Generalized uncertainty principle and elliptic flow in relativistic heavy-ion collisions

Elliptic flow is a central manifestation of collective behavior in relativistic heavy-ion collisions and is typically understood through relativistic hydrodynamics. At the same time, generalized uncertainty principles (GUPs) motivated by quantum gravity modify canonical commutators, dispersion relations and phase-space measures. We investigate how a rotationally invariant, minimal-length GUP influences the extraction and interpretation of elliptic flow. Using the GUP-deformed Cooper–Frye prescription derived from the Ali–Das–Vagenas framework, we analyze the azimuthal structure of the freeze-out spectrum and show that, to leading order in the deformation parameter and for fixed hydrodynamic freeze-out fields, all harmonic flow coefficients remain exactly unchanged. The GUP correction factor is azimuthally isotropic and cancels identically in the definition of the flow harmonics, including elliptic flow. Although the freeze-out definition is thus protected against isotropic GUP effects, indirect modifications can still arise through the hydrodynamic evolution. Combining a GUP-corrected equation of state for a massless gas with a simple eccentricity-driven response model, we estimate a modest suppression of elliptic flow driven by the reduced speed of sound. These results indicate that any observable GUP imprint on anisotropic flow must originate from altered QCD medium dynamics rather than from kinematic modifications of the momentum distribution at freeze-out.