ratio $\rm BR=1$ is used for each of the channels in Expression \[benchch\]. Beyond-the-SM particle physics with $\rm BR<1$ can be accommodated by scaling the fluxes in Equation \[nuoscs\] linearly with the appropriate branching ratio.

[./MC\_QFit\_Q\_New.eps]{} (15,60) [$\displaystyle QFit$]{}

[./MC\_LambdaFit\_Lambda\_New.eps]{} (85,60) [$\displaystyle\Lambda Fit$]{}

[./MC\_QFit\_costh\_New.eps]{} (15,60) [$\displaystyle QFit$]{}

[./MC\_LambdaFit\_costh\_New.eps]{} (85,60) [$\displaystyle\Lambda Fit$]{}

The main backgrounds for this analysis are atmospheric muons and neutrinos, both produced in the interactions of cosmic rays with the Earth’s atmosphere. Downgoing atmospheric muons dominate the trigger rate, which ranges from $3$ to $10$ Hz depending on the trigger conditions. They are simulated using MUPAGE [@mupage]. Upgoing atmospheric neutrinos, which are recorded at a rate of $\sim$50 $\mu$Hz (about four per day), are simulated according to the parameterisation of the atmospheric $\rm \nu_{\mu}$ flux from Ref. [@bartol] in the energy range from 10 GeV to 10 PeV using GENHEN [@genhen]. Furthermore, the propagation of muon tracks is simulated with the KM3 package [@genhen]. The Cherenkov light produced in the vicinity of the detector is propagated taking into account light absorption and scattering in sea water [@transmission]. The characteristics of the PMTs are taken from Ref. [@OM] and the overall geometry corresponds to the different layouts of the 