First bounds on effective muon interactions using the NA64$μ$ experiment at CERN

TL;DR

This work reframes NA64$\mu$ data within the Standard Model Effective Field Theory (SMEFT) and its extension with light SM-singlet fermions (νSMEFT) to bound dimension-6 muon-related four-fermion operators. Using a Weizsäcker–Williams factorization and missing-energy signatures, the authors derive 90% CL bounds on SMEFT combinations $|[c_{LL}]_{\mu\mu\alpha\alpha}/v^2|^2$ and $|[c_{L\ell}]_{\\alpha\alpha\mu\mu}/v^2|^2$, as well as νSMEFT coefficients $|C_{LN}^{\mu}|/\Lambda^2$, with current data and projected upgrades up to $N_{\rm MOT}\sim 10^{14}$. They identify that NA64$\mu$ can access previously unbounded operators such as $[\mathcal{O}_{LL}]_{\mu\mu\tau\tau}$ and $[\mathcal{O}_{L\ell}]_{\tau\tau\mu\mu}$ and can help break flat directions in muon-only operator spaces, achieving NP scales $\Lambda$ of order tens to a few hundred GeV. The results thus bridge low-energy indirect searches with the physics reach of future muon colliders and demonstrate the complementary role of NA64$\mu$ in exploring muon-specific New Physics and light sterile states.

Abstract

We analyze how NA64$μ$ can contribute to the global SMEFT program demonstrating that it can probe two effective four lepton operators completely unbounded so far and break one of the current flat directions. Furthermore, we also study an extension of SMEFT that includes fermion singlets of the SM gauge group in the low energy field content. This effective field theory, usually dubbed $ν$SMEFT, is well motivated by the observation of light neutrino masses and leptonic mixing. We find that NA64$μ$ can constrain three unbounded four fermion operators of the $ν$SMEFT. We derive the current leading bounds on these operators and compute the future sensitivity. Our results fill the gap between the current experimental program and a possible future muon collider able to probe this type of New Physics.

Figures (6)

• Figure 1: Feynman diagrams for the two to four neutrino and HNL production processes at NA64$\mu$ mediated by the indicated effective operators of the SMEFT and $\nu$SMEFT (see Table \ref{['tab:operators']}). For simplicity we omit the analogous diagrams in which the photon is interchanged with the nucleus "before" the HNL and/or neutrino emission.
• Figure 2: Schematic illustration of the NA64$\mu$ set-up in pre-LS3 runs. The spectrometer in the upstream region (MS1) is used for identifying incoming muons with momentum $p_\text{in}\simeq160$ GeV. The downstream part composed of calorimeters and a second spectrometer (MS2) measures the momentum of the scattered muons in the ECAL serving as an active target to search for the production of new light feebly interacting particles.
• Figure 3: Feynman diagrams contributing to neutral fermion production in the EFT at NA64$\mu$ using the WW approximation. We denote $\chi_1$ and $\chi_2$ as generic neutral fermions (in our case SM neutrinos or HNLs depending on the effective operator mediating the process).
• Figure 4: Geometrical acceptance on the signal efficiency as a function of $k^2$. The magenta solid line is the acceptance for published data extracted from NA64:2024nwj. The yellow dashed line and the purple dotted line indicate the expected curve for the ongoing analysis, and the future expected acceptance respectively.
• Figure 5: 90% CL NA64$\mu$ sensitivity to the WC of the SMEFT operators given in Eq. (\ref{['eq:Osmeft']}) for the three data sets introduced in Sec. \ref{['sec:na64']}.