Summary
Rigorous bounds on physical-region averages of real parts of ππ amplitudes are obtained in terms of theD-wave scattering lengths. Our bounds provide consistency checks on ππ scattering data, the experimental information on which is not in a satisfactory state. An example of our bounds is (in units with ħ=c=m π=1 ands=(c.m. energy)2)\( - 0.013 \leqslant g \equiv (3/32^3 )\int\limits_4^8 {ds} (s + 4)(8 - s)\{ - 2(s - 4) Re F^{(0)} (s,0) + 3(3s - 4) \cdot Re F^{(1)} (s,0) + 5(s - 4) Re F^{(2)} (s,0)\} \leqslant 0.019\), whereF (I)(s, t) are isospin-I ππ amplitudes. From the CERN-Munich experiment, the value ofg would be in the range 0.018±0.008 to 0.029±0.007 depending upon the value of theI=2,S-wave scattering length.
Riassunto
Si ottengono limiti rigorosi sulle medie delle regioni fisiche delle parti reali delle ampiezze ππ in termini delle lunghezze di scattering dell’ondaD. Questi limiti forniscono controlli di consistenza sui dati di scattering ππ, sui quali l’informazione sperimentale non è in uno stato soddisfacente. Un esempio di questi limiti (espressi in unità con ħ=c=m π=1 es=(energia del centro di massa)2)\( - 0.013 \leqslant g \equiv (3/32^3 )\int\limits_4^8 {ds} (s + 4) \cdot (8 - s)\{ - 2(s - 4) Re F^{(0)} (s,0) + 3(3s - 4) Re F^{(1)} (s,0) + 5(s - 4) Re F^{(2)} (s,0)\} \leqslant 0.019\) doveF (I) (s, t) sono le ampiezze ππ di isospinI. In base all’esperimento del CERN-Monaco, il valore dig dovrebbe essere nell’intervallo da 0.018±0.008 a 0.029±0.007 che dipende dal valore della lunghezza di scattering dell’ondaS perI=2.
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Gangal, A.D. Rigorous bounds on ππ amplitudes in terms of theD-wave scattering lengths. Nuov Cim A 74, 117–127 (1983). https://doi.org/10.1007/BF02829861
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DOI: https://doi.org/10.1007/BF02829861