Muon Survival and Flux Workbench

01The actual count model

A device prediction must be calculated by bin:

$N_i=T\int dE\,d\Omega\,dh\;\Phi_0(E,\Omega,h)\,P(E,\Omega,h)\,A_{\rm eff}(E,\Omega,h)\,R_i(E,\Omega,h)+B_i.$

Here $\Phi_0$ is production, $A_{\rm eff}$ includes geometry and efficiency, $R_i$ reconstruction migration and $B_i$ background. With energy loss, the comparison survival law uses transported $\beta(s),\gamma(s)$: $P_{\rm SR}=\exp[-\int ds/(\beta\gamma c\tau_\mu)]$. ASD must independently derive its decay law; a path factor cannot simply be inserted into the exponential.

02Existing LVE content and the gap

The example gives $L/L'=\gamma(1+\beta)$. Whether $L'$ denotes a single event, a mean or a lifetime-related path remains to be fixed. Without aligned statistics, it is premature to claim a different survival prediction. The original matrix's TENSION status is retained.

03Data selection and errors

The PDG 2024 cosmic-ray review supplies measurement and transport references; it is not a curated event input for this apparatus. Prefer tables with defined momentum/angle, exposure, efficiency and systematics. Ground spectra cannot directly substitute for undecayed production spectra. Reproduce the comparison model before adding ASD.

The workbench uses reference inputs $m_\mu c^2=0.1056583755\,\mathrm{GeV}$ and $\tau_\mu=2.1969811\,\mu\mathrm s$, not ASD outputs. Its constant-energy, single-height curve is an algebraic baseline. The kit also provides a binned acceptance-folding example, explicitly using synthetic inputs.

04Discrimination and the next deliverable

Release bin residuals and a shared likelihood; propagate production, atmosphere, energy-loss and acceptance uncertainties. Freely normalizing every bin can destroy identifiability. The next deliverable is a statistical definition of L′, an ASD hazard law and one traceable dataset; see OP-LVE-01 · Chinese original.

Reference constants: PDG 2024 muon.