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Unitarization of infinite-range forces: graviton-graviton scattering | | Diego Blas
; Jorge Martin Camalich
; Jose Antonio Oller
; | | Date: |
23 Oct 2020 | | Abstract: | A method to unitarize the scattering amplitude produced by infinite-range
forces is developed and applied to Born terms. In order to apply $S$-matrix
techniques, based on unitarity and analyticity, we first derive an $S$-matrix
free of infrared divergences. This is achieved by removing a divergent phase
factor due to the interactions mediated by the massless particles in the
crossed channels, a procedure that is related to previous formalisms to treat
infrared divergences. We apply this method in detail by unitarizing the Born
terms for graviton-graviton scattering in pure gravity and we find a scalar
graviton-graviton resonance with vacuum quantum numbers ($J^{PC}=0^{++}$) that
we call the extit{graviball}. Remarkably, this resonance is located below the
Planck mass but deep in the complex $s$-plane (with $s$ the usual Mandelstam
variable), so that its effects along the physical real $s$ axis peak for values
significantly lower than this scale. We argue that the position and width of
the graviball are reduced when including extra light fields in the theory. This
could lead to phenomenological consequences in scenarios of quantum gravity
with a large number of such fields or, in general, with a low-energy
ultraviolet completion. We also apply this formalism to two non-relativistic
potentials with exact known solutions for the scattering amplitudes: Coulomb
scattering and an energy-dependent potential obtained from the Coulomb one with
a zero at threshold. This latter case shares the same $J=0$ partial-wave
projected Born term as the graviton-graviton case, except for a global factor.
We find that the relevant resonance structure of these examples is reproduced
by our methods, which represents a strong indication of their robustness. | | Source: | arXiv, 2010.12459 | | Services: | Forum | Review | PDF | Favorites | |
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