DRalgo: A package for effective field theory approach for thermal phase transitions

DRalgo is an algorithmic implementation that constructs an effective, dimensionally reduced, high-temperature field theory for generic models. The corresponding Mathematica package automatically performs the matching to next-to-leading order. This includes two-loop thermal corrections to scalar and Debye masses as well as one-loop thermal corrections to couplings. DRalgo also allows for integrating out additional heavy scalars. Along the way, the package provides leading-order beta functions for general gauge-charges and fermion-families; both in the fundamental and in the effective theory. Finally, the package computes the finite-temperature effective potential within the effective theory. The article explains the theory of the underlying algorithm while introducing the software on a pedagogical level. Program summary: Program title: Dimensional Reduction algorithm (DRalgo) 1.0 CPC Library link to program files: https://doi.org/10.17632/k66j9vmh9r.1 Developer's repository link: https://github.com/DR-algo/DRalgo Licensing provisions: GNU General Public License 3 Programming language: Mathematica External routines/libraries: GroupMath [1] Nature of problem: Construction of high-temperature effective field theories for beyond the Standard Model physics. Solution method: Matching of n-point correlation functions using tensor-notation of couplings [2–6] Additional comments including restrictions and unusual features: Mathematica version 12 or above. References: [1] R. M. Fonseca, Comput. Phys. Commun. 267 (2021) 108085, arXiv:2011.01764. [2] S. P. Martin, Phys. Rev. D 96 (2017) 096005, arXiv:1709.02397. [3] S. P. Martin and H. H. Patel, Phys. Rev. D 98 (2018) 076008, arXiv:1808.07615. [4] M. E. Machacek and M. T. Vaughn, Nucl. Phys. B 249 (1985) 70. [5] M. E. Machacek and M. T. Vaughn, Nucl. Phys. B 236 (1984) 221. [6] M. E. Machacek and M. T. Vaughn, Nucl. Phys. B 222 (1983) 83.