Positivity and geometric function theory constraints on pion scattering

Zahed, Ahmadullah

doi:10.1007/jhep12(2021)036

Cited by 27 publications

(23 citation statements)

References 52 publications

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“…A preliminary study of the more general conditions did suggest that stronger results are possible. In [46], the techniques used in this paper will be applied for the full pion scattering amplitude and useful and interesting inequalities for all physical pion scattering (e.g. π + π − → π 0 π 0 ) will be derived.…”

Section: Jhep12(2021)203mentioning

confidence: 99%

QFT, EFT and GFT

Raman

Sinha

2021

J. High Energ. Phys.

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We explore the correspondence between geometric function theory (GFT) and quantum field theory (QFT). The crossing symmetric dispersion relation provides the necessary tool to examine the connection between GFT, QFT, and effective field theories (EFTs), enabling us to connect with the crossing-symmetric EFT-hedron. Several existing mathematical bounds on the Taylor coefficients of Typically Real functions are summarized and shown to be of enormous use in bounding Wilson coefficients in the context of 2-2 scattering. We prove that two-sided bounds on Wilson coefficients are guaranteed to exist quite generally for the fully crossing symmetric situation. Numerical implementation of the GFT constraints (Bieberbach-Rogosinski inequalities) is straightforward and allows a systematic exploration. A comparison of our findings obtained using GFT techniques and other results in the literature is made. We study both the three-channel as well as the two-channel crossing-symmetric cases, the latter having some crucial differences. We also consider bound state poles as well as massless poles in EFTs. Finally, we consider nonlinear constraints arising from the positivity of certain Toeplitz determinants, which occur in the trigonometric moment problem.

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Section: Jhep12(2021)203mentioning

confidence: 99%

QFT, EFT and GFT

Raman

Sinha

2021

J. High Energ. Phys.

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“…Another approach to obtaining bounds on EFT couplings, using geometric function theory, has been recently developed in Refs. [42][43][44][45]. Here one trades manifest locality for manifest crossing symmetry, and uses so-called Bieberbach bounds to constrain EFT coefficients.…”

Section: Discussionmentioning

confidence: 99%

(Non)-projective bounds on gravitational EFT

Chiang¹,

Huang²,

Li³

et al. 2022

Preprint

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In this paper we study both projective and non-projective constraints on gravitational effective fields theories implied from unitarity, causality and crossing. We derive bounds on the Wilson coefficients of D 2n R 4 from its dispersive representation, utilizing both numerical semi-definite programming and analytic geometry analysis. From the former, we derive projective bounds on ratios of couplings and observe that generic boundary spectrums exhibit accumulation points. For the latter we consider the non-projective geometry of the EFThedron, which we relate to the known L-moment problem in the literature. This allows us to move beyond positivity and incorporate the upper bound from unitarity on the spectral functions. This leads to sharp bounds on individual coefficients, which are of order unity when normalized with respect to the UV scale. Finally, the non-projective geometry also allows us to derive optimal bounds reflecting assumptions of low-spin dominance, improving previous results. We complement the analytic derivations with a simple linear programming approach that can efficiently solve such non-projective conditions.

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“…In [33] this approach was extended to O(N ) theories building on the work of [34]. It will be interesting to see how the crossing antisymmetric dispersion relation can be tied into the GFT framework and if the associated constraints/sum rules are connected to [33,34] or independent ones. [37][38][39]) for other cases this is harder (e.g.…”

Section: Jhep01(2022)005mentioning

confidence: 99%

Crossing antisymmetric Polyakov blocks + dispersion relation

Kaviraj

2022

J. High Energ. Phys.

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Many CFT problems, e.g. ones with global symmetries, have correlation functions with a crossing antisymmetric sector. We show that such a crossing antisymmetric function can be expanded in terms of manifestly crossing antisymmetric objects, which we call the ‘+ type Polyakov blocks’. These blocks are built from AdSd+1 Witten diagrams. In 1d they encode the ‘+ type’ analytic functionals which act on crossing antisymmetric functions. In general d we establish this Witten diagram basis from a crossing antisymmetric dispersion relation in Mellin space. Analogous to the crossing symmetric case, the dispersion relation imposes a set of independent ‘locality constraints’ in addition to the usual CFT sum rules given by the ‘Polyakov conditions’. We use the Polyakov blocks to simplify more general analytic functionals in d > 1 and global symmetry functionals.

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Positivity and geometric function theory constraints on pion scattering

Cited by 27 publications

References 52 publications

QFT, EFT and GFT

QFT, EFT and GFT

(Non)-projective bounds on gravitational EFT

Crossing antisymmetric Polyakov blocks + dispersion relation

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