Agradecimentos: The authors acknowledge the computing time provided by the Laboratory for Advanced Computing at the University of Coimbra (FCT contracts 2021.09759.CPCA and 2022.15892.CPCA.A2). Work supported by FCT contracts CERN/FIS-PAR/0023/2021, UIDB/04564/2020, and UIDP/04564/2020. P. J. S. acknowledges financial support from FCT under Contract No. CEECIND/00488/2017. A. C. A is supported by the CNPq grant 310763/2023-1, and acknowledges financial support from project 464898/2014-5 (INCT-FNA). M. N. F. and J. P. are supported by the Spanish MICINN grant PID2020-113334GB-I00. M. N. F. acknowledges financial support from Generalitat Valenciana through contract CIAPOS/2021/74. J. P. also acknowledges funding from the Generalitat Valenciana grant CIPROM/2022/66. This work was granted access to the HPC resources of the PDC Center for High Performance Computing at the KTH Royal Institute of Technology, Sweden, made available within the Distributed European Computing Initiative by the PRACE-2IP, receiving funding from the European Community's Seventh Framework Programme (FP7/ 2007-2013) under grant agreement No. RI-283493. The use of Lindgren has been provided under DECI-9 project COIMBRALATT. We acknowledge that the results of this research have been achieved using the PRACE-3IP project (FP7 RI- 312763) resource Sisu based in Finland at CSC. The use of Sisu has been provided under DECI-12 project COIMBRALATT2 Ver menos

Abstract: The Batalin-Vilkovisky function is a central component in the modern formulation of the background field method and the physical applications derived from it. In the present work we report on novel lattice results for this particular quantity, obtained by capitalizing on its equality with the Kugo-Ojima function in the Landau gauge. The results of the lattice simulation are in very good agreement with the predictions derived from a continuum analysis based on the corresponding Schwinger-Dyson equations. In addition, we show that an important relation connecting this function with the ghost propagator is fulfilled rather accurately. With the aid of these results, we carry out the first completely lattice-based determination of the process-independent strong running interaction, employed in a variety of phenomenological studies Ver menos