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The antineutrino associated with the muon flavour of the weak charged current has zero electric charge and lepton number $-1$ in the usual production-and-detection description. A negative muon decays to an electron, an electron antineutrino and a muon neutrino; the charge-conjugate process instead produces the muon antineutrino.

Use the inverse beta decay threshold, with the charged-lepton mass generalized to $m_{\ell }$. For a stationary proton and a massless incident antineutrino, the Mandelstam invariant is $s=m_p^2+2m_p{E}_{\nu }$. At threshold the final particles have no relative momentum in their centre-of-momentum frame, so $s_{\mathrm{thr}}=(m_n+m_{\ell }{)}^2$. ThereforeUsing the supplied, rounded masses givesThe second term is the recoil correction; setting the threshold equal just to the final rest-mass excess would miss it.

Reactor electron antineutrinos have energies of a few million electronvolts. They can produce a Positron through inverse beta decay above the first threshold, but cannot produce a muon. Thus reactor neutrino oscillations are measured primarily as electron-antineutrino disappearance, through the event rate and energy spectrum relative to the unoscillated prediction. An oscillated muon antineutrino cannot be identified by the proposed muon-production channel at reactor energies; disappearance alone does not distinguish all possible final flavours.

Strike a target with high-energy protons, collect negative pions and kaons with magnetic horns, and let them decay in a long evacuated decay tunnel: ${\pi }^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }$ and $K^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }$. Absorb residual hadrons and range out muons in shielding. Focusing selects the negative parent sign and therefore enriches muon antineutrinos; other parent decays leave a finite contamination. Monitor the parent flux and use a near detector to constrain the unoscillated spectrum.

A massive segmented calorimeter supplies interaction probability and measures the hadronic shower. Alternate dense absorber plates with scintillation counters or tracking planes, and magnetize the iron or add a downstream magnetic muon detector. The signal is a positive muon plus a hadronic shower; the sign rejects much of the muon neutrino contamination. For a contained muon, its range gives energy; for a penetrating track, curvature gives $p_{\perp }[\mathrm{GeV}]=0.2998B[\mathrm{T}]R[\mathrm{m}]$. Multiple measurements and a field map determine the fitted momentum and sign. Summed calibrated shower response estimates the struck quark's visible hadronization energy, not the energy of a free observable quark. Correct for invisible nuclear losses, noncompensating response, leakage and acceptance. Neglecting target recoil corrections, $E_{\nu }\simeq E_{\mu }+E_{\mathrm{had}}$ and $y\simeq E_{\mathrm{had}}/E_{\nu }$.

The Fermilab primary proton beam strikes a target, producing secondary pions and kaons. Horn focusing selects positive parents; their decays ${\pi }^{+}\to {\mu }^{+}{\nu }_{\mu }$ and $K^{+}\to {\mu }^{+}{\nu }_{\mu }$ produce a predominantly muon neutrino beam. A decay tunnel permits decay before the remaining charged secondaries encounter an absorber. A near detector constrains the flux and interaction spectrum, while the distant MINOS detector measures its change.

The alternating scintillation counters and magnetized iron give a sampling calorimeter and a magnetic tracking volume. A charged current ${\nu }_{\mu }N\to {\mu }^{-}X$ event has a long negative muon track and a localized hadronic shower. Estimate $E_{\mu }$ by range if contained or magnetic curvature if exiting, and $E_X$ by the calibrated scintillator pulse-height sum. Reconstruct $E_{\nu }\simeq E_{\mu }+E_X$, with corrections for nuclear binding, invisible energy and detector response. The muon charge separates most wrong-sign muon antineutrino events; short showers without the track are primarily neutral current candidates. The source's $730\mathrm{km}$ baseline is used in the calculations below.

A fission reactor supplies predominantly electron antineutrinos, with typical energies of a few MeV. Even if they oscillate to muon antineutrinos, producing a real muon through a charged current requires roughly the muon rest energy, over $100$ MeV for a free nucleon target. For example,Thus a muon spectrometer cannot observe this appearance channel from a reactor. Measure electron antineutrino disappearance instead, most commonly through inverse beta decay, ${\bar{\nu }}_{e}p\to e^{+}n$, using the prompt Positron and delayed neutron signal.