Positive moments for scattering amplitudes

Bellazzini, Brando; Miró, Joan Elias; Rattazzi, Riccardo; Riembau, Marc; Riva, Francesco

doi:10.1103/physrevd.104.036006

Cited by 156 publications

(196 citation statements)

References 40 publications

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“…• Positivity bounds have become a powerful tool in the S-matrix programme given their power to constrain low-energy effective field theory couplings from some mild assumptions about the UV, see e.g. [70][71][72][73][74][75][76][77][78] and references therein. Very recently these bounds have been applied to boost-breaking amplitudes as relevant for the sub-horizon limit of the effective field theory of inflation [79,80].…”

Section: Jhep10(2021)065mentioning

confidence: 99%

From locality and unitarity to cosmological correlators

Jazayeri

Pajer

Stefanyszyn

2021

J. High Energ. Phys.

118

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In the standard approach to deriving inflationary predictions, we evolve a vacuum state in time according to the rules of a given model. Since the only observables are the future values of correlators and not their time evolution, this brings about a large degeneracy: a vast number of different models are mapped to the same minute number of observables. Furthermore, due to the lack of time-translation invariance, even tree-level calculations require an increasing number of nested integrals that quickly become intractable. Here we ask how much of the final observables can be “bootstrapped” directly from locality, unitarity and symmetries.To this end, we introduce two new “boostless” bootstrap tools to efficiently compute tree-level cosmological correlators/wavefunctions without any assumption about de Sitter boosts. The first is a Manifestly Local Test (MLT) that any n-point (wave)function of massless scalars or gravitons must satisfy if it is to arise from a manifestly local theory. When combined with a sub-set of the recently proposed Bootstrap Rules, this allows us to compute explicitly all bispectra to all orders in derivatives for a single scalar. Since we don’t invoke soft theorems, this can also be extended to multi-field inflation. The second is a partial energy recursion relation that allows us to compute exchange correlators. Combining a bespoke complex shift of the partial energies with Cauchy’s integral theorem and the Cosmological Optical Theorem, we fix exchange correlators up to a boundary term. The latter can be determined up to contact interactions using unitarity and manifest locality. As an illustration, we use these tools to bootstrap scalar inflationary trispectra due to graviton exchange and inflaton self-interactions.

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Section: Jhep10(2021)065mentioning

confidence: 99%

From locality and unitarity to cosmological correlators

Jazayeri

Pajer

Stefanyszyn

2021

J. High Energ. Phys.

118

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“…Similar variables to a n ( ) where recently used in [18], there named arcs, to study the positivity constraints of operator's Wilson coefficients along the Rernormalization Group flow. In this work, thanks to our knowledge of the low energy expansion (2.3), we have introduced subtractions in the definition of a n ( ) such that we get (2.14).…”

Section: Jhep10(2021)126mentioning

confidence: 99%

“…n max → ∞ and N * → ∞). We have also performed an extrapolation of the primal numerics in n max , 18 shown with a black curve in figure 2. Interestingly, we find that the extrapolation of the primal falls nearly on top of the boundary of the exclusion region.…”

Section: Jhep10(2021)126mentioning

confidence: 99%

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Dual EFT bootstrap: QCD flux tubes

Miró

Guerrieri

2021

J. High Energ. Phys.

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We develop a bootstrap approach to Effective Field Theories (EFTs) based on the concept of duality in optimisation theory. As a first application, we consider the fascinating set of EFTs for confining flux tubes. The outcome of our analysis are optimal bounds on the scattering amplitude of Goldstone excitations of the flux tube, which in turn translate into bounds on the Wilson coefficients of the EFT action. Finally, we comment on how our approach compares to EFT positivity bounds.

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“…3. Dimension-eight operators are subject to positivity bounds [31][32][33][34][35][36][37]. Thus, precisely because dimension-six interactions mix into dimension-eight ones, it is a priori conceivable that theoretical constraints on combinations of dimension-six Wilson coefficients can be established if the corresponding renormalisation group equations (RGEs) are precisely known.…”

Section: Introductionmentioning

confidence: 99%

Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I

et al. 2021

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We compute the one-loop renormalisation group running of the bosonic Standard Model effective operators to order v^4/\Lambda^4v4/Λ4, with v\sim 246v∼246 GeV being the electroweak scale and \LambdaΛ the unknown new physics threshold. We concentrate on the effects triggered by pairs of the leading dimension-six interactions, namely those that can arise at tree level in weakly-coupled ultraviolet completions of the Standard Model. We highlight some interesting consequences, including the interplay between positivity bounds and the form of the anomalous dimensions; the non-renormalisation of the SS and UU parameters; or the importance of radiative corrections to the Higgs potential for the electroweak phase transition. As a byproduct of this work, we provide a complete Green basis of operators involving only the Higgs and derivatives at dimension-eight, comprising 13 redundant interactions.

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Positive moments for scattering amplitudes

Cited by 156 publications

References 40 publications

From locality and unitarity to cosmological correlators

From locality and unitarity to cosmological correlators

Dual EFT bootstrap: QCD flux tubes

Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I

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