RG evolution and effect of intermediate new physics on ∆B = 2 six-quark operators

The recent observation of possible 11 neutron-antineutron (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \text- \overline{n }$$\end{document}) oscillation candidates with an expected background of 9.3 ± 2.7 events at Super-Kamiokande has renewed the interest in ∆B = 2 transitions. In this work, we analyze the Renormalization Group (RG) running of mass dimension-9 six-quark operators, in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{M }S$$\end{document} scheme, that generate processes like nn → π0π0, deuteron decay, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \text- \overline{n }$$\end{document} oscillations etc, evolving them from the electroweak scale to baryon number violation (BNV) scale (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{O}$$\end{document}(103 TeV)). Our goal is to systematically account for the influence of potential new physics at intermediate energies (≳ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{O}$$\end{document}(10 TeV)), especially given the fact that Large Hadron Collider has not ruled out new physics beyond ~ 10 TeV. To comprehensively investigate their influence, we consider two scenarios: (i) a minimal setup with only Standard Model degrees of freedom up to the high scale at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{O}$$\end{document}(103 TeV), and (ii) an extended framework involving scalar and vector bosons above ~ 10 TeV up till BNV scale. To facilitate further studies, we also provide a Python script that performs RG evolution of the BNV Wilson coefficients in the presence of generic bosonic new physics at any intermediate energy scale. It can be modified easily to meet the needs of the user to investigate the running of the BNV Wilson coefficients. We then compare the result with the experimental bound from the neutron-antineutron oscillation process and constrain the scale of baryon number violating new physics. The code and instructions can be downloaded from https://github.com/rp-winter/bnv-running.