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Register a new userNatural Selection Rules: New Positivity Bounds for Massive Spinning Particles
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We derive new effective field theory (EFT) positivity bounds on the elastic $2to2$ scattering amplitudes of massive spinning particles from the standard UV properties of unitarity, causality, locality and Lorentz invariance. By bounding the $t$ derivatives of the amplitude (which can be represented as angular momentum matrix elements) in terms of the total ingoing helicity, we derive stronger unitarity bounds on the $s$- and $u$-channel branch cuts which determine the dispersion relation. In contrast to previous positivity bounds, which relate the $t$-derivative to the forward-limit EFT amplitude with no $t$ derivatives, our bounds establish that the $t$-derivative alone must be strictly positive for sufficiently large helicities. Consequently, they provide stronger constraints beyond the forward limit and can be used to constrain dimension-6 interactions with a milder assumption about the high-energy growth of the UV amplitude.
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We apply positivity bounds directly to a $U(1)$ gauge theory with charged scalars and charged fermions, i.e. QED, minimally coupled to gravity. Assuming that the massless $t$-channel pole may be discarded, we show that the improved positivity bounds are violated unless new physics is introduced at the parametrically low scale $Lambda_{rm new} sim (e m M_{rm pl})^{1/2}$, consistent with similar results for scalar field theories, far lower than the scale implied by the weak gravity conjecture. This is sharply contrasted with previous treatments which focus on the application of positivity bounds to the low energy gravitational Euler-Heisenberg effective theory only. We emphasise that the low-cutoff is a consequence of applying the positivity bounds under the assumption that the pole may be discarded. We conjecture an alternative resolution that a small amount of negativity, consistent with decoupling limits, is allowed and not in conflict with standard UV completions, including weakly coupled ones.
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 $M_{rm pl}^{-2}alpha$ where $alpha$ 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.
In this paper the general form of scattering amplitudes for massless particles with equal spins s ($s s to s s$) or unequal spins ($s_a s_b to s_a s_b$) are derived. The imposed conditions are that the amplitudes should have the lowest possible dimension, have propagators of dimension $m^{-2}$, and obey gauge invariance. It is shown that the number of momenta required for amplitudes involving particles with s > 2 is higher than the number implied by 3-vertices for higher spin particles derived in the literature. Therefore, the dimension of the coupling constants following from the latter 3-vertices has a smaller power of an inverse mass than our results imply. Consequently, the 3-vertices in the literature cannot be the first interaction terms of a gauge-invariant theory. When no spins s > 2 are present in the process the known QCD, QED or (super) gravity amplitudes are obtained from the above general amplitudes.
We derive the first positivity bounds for low-energy Effective Field Theories (EFTs) that are not invariant under Lorentz boosts. Positivity bounds are the low-energy manifestation of certain fundamental properties in the UV -- to date they have been used to constrain a wide variety of EFTs, however since all of the existing bounds require Lorentz invariance they are not directly applicable when this symmetry is broken, such as for most cosmological and condensed matter systems. From the UV axioms of unitarity, causality and locality, we derive an infinite family of bounds which (derivatives of) the $2to2$ EFT scattering amplitude must satisfy even when Lorentz boosts are broken (either spontaneously or explicitly). We apply these bounds to the leading-order EFT of both a superfluid and the scalar fluctuations produced during inflation, comparing in the latter case with the current observational constraints on primordial non-Gaussianity.
We derive constraints on scalar field theories coupled to gravity by using recently developed positivity bounds in the presence of gravity. It is found that a canonically-normalized real scalar cannot have an arbitrarily flat potential unless some new physics enters well below the Planck scale. An upper bound on the scale of new physics is determined by loop corrections to the self-energy. Our result provides a swampland condition for scalar potentials.
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