Experimental behaviour of the P-wave isovector ππ phase shift and the pion form factor left hand cut contribution

Using the experimental data on the P-wave isovector ππ phase shift delta11 the importance of the pion form factor left hand cut contribution of the second Riemann sheet is investigated. Starting with the pion form factor phase representation, finding the suitable parametrization of the phase shift delta11 and calculating the corresponding integral in the pion c.m. momentum plane, one zero and two poles are found on the negative imaginary axis. The appearance of these poles and zero reveals that the contribution of the left hand cut of the second Riemann sheet to the pion form factor behaviour at the elastic region is non-negligible. (author)