Abstract
Starting from the ACV approach to transplanckian scattering, we present a development of the reduced-action model in which the (improved) eikonal representation is able to describe particles’ motion at large scattering angle and, furthermore, UV-safe (regular) rescattering solutions are found and incorporated in the metric. The resulting particles’ shock-waves undergo calculable trajectory shifts and time delays during the scattering process — which turns out to be consistently described by both action and metric, up to relative order R 2 /b 2 in the gravitational radius over impact parameter expansion. Some suggestions about the role and the (re)scattering properties of irregular solutions — not fully investigated here — are also presented.
Highlights
Series and is unitary, while for b < bc the field solutions are complex-valued and the elastic
Starting from the ACV approach to transplanckian scattering, we present a development of the reduced-action model in which the eikonal representation is able to describe particles’ motion at large scattering angle and, UV-safe rescattering solutions are found and incorporated in the metric
The main motivation of the present paper is to improve and complete some unsatisfactory aspects of the reduced-action model which might be crucial at planckian distances, but show up already at distances of order R ≡ 4GE, the gravitational radius
Summary
ACV [6] have shown that the leading contributions to the high-energy elastic scattering amplitude come from the s-channel iteration of soft-graviton exchanges, which can be represented by effective ladder diagrams as in figure 1. The purpose of the present section is to recall the method of resumming the effective ladder contributions to all orders so as to provide the so-called eikonal representation for the elastic S matrix. This representation is here “improved” in the sense that we do not make a separation of longitudinal and transverse variables by neglecting the leading scattering angle. For the same reason, the two external mass-shell deltas in eq (2.2) constrain Q0 = 0, cos θQ ≡ p1 · Q = |Q|/2E, Q2 = −Q2 In this way, the 4D integration d4q = dq0 |q|2 d|q| d cos θ dφ reduces to a 2D integral. Both issues will be discussed in detail
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