Recently, a new family of observables consisting of azimuthal-angle generalized ratios was proposed in a kinematical setup that resembles the usual Mueller-Navelet jets but with an additional tagged jet in the central region of rapidity. Nontagged minijet activity between the three jets can affect significantly the azimuthal angle orientation of the jets and is accounted for by the introduction of two Balitsky-Fadin-Kuraev- Lipatov (BFKL) gluon Green functions. Here, we calculate the, presumably, most relevant higher order corrections to the observables by now convoluting the three leading order jet vertices with two gluon Green functions at next-to-leading logarithmic approximation. The corrections appear to be mostly moderate, giving us confidence that the recently proposed observables are actually an excellent way to probe the BFKL dynamics at the LHC. Furthermore, we allow for the jets to take values in different rapidity bins in various configurations such that a comparison between our predictions and the experimental data is a straightforward task.
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