An EFT toolbox for baryon and lepton number violating dinucleon to dilepton decays

In this paper we systematically consider the baryon (B) and lepton (L) number violating dinucleon to dilepton decays (pp → ℓ+ℓ′+, pn → $$ {\mathrm{\ell}}^{+}\overline{\nu}^{\prime } $$ ℓ + ν ¯ ′ , nn → $$ \overline{\nu}\overline{\nu}^{\prime } $$ ν ¯ ν ¯ ′ ) with ∆B = ∆L = −2 in the framework of effective field theory. We start by constructing a basis of dimension-12 (dim-12) operators mediating such processes in the low energy effective field theory (LEFT) below the electroweak scale. Then we consider their standard model effective field theory (SMEFT) completions upwards and their chiral realizations in baryon chiral perturbation theory (BχPT) downwards. We work to the first nontrivial orders in each effective field theory, collect along the way the matching conditions, and express the decay rates in terms of the Wilson coefficients associated with the dim-12 operators in the SMEFT and the low energy constants pertinent to BχPT. We find the current experimental limits push the associated new physics scale larger than 1 − 3 TeV, which is still accessible to the future collider searches. Through weak isospin symmetry, we find the current experimental limits on the partial lifetime of transitions pp → ℓ+ℓ′+, pn → $$ {\mathrm{\ell}}^{+}\overline{\nu}^{\prime } $$ ℓ + ν ¯ ′ imply stronger limits on nn → $$ \overline{\nu}\overline{\nu}^{\prime } $$ ν ¯ ν ¯ ′ than their existing lower bounds, which are improved by 2−3 orders of magnitude. Furthermore, assuming charged mode transitions are also dominantly generated by the similar dim-12 SMEFT interactions, the experimental limits on pp → e+e+, e+μ+, μ+μ+ lead to stronger limits on pn → $$ {\mathrm{\ell}}_{\alpha}^{+}{\overline{\nu}}_{\beta } $$ ℓ α + ν ¯ β with α, β = e, μ than their existing bounds. Conversely, the same assumptions help us to set a lower bound on the lifetime of the experimentally unsearched mode pp → e+τ+ from that of pn → $$ {e}^{+}{\overline{\nu}}_{\tau } $$ e + ν ¯ τ , i.e., $$ {\Gamma}_{pp\to {e}^{+}{\tau}^{+}}^{-1}\gtrsim 2\times {10}^{34} $$ Γ pp → e + τ + − 1 ≳ 2 × 10 34 yr.