On the N-pion extension of the Lovelace-Shapiro model

Bianchi, Massimo; Consoli, Dario; Vecchia, P. Di

doi:10.1007/jhep03(2021)119

Cited by 16 publications

(18 citation statements)

References 37 publications

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“…In this section, we will verify our various formulas for the Lovelace-Shapiro model [36,[59][60][61].…”

Section: Jhep12(2021)036mentioning

confidence: 91%

Positivity and geometric function theory constraints on pion scattering

Zahed

2021

J. High Energ. Phys.

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This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with O(N) global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion relation in the z-variable, rather than the fixed channel dispersion relation. We have written down fully crossing symmetric dispersion relation for O(N) model in z-variable for three independent combinations of isospin amplitudes. We have presented three independent sum rules or locality constraints for the O(N) model arising from the fully crossing symmetric dispersion relations. We have derived three sets of positivity conditions. We have obtained two-sided bounds on Taylor coefficients of physical Pion amplitudes around the crossing symmetric point (for example, π+π−→ π0π0) applying the positivity conditions and the Bieberbach-Rogosinski inequalities from geometric function theory.

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“…In this section, we will verify our various formulas for the Lovelace-Shapiro model [36,[59][60][61].…”

Section: Jhep12(2021)036mentioning

confidence: 91%

Positivity and geometric function theory constraints on pion scattering

Zahed

2021

J. High Energ. Phys.

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“…It would also be interesting to study the Coon version of the Lovelace-Shapiro amplitude [39,40]. This amplitude, only recently understood from string theory [41], constitutes an interesting example where the N -point function shows defaults of unitarity.…”

Section: Perspectivesmentioning

confidence: 99%

On the unitarity and low energy expansion of the Coon amplitude

Figueroa¹,

Tourkine²

2022

Preprint

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The Coon amplitude is a deformation of the Veneziano amplitude with logarithmic Regge trajectories and an accumulation point in the spectrum, which interpolates between string theory and field theory. With string theory, it is the only other solution to duality constraints explicitly known and it constitutes an important data point in the modern S-matrix bootstrap. Yet, its basics properties are essentially unknown. In this paper we fill this gap and derive the conditions of positivity and the low energy expansion of the amplitude. On the positivity side, we discover that the amplitude switches from a regime where it is positive in all dimensions to a regime with critical dimensions, that connects to the known d = 26, 10 when the deformation is removed. En passant, we find that the Veneziano amplitude can be extended to massive scalars of masses up to m 2 = 1/3, where it has critical dimension 6.3. On the low-energy side, we compute the first few coupligs of the theory in terms of q-deformed analogues of the standard Riemann zeta values of the string expansion. We locate their location in the EFT-hedron, and find agreement with a recent conjecture that theories with accumulation points populate this space. We also discuss their relation to low spin dominance.

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“…In [9], in addition to the conditions above, dispersion relations and χPT motivated inequalities constrained the lake further leading to a "river" like allowed region. The D-wave inequalities were found using the Froissart-Gribov representation which rely on subtractions- 1 See for example, [11]. 2 Since each point inside the river corresponds to infinitely many allowed S-Matrices, there is no unique S-Matrix which describes two-loop χ P T in our current formulation.…”

Section: S-matrix Bootstrap Reloadedmentioning

confidence: 99%

“…Here, we will briefly discuss the Lovelace-Shapiro (LS) model. We start with the form of the amplitude in the LS model as [3,4,11,31]…”

Section: B2 Linearity Of Even and Odd Trajectoriesmentioning

confidence: 99%

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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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On the N-pion extension of the Lovelace-Shapiro model

Cited by 16 publications

References 37 publications

Positivity and geometric function theory constraints on pion scattering

Positivity and geometric function theory constraints on pion scattering

On the unitarity and low energy expansion of the Coon amplitude

Selection rules for the S-Matrix bootstrap

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