Search Method
6.4 Hypothtsis atjtrtion
7.1.1 An e btansalont Analysis
In the A standalone analysis, the test statistic is ited for each parametrization of the background of the unblinded data, the distribution is shown in igureα7.1. hen, the average of these test statistics is used as the unblinded test statistic,⟨�ANTdata⟩ = �.65. he number of ited tracks and showers are obtained in the same way,⟨ Tr⟩ = � · ��−3≈ �and⟨ Sh⟩ = �.9.
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Figurt 7.2– Log-liktlihoos ratio rurvts as a uunrtion ou tht normalization ou tht lux uor siu-utrtnt bakgrouns paramttrizations. he curve corresponding to the ited systematic efects is represented by triangles.
Figurt 7.3–btnsitivitits ou tht rombints analysisfor each sample, each experiment, and the total.
cablt 7.1–btnsitivity, txptrtts lux ans rtsultsof the combined, A aloneα[102] and I C aloneα[97] analyses on the KRA model with the 5 and 50 PeV cutofs. he A alone sensitivity is deined as the average upper limit, the I C and combined ones are deined as the median upper limit. For the A standalone analysis the expected luxes are given in a number of tracks ⁸Tr⁹ and showers ⁸Sh⁹.
Energycutof Analysis Sensitivity Expected lux Fited lux[ΦKRA ] -value Upper limit[ΦKRA ] 5 PeV A 140 ⁵ 9.3αTr, 2.3αSh 0 ⁵ Tr, 83 ⁵ Sh 67 ⁵ 110 ⁵
Combined 81 ⁵ ΦKRA 5 47 ⁵ 29 ⁵ 119 ⁵
50 PeV A 105 ⁵ 11αTr, 2.8αSh 0 ⁵ Tr, 93 ⁵ Sh 54 ⁵ 120 ⁵
I C 79 ⁵ 213αTracks 46 ⁵ 29 ⁵ 120 ⁵
Combined 57 ⁵ ΦKRA 50 37 ⁵ 26 ⁵ 90 ⁵
luxα[100]. In any case, as shown in the following section, only upper limits are put here so this is not an issue.
7.3 atsults
he sensitivities and results obtained for both analyses as well as the I C standalone analy-sisα[97] are summarized in Tableα7.1. Systematic uncertainties on the acceptance of the A
optical modules are included in the analysis as explained in sectionα6.2. For what concerns I -C , systematic efects lead to an uncertainty on the luxes of 11 ⁵ as described inα[101], it is not included here.
Some signal is ited in the shower channel of the A standalone analysis but not in the track channel. his could be an under-luctuation in the track channel coupled to the bias that you can see in igureα6.15bwhen the signal is weak ⁸�.�5 × ΦKRA 5⁹. As said earlier, this bias being present in the pseudo-experiments, it is taken into account in the upper limit.
Although the ited number of shower is close to the expected lux, the -value is still very background-like as most of the sensitivity comes from tracks. Nevertheless, the lower propor-tion of showers ited for the KRA model improves the upper limit in comparison with the KRA ⁰ model, leading to�.� × ΦKRA 5.
he I C standalone analysis did not test the KRA model. heir sensitivity on the other model, KRA ⁰, is beter than the A one but the limit is the same. his can be explained by the high number of events they ited. Indeed, Tableα7.1shows that I C analysis has a p-value nearly twice lower than A .
he combination leads to much beter sensitivities. he upper limit is under the lux nor-malization for the KRA ⁰ model which is rejected with a 92 ⁵ conidence level. As explained in chapterα4, the 50 PeV cutof represents an extreme tuning of the acceleration parameters for the Galactic cosmic rays, so the rejection of this version of the model might not be surprising.
On the other hand, the KRA model is not rejected and the combined upper limit obtained is
actually worse than the A alone upper limit. his is partly due to the over-luctuation in I C data, but also because of the diference in the deinition of the test statistic explained in sectionα6.1.2. Indeed, the upper limit worsens1when changing only the combined test statistic
�Combto�ANTin the implementation of the analysis for the A samples. his is because
�Combuses the information of the shape of each curve and not only the maximum as does�ANT. In the speciic case of a null lux ited in one of the two samples ⁸tracks here⁹, it can give distinct results depending on the slope of the curve of the null-lux sample. If the A tracks curve of the igureα6.5was decreasing faster,�Combwould be lower while it would not inluence�ANT if the maximum of the A track sample was zero ⁸which is the case for the nine years sampleα[102]⁹.
he upper limits are presented in igureα11.2in comparison with the model predictions. he previous A upper limit on the KRA model is also shown as well as the I C up-per limit on KRA ⁰. he boxes represent the isotropic difuse astrophysical neutrino luxes measured by I C with starting eventsα[35] and upward-going tracksα[32]. he I C data combining diferent samples from the whole sky are shown simultaneously with the cor-responding it and the it of the eight year muon sample from the Northern sky.
Considering that KRA ⁰ is excluded, the KRA model gives a more intense difuse Galactic neutrino lux than all other available models. In particular, the lux in the central ridge where a hardening of the cosmic rays is reproduced is the most intense. As a consequence, the limits presented here further constrain the possible contribution of the Galactic difuse emission to the I C spectral anomalyα[32] ⁸see sectionα1.6⁹. In the six-year HESE sample2, 47.0αevents are expected to be of cosmic origin above 60 TeVα[103]. he combined analysis implies that a maximum of 4.5 events originate from difuse Galactic cosmic ray interactions. It corresponds to 9.6 ⁵ of the total HESE lux. his limit is more restrictive than the one previously derived byα[27,91].
With the rejection of the KRA ⁰ version of the model, its constraints are extended in an energy range from tens of GeV with theFermi-LAT data up to hundreds of TeV. his is the irst combined constraint on difuse Galactic neutrino emission by I C and A . While it is challenging to infer the energy break between Galactic and Extragalactic cosmic ray spectra with the gamma-ray observations, crucial informations can be expected with the incoming neutrino analyses including the I C shower events or, on a longer time-scale, with KM3NeT.
1But the sensitivity does not change signiicantly.
2HESE stands for High-Energy Starting Events, this sample corresponds to high-energy events whose interac-tion vertex is contained inside of the detector in order to reject at most the background. his sample is sensitive to the whole sky.