Rare fluctuations of the S matrix at NLO in QCD

We calculate the rare fluctuations of the S matrix for high-energy dipole-dipole scattering on top of the full next-to-leading-order corrections in the center of mass frame. The relevant result in the saturation regime shows that the exponential factor of the S matrix is root 2., as large as the result which emerges when the rare fluctuation effects are taken into account. We find that the factor of root 2 change of the exponential factor is induced by the gluon loop corrections which compensate for part of the rapidity decrease of the S matrix made by quark loops and lead to the rare fluctuations becoming important again. To ensure the relevant results of the S matrix are independent of the frame choice, the rare fluctuations of the S matrix are also derived in a general frame. It is found that all the results are consistent with each other in both frames.