Causality, unitarity and symmetry in effective field theory

Abstract

Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the S-matrix, these imply that the size of higher dimensional corrections to transition amplitudes between different states is bounded by the strength of their contributions to elastic forward scattering processes. This places fundamental limits on the extent to which hypothetical symmetries can be broken by effective interactions. All analysis is for dimension 8 operators in the forward limit. Included is a thorough derivation of all positivity bounds for a chiral fermion in SU(2) and SU(3) global symmetry representations resembling those of the Standard Model, general bounds on flavour violation, new bounds for interactions between particles of different spin, inclusion of loops of dimension 6 operators and illustration of the resulting strengthening of positivity bounds over tree-level expectations, a catalogue of supersymmetric effective interactions up to mass dimension 8 and 4 legs and the demonstration that supersymmetry unifies the positivity theorems as well as the new bounds.

Natural selection rules: new positivity bounds for massive spinning particles

“…(3.12) 13 As with (2.14), (3.8) should be understood as first differentiating and setting t = 0, and then taking the absorptive part.…”

“…Rather than match EFT coefficients to a particular UV model, so-called "positivity bounds" instead leverage such fundamental UV properties to constrain the EFT coefficient space. In this work, we derive new and more general positivity bounds on EFTs for massive spinning particles, adding to the rapidly growing list of available bounds developed recently in [5][6][7][8][9][10][11][12][13][14][15][16].…”

“…In fact, since Absu A h 1 h2 h 1 h2 (s, 0) > 0 in the forward limit, there is no need to perform the helicity sum (3.11) since every elastic A (2N )h 1 h 2 h 1 h 2 (s0, 0; µ) is monotonic[5]. In fact, the elastic scattering of any superposition of helicity states is also monotonic[33], and more recently bounds have also been placed on the inelastic configurations[13,89].…”

Positivity bounds from multiple vacua and their cosmological consequences

“…By using these bounds, we can carve the EFT parameter space into regions which could admit a standard Wilsonian UV completion, and regions which could never be embedded in a high-energy theory (in a way consistent with these standard axioms). This positivity technology has recently been applied to a number of different low-energy EFTs, ranging from particle physics [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] to cosmology [49][50][51][52][53][54][55][56][57][58][59][60][61][62]. However, these previous applications have focussed on scattering fluctuations around a trivial vacuum configuration, such as φ = 0.…”

SMEFTs living on the edge: determining the UV theories from positivity and extremality

“…The first issue is relatively better studied. Recent progresses in extending the scope of positivity bounds can be categorized in three directions: the inclusion of higher-dimensional operators (or higher powers of s dependence) [59,60], the inclusion of higher-angular momenta in the scattering (or higher powers of t dependence) [52,53] (see also [54][55][56][57][58]), and the inclusion of multiple particle species [46,47] (see also [39,48,[67][68][69][70][71][72][73][74][75][76]). Progress in the 3rd direction is the most relevant in the inverse problem, as it allows us to discuss the boundary of SMEFTs in a large-dimensional parameter space, and therefore to infer how a UV particle interacts with multiple SM species.…”