Singular lensing from the scattering on special space–time defects

Abstract

It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space-times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent ("singular lensing"). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space-time, and thus the disappearance of the lensing phenomenon, in the nodefect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals.

Constraining D-foam via the 21-cm line

“…(A.3), (A.6)), we observe that this is suppressed compared to (3.14) as we mentioned previously, despite the v −2 behaviour. We note for completeness that, with our regularisation, the total cross-section σ total = dΩ|f (θ)| 2 is which is finite like the transport cross-section and, as with σ t , also vanishes in the no-defect limitα → 0, providing a self-consistency check of the approach [42].…”

“…Thus there are at least four orders of magnitude difference between these two parameters of the D-foam 11 . As discussed in [41,42], the propagation of particles in topologically non-trivial space-times of the form (A.1) results in non-trivial scattering, whereby the defect 'lenses' the particles, in the sense of inducing singular scattering amplitudes for scattering angles θ = π(1 − b −1 ). Such cross-sections are not of Coulombic Type, in the sense of scaling as | p| −2 rather than | p| −4 , where | p| is the magnitude of the spatial momentum of the particle in the frame where the defect is at rest, in contrast to the standard millicharged DM interactions that scale like v −4 .…”

“…Nonetheless, such an effect should in general be taken into account, especially in Type-IA models of D-foam, where there is no direct interaction of baryons with the D-particles. In such models the baryons simply feel the effects associated with the non-trivial topology of the 'fuzzy' space time (A.1) via the induced cross-sections of [41,42]. In addition, in such space-times, the separation of the energy levels of atoms such as hydrogen, of relevance to us here, will be modified compared to the non-defect limit [43].…”

“…. represent singular terms arising from the δ-function term in the scattering amplitude (A.7), which need proper regularization in the θ = 0 (forward scattering) region, as discussed in [42]. This is essential for yielding the correct vanishing result for the scattering amplitude in the no-defect limit, where f (θ) | no−defect =0, and hence the suppression of the cross-sections for vanishingly-small deficits.…”

Searches for Magnetic Monopoles: A Review

“…These monopoles carry no magnetic charge, yet gravitational effects away from their centre are significant, leading to a deficit angle in the (non-Minkowski) space-time. Such an effect may modify the forward scattering amplitude of Standard Model (SM) background particles, creating ring-like angular regions with very large scattering amplitude [28,29]. Such peculiar scattering patterns of ordinary SM particles may indicate indirectly the presence of a neutral global monopole in collider detectors, where they may be pair-produced [27,30].…”