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Rotational structures have been measured using the Jurogam II and GAMMASPHEREarrays at low spin following the 155Gd({\alpha},2n)157Dy and 148Nd(12C,5n)155Dy reactions at 25 and 65 MeV, respectively. We report high-K bands,which are conjectured to be the first candidates of a K{\pi}= 2+ {\gamma}vibrational band, built on the [505]11/2- neutron orbital, in both odd-A 155,157Dy isotopes. The coupling of the first excited K=0+ states or the so-called\b{eta} vibrational bands at 661 and 676 keV in 154Dy and 156Dy to the[505]11/2- orbital, to produce a K{\pi}=11/2- band, was not observed in both155Dy and 157Dy, respectively. The implication of these findings on theinterpretation of the first excited 0+ states in the core nuclei 154Dy and156Dy are also discussed.

First candidates for {\gamma} vibrational bands built on the [505]11/2- neutron orbital in odd-A Dy isotopes