Analyticity, unitarity and crossing-symmetry constraints for pion-pion partial wave amplitudes

1971 ◽  
pp. 22-40 ◽  
Author(s):  
G. Wanders
Keyword(s):  
Partial Wave ◽  
Crossing Symmetry ◽  
Symmetry Constraints

scholarly journals Crossing-symmetry constraints on partial-wave amplitudes and their physical content

1969 ◽  
Vol 64 (3) ◽  
pp. 585-602 ◽  
Author(s):  
J. L. Basdevant ◽  
G. Cohen-Tannoudji ◽  
A. Morel
Keyword(s):  
Partial Wave ◽  
Physical Content ◽  
Crossing Symmetry ◽  
Symmetry Constraints

Unitarized VenezianoππScattering Amplitude Consistent with Positivity and Crossing-Symmetry Constraints

1971 ◽  
Vol 4 (10) ◽  
pp. 3005-3011 ◽  
Author(s):  
Kyungsik Kang ◽  
M. Lacombe ◽  
R. Vinh Mau
Keyword(s):  
Crossing Symmetry ◽  
Symmetry Constraints

scholarly journals NEW DISPERSION RELATIONS IN THE DESCRIPTION OF ππ SCATTERING AMPLITUDES

2009 ◽  
Vol 24 (02n03) ◽  
pp. 402-409 ◽  
Author(s):  
R. KAMIŃSKI ◽  
R. GARCIA-MARTIN ◽  
P. GRYNKIEWICZ ◽  
J. R. PELAEZ ◽  
F. YNDURAIN
Keyword(s):  
Scattering Amplitudes ◽  
Partial Wave ◽  
Dispersion Relations ◽  
Crossing Symmetry ◽  
Stringent Test

We present a set of once subtracted dispersion relations which implement crossing symmetry conditions for the ππ scattering amplitudes below 1 GeV. We compare and discuss the results obtained for the once and twice subtracted dispersion relations, known as Roy's equations, for three ππ partial JI waves, S0, P and S2. We also show that once subtracted dispersion relations provide a stringent test of crossing and analyticity for ππ partial wave amplitudes, remarkably precise in the 400 to 1.1 GeV region, where the resulting uncertainties are significantly smaller than those coming from standard Roy's equations, given the same input.

scholarly journals Dispersion relations for hadronic light-by-light scattering and the muon g – 2

2018 ◽  
Vol 166 ◽  
pp. 00014 ◽  
Author(s):  
Massimiliano Procura ◽  
Gilberto Colangelo ◽  
Martin Hoferichter ◽  
Peter Stoffer
Keyword(s):  
Partial Wave ◽  
Form Factors ◽  
Pion Pole ◽  
Vector Form ◽  
Partial Wave Expansion ◽  
Left Hand ◽  
Pion Polarizability ◽  
Pion Loop ◽  
Crossing Symmetry ◽  
The One

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g – 2)μ come from hadronic effects, and in a few years the subleading hadronic light-by-light (HLbL) contribution might dominate the theory error. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. This opens up the possibility of a data-driven determination of the HLbL contribution to (g – 2)μ with the aim of reducing model dependence and achieving a reliable error estimate. Our dispersive approach defines unambiguously the pion-pole and the pion-box contribution to the HLbL tensor. Using Mandelstam double-spectral representation, we have proven that the pion-box contribution coincides exactly with the one-loop scalar-QED amplitude, multiplied by the appropriate pion vector form factors. Using dispersive fits to high-statistics data for the pion vector form factor, we obtain [see formula in PDF]. A first model-independent calculation of effects of ππ intermediate states that go beyond the scalar-QED pion loop is also presented. We combine our dispersive description of the HLbL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. After constructing suitable input for the γ*γ* → ππ helicity partial waves based on a pion-pole left-hand cut (LHC), we find that for the dominant charged-pion contribution this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate S-wave rescattering effects to the full pion box and leads to [see formula in PDF].

Physical pion-pion partial-wave equations based on three channel crossing symmetry

1974 ◽  
Vol 70 (2) ◽  
pp. 297-316 ◽  
Author(s):  
G. Mahoux ◽  
S.M. Roy ◽  
G. Wanders
Keyword(s):  
Partial Wave ◽  
Wave Equations ◽  
Physical Pion ◽  
Crossing Symmetry
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