Uncharted Logarithmic Structures in QCD Transverse-Energy Flow

We investigate the QCD transverse-energy ($E_T$) flow distribution within an azimuthal region of phase space, defined by an angular interval $\Delta \phi$ on the plane transverse to a chosen jet axis. Vetoes on the resulting $E_T$ are widely employed at the LHC to isolate missing transverse momentum in final states with invisible particles. We show that this observable has logarithmic structures never seen before in QCD calculations. Notably, its description involves the resummation of non-global and coherence-violating logarithmic contributions that are more singular than any reported to date. We analyze its all-orders behavior, providing analytical resummations at next-to-double-logarithmic accuracy for $e^+e^-$ and $pp$ collisions, and numerical resummations at leading-logarithmic accuracy in the Veneziano limit for $pp$ collisions. We further present a computation of the leading coherence-violating correction for $pp$ collisions. The intricate structure of vetoes in azimuthal gaps reveals new aspects of QCD dynamics and offers a novel probe of collinear-factorization breaking at the LHC.