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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>P</mml:mi></mml:math>wave<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>amplitude from dispersion relations
We solve the dispersion relation for the $P$-wave $\ensuremath{\pi}\ensuremath{\pi}$ amplitude. We discuss the role of the left-hand cut vs the Castillejo-Dalitz-Dyson pole contribution and compare the solution with a generic quark model description. We review the generic properties of analytical partial wave scattering and production amplitudes and discuss their applicability …