The transverse emittance growth rate of colliding hadron beams driven by external sources of noise is investigated based on existing analytical model as well as on macro-particle simulations and comparison to experimental data at the Large Hadron Collider (LHC). It is shown that an analytical description of the emittance growth rate neglecting the existence coherent beam-beam mode can nevertheless provide accurate estimate for operational conditions, featuring notably a high chromaticity. The model is used to investigate the level of noise experienced by the LHC beams. The results indicate that a significant reduction of the noise floor of the transverse feedback's beam position monitor is required for operation with a large beam-beam tune shift, as the one anticipated for the High Luminosity LHC (HL-LHC).