RG evolution and effect of intermediate new physics on $ΔB=2$ six-quark operators

TL;DR

This work studies the RG evolution of $\Delta B=2$ dimension-9 six-quark operators from the electroweak scale to $\mathcal{O}(10^3~\text{TeV})$, accounting for possible intermediate-scale new physics. It constructs the operator basis, computes the one-loop anomalous dimensions in the SM and in scenarios with extra $U(1)$ gauge factors and scalar doublets, and connects Wilson coefficients to hadronic matrix elements through Chiral Perturbation Theory to bound the NP scale $\Lambda$. The analysis shows that intermediate NP can significantly modify the running and alter the bounds on $\Lambda$ depending on the operator, with a publicly available Python RG tool for general NP setups. These results inform the interpretation of neutron-antineutron oscillation bounds and provide a practical framework for model-building in $\Delta B=2$ processes and future experimental planning.

Abstract

The recent identification of possible 11 neutron-antineutron ($n$-$\bar{n}$) oscillation candidate events at Super-Kamiokande has renewed the interest in $ΔB = 2$ transitions. In this work, we analyze the Renormalization Group (RG) running of mass dimension-9 six-quark operators, in $\bar{MS}$ scheme, that generate processes like $nn\to π^0π^0$, deuteron decay, $n$-$\bar{n}$ oscillations etc, evolving them from the electroweak scale to baryon number violating scale ($\mathcal{O}(10^3~\text{TeV})$). Our goal is to systematically account for the influence of potential new physics at intermediate energies ($\gtrsim \mathcal{O}(10~ \text{TeV})$), especially given the fact that {\it Large Hadron Collider} has not ruled out new physics beyond $\sim 10~\text{TeV}$. 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 $\mathcal{O}(10^3~\text{TeV})$, and (ii) an extended framework involving scalar and vector bosons above $\sim 10~\text{TeV}$ 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.

Figures (12)

• Figure 1: Intermediate scale new physics dimension-6 $(\overline{q}q)(\overline{q}q)$ effective field theory operators at entering the RG running of the dimension-9 baryon number violating operators.
• Figure 2: All possible 1-boson-exchange diagrams for $3q\rightarrow3\overline{q}$ processes.
• Figure 3: Running of Wilson coefficients of all nine operators as functions of the energy scale $\mu$ under various initial conditions and parameter configurations: Case 1(RGE with only SM) Case 2(RGE with $U(1)$ abelian gauge boson at every 10 TeV till 700 TeV) Case 3(RGE with doublet scalar boson at every 10 TeV till 700 TeV) Case 3(RGE with $U(1)$ abelian gauge boson and doublet scalar boson at every 10 TeV till 700 TeV).
• Figure 4: Correlation matrix $\rho$ for dimension-9 six-quark operators under SM at low scale.
• Figure 5: (a) Limits on the UV scale $\Lambda^{(n)}$ for each of the nine operators without (with) RGE effects in dark blue(Violet) with only the SM. (b) Correlation matrix for dimension-9 six-quark operators under Standard Model RG evolution at the high scale $\mu = 700$ TeV.