Cornering large-Nc QCD with positivity bounds

Abstract

The simple analytic structure of meson scattering amplitudes in the large-Nc limit, combined with positivity of the spectral density, provides precise predictions on low-energy observables. Building upon previous studies, we explore the allowed regions of chiral Lagrangian parameters and meson couplings to pions. We reveal a structure of kinks at all orders in the chiral expansion and develop analytical tools to show that kinks always correspond to amplitudes with a single light pole. We build (scalar- and vector-less) deformations of the Lovelace-Shapiro and Coon UV-complete amplitudes, and show that they lie close to the boundaries. Moreover, constraints from crossing-symmetry imply that meson couplings to pions become smaller as their spin increases, providing an explanation for the success of Vector Meson Dominance and holographic QCD. We study how these conclusions depend on assumptions about the high-energy behavior of amplitudes. Finally, we emphasize the complementarity between our results and Lattice computations in the exploration of large-Nc QCD.

Flattening of the EFT-hedron: supersymmetric positivity bounds and the search for string theory

“…Our analysis shares many features with the pion-bootstrap papers [7,8]. One difference is that supersymmetry effectively imposes additional constraints and allows us to bound all nonzero Wilson coefficients without having to assume a stronger Froissart bound.…”

“…Finally, it is unclear how generic the flattening phenomenon is. For example, it would be interesting to examine whether flattening also occurs in the pion bootstrap [5][6][7][8][9][10] or for abelian scalar models [3].…”

“…These basic high-energy assumptions facilitate a dispersive representation of the Wilson coefficients which implies that they must lie in a convex region sometimes called the "EFT-hedron" [2]. The allowed region of Wilson coefficients has been explored recently for theories of massless particles, including for scalars [2][3][4], massless pions [5][6][7][8][9][10], photons [11][12][13][14][15], and gravitons [16,17].…”

Spinning partial waves for scattering amplitudes in d dimensions

“…Consider a Cartan decomposition G = KA p K and let h ∈ A p be a generic element of A p . 25 The universal enveloping algebra U(g c ) admits a factorisation…”

“…This has led to a number of important outcomes, including a demonstration that S-matrix consistency implies two-sided bounds on ratios of EFT coefficients, essentially "proving" the intuition of dimensional analysis above, as well as a precise numerical recipe for obtaining optimal bounds [19][20][21][22][23]. This technique has recently also been applied to pion scattering [24,25] but also photons [26,27] and gravitons [28][29][30].…”