The high energy neutrino detection by a km^3 Neutrino Telescope placed in the
Mediterranean sea provides a unique tool to both determine the diffuse
astrophysical neutrino flux and the neutrino-nucleon cross section in the
extreme kinematical region, which could unveil the presence of new physics.
Here is performed a brief analysis of possible NEMO site performances.Comment: 4 pages, 3 figures, Proceedings of the 30th ICRC 200

Borriello, E.

Cuoco, A.

Mangano, G.

Miele, G.

Pastor, S.

Pisanti, O.

Serpico, P. D.

English

arXiv

The high energy neutrino detection by a km{sup 3} Neutrino Telescope placed in the Mediterranean sea provides a unique tool to both determine the diffuse astrophysical neutrino flux and the neutrino nucleon cross section in the extreme kinematical region, which could unveil the presence of new physics. Here is performed a brief analysis of possible NEMO site performances

Pastor, Sergio

Serpico, Pasquale Dario

UNT (University of North Texas) Digital Library

30TH INTERNATIONAL COSMIC RAY CONFERENCEHigh Energy Neutrinos with a Mediterranean Neutrino TelescopeE. BORRIELLO1,2, A. CUOCO3 , G. MANGANO1 , G. MIELE1,2, S. PASTOR2 , O. PISANTI1 ,P. D. SERPICO41Dipartimento di Scienze Fisiche, Universita` di Napoli “Federico II” and INFN Sezione di Napoli, Com-plesso Universitario di Monte S. Angelo, Via Cintia, Napoli, 80126, Italy2Instituto de Fı´sica Corpuscular (CSIC-Universitat de Vale`ncia), Ed. Institutos de Investigacio´n, Apdo.22085, E-46071 Valencia, Spain3Institut for Fysik og Astronomi, Aarhus Universitet Ny Munkegade, Bygn. 1520 8000 Aarhus Denmark4Center for Particle Astrophysics, Fermi National Accelerator Laboratory, Batavia, IL 60510-0500, USApisanti@na.infn.it FERMILAB-CONF-07-139-AAbstract: The high energy neutrino detection by a km3 Neutrino Telescope placed in the Mediterraneansea provides a unique tool to both determine the diffuse astrophysical neutrino flux and the neutrino-nucleon cross section in the extreme kinematical region, which could unveil the presence of new physics.Here is performed a brief analysis of possible NEMO site performances.IntroductionNeutrinos are one of the main components of thecosmic radiation in the high energy regime. Al-though their fluxes are uncertain and depend on theproduction mechanism, their detection can provideinformation on the sources and origin of the highenergy cosmic rays.From the experimental point of view the detectionperspectives are stimulated by the Neutrino Tele-scopes (NT’s) constructed, like Baikal [1] andAMANDA [2], or under construction like IceCube[3] under the ice and ANTARES [4] in the deep wa-ter of the Mediterranean sea. Here, also the exper-iments NESTOR [5] and NEMO [6] are in the R&Dphase and, together with ANTARES, in the futurecould lead to the construction of a km3 telescopeas pursued by the KM3NeT project [7].Although NT’s were originally thought as νµ de-tectors, their capability as ντ detectors has becomea hot topic in view of the fact that flavor neu-trino oscillations lead to nearly equal astrophysi-cal fluxes for the three neutrino flavors. Despitethe different behavior of the produced tau leptonswith respect to muons in terms of energy loss anddecay length, both νµ and ντ event detection ratesare sensitive to the matter distribution near the NTarea. In principle, the elevation profile of the Earthsurface around the detector may be relevant. InRef. [8], some of the present authors calculatedthe aperture of the Pierre Auger Observatory [9]for Earth-skimming UHE ντ ’s, by using the Digi-tal Elevation Map (DEM) of the site (GTOPO30)[10]. In Ref. [11] the DEM’s of the under-waterEarth surface, provided by the Global Relief Datasurvey (ETOPO2) [12], was used to estimate theeffective aperture for ντ and νµ detection of a km3NT in the Mediterranean sea placed at any of thethree locations proposed by the ANTARES, NEMOand NESTOR collaborations. In the present pa-per we further develop the approach of Ref. [11]to evaluate the performances of a MediterraneanNT in the simultaneous determination of the neu-trino flux and the ν-Nucleus cross section in ex-treme kinematical regions (which may probe newphysics, see e.g. [13]). Since the three differentproposed sites for the under-water km3 telescopeshow event rate differences of the order of 20%, forthe sake of brevity we report the results our analy-sis for the NEMO site only, which presents interme-diate performances.FERMILAB-CONF-07-139-AHIGH ENERGY NEUTRINOS WITH A MEDITERRANEAN NEUTRINO TELESCOPEFormalism and resultsFollowing the formalism developed in [8, 11] wedefine the km3 NT fiducial volume as that boundedby the six lateral surfaces Σa (the index a=D, U, S,N, W, and E labels each surface through its orien-tation: Down, Up, South, North, West, and East),and indicate with Ωa ≡ (θa, φa) the generic direc-tion of a track entering the surface Σa (see Figure4 of Ref. [11] for notations). We introduce all rele-vant quantities with reference to ντ events, the caseof νµ being completely analogous.Let dΦν/(dEν dΩa) be the differential flux ofUHE ντ + ν¯τ . The number per unit time of τ lep-tons emerging from the Earth surface and enteringthe NT through Σa with energy Eτ is given by(dNτdt)a=∫dΩa∫dSa∫dEνdΦν(Eν ,Ωa)dEν dΩa∫dEτ cos (θa) kτa(Eν , Eτ ;~ra,Ωa). (1)The kernel kτa(Eν , Eτ ;~ra,Ωa) represents the pro-bability that an incoming ντ crossing the Earth,with energy Eν and direction Ωa, produces a τ -lepton which enters the NT fiducial volume th-rough the lateral surface dSa at the position ~ra withenergy Eτ . For an isotropic flux and an exposuretime T , the total number of τ leptons (and similarlyfor muons) crossing the NT isNτ = T∑a∫dΩa∫dSa∫dEν∫dEτ(14pidΦν(Eν)dEν)cos (θa) kτa(Eν , Eτ ;~ra,Ωa). (2)Although the exact dependence of Eq. (2) onthe neutrino flux and the neutrino-nucleon chargedcurrent cross section σνNCC may be quite compli-cated, basic physical considerations show that evena rough binning of the events for energy loss andarrival direction may be used to obtain informationon both these quantities (see e.g. [14, 15]). In par-ticular, in the following we shall consider the sumof the µ and τ contributions as the experimentalobservable, namely the energy deposited in the de-tector and not the energy and/or the nature of thecharged lepton crossing the NT. In fact, only for aminor fraction of the detected events the nature ofthe charged lepton can be reliably established.According to Ref.s [16, 17], the differential energyloss of the τ leptons per unit of length in an un-derwater NT can be simply taken as dEτ/dλ =−βτ Eτ%w, with βτ = 0.71 × 10−6 cm2 g−1 and%w denoting the water density. Analogously, formuons one just needs to replace βτ with the corre-sponding value βµ = 0.58 × 10−5 cm2 g−1. As-suming that the lepton energy loss in the NT bye.m. interactions, ∆El, is just a small fraction ofits energy at the entrance, El, we simply obtain∆El = λ(~ra,Ωa)βlEl %w, where λ(~ra,Ωa) is thelength crossed in the NT by the lepton whose trackis defined the geometrical quantities ~ra,Ωa.Using these relations one can derive the spectrumof leptons detected in the NT as a function of theirdeposited energy, ∆E, and their arrival direction,Ω ≡ (θ, φ), measured in the zenith-azimuth refer-ence framed2Nd(∆E)dΩ= T∑α=µ,τ∑a∫dSa∫dEν14pidΦν(Eν)dEνcos (θa) kαaλ(~ra,Ωa)βα %w. (3)By denoting with Xi a given bin in energy loss,and with Yj the one for the zenithal angle, we canintegrate the expression (3) to get the number ofexpected events in Xi × Yj ,Nij = T∑α=µ,τ∑a∫Xid(∆E)∫YjdΩ (4)∫dSa∫dEν14pidΦν(Eν)dEνcos (θa) kαaλ(~ra,Ωa)βα %w.To take into account the underwater surface profileone can numerically compute the above integral asdescribed in Ref. [8]: by using the available DEMof the area near the NEMO site, one can isotrop-ically generate a large number of oriented trackswhich cross the NEMO fiducial volume (see Figure4 of Ref. [11]) and sample the above integrand.This technique allows also to account for the radialdensity profile of the Earth (we use the formula re-ported in [18]).In order to study the sensitivity to both neutrinoflux and σνNCC it is necessary to parameterize theirstandard expressions and the possible departuresfrom them. In particular, we parameterize the fluxas dΦν/dEν dΩa = C ·1.3 ·10−8 (Eν/GeV)−2D30TH INTERNATIONAL COSMIC RAY CONFERENCE0 Π4Π23 Π4ΠΘ01020304050dNidΘN1 = 39.105.5 GeV < DEl < 106.0 GeVN11 = 29.N12 = 10.N2 = 43.DEl > 106.0 GeVN21 = 37.N22 = 6.j=1 j=2Figure 1: Angular distributions of (µ + τ ) eventscollected in five years from a km3 NT placed at theNEMO site (see text).GeV−1 cm−2 s−1 sr−1, which gives a standardWaxman-Bahcall flux [19] for C = D = 1. Forthe neutrino-nucleon cross section we use:σνNCC0.344 nb =(EνE1)0.492AEν ≤ E2(E2E1)0.492A (EνE2)0.492BEν > E2where E1 = 105.5 GeV is the energy below whichthe atmospheric flux is expected to dominate (sowe consider only the region E > E1) and E2 =106.0 GeV. In the low-energy bin this cross-sectionmatches the standard expression [20] for A = 1.A value of B significantly larger than 1 may beassociated with new physics. Note that the factorConly enters via the product CT as a normalizationand can be fixed to C = 1, considering instead theexposure time T as the effective variable.For illustrative purposes, in Figure 1 we report theevent angular distribution, for a km3 NT placed atthe NEMO site in five years of operations. The solidand dashed lines correspond to events whose en-ergy loss in the detector belongs to the intervals105.5-106 GeV or > 106 GeV, respectively. Thepredictions are obtained for standard flux and crosssection (A = B = C = 1). In the plot are also re-ported the number of eventsNij (see Eq. (4)) whenwe consider i = 1, 2 for the previous two energy0.5 0.75 1 1.25 1.5D10-11510CTHyrLD < 1.44N2 j = 1N1 j = 1æCTHyrLFigure 2: (CT,D) region corresponding to the ob-servation of at least one event in each bin (for stan-dard cross section).bins and j = 1, 2 when the zenith arrival directionis between 0◦ and 90◦ or 90◦ and 180◦.Clearly, for a very steep flux power-law index D,the number of events decreases. We shall re-quire that at least one event falls in each bin, inT years of running, in the case of standard cross-section; this rough criterion constrains the parame-ter range that one experiment is able to explore tothe brighter region of Fig. 2, corresponding to theintersection of the regions where Nij ≥ 1, for alli, j.As a preliminary result, in Fig. 3 we show theconstraints (contours at the 68 % and 95 % CL)which can be obtained on the physical parametersA and D after the marginalization over C is made.Here we are assuming B = A, so that the plotrepresents the capability of the telescope to dis-entangle the energy dependence of the flux fromthe energy dependence of the cross-section (in thetoy model where both are described by a singleparameter). We performed a multi-Poisson like-lihood analysis [21], in which the likelihood func-tion, L = exp(−χ2/2), is defined using the fol-lowing expression for the χ2 (N0ij being the eventnumbers of the reference model):χ2 = 2∑ij[(Nij −N0ij) +N0ij ln(N0ij/Nij)].(5)HIGH ENERGY NEUTRINOS WITH A MEDITERRANEAN NEUTRINO TELESCOPE0.5 1.0 1.5A0.901.001.101.201.301.40D95%68%Figure 3: Marginalized contour levels in the(A,D) plane (for A = B) (see text for details).ConclusionsWe have performed an analysis of the capability ofa km3 NT in the Mediterranean to disentangle thehigh energy neutrino flux and neutrino-nucleoncross section in an unexplored kinematical region.Our statistical analysis exploits the dependence ofobservables on energy and arrival direction (underthe hypothesis of an isotropic diffuse flux). Usinga simplified toy model to parameterize fluxesand cross-sections, preliminary results confirmthat this approach is very promising, and couldpotentially detect hints of new physics. Of coursethe real feasibility of such measurements willdepend crucially on the size of the neutrino fluxwhich fixes the time required to reach a reasonablestatistics. A complete account of this research willbe reported in a forthcoming publication.Acknowledgements: P.S. acknowledges sup-port by the US Department of Energy and byNASA grant NAG5-10842. G. Miele acknowl-edges support by Generalitat Valenciana (ref.AINV/2007/080 CSIC).References[1] V. A. Balkanov et al. [Baikal Collabora-tion], Phys. Atom. Nucl. 63, 951 (2000)[Yad. Fiz. 63N6, 1027 (2000)] [arXiv:astro-ph/0001151].[2] E. Andres et al., Astropart. Phys. 13, 1 (2000)[arXiv:astro-ph/9906203].[3] J. Ahrens et al. [IceCube Collaboration], As-tropart. Phys. 20, 507 (2004) [arXiv:astro-ph/0305196].[4] M. Spurio [ANTARES Collaboration],arXiv:hep-ph/0611032.[5] G. Aggouras et al. [NESTOR Collaboration],Nucl. Instrum. Meth. A 567, 452 (2006).[6] P. Piattelli [NEMO Collaboration], Nucl.Phys. Proc. Suppl. 165, 172 (2007).[7] U. F. 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High Energy Neutrinos with a Mediterranean Neutrino Telescope

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