Unitarized one-loop graviton-graviton scattering

Abstract

In this work we interpret the Einstein-Hilbert (EH) Lagrangian of gravitation as the first term of a low-energy effective theory similar to those considered in the chiral Lagrangian approach to low-energy hadron physics or the electroweak chiral Lagragians describing the symmetry breaking sector of the Standard Model (SM). Starting from the one-loop computation of the elastic gravitongraviton scattering amplitude by Dunbar and Norridge, we unitarize the IR regularized partial waves by using the Inverse Amplitude Method (IAM). This method enlarges the regime of applicability of the perturbative results to higher energies of the order of the Plank scale MP and allows for the possibility of poles in the second Riemann which have the natural interpretation of dynamical resonances. In this work we look for these possible resonances for the ++++ and −−−− helicity channels and the J = 0, 2 and 4 partial waves.

Unitarizing infinite-range forces: Graviton-graviton scattering, the graviball, and Coulomb scattering

“…With the perturbatively calculated F (1) 0 and F (2) 0 , in terms of a finite but vanishing photon mass, one can apply and test for Coulomb scattering the method advocated in Ref. [36] for unitarizing graviton-graviton scattering. In terms of those perturbative PWAs the unitarized formula for T 0 (p) reads T 0 (p) = F (1) 0 (p) 2 F (1) 0 (p) − F (2) 0 (p) ,…”

“…Therefore, the method of Ref. [36] fails to reproduce Coulomb scattering and, in general, is not suitable to unitarize infinite range interactions.…”

“…Two popular algebraic unitarization methods fulfilling these requirements are the IAM and the algebraic-N/D methods. The IAM [20][21][22][23] can be straightforwardly obtained by performing the expansion in powers of G of 1/A J up to NLO, and then directly inverting the outcome. The PWA obtained is denoted by A J IAM (s) and is given by…”

“…The parameter ln a emerges in the process of removing the infrared divergences. We also compare the results between different unitarization methods [15,16]: The algebraic N/D method [17,18], the 1st-iterated N/D method [19], and the Inverse Amplitude Method (IAM) [20][21][22][23]. Our benchmark results are those obtained by applying the IAM because this method has the practical advantage of not introducing any unitarization scale, at around Q 2 .…”