].…”

Double‐Twisted Spectroscopy with Delocalized Atoms

“…If the initial photons are in Bessel twisted states, we represent each photon, neglecting its polarization degrees of freedom, as a superposition of plane waves [ 28,36–38 ] : $$\begin{equation} |\varkappa ,m\rangle = e^{-i \omega t + i k_z z} \int {\text{d}^2 k_\perp \over (2\pi )^2}a_{\varkappa m}({\bf k}_\perp ) e^{i{\bf k}_\perp {\bf r}_\perp } \end{equation}$$where $$\begin{equation} a_{\varkappa m}({\bf k}_\perp )= (-i)^m e^{im\varphi _k}\sqrt {2\pi \over \varkappa }\; \delta (|{\bf k}_\perp |-\varkappa ) \end{equation}$$is the corresponding Fourier amplitude. The S ‐matrix element of the two twisted photon excitation is $$\begin{eq...$$…”

“…Since they lead to the same final state, the two PW configurations interfere. Squaring (8) and following the standard regularization, [ 28,36–38 ] we obtain the generalized cross section in the form $$\begin{eqnarray} && d\sigma \propto \delta (\Sigma E)\cdot \delta (\Sigma k_z)\, |{\cal J}|^2 \, d^3K = \delta (E_i + \omega _1 +\omega _2 - E_f)\, |{\cal J}|^2 \, d^2{\bf K}_\perp \nonumber\\ \end{eqnarray}$$The energy conservation law expressed in Equation (5) still holds. However, unlike the plane‐wave collision where the final momentum was completely fixed by the initial kinematics, we have here a distribution over $${\bf K}_\perp$$ inside the annular region defined by Equation (11).…”