NCN grant Opus 2018-2023, 2017/25/B/ST2/01987, “The Z-boson resonance at three loops and New Physics effects” – results and output data.
In this project, we have undertaken studies to understand better the theory known as the Standard Model (SM) of elementary particles and its possible generalizations. The project resulted in the publishing of ten articles in peer-reviewed, prestigious journals (PRD, JHEP, PLB), seven post-conference publications, and many talks at conferences, seminars, and lectures in Poland and abroad. Part of the project’s outcome is two master’s theses and one PhD thesis. Finally, a textbook on methods for calculating multidimensional Feynman integrals by the Mellin-Barnes method was published by Springer \colbref{https://inspirehep.net/literature/2593456}.
The grant led by prof. Janusz Gluza from the University of Silesia in Katowice was implemented with prof. Ayres Freitas (U. Pittsburgh, USA), Dr. Tord Riemann (DESY, Germany), Dr. Johann Usovitsch (CERN, Switzerland), Dr. Martijn Hidding (U. Uppsala, Sweden), Dr. Ievgen Usovitsch (University of Silesia, Katowice).
The remarkable precision of LEP at CERN and other lepton colliders has historically been instrumental in testing and understanding the Standard Model of fundamental interactions.
Future accelerators such as FCC-ee, also planned at CERN, will allow $e^+e^-$ collisions to produce, among other things, $10^{12}$ Z bosons in clean and precise experimental conditions, which in turn will give the ability to study the production of new elusive particles that can interact extremely weakly with the $Z$ boson (e.g. extra massive neutrinos), or discover the existence of new heavy particles through their indirect effects (a.k.a `loops’) on ultra-precise measurements. The planned experimental precision of future accelerators exceeds the current accuracy of theoretical calculations, hence in the project, we calculated, inter alia, quantum two- and three-loop effects in the production and decay of Z particles, where virtual particles involved in the process “draw”\; two or three loops in space. Mathematically, this situation corresponds to the calculation of the corresponding multidimensional integrals.
Within a few years, partly thanks to the grant from the National Science Centre, it was possible to develop the numerical calculation of such integrals with very high accuracy (now we can calculate these integrals numerically with the precision of many significant digits, \colbref{https://doi.org/10.1103/ PhysRevD.106.L111301}).
The results were obtained thanks to the team’s development of advanced methods for calculating these integrals (Mellin-Barnes representation method, sectors decomposition, differential equations). The three-loop calculations, together with the methods used and the developed software, will undoubtedly enter the canon of theoretical studies and will become one of the milestones confirming from the point of view of the theory the legitimacy of building the future precision frontier accelerator, whose construction cost is estimated at several billion euros.
Concerning precise calculations related to non-standard physics, it is our achievement to show that by using the PMNS neutrino matrix analysis based on the concepts of singular values and unitary dilation, a formalism developed by Katowice grant’s team, new restrictions on the mixing of active neutrinos with an additional massive neutrino state was obtained (publication \colbref{https://doi.org/10.1007/JHEP03(2020)169}).
Publications:
Physics Letters B, 2018 and 2019 https://doi.org/10.1016/j.physletb.2018.06.037, https://doi.org/10.1016/j.physletb.2019.02.044
Journal of High Energy Physics 2019 and 2*2020 https://link.springer.com/content/pdf/10.1007/JHEP08(2019)113.pdf, https://link.springer.com/content/pdf/10.1007/JHEP01(2020)024.pdf, https://link.springer.com/article/10.1007/JHEP03(2020)169
Chinese Physics C, 2021 https://iopscience.iop.org/article/10.1088/1674-1137/abcd2f
Symmetry 2021 https://doi.org/10.3390/sym13060975
Physical Review D Letters 2022, https://journals.aps.org/prd/abstract/10.1103/PhysRevD.106.L111301
arxiv, 2022, 2023 https://arxiv.org/pdf/2206.14790, https://arxiv.org/pdf/2301.07168
Book: “Mellin-Barnes Integrals: A Primer on Particle Physics Applications”, Lecture Notes
in Physics, Springer, https://arxiv.org/pdf/2211.13733 and https://link.springer.com/book/10.1007/978-3-031-14272-7
Results: