Constraining lepton flavor violating SMEFT $2q2\ell$ operators from low-energy cLFV processes

TL;DR

The paper develops and applies a SMEFT-based framework to constrain lepton-flavour-violating 2q2ℓ operators using low-energy observables. It performs a detailed match-and-run procedure to LEFT, uses Flavio for predictions, and implements several LFV decay modes not previously available in the package, enabling a comprehensive 1-D and 2-D operator-by-operator analysis. The results show that μ–e observables, particularly muon-to-electron conversion and kaon decays, yield the strongest bounds on many operators, while τ–ℓ channels are comparatively less constrained but provide valuable complementary information; CKM rotations and RGE running induce significant interdependencies among operators. The study quantifies the NP scales that can be probed by different 2q2ℓ structures, highlights flat directions arising from operator interferences, and offers a practical framework for interpreting future experimental improvements in LFV searches. Overall, this work advances precision constraints on SMEFT LFV operators and informs both model-building and experimental prioritization in the search for new physics.

Abstract

Charged lepton flavour-violating (cLFV) processes, which are definite proof of new physics beyond the Standard Model, have remained elusive experimentally till now. Effective Field Theory (EFT) has been very useful in providing information about such new physics through the higher-dimensional operators. These operators respect SM gauge invariance, and they are suppressed by appropriate powers of the energy scale $Λ$. In regard to lepton flavour violating (LFV) processes, the Standard Model Effective Field Theory (SMEFT) is shown to be a useful tool for estimating any new physics effect at the scale $Λ$. It is worth noticing that a large class of cLFV processes involve both quarks and leptons and thus low-energy observables play a significant role in providing bounds on lepton-flavour-violating 2-quark-2-lepton ($2q2\ell$) operators. Therefore, in this work, we have collected several low-energy cLFV processes that can be addressed within the SMEFT framework and also collected the set of operators responsible for such processes. Keeping in mind the correlation that exists among the SMEFT operators, we want to extract the strongest constraints on these $2q2\ell$ operators.

Figures (18)

• Figure 1: Effective vertex for a LFV semi-leptonic decay of a pseudoscalar meson $\mathcal{P}$ to a pseudoscalar $\mathcal{P}^{\prime}$ or a vector meson $\mathcal{V}$. The (anti-)quark $q_i$ converts into another (anti-)quark $q_j$ and two different flavors of leptons $\ell_\alpha,\ell_\beta$. The other (anti-)quark $q_s$ represents the spectator (anti-)quark.
• Figure 2: Effective vertex of pseudoscalar/vector meson (or quarkonium) $(\mathcal{P}/\mathcal{V})$ LFV decay to a pair of leptons via $(2q2\ell)$ operators.
• Figure 3: Feynman diagram of LFV hadronic $\tau$ decays. The blob indicates the charged LFV vertex.
• Figure 4: Effective vertex of muon to electron conversion at a nucleus ($N$). $q\in\{u,d\}$ represents quarks with $q_{\rm int}$ and $q_{\rm sp}$, meaning interacting and spectator quarks respectively. Apart from the interaction with the valence quarks as shown, a muon can also interact with the sea quarks, resulting in scalar contributions from $s$-quarks as well Kuno:1999jp.
• Figure 5: Upper bounds on the $2q2\ell$ Wilson coefficient ($\mathcal{C}_{\rm max}$) involving first- and second-generation charged leptons ($e^\pm$, $\mu^\pm$), considering one at a time at scale $\Lambda=1$ TeV. Each box shows the constraint from a specific observable, colour-coded accordingly. The numerical value of the limit is given as $\mathcal{C}_{\rm max} = 10^{x}$, where $x$ is the value displayed in the box. The blank spaces indicate that the observable does not constrain the corresponding WC.