Abstract
4-Derivative gravity provides a renormalizable theory of quantum gravity at the price of introducing a physical ghost, which could admit a sensible positive-energy quantization. To understand its physics, we compute ghost-mediated scatterings among matter particles at tree-level, finding a new power-like infra-red enhancement typical of 4-derivative theories, that we dub ‘ghostrahlung’. Super-Planckian scatterings get downgraded to Planckian by radiating hard gravitons and ghosts, which are weakly coupled and carry away the energy.
Highlights
We find a new kind of IR enhancement related to the 4-derivative structure and to the consequent gravi-ghost propagator of Eq (1)
While purely gravitational cross sections can remain smaller than in Einstein theory, cross sections mediated by large matter couplings look as bad as those in UV-divergent Einstein theory, which violate naive perturbative unitarity
This comes together with the extra issue of understanding what a ‘ghost’ is, that we addressed by treating the gravi-ghosts as virtual particles in scatterings among matter particles, finding that 4-derivative gravity contains power-like IR enhancements at small k2
Summary
Where the first two terms, suppressed by the dimensionless gravitational couplings f0 and f2, are the 4-derivative graviton kinetic terms; the latter term Lmatter is the part of the Lagrangian that depends on the matter fields (scalars S, fermions ψ, vectors V with gauge-covariant kinetic terms, Yukawa couplings, quartic scalars, scalar couplings to gravity, −ξS|S|2 R and possibly with super-renormalizable terms). The gravi-ghost propagator is (in the gauge ξh = cg = 0 of [2]). The cross section is dσ/d = |A |2/4I , where I ≡ ( p1 · p2)2 − m21m22 is the usual flux factor (I = s/2 for massless particles with s = ( p1 + p2)2) and d is the usual relativistic phase space. The cross section is well defined despite the virtual gravi-ghost, which gets indirectly defined by what it does. In order to proceed in understanding the ghost, we decompose the scattering amplitude A as the amplitude Sμν for the ‘scattering’ times the gravi-ghost propagator Pμναβ of Eq (3), times the amplitude Dαβ for the ‘decay’: Fig. 2 A generic process among matter particles mediated by one gravi-ghost, denoted as a double wave where kμ is the quadri-momentum, c0 = 1, c2 = −2 (this sign is crucial) and.
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