Perturbative S-matrix unitarity (S†S = 1) in Rμν2 gravity

Abstract

We show that in the quadratic curvature theory of gravity, or simply [Formula: see text] gravity, the tree-level unitarity bound (tree unitarity) is violated in the UV region but an analog for [Formula: see text]-matrix unitarity [Formula: see text] is satisfied. This theory is renormalizable, and hence the failure of tree unitarity is a counter example of Llewellyn Smith’s conjecture on the relation between them. We have recently proposed a new conjecture that [Formula: see text]-matrix unitarity gives the same conditions as renormalizability. We verify that [Formula: see text]-matrix unitarity holds in the matter-graviton scattering at the tree level in the [Formula: see text] gravity, demonstrating our new conjecture.

High-energy properties of the graviton scattering in quadratic gravity

“…The reason why we consider both is that the former is a non-renormalizable theory while the latter is a renormalizable one. A part of our results has been reported briefly in [14]. In the present paper we obtain the matter-graviton scattering amplitudes in full, and study how the perturbative S-matrix unitarity is obeyed, even though the tree unitarity fails, in quadratic gravity.…”

“…Berends and Gastmans use σ = +2, −2 as basis elements [16]. We use those constructed from the vector elements [14,47], given in eqs. (A.30) of appendix A.…”

“…The tree unitarity fails for QFT with higher derivative kinetic terms, including Lee-Wick type QFT [9,10] and R 2 µν gravity [11,12], because of negative norm field (ghost). The tree unitarity can be extended to perturbative S-matrix unitarity (SS † = 1) for higher-derivative QFT [13,14].…”

Neutrino physics: Experimental and theoretical challenges

“…Reactor experiments are usually categorized as short baseline (SBL) and long baseline (LBL). SBL experiments, like RENO (Bak et al 2018) and Daya‐Bay (Adey et al 2018), are sensitive to the mixing angle $$$ {\theta}_{13} $$$ and to a mass splitting combination involving $$$ {\theta}_{12} $$$, $$$ \Delta {m}_{31}^2 $$$, and $$$ \Delta {m}_{32}^2 $$$, while the LBL experiment KamLAND (Abe et al 2008; Gando et al 2011) is more sensitive to $$$ {\theta}_{12} $$$ and $$$ \Delta {m}_{21}^2 $$$. The new SBL experiments NEOS (Ko et al 2017), DANSS (Alekseev et al 2018), STEREO (Almazán et al 2020), PROSPECT (Andriamirado et al 2021), NEUTRINO‐4 (Serebrov et al 2021), and SoLid (Abreu et al 2021) will be able to probe a mass splitting beyond the standard three active neutrino picture, with $$$ \Delta {m}^2\sim 1 $$$ eV$$$ {}^2 $$$.…”

Scalar and fermion on-shell amplitudes in generalized Higgs effective field theory

“…2 This condition guarantees the absence of ghost particles in GHEFT framework. See [62,63] for the discussion on the pseudo unitarity in theories with ghost particles.…”