Abstract
We study the validity of positivity bounds in the presence of a massless graviton, assuming the Regge behavior of the amplitude. Under this assumption, the problematic t-channel pole is canceled with the UV integral of the imaginary part of the amplitude in the dispersion relation, which gives rise to finite corrections to the positivity bounds. We find that low-energy effective field theories (EFT) with “wrong” sign are generically allowed. The allowed amount of the positivity violation is determined by the Regge behavior. This violation is suppressed by {M}_{mathrm{pl}}^{-2}alpha^{prime } where α′ is the scale of Reggeization. This implies that the positivity bounds can be applied only when the cutoff scale of EFT is much lower than the scale of Reggeization. We then obtain the positivity bounds on scalar-tensor EFT at one-loop level. Implications of our results on the degenerate higher-order scalar-tensor (DHOST) theory are also discussed.
Highlights
Must possess correct sign if one requires the existence of standard UV completions
We study the validity of positivity bounds in the presence of a massless graviton, assuming the Regge behavior of the amplitude
We have studied the validity of the positivity bounds in the presence of a massless graviton, by considering the 2 to 2 scattering of a light scalar field φ
Summary
We briefly review the derivation of positivity bounds for scalar EFT without gravity following [1, 15]. This scattering amplitude can be expressed as a function of Mandelstam invariants (s, t, u) thanks to the Lorentz invariance The definition of these variables are s := −(p1 + p2), t := −(p1 − p3), and u := −(p1 − p4), where (p1, p2) and (p3, p4) denote a set of ingoing and outgoing four momenta, respectively. Supposing that perturbative EFT computations are valid up to the scale ΛEFT, we obtain the following improved positivity bounds for t < 4m2φ. From the definition of ΛEFT one can evaluate the left-hand side of eq (2.8) These bounds can be useful constraints on EFT. We briefly review the derivation of these bounds in the appendix A.1, and see [15] for details
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