We show that the excess of high energy neutrinos observed by the IceCube
collaboration at energies above 100 TeV might originate from baryon number
violating decays of heavy shadow baryons from mirror sector, which in turn
constitute Dark Matter. Due to tiny mixing between mirror and ordinary
neutrinos, it is possible to explain the specific features of the IceCube
events spectrum.Comment: 5 pages, 3 figures. Talk given at IFAE 2014 conference 9-11 April
  2014 Gran Sasso Science Institute And Laboratori Nazionali del Gran Sasso.
  The work is done in collaboration with authors of arXiv:1506.09040. arXiv
  admin note: substantial text overlap with arXiv:1506.09040 by other author

Biondi, Riccardo

English

arXiv

We show that the excess of high energy neutrinos observed by

the IceCube collaboration at energies above 100TeV might originate from baryon number violating decays of heavy shadow baryons from mirror sector, which in turn constitute Dark Matter. Due to tiny mixing between mirror and ordinary neutrinos, it is possible to explain the specific features of the IceCube events spectrum

Biondi, R.

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2015-15031-4Colloquia: IFAE 2014IL NUOVO CIMENTO 38 C (2015) 31Dark matter and IceCube neutrinosR. BiondiDipartimento di Scienze Fisiche e Chimiche, Universita` degli Studi di L’Aquila, 67100 L’Aquila(AQ), ItalyINFN, Laboratori Nazionali del Gran Sasso (LNGS), 67100 Assergi (AQ), Italyreceived 7 January 2015Summary. — We show that the excess of high energy neutrinos observed bythe IceCube collaboration at energies above 100TeV might originate from baryonnumber violating decays of heavy shadow baryons from mirror sector, which in turnconstitute Dark Matter. Due to tiny mixing between mirror and ordinary neutrinos,it is possible to explain the specific features of the IceCube events spectrum.PACS 14.60.Pq – Neutrino mass and mixing.PACS 14.60.St – Non-standard-model neutrinos, right-handed neutrinos, etc.Discovery of high-energy neutrino events by the IceCube Collaboration [1] opened anew era of experimental high-energy neutrino astrophysics. Recently the collaborationpublished the three year data collected between 2010 and 2013, containing 37 candidatein the energy range from 30TeV to 2PeV. While the number of events with energiesbelow 100TeV or so is compatible with the background expectations, there is an evidentexcess of the events with E > 100TeV or so. On the other hand, no events were observedin the gap between 400TeV and 1PeV, but three most energetic shower events emergedat the end of the spectrum with energies 1.04PeV, 1.14PeV and 2.0PeV where theatmospheric background is practically vanishing. On the other hand, the spectrum isapparently cut off at energies larger than about 2PeV. The gap in the energy spectrumis difficult to explain in known models of high-energy neutrinos of astrophysical origin.The model that may explain such a spectrum was suggested in ref. [2]. Here wepresent main guidelines of this model. Nowadays it becomes popular the idea that darkmatter of the universe can emerge from a parallel gauge sector, with particles and in-teractions sharing many similarities with ordinary particle sector. Such a shadow sectorwould contain particles like quarks which form composite baryons, as well as leptons andneutrinos which are all sterile for ordinary gauge interactions. In particularly interestingexample is represented by so-called mirror world [3], which has the content of particlesand interactions exactly identical to that of ordinary sector, with the same gauge andYukawa coupling constants. Taking into consideration also attractive possibilities for par-ticle physics beyond the Standard Model related to supersymmetric grand unified theoryCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 R. BIONDI(SUSY GUT), one can consider that at higher energies both ordinary and mirror sectorsare presented by identical GUTs, e.g. SU(5) and SU(5)′ or SU(6) and SU(6)′, which inboth sectors break down to their Standard Model subgroups SU(3)×SU(2)×U(1) at thescale MG ∼ 1016 GeV. However, following refs. [4, 5], one can assume that later on thesymmetry between two sectors is broken so that the electroweak symmetry breaking scaleV in mirror sector is much larger than in the Standard Model, v = 174GeV. Namely,if V ∼ 1011 GeV, then the lightest shadow baryons should have mass order few PeV.Due to baryon violating GUT gauge bosons, they decay with τdec ∼ tU producing ener-getic shadow neutrinos which oscillate into active neutrinos (with oscillation probabilities∼ 10−10 or so) transferring their spectrum to the latter.Let us consider, for simplicity, a supersymmetric grand unification theory SU(5) ×SU(5)′ (1). Consider a situation when in both sectors the GUT symmetries are brokenat the scale MG  2 × 1016 GeV, SU(5) → SU(3) × SU(2) × U(1) and SU(5)′ →SU(3)′×SU(2)′×U(1)′. Below this scale our sector is represented by MSSM with chiralsuperfields of quarks qi = (u, d)i, uci , dci and leptons li = (ν, e)i, eci , i = 1, 2, 3 beingfamily index, and two Higgs superfields h1, h2. As for parallel sector we have the similarparticle content, quarks Qi = (U,D)i, U ci ,Dci , leptons Li = (N,E)i, Eci , and two HiggsesH1,H2. At the scale μ = MG all gauge coupling constants are equal and the Yukawacouplings have the same pattern for ordinary and shadow fermions:(1) (Y eij liecjh1 + Ydijqidch1 + Y uijqiucjh2) + (YeijLiEcjH1 + YdijQiDcH1 + Y uijQiUcj H2).As for the neutrinos, their masses emerge from the following D = 5 operators [4]:(2)αijM(lh2)(lh2) +αijM(LH2)(LH2) +βijM(lh2)(LH2),where M is an effective scale of the order of Planck scale MPl [5]. The first two terms givethe Majorana masses respectively to ordinary neutrinos νe,μ,τ and their shadow (sterile)partners while third term induces the mixing between ordinary and shadow neutrinos.Below GUT scale, the gauge coupling constants of two sectors, respectively g3,2,1and g′3,2,1 evolve down in energies in both sectors in the same way (see fig. 1). Forordinary sector we follow to the standard paradigm. Supersymmetry is broken at thescale MS ∼ 1TeV, the Higgses are not protected anymore to be massless and they getVEVs v1 = v cosβ, v2 = v sinβ, where v = 174GeV, which induce the electroweaksymmetry breaking and generate the fermion masses.As for parallel sector, let us assume now that mirror symmetry between two sectorsis spontaneously broken in the following way. Imagine that supersymmetry is broken inshadow sector at the scale M ′S ∼ 1011 GeV, supposedly due to non-zero F or D termsof some auxiliary fields, so that shadow scalars, including squarks and leptons as wellas Higgs doublets H1 and H2 acquire soft masses order MS (2). Respectively shadowHiggses Get VEVs V1 = V cosβ′ and V2 = V sinβ′, and electroweak symmetry is broken(1) As discussed in ref. [2], our proposal can be more nicely realized in SUSY SU(6) theory [6]which gives natural solution to the so-called hierarchy and doublet-triplet splitting problems byrelating the electroweak symmetry breaking scale to the supersymmetry breaking scale MS ∼1TeV and naturally explains the fermion mass spectrum.(2) Interestingly, if supersymmetry breaking is transferred to our sector via gravity or otherPlanck scale mediators, this would explain ordinary soft masses order MS ∼M ′2S /MPl ∼ 1TeV.DARK MATTER AND ICECUBE NEUTRINOS 3Fig. 1. – Running of gauge couplings below the GUT scale, αi = g2i /4π and α′i = g′2i /4π.at the scale V ≤ M ′S . Therefore, the masses of shadow fermions are rescaled, modulorenormalization factors order 1, by a factor ξ = V/v with respect to ordinary fermionmasses. Namely, taking V/v = 109 and assuming tanβ′ = tanβ, by the RG runningof gauge and Yukawa constants from the GUT scale down in energies, one obtains forthe shadow electron mass ME  0.4PeV, MD  1.1PeV and MU  1.9PeV, againstme = 0.5MeV, md  5MeV and mu  3MeV for ordinary electron and quarks. On theother hand, the RG evolution shows that the shadow QCD scale becomes Λ′ ∼ 100TeV(c.f. Λ  200MeV in ordinary QCD). Therefore, Λ′  MU ,MD and the shadow QCDlooks like a rescaled version of our QCD without light quarks, but only with heavy quarkslike c and b. Notice also that in shadow sector up quark U becomes heavier than thedown quark D [2], and MU,D/Λ′ is of the same order as mb,c/Λ in ordinary QCD.The lightest state would appear to be a shadow Δ− baryon of spin 3/2, consisting ofthree down quarks D and having mass MΔ ≈ 3MD = 3.3PeV. All states, containing upquark U , will be unstable against weak decays, U → DE¯N . As for mesons, the lightestpseudoscalar is shadow neutral pion π0 consisting of DD¯, with mass M0 ≈ 2MD =2.2PeV, while the lightest vector meson ρ0(DD¯) is slightly heavier than π0. ChargedPion π− as well as ρ−-meson consisting of DU¯ will have mass M MU + MD = 3PeV,with ρ− a bit heavier than π−. All pseudoscalar and vector mesons have excited stateswith mass gap order Λ′ between the levels, just like cc¯ or bb¯ states in ordinary QCD.Now we come to the role of baryon violation and proton decay which is fundamen-tal prediction of the GUTs. The heavy gauge bosons of SU(5) with baryon violatingcouplings between quarks and leptons induce the decay of the lightest ordinary baryons(proton, or neutron bound in nuclei), with lifetime τp ∼M4G(α25m5p)−1 ∼ 1031 Gyr or so,where α5 is SU(5) coupling constant at the GUT scale MG ∼ 2× 1016 GeV [7].In the shadow sector, the similar couplings of GUT gauge bosons should destabilize theshadow baryon. However, taking into account that shadow Δ baryon is much heavier thanthe ordinary proton, MΔ/mp ∼ 106, its lifetime must be about 30 orders of magnitudesmaller than the proton lifetime. Hence we get τΔ ∼M4G(α25m5Δ)−1 ∼ 10Gyr or so, withlifetime comparable to the age of the Universe tU  14Gyr.The principal decay mode of Δ baryon is in vector mesons, Δ− → ρ−a +N¯x, where theneutrino state Nx is generically a superposition of shadow neutrino flavor eigenstates.However, taking into account the active sterile mixing ∼ βv/αV due to operators (2), itcontains also small admixture of ordinary neutrinos. Each decay produces monoenergeticneutrinos Nx with energies Ea = 12MΔ(1−M2a/M2Δ), where M0 is the mass of ρ− mesonand M1,2,... are the masses of its excitations. In fig. 2(a) the spectrum of neutrinosproduced by decay of galactic dark matter is shown by sharp peaks (solid blue) for4 R. BIONDI(a) (b)Fig. 2. – (a) Shadow neutrino spectrum produced by Δ-barion decay and subsequent decay ofshadow pions. (b) Spectrum of VHE neutrino events as predicted in our model.M0,M1,M2, respectively, being 3.0, 3.1 and 3.2PeV. Due to close degeneracy betweenthe masses of Δ-baryon and ρ−a mesons, the neutrino energies are Ea  1PeV while themost of initial energy = MΔ is taken away by mesons ρ−a .Vector mesons promptly decay into mirror pion and photon, ρ−a → π− + γ′, and sub-sequent decay of the pion produces the neutrino once again (solid red curves in fig. 2(a)).Shadow π− has two decay modes, two body π− → EN¯E and three body π− → π0EN¯E .Interestingly, their branching ratios are comparable which fact is intimately related tothe value Λ′ ∼ 100TeV [2]. Two body decay produces neutrinos with a narrow energyspectrum concentrated around MΔ/2  1.6PeV, while the three body decay, due tosmaller phase space, produces less energetic neutrinos with a wide spectrum extendingup to the value Emax = M− −M0 −ME MU −MD −ME  0.4PeV.Figure 2(a) shows the final spectrum including the neutrinos produced by the decayof dark matter in the galactic halo, and extragalactic neutrinos produced by the decayof cosmological dark matter at large redshifts. The fraction of extragalactic neutrinosstrongly depends on the decay time τΔ (in fig. 2 we take τΔ = 10tU ). Figure 2(b) showshow such a spectrum will be seen by the IceCube provided that active-shadow neutrinomixing angles are order 10−5. Here the effective areas for the neutrino detection byIceCube [1] and characteristic error bars in estimation of neutrino energies (of about13%) are taken into account. Needless to say, that the obtained spectrum of events lookvery much like the spectrum observed by the IceCube [1]. The validity of our model willbe tested with increasing statistics by the IceCube collaboration.REFERENCES[1] Aartsen M. G. et al. [IceCube Collaboration], Science, 342, no. 6161 (2013) 1242856;Phys. Rev. Lett., 113 (2014) 101101.[2] Berezhiani Z., Biondi R., Di Panfilo G. and Gazizov A., in press.[3] For a review, see e.g. Berezhiani Z., Int. J. Mod. Phys. A, 19 (2004) 3775; hep-ph/0508233.[4] Berezhiani Z. and Mohapatra R. N., Phys. Rev. D, 52 (1995) 6607; Berezhiani Z.,Dolgov A. D. and Mohapatra R. N., Phys. Lett. B, 375 (1996) 26.[5] Akhmedov E. K., Berezhiani Z. and Senjanovic G., Phys. Rev. Lett., 69 (1992) 3013.DARK MATTER AND ICECUBE NEUTRINOS 5[6] Berezhiani Z. and Dvali G., Bull. Lebedev Phys. Inst., 5 (1989) 55; Barbieri R. et al.,Nucl. Phys. B, 432 (1994) 49; Berezhiani Z. et al., Nucl. Phys. B, 444 (1995) 61.[7] For a review, see e.g. Nath P. and Fileviez Perez P., Phys. Rep., 441 (2007) 191.

Dark matter and IceCube neutrinos

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