Forward dispersion relation constraints on the pion-nucleon p-wave and d-wave scattering lengths

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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Comments on the calculation of the pion-nucleon coupling constant and s-wave scattering lengths

Nuclear Physics B ◽

10.1016/0550-3213(74)90087-x ◽

1974 ◽

Vol 75 (3) ◽

pp. 455-460 ◽

Cited By ~ 15

Author(s):

W.S. Woolcock

Keyword(s):

Wave Scattering ◽

Coupling Constant ◽

S Wave ◽

Pion Nucleon ◽

Scattering Lengths

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Padé Approximant Calculation of p-Wave π–π Scattering with a σ Model Lagrangian

Canadian Journal of Physics ◽

10.1139/p71-042 ◽

1971 ◽

Vol 49 (3) ◽

pp. 360-366

Author(s):

D. K. Elias

Keyword(s):

Padé Approximants ◽

Padé Approximant ◽

P Wave ◽

Pade Approximants ◽

Pade Approximant ◽

Wave Channel ◽

Wave Resonance ◽

Text Interaction ◽

Range Of Values ◽

D Wave

A π–π it interaction via a scalar I = 0, σ exchange is considered. The contribution of the t and u channel exchanges of the σ to the p-wave, I = 1 amplitude is calculated using Padé approximants. A p-wave resonance, interpreted as the p meson, the width of which depends on the mass of the input a meson, is found; for a certain range of values of the σ mass the ρ width compares not unfavorably with similar calculations using a [Formula: see text] interaction. However, for the range of masses considered the width is considerably smaller than the experimental value. The I = 0, d-wave channel is also considered and a resonance, interpreted as the ƒ0(1260), is found.

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