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Spin correlations are considered now as the only possible source ofdispersion of the polaronic band in ARPES spectra of cuprates. However, thesame dispersion is observed experimentally for broad O 2p{\pi} band in ARPESspectra of cuprates [Phys. Rev. B 75, 075115 (2007)] although the O 2p{\pi}states do not experience any coupling to the low-energy spin degrees offreedom. The aim of the present report is exploring dispersion of the polaronicband in ARPES spectrum in the frames of Frohlich-Pekar polaron model where thisband is calculated analytically [Phys. Rev. B 77, 165136 (2008)]. We improvethe method by taking into account the momentum of the recoil and obtain newanalytical expression for the photoelectron rate as function of binding energyand momentum. Calculated according to it polaronic band demonstrates dispersionand broadening being in good agreement with the experiment. The dispersion iscaused by the momentum of the recoil and can be used to extract the polaroneffective mass from the experimental ARPES spectra. We also supplement theFranck-Condon principle by indication that if the phonon field is in a coherentstate then during rapid (photo) transition the average coordinates of thephonon field harmonics do not change, but their average momentums are changeddue to the recoil momentum.

On the nature of dispersion of the polaronic bands in ARPES spectra of cuprates: supplement of the Franck-Condon principle