Pion-pion scattering amplitude

Journal Article · Fri Apr 01 04:00:00 EST 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.71.074016· OSTI ID:20708987

Pelaez, J R; Yndurain, F J ^[1]

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1. Departamento de Fisica Teorica, II (Metodos Matematicos), Facultad de Ciencias Fisicas, Universidad Complutense de Madrid, E-28040, Madrid (Spain)

We obtain reliable {pi}{pi} scattering amplitudes consistent with experimental data, both at low and high energies, and fulfilling appropriate analyticity properties. We do this by first fitting experimental low energy (s{sup 1/2}{<=}1.42 GeV) phase shifts and inelasticities with expressions that incorporate analyticity and unitarity. In particular, for the S wave with isospin 0, we discuss in detail several sets of experimental data. This provides low energy partial wave amplitudes that summarize the known experimental information. Then, we impose Regge behavior as follows from factorization and experimental data for the imaginary parts of the scattering amplitudes at higher energy, and check fulfillment of dispersion relations up to 0.925 GeV. This allows us to improve our fits. The ensuing {pi}{pi} scattering amplitudes are then shown to verify dispersion relations up to 1.42 GeV, as well as s-t-u crossing sum rules and other consistency conditions. The improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test chiral perturbation theory calculations, pionium decays, or use as input for CP-violating K decays. In this respect, we find [a{sub 0}{sup (0)}-a{sub 0}{sup (2)}]{sup 2}=(0.077{+-}0.008)M{sub {pi}}{sup -2} and {delta}{sub 0}{sup (0)}(m{sub K}{sup 2})-{delta}{sub 0}{sup (2)}(m{sub K}{sup 2})=52.9{+-}1.6{sup o}.

• OSTI ID: 20708987
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 7 Vol. 71; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRAL SYMMETRY
CHIRALITY
CP INVARIANCE
DISPERSION RELATIONS
FACTORIZATION
GEV RANGE
ISOSPIN
KAONS
PARTICLE DECAY
PERTURBATION THEORY
PHASE SHIFT
PION-PION INTERACTIONS
PIONIUM
PIONS
QUANTUM FIELD THEORY
S WAVES
SCATTERING AMPLITUDES
SUM RULES
UNITARITY