Abstract
We calculate the rare fluctuations of the $S$-matrix 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 $\sqrt{2}$ as large as the result which emerges when the rare fluctuation effects are taken into account. We find that the factor of $\sqrt{2}$ change of the exponential factor is induced by the gluon loop corrections which compensate part of 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.
Highlights
In high-energy QCD, one of the most challenging problem has been to study theoretically and experimentally the parton saturation
In the fixed coupling case, the S matrix obtained from the BK equation shows a quadratic rapidity dependence in its exponent, and it was found that the exponential factor of the S matrix (∼ exp 1⁄2−c1α 2sðY − Y0Þ2=2) is twice as large as the one which takes into account the rare fluctuation effects [20], where αs is the coupling constant, and c1 is a constant which is not important in this paper
To reveal which one is the dominant effect, we studied the rare fluctuations on top of the running coupling effect in Ref. [11]
Summary
In high-energy QCD, one of the most challenging problem has been to study theoretically and experimentally the parton saturation. In the fixed coupling case, the S matrix obtained from the BK equation shows a quadratic rapidity dependence in its exponent, and it was found that the exponential factor of the S matrix (∼ exp 1⁄2−c1α 2sðY − Y0Þ2=2) is twice as large as the one which takes into account the rare fluctuation effects [20], where αs is the coupling constant, and c1 is a constant which is not important in this paper This result shows that the rare fluctuations reduce the evolution speed of the dipole scattering amplitude with respect to rapidity. The result shows that the influence of the rare fluctuations in the NLO BK case on the S matrix are greater than that in the running coupling BK case, which indicates that the rare fluctuations are important in the NLO BK case, it is not as significant as the LO BK case
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
