  We report on high-field electron spin resonance (ESR) studies of magnetic
excitations in the spin-1/2 triangular-lattice antiferromagnet Cs$_2$CuBr$_4$.
Frequency-field diagrams of ESR excitations are measured for different
orientations of magnetic fields up to 25 T. We show that the substantial
zero-field energy gap, $\Delta\approx9.5$ K, observed in the low-temperature
excitation spectrum of Cs$_2$CuBr$_4$ [Zvyagin $et~al.$, Phys. Rev. Lett. 112,
077206 (2014)], is present well above $T_N$. Noticeably, the transition into
the long-range magnetically ordered phase does not significantly affect the
size of the gap, suggesting that even below $T_N$ the high-energy spin dynamics
in Cs$_2$CuBr$_4$ is determined by short-range-order spin correlations. The
experimental data are compared with results of model spin-wave-theory
calculations for spin-1/2 triangle-lattice antiferromagnet.
