Dual S-matrix bootstrap. Part I. 2D theory

Guerrieri, Andrea L.; Homrich, Alexandre; Vieira, Pedro

doi:10.1007/jhep11(2020)084

Cited by 41 publications

(34 citation statements)

References 26 publications

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“…From a practical point of view, to investigate the physics considered in this paper further, it would be desirable to have better and faster numerical approaches, perhaps building on the recent proposals in [23,24,32]; for instance, using the current methods, the decay widths appear to be quite sensitive to N ma x . Furthermore, it may also be beneficial to consider a better starting point inspired by the narrow resonance approximation.…”

Section: Future Directionsmentioning

confidence: 99%

Selection rules for the S-Matrix bootstrap

2021

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We examine the space of allowed S-matrices on the Adler zeros' plane using the recently resurrected (numerical) S-matrix bootstrap program for pion scattering. Two physical quantities, an averaged total scattering cross-section, and an averaged entanglement power for the boundary S-matrices, are studied. Emerging linearity in the leading Regge trajectory is correlated with a reduction in both these quantities. We identify two potentially viable regions where the S-matrices give decent agreement with low energy S- and P-wave scattering lengths and have leading Regge trajectory compatible with experiments. We also study the line of minimum averaged total cross section in the Adler zeros' plane. The Lovelace-Shapiro model, which was a precursor to modern string theory, is given by a straight line in the Adler zeros' plane and, quite remarkably, we find that this line intersects the space of allowed S-matrices near both these regions.

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Section: Future Directionsmentioning

confidence: 99%

Selection rules for the S-Matrix bootstrap

2021

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“…Systematic implementations of the primal problem have been proposed for generic field theories (without a large gap M ) [30,31]. Convergence of the dual and primal problems have also been studied for two-dimensional S-matrices [29,32]. We will not attempt to adapt these methods to our problem, but we will study simple special theories which can be ruled in analytically.…”

mentioning

confidence: 99%

Extremal effective field theories

Caron-Huot

Duong

2021

J. High Energ. Phys.

156

327

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Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known. Previous work showed that EFT coefficients must obey certain positivity constraints if causality and unitarity are satisfied at all scales. We explore those constraints from the perspective of 2 → 2 scattering amplitudes of a light real scalar field, using semi-definite programming to carve out the space of allowed EFT coefficients for a given mass threshold M. We point out that all EFT parameters are bounded both below and above, effectively showing that dimensional analysis scaling is a consequence of causality. This includes the coefficients of s2 + t2 + u2 and stu type interactions. We present simple 2 → 2 extremal amplitudes which realize, or “rule in”, kinks in coefficient space and whose convex hull span a large fraction of the allowed space.

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“…In this case, convergence will be "quadratic". 12 Convergence of the Newton method is a rich mathematical domain. One famous result that maybe illustrates this point best is the fractal structure of the basins of attraction of the method to determine complex roots of polynomials, see appendix C…”

Section: Newton's Methodsmentioning

confidence: 99%

“…It does not necessarily describe scattering in some physical theory, but the converse is definitely true: every physical scattering amplitude is an amplitude-function. Constructing amplitudefunctions and characterizing the space of physical parameters that they span, which we can loosely call the space of couplings, is an interesting and important problem, sometimes also called the primal problem, see [12] for the recent discussion of both the primal and dual problems in 2d. Even more ambitiously, by exploring the space of the amplitude-functions, we might hope to find physical theories at its boundary and in this way try to solve them.…”

Section: Introductionmentioning

confidence: 99%

Scattering from production in 2d

Tourkine

Zhiboedov

2021

J. High Energ. Phys.

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In 1968, Atkinson proved the existence of functions that satisfy all S-matrix axioms in four spacetime dimensions. His proof is constructive and to our knowledge it is the only result of this type. Remarkably, the methods to construct such functions used in the proof were never implemented in practice. In the present paper, we test the applicability of those methods in the simpler setting of two-dimensional S-matrices. We solve the problem of reconstructing the scattering amplitude starting from a given particle production probability. We do this by implementing two numerical iterative schemes (fixed-point iteration and Newton’s method), which, by iterating unitarity and dispersion relations, converge to solutions to the S-matrix axioms. We characterize the region in the amplitude-space in which our algorithms converge, and discover a fractal structure connected to the so-called CDD ambiguities which we call “CDD fractal”. To our surprise, the question of convergence naturally connects to the recent study of the coupling maximization in the two-dimensional S-matrix bootstrap. The methods exposed here pave the way for applications to higher dimensions, and expose some of the potential challenges that will have to be overcome.

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Dual S-matrix bootstrap. Part I. 2D theory

Cited by 41 publications

References 26 publications

Selection rules for the S-Matrix bootstrap

Selection rules for the S-Matrix bootstrap

Extremal effective field theories

Scattering from production in 2d

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