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A reanalysis of $\pi\pi$ amplitudes for all important partial-waves belowabout 2 GeV is presented. A set of once subtracted dispersion relations withimposed crossing symmetry condition is used to modify unitary multi-channelamplitudes in the $S$, $P$, $D$, and $F$ waves. So far, these specificamplitudes constructed in our works and many other analyzes have been fittedonly to experimental data and therefore do not fulfill the crossing symmetrycondition. In the present analysis, the self consistent, i.e. unitary andfulfilling the crossing symmetry, amplitudes for the $S$, $P$, $D$, and $F$waves are formed. The proposed very effective and simple method of modificationof the $\pi\pi$ amplitudes does not change their previous-original mathematicalstructure and the method can be easily applied in various other analyzes.

Dispersive analysis of the $S$-, $P$-, $D$-, and $F$-wave $\pi\pi$ amplitudes