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Scalar resonance in graviton-graviton scattering at high-energies: the graviball

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 نشر من قبل Jose Antonio Oller
 تاريخ النشر 2020
  مجال البحث فيزياء
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We study graviton-graviton scattering in partial-wave amplitudes after unitarizing their Born terms. In order to apply S-matrix techniques, based on unitarity and analyticity, we introduce an S-matrix free of infrared divergences. This is achieved by removing a diverging phase factor related to the infinite-range character of the interactions mediated by graviton exchange in the crossed channels. A scalar graviton-graviton resonance with vacuum quantum numbers (J^{PC}=0^{++}) is obtained as a pole in the nonperturbative S-wave amplitude, which we call the {it graviball}. Its resonant effects along the physical real s axis may peak at values much lower than the UV cutoff of the theory. For some scenarios, this phenomenon could have phenomenological consequences at relatively low-energy scales.



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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 diver gences. 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 textit{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.
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