The recent observation of the blazar TXS 0506+056 suggests the presence of a hard power-law component in the extraterrestrial TeV-PeV neutrino flux, in agreement with the IceCube analysis on the 8-year through-going muon neutrinos from the Northern Sky. This is slightly in tension with the soft power-law neutrino flux deduced by the IceCube 6-year High Energy Starting Events data. A possible solution to such a puzzle is assuming a two-component neutrino flux. In this paper, we focus on the case where, in addition to an astrophysical power-law, the second component is a pure neutrino line produced by decaying Dark Matter particles. We investigate how to realize a neutrinophilic decaying Dark Matter in an extension of the Standard Model. The main features of the model are: i) the requirement of a new symmetry like a global $U(1)$ charge; ii) the Dirac nature of active neutrinos; iii) a low-reheating temperature of the Universe of about 1 TeV. We perform a likelihood statistical analysis to fit the IceCube data according to the present Fermi-LAT gamma-rays constraints.
The non-observation of neutrinos by the IceCube at the Glashow resonance energy of 6.3 PeV has been a long standing unresolved issue. In this paper we propose a t-channel neutrino absorption by the C$ν$B, which causes a cutoff at 4.5 PeV neutrino energy, to explain the IceCube observations. We present a neutrinophilic 2HDM where the neutrino masses are generated by a low scale seesaw mechanism. A $\mathcal{O}$(10) MeV scalar mediates the interactions between left and right handed neutrinos and generates the t-channel diagram used for explaining the absence of Glashow resonance. The same scalar…
Extensions of the Standard Model with charged Higgs, having a non-negligible coupling with neutrinos, can have interesting implications vis-à-vis neutrino experiments. Such models can leave their footprints in the ultra-high energy neutrino detectors like IceCube in the form of neutrino non-standard interactions (NSIs) which can also be probed in lower energy neutrino experiments. We consider a model based on the neutrinophilic two-Higgs doublets and study its imprints in the recently reported excess neutrino events in the PeV energy bins at the IceCube. An additional signature of the model is…
The mass of primordial dark matter (DM) protohalos remains unknown. However, the missing satellites problem may be an indication that they are quite large. In this paper, we use effective field theory to map constraints on dark matter-SM interactions into limits on the mass of DM protohalos. Given that leptons remain in the thermal bath until late times, we focus on their interactions with DM. To illustrate the method, we use the null results of LEP missing energy searches along with Fermi-LAT searches for DM annihilation in nearby dwarf galaxies, to derive limits on the protohalo mass, $\less…
Two of the key unresolved issues facing Standard Model physics are (i) the appearance of a small but non-zero neutrino mass, and, (ii) the missing mass problem in the Universe. The focus of this paper is a previously proposed low energy effective theory that couples a dark scalar to Standard Model neutrinos. This provides a stable dark matter candidate as well as radiatively generating a neutrino mass. Within this framework we will then construct an entirely new bound from the IceCube-170922A event which takes into account (i) the possible neutrino mass hierarchies, (ii) the effect of cosmolog…
We study a supersymmetric neutrinophilic Higgs model with large neutrino Yukawa couplings where neutrinos are Dirac particles and the lightest right-handed (RH) sneutrino is the lightest supersymmetric particle (LSP) as a dark matter candidate. Neutrinophilic Higgs bosons need to be rather heavy by the precise determination of the muon decay width and dark radiation constraints for large Yukawa couplings. From the Large Hadron Collider constraints, neutrinophilic Higgsino mass need to be heavier than several hundred GeV or close to the RH sneutrino LSP mass. The latter case is interesting beca…
It has been suggested that the baseline scenario of collisionless cold dark matter over-predicts the numbers of satellite galaxies, as well as the dark matter (DM) densities in galactic centers. This apparent lack of structure at small scales can be accounted for if one postulates neutrino-DM and DM-DM interactions mediated by light O(MeV) force carriers. In this letter, we consider a simple, consistent model of neutrinophilic DM with these features where DM and a "secluded" SM-singlet neutrino species are charged under a new $U(1)$ gauge symmetry. An important ingredient of this model is that…
We discuss how to constrain new physics in the neutrino sector using multimessenger astronomical observations by the IceCube experiment. The information from time and direction coincidence with an identifiable source is used to improve experimental limits by constraining the mean free path of neutrinos from these sources. Over the coming years, IceCube is expected to detect neutrinos from a variety of neutrino-producing sources, and has already identified the Blazar TXS 0506+056 as a neutrino-producing source. We explore specific phenomenological models: additional neutrino interactions, neutr…
We test the hypothesis of non-radiative neutrinos decay using the latest IceCube data. Namely, we calculate the track-to-shower ratio expected in IceCube for the normal and inverted neutrino mass hierarchy taking into account the uncertainties in neutrino oscillation parameters. We show that the subset of data with energy above 60 TeV actually excludes the possibility of a neutrinos decay at the 1 sigma level of significance for both neutrino mass hierarchies.
IceCube has detected many TeV--PeV neutrinos, but their astrophysical origins remain largely unknown. Motivated by the observed late-time X-ray/optical bumps in some gamma-ray bursts (GRBs), we examine the correlation between IceCube neutrinos and GRBs allowing delayed neutrinos $\sim$days after the prompt gamma rays. Although we have not found any definitive correlation, up to $\sim$10\% of the events observed so far at IceCube may have been neutrinos produced by the late-time GRB activities at $\sim$1 day. Assuming a connection between some IceCube events and the late GRB bumps, we show in a…
Recent IceCube search results for sterile neutrino increased tension between the combined appearance and disappearance experiments. On the other hand, MiniBooNE latest data confirms at $4.9σ$ CL the short-baseline oscillation anomaly. We analyze published IceCube data based on two different active-sterile mixing schemes using one additional sterile neutrino flavor. We present exclusion regions in the parameter ranges $0.01 \le \sin^2 θ_{24} \le 0.1$ and $0.1~{\rm eV}^2 \le Δm^2_{42} \le 10~{\rm eV}^2$ for the mass-mixing and flavor-mixing schemes. Under the more conservative mass-mixing scheme…
We present an interpretation of searches for Dark Matter in a simplified model approach. Considering Majorana fermion Dark Matter and a neutral vector mediator with axial-vector interactions we explore mono-jet searches at the LHC and searches for neutrinos from Dark Matter annihilation in the Sun at IceCube and place new limits on model parameter space. Further, we compare the simplified model with its effective field theory approximation and discuss the validity of the latter one.
A signal of high-energy extraterrestrial neutrinos from unknown source(s) was recently discovered by the IceCube experiment. Neutrinos are always produced together with gamma-rays, but the gamma-ray flux from extragalactic sources is suppressed due to attenuation in the intergalactic medium. We report the discovery of a gamma-ray excess at high Galactic latitudes starting at energies 300 GeV in the data of the Fermi telescope. We show that the multi-TeV gamma-ray diffuse emission has spectral characteristics at both low and high Galactic latitudes compatible with those of the IceCube high neut…
We compute the gamma-ray and neutrino diffuse emission of the Galaxy on the basis of a recently proposed phenomenological model characterized by radially dependent cosmic-ray (CR) transport properties. We show how this model, designed to reproduce both Fermi-LAT gamma-ray data and local CR observables, naturally reproduces the anomalous TeV diffuse emission observed by Milagro in the inner Galactic plane. Above 100 TeV our picture predicts a neutrino flux that is about five (two) times larger than the neutrino flux computed with conventional models in the Galactic Center region (full-sky). Exp…
Cosmic ray accelerators like supernova and hypernova remnants in star forming galaxies are one of the most plausible sources of the IceCube observed diffuse astrophysical neutrinos. The neutrino producing hadronic processes will also produce a diffuse gamma ray flux, constrained by the Fermi-LAT bounds. The fact that point sources like blazars also contribute to the diffuse gamma ray flux implies large gamma opacity of the neutrino sources. Indeed, for these high redshift star forming galaxies the gamma absorption during the intergalactic propagation can be significant. In addition, large gamm…
We show that the Galactic latitude distribution of IceCube astrophysical neutrino events with energies above 100~TeV is inconsistent with the isotropic model of the astrophysical neutrino flux. Namely, the Galactic latitude distribution of the events shows an excess at low latitudes |b|<10 degrees and a deficit at high Galactic latitude |b|> 50 degrees. We use Monte-Carlo simulations to show that the inconsistency of the isotropic signal model with the data is at > 3 sigma level, after the account of trial factors related to the choice of the low-energy threshold and Galactic latitude binning …
The IceCube Collaboration has observed 37 neutrino events in the energy range $30\, TeV\leq E_ν \leq 2$ PeV and the sources of these neutrinos are unknown. Here we have shown that positions of 12 high energy blazars and the position of the FR-I galaxy Centaurus A, coincide within the error circles of ten IceCube events, the later being in the error circle of the highest energy event so far observed by IceCube. Two of the above blazars are simultaneously within the error circles of the Telescope Array hotspot and one IceCube event. We found that the blazar H2356-309 is within the error circles …
Starburst galaxies, which are known as "reservoirs" of high-energy cosmic-rays, can represent an important high-energy neutrino "factory" contributing to the diffuse neutrino flux observed by IceCube. In this paper, we revisit the constraints affecting the neutrino and gamma-ray hadronuclear emissions from this class of astrophysical objects. In particular, we go beyond the standard prototype-based approach leading to a simple power-law neutrino flux, and investigate a more realistic model based on a data-driven blending of spectral indexes, thereby capturing the observed changes in the proper…
We extend the colored Zee-Babu model with a gauged $U(1)_{B-L}$ symmetry and a scalar singlet dark matter (DM) candidate $S$. The spontaneous breaking of $U(1)_{B-L}$ leaves a residual $Z_2$ symmetry that stabilizes the DM and generates tiny neutrino mass at the two-loop level with the color seesaw mechanism. After investigating dark matter and flavor phenomenology of this model systematically, we further focus on its imprint on two of cosmic-ray anomalies: the Fermi-LAT gamma-ray excess at the Galactic Center (GCE) and the PeV ultra-high energy (UHE) neutrino events at the IceCube. We found t…
Superheavy dark matter may show its presence in high energy neutrino signals detected on earth. From the latest results of IceCube, we could set the strongest lower bound on the lifetime of dark matter beyond 100 TeV around $10^{28} {\rm sec}$. The excess around a PeV is noticed and may be interpreted as the first signal of DM even though further confirmation and dedicated searches are invited.
Late time decay of very heavy dark matter is considered as one of the possible explanations for diffuse PeV neutrinos observed in IceCube. We consider implications of multimessenger constraints, and show that proposed models are marginally consistent with the diffuse gamma-ray background data. Critical tests are possible by a detailed analysis and identification of the sub-TeV isotropic diffuse gamma-ray data observed by Fermi and future observations of sub-PeV gamma rays by observatories like HAWC or Tibet AS+MD. In addition, with several-year observations by next-generation telescopes such a…
The assumption of a single astrophysical power-law flux to explain the IceCube 6-year HESE extraterrestrial events yields a large spectral index that is in tension with gamma-ray observations and the 6-year up-going muon neutrinos data. Adopting a spectral index belonging to the range $\left[2.0,2.2\right]$, which is compatible with the one deduced by the analysis performed on the 6-year up-going muon neutrinos data and with $p$-$p$ astrophysical sources, the latest IceCube data show an up to $2.6\,σ$ excess in the number of events in the energy range 40--200 TeV. We interpret such an excess a…
The 6-year dataset of high-energy starting events (HESE) at IceCube indicates a spectrum of astrophysical neutrinos much softer than expected from the Fermi shock acceleration mechanism. On the other hand, IceCube's up-going muon neutrino dataset and Fermi-LAT's gamma-ray spectrum point to an $E^{-2}$ neutrino spectrum. If the HESE data above 200 TeV are fit with the latter flux, an excess at lower energies ensues, which then suggests a multicomponent spectrum. We show that the HESE dataset can be explained by a single $E^{-2}$ power-law neutrino flux from a muon-damped $pγ$ source if neutrino…
High energy neutrino astrophysics has come of age with the discovery by IceCube of neutrinos in the TeV to PeV energy range attributable to extragalactic sources at cosmological distances. At such energies, astrophysical neutrinos must have their origin in cosmic ray interactions, providing information about the sources of high energy cosmic rays, as well as leading to the co-production of high energy gamma-rays. The intimate link with these latter two independently observed types of radiation provides important tools in the search for identifying and understanding the nature of their astrophy…
Despite the spectacular discovery of an astrophysical neutrino flux by IceCube in 2013, its origin remains a mystery. Whatever its sources, we expect the neutrino flux to be accompanied by a comparable gamma-ray flux. These photons should be degraded in energy by electromagnetic cascades and contribute to the diffuse GeV-TeV flux precisely measured by the Fermi-LAT. Population studies have also permitted to identify the main classes of contributors to this flux, which at the same time have not been associated with major neutrino sources in cross-correlation studies. These considerations allow …
Cosmological parameters deduced from the Planck measurements of anisotropies in the cosmic microwave background are at some tension with direct astronomical measurements of various parameters at low redshifts. Very recently, it has been conjectured that this discrepancy can be reconciled if a certain fraction of dark matter is unstable and decays between recombination and the present epoch. Herein we show that if the superheavy relics have a branching into neutrinos B (X \to ν\bar ν) \sim 3 \times 10^{-9}, then this scenario can also accommodate the recently discovered extraterrestrial flux of…
The recent high-statistics high-energy atmospheric neutrino data collected by IceCube open a new window to probe new physics scenarios that are suppressed in lower energy neutrino experiments. In this paper we analyze the IceCube atmospheric neutrino data to constrain the Violation of Equivalence Principle (VEP) in the framework of three neutrinos with non-universal gravitational couplings. In this scenario the effect of VEP on neutrino oscillation probabilities can be parametrized by two parameters $Δγ_{21}\equiv γ_2-γ_1$ and $Δγ_{31}\equiv γ_3-γ_1$, where $γ_i$'s denote the coupling of neutr…
The center of the Milkyway is a host to energetic phenomena across many electromagnetic wave-bands and now possibly of high-energy neutrinos. We show that 5 out of 21 IceCube shower-like events, including a PeV event, likely originated from the Galactic Center region. Hard spectrum and flux inferred from these events are inconsistent with atmospheric neutrinos. The flux of these neutrinos is consistent with an extrapolation of the gamma-ray flux measured by Fermi-LAT from the inner Galactic region. This indicates a common hadronic origin of both, powered by supernovae. Three other shower-like …
We analyze the energy and zenith angle distributions of the latest 2-year IceCube dataset of upward going atmospheric neutrinos to constrain sterile neutrinos at the eV scale in the 3+1 scenario. We find that the parameters favored by a combination of LSND and MiniBooNE data are excluded at more than the 99% C.L. We explore the impact of nonstandard matter interactions on this exclusion, and find that the exclusion holds for nonstandard interactions (NSI) that are within the stringent model-dependent bounds set by collider and neutrino scattering experiments. However, for large NSI parameters …
We analyse the sensitivity of IceCube-DeepCore to annihilation of neutralino dark matter in the solar core, generated within a 25 parameter version of the minimally supersymmetric standard model (MSSM-25). We explore the 25-dimensional parameter space using scanning methods based on importance sampling and using DarkSUSY 5.0.6 to calculate observables. Our scans produced a database of 6.02 million parameter space points with neutralino dark matter consistent with the relic density implied by WMAP 7-year data, as well as with accelerator searches. We performed a model exclusion analysis upon th…
We discuss the event rate in DeepCore array due to neutrino flux produced by annihilations and decays of galactic dark matter. This event rate is calculated with a 10 GeV threshold energy, which is smaller than the threshold energy taken in previous works. Taking into account the background event rate due to the atmospheric neutrino flux, we evaluate the sensitivity of DeepCore array for probing dark matter annihilation cross section and decay time. The sensitivity studies include the annihilation modes $χχ\to b\bar{b}, \ τ^+ τ^-$, \ $μ^+μ^-$, and $ν\barν$, and decay modes $χ\to b\bar{b}, \ τ^…
The Zwicky Transient Facility (ZTF) follow-up campaign of alerts released by the IceCube Neutrino Observatory has led to the likely identification of the transient AT2019fdr as the source of the neutrino event IC200530A. AT2019fdr was initially suggested to be a tidal disruption event in a Narrow-Line Seyfert 1 galaxy. However, the combination of its spectral properties, color evolution, and feature-rich light curve suggests that AT2019fdr may be a Type IIn superluminous supernova. In the latter scenario, IC200530A may have been produced via inelastic proton-proton collisions between the relat…
The origin of neutrino flux observed in IceCube is still mainly unknown. Typically two flux components are assumed, namely: atmospheric neutrinos and an unknown astrophysical term. In principle the latter could also contain a top-down contribution coming for example from decaying dark matter. In this case one should also expect prompt and secondary gammas as well. This leads to the possibility of a multimessenger analysis based on the simultaneous comparison of the Dark Matter hypothesis both with neutrino and high energy gamma rays data. In this paper, we analyze, for different decaying Dark …
It has been speculated that Lorentz-invariance violation (LIV) might be generated by quantum-gravity (QG) effects. As a consequence, particles may not travel at the universal speed of light. In particular, superluminal extragalactic neutrinos would rapidly lose energy via the bremssthralung of electron-positron pairs (nu -> nu e+ e-), damping their initial energy into electromagnetic cascades, a figure constrained by Fermi-LAT data. We show that the two cascade neutrino events with energies around 1 PeV recently detected by IceCube -if attributed to extragalactic diffuse events, as it appears …
We show that a Dirac right-handed scalar neutrino can be weakly interacting massive particle in the neutrinophilic Higgs model. When the additional Higgs fields couple only to the leptonic sector through neutrino Yukawa couplings, the right number of relic density of dark matter can be obtained from thermal freeze-out of the dark matter annihilation into charged leptons and neutrinos. At present, this annihilation is suppressed by the velocity of dark matter. However one-loop annihilation cross section into $γγ$ can be larger than that of the helicity suppressed annihilation into fermions, bec…
We perform a combined likelihood analysis for the IceCube 6-year high-energy starting events (HESE) and 8-year throughgoing muon events above 10 TeV using a two-component neutrino flux model. The two-component flux can be motivated either from purely astrophysical sources or due to a beyond Standard Model contribution, such as decaying heavy dark matter. We find that the astrophysical plus dark matter interpretation is mildly preferred by the current data over the purely astrophysical explanation. As for the astrophysical neutrinos, we consider two different source flavor compositions correspo…
We have determined the currently allowed regions of the parameter spaces of two representative models of diffuse neutrino flux from active galactic nuclei (AGN): one by Koers & Tinyakov (KT) and another by Becker & Biermann (BB). Our observable has been the number of upgoing muon-neutrinos expected in the 86-string IceCube detector, after 5 years of exposure, in the range 10^5 < E/GeV < 10^8. We have used the latest estimated discovery potential of the IceCube-86 array at the 5-sigma level to determine the lower boundary of the regions, while for the upper boundary we have used either the AMAN…
Excesses on positron and electron fluxes measured by ATIC, and the PAMELA and Fermi--LAT telescopes can be explained by dark matter annihilation in our Galaxy. However, this requires large boosts on the dark matter annihilation rate. There are many possible enhancement mechanisms, such as the Sommerfeld effect or the existence of dark matter clumps in our halo. If enhancements on the dark matter annihilation cross section are taking place, the dark matter annihilation in the core of the Earth should also be enhanced. Here we use recent results from the IceCube 40-string configuration to probe …
We consider a simple extension of the minimal left-right symmetric model (LRSM) in order to explain the PeV neutrino events seen at the IceCube experiment from a heavy decaying dark matter. The dark matter sector is composed of two fermions: one at PeV scale and the other at TeV scale such that the heavier one can decay into the lighter one and two neutrinos. The gauge annihilation cross sections of PeV dark matter are not large enough to generate its relic abundance within the observed limit. We include a pair of real scalar triplets $Ω_{L,R}$ which can bring the thermally overproduced PeV da…
In view of the IceCube's 6-year high-energy starting events (HESE) sample, we revisit the possibility that the updated data may be better explained by a combination of neutrino fluxes from dark matter decay and an isotropic astrophysical power-law than purely by the latter. We find that the combined two-component flux qualitatively improves the fit to the observed data over a purely astrophysical one, and discuss how these updated fits compare against a similar analysis done with the 4-year HESE data. We also update fits involving dark matter decay via multiple channels, without any contributi…
We explore the correlation of $γ$-ray emitting blazars with IceCube neutrinos by using three very recently completed, and independently built, catalogues and the latest neutrino lists. We introduce a new observable, namely the number of neutrino events with at least one $γ$-ray counterpart, $N_ν$. In all three catalogues we consistently observe a positive fluctuation of $N_ν$ with respect to the mean random expectation at a significance level of $0.4 - 1.3$ per cent. This applies only to extreme blazars, namely strong, very high energy $γ$-ray sources of the high energy peaked type, and implie…
Recent analyses of the diffuse TeV-PeV neutrino flux highlight a tension between different Ice-Cube data samples that strongly suggests a two-component scenario rather than a single steep power-law flux. Such a tension is further strengthened once the latest ANTARES data are also taken into account. Remarkably, both experiments show an excess in the same energy range (40-200 TeV), whose origin could intriguingly be related to dark matter. In this paper, I discuss the combined analysis of IceCube and ANTARES data, highlighting the presence of the low-energy excess. Moreover, I update the result…
We study the contribution of Galactic sources to the flux of astrophysical neutrinos recently observed by the IceCube Collaboration. We show that in the simplest model of homogeneous and isotropic cosmic ray diffusion in the Milky Way the Galactic diffuse neutrino emission consistent with $γ$-ray (Fermi-LAT) and cosmic ray data (KASCADE, KASCADE-Grande and CREAM) is expected to account for only $4\%-8\%$ of the IceCube flux above 60 TeV. Direct neutrino emission from cosmic ray-gas ($pp$) interactions in the sources would require an unusually large average opacity above 0.01. On the other hand…
The Fermi Bubbles have been imaged in sub-TeV gamma rays at Fermi-LAT, and, if their origin is hadronic, they might have been seen with low statistics in $\sim 0.1- 1$ PeV neutrinos at IceCube. We discuss the detectability of these objects at the new High Altitude Water Cherenkov (HAWC) gamma ray detector. HAWC will view the North Bubble for $\sim 2-3$ hours a day, and will map its spectrum at 0.1-100 TeV. For the hard primary proton spectrum required to explain five events at IceCube, a high significance detection at HAWC will be achieved in less than 30 days. The combination of results at HA…
The observation of very high energy neutrino events at IceCube has grasped a lot of attention in the fields of both astrophysics and particle physics. It has been speculated that these high energy neutrinos might originate either from purely conventional astrophysical sources or from the late decay of a super heavy (PeV scale) dark matter (DM) particle. In order for decaying DM to be a dominant source of the IceCube high-energy neutrinos, it would require an unusually suppressed value of the coupling of DM to neutrinos. We attempt to explain this small coupling in the context of an $R$-parity …
Developments in neutrino astronomy have been to a great extent motivated by the search for the sources of the cosmic rays, leading at a very early stage to the concept of a cubic kilometer neutrino detector. Almost four decades later such an instrument, IceCube, is taking data and has produced the first evidence for a flux of high-energy neutrinos of cosmic origin. After a brief review of the history of the field, we will introduce IceCube and describe the first analysis of data taken with the completed instrument. The atmospheric neutrino flux cannot accommodate an excess of 28 neutrinos obse…
Recently the atmospheric muon spectra at high energies were reconstructed for two ranges of zenith angles, basing on the events collected with the IceCube detector. These measurements reach high energies at which the contribution to atmospheric muon fluxes from decays of short-lived hadrons is expected. Latest IceCube measurements of the high-energy atmospheric muon spectrum indicate the presence of prompt muon component at energies above 500 TeV. In this work, the atmospheric conventional muon flux in the energy range 10 GeV - 10 PeV is calculated using a set of hadronic models in combination…
Gamma-ray bursts (GRBs) have been suggested as possible sources of the high-energy neutrino flux recently detected by the IceCube telescope. We revisit the fireball emission model and elaborate an analytical prescription to estimate the high-energy neutrino prompt emission from pion and kaon decays, assuming that the leading mechanism for the neutrino production is lepto-hadronic. To this purpose, we include hadronic, radiative and adiabatic cooling effects and discuss their relevance for long- (including high- and low-luminosity) and short-duration GRBs. The expected diffuse neutrino backgrou…
Dark matter (DM) annihilations in the Galaxy may produce high energy neutrinos, which can be detected by the neutrino telescopes, for example IceCube, ANTARES and Super-Kamiokande. The neutrinos can also arise from hadronic interaction between cosmic ray and atmosphere around the Earth, known as atmospheric neutrino. Current measurements on neutrino flux is consistent with theoretical prediction of atmospheric neutrino within the uncertainties. In this paper, by requiring that the DM annihilation neutrino flux is less than the current measurements, we obtain an upper bound on the cross section…
