Presented at the Seventh Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 20-24, 2016Presented at the Seventh Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 20-24, 2016G.C., C.A., and J.C. are
supported by NSF grants 1505858 and 1505855. T.K. is supported by the
Science and Technology Facilities Council, UK. A.K. was supported in part
by the NSF under grants 0937462 and 1306958 and by the University of
Wisconsin Research Committee

Arguelles, CA

Collin, GH

Conrad, JM

Katori, T

Kheirandish, A

arXiv

Queen Mary Research Online

Search for Lorentz Violation in km$^3$-Scale Neutrino TelescopesArgüelles, CA; Collin, GH; Conrad, JM; Katori, T; Kheirandish, A       For additional information about this publication click this link.http://qmro.qmul.ac.uk/xmlui/handle/123456789/15967   Information about this research object was correct at the time of download; we occasionallymake corrections to records, please therefore check the published record when citing. Formore information contact scholarlycommunications@qmul.ac.ukarXiv:1608.02946v1  [hep-ph]  9 Aug 2016Proceedings of the Seventh Meeting on CPT and Lorentz Symmetry (CPT’16), Indiana University, Bloomington, June 20-24, 20161Search for Lorentz Violation in km3-Scale Neutrino TelescopesC.A. Argu¨elles,1 G.H. Collin,1 J.M. Conrad,1 T. Katori,2 and A. Kheirandish31Physics Department, Massachusetts Institute of TechnologyCambridge, MA 02139, USA2School of Physics and Astronomy, Queen Mary University of LondonLondon E1 4NS, UK3Department of Physics and Wisconsin IceCube Particle Astrophysics CenterUniversity of Wisconsin, Madison, WI 53706, USAKilometer3-scale neutrino detectors such as IceCube, ANTARES, and the pro-posed Km3Net neutrino observatory in the Mediterranean have measured, andwill continue to characterize, the atmospheric neutrino spectrum above 1 TeV.Such precise measurements enable us to probe new neutrino physics, in par-ticular, those that arise from Lorentz violation. In this paper, we first relatethe effective new physics hamiltonian terms with the Lorentz violating litera-ture. Second, we calculate the oscillation probability formulas for the two-levelνµ − ντ sector. Finally, we comment on some of the challenges and outlook forthis analysis.Neutrino oscillations arise from the non-alignment of the propagation andthe weak-interaction hamiltonian eigenstates. In vacuum, the former basisis given by the neutrino mass eigenstates and scales as 1/E. This scalingimplies that precise observation of the properties of high energy neutrinosshould explore small perturbations due to new physics. Such cases havebeen studied in the context of astrophysical neutrinos.1–4 Furthermore, thehigh energy component of the atmospheric neutrino spectrum — before theonset of the astrophysical component — is well understood and can also beused to look for small perturbations in the standard hamiltonian. In thiswork we calculate the oscillation probabilities that affect those high energyatmospheric neutrinos in the presence of Lorentz violation.One of the most generic ways to introduce new physics in neutrinooscillations is to extend the hamiltonian that drives neutrino oscillations inProceedings of the Seventh Meeting on CPT and Lorentz Symmetry (CPT’16), Indiana University, Bloomington, June 20-24, 20162the following way,H = Hstd +∑n(EΛn)nU˜ †nOnU˜n, (1)where the first term is the standard neutrino hamiltonian and the secondterm has the following components: On = diag(On,1, On,2, On,3) and U˜nis a unitary matrix. On and Λn set the scale of the new physics and U˜nis the mixing matrix describing the new physics flavor structure.1,2 Suchnew operators are explicitly introduced in the context of Lorentz symme-try violation and, in general, depend on the neutrino four-momentum, pµ.In the minimal Standard-Model Extension (SME), which restricts itselfto dimension-four operators, only two terms are introduced:5 those corre-sponding to n = 0 and n = 1. In the SME notation they are, respectively,denoted by aλαβ and cλσαβ ; where α, β = e, µ, τ are indices that dictate theflavor structure and λ, σ are Lorentz indices. These terms can be explicitlywritten in the following wayH = Hstd +pλE aλee aλeµ aλeτaλ∗eµ aλµµ aλµτaλ∗µτ aλ∗eτ aλττ− pλpσE cλσee cλσeµ cλσeτcλσ∗eµ cλσµµ cλσµτcλσ∗µτ cλσ∗eτ cλσττ , (2)where pλ = (E, ~p) is the neutrino four-momentum. In this work we willimpose the simplifying assumption that aλαβ and cλσαβ are isotropic tensors,i.e., they only have time components.6 In this scenario, the spatial depen-dence is neglected and is called isotropic Lorentz violation. Further, as theterms need to be traceless in the Lorentz indices, a factor of 4/3 needs tobe included. With these assumptions, Eq. (2) simplifies toH = Hstd + aαβ −43Ecαβ . (3)Under this simplification, the relationship between Eqs. (1) and (2) is nowapparent. In order to make it more comparable we choose to redefine−4cαβ/3→ cαβ in what follows in this paper.Having introduced these new terms in the hamiltonian, we must nowconsider where they are relevant. The standard hamiltonian comprisestwo pieces: Hvac and Hmatter. The first term scales like ∆m2/E, while thesecond one is proportional to the matter density. The largest squared-mass-difference makes Hvac ∼ 10−24(TeV/E) GeV. Within the Earth, Hmatterhas only one relevant component which is Heematter ∼ 10−23 GeV. If we thenrestrict ourselves to scenarios in which we consider only the νµ-ντ sector,then only the Hvac scaling matters. This scenario leads to a back of the en-velope SME parameter sensitivity estimation of a ∼ 10−24-10−27 GeV andProceedings of the Seventh Meeting on CPT and Lorentz Symmetry (CPT’16), Indiana University, Bloomington, June 20-24, 20163c ∼ 10−27-10−32, where the upper and lower sensitivity ranges correspondto neutrino energies of 1 TeV and 1 PeV.Now that we have established the scale of our search, we proceed tocalculate the oscillation probabilities in this regime. Since, in the νµ-ντsector, the matter potential drops out of the hamiltonian we can write itin the following way,7H =12EU †(θ)(0 00 ∆m2)U(θ) + En(δµµ δµτδ∗µτ −δµµ), (4)where δαβ is the CPT conserving a-term, for n = 0, and the CPT violatingc-term, for n = 1, respectively. Then the transition probabilities are7Pνµ→νµ = 1− sin2 2Θ sin2(∆m2L4ER), (5)wheresin2 2Θ =1R2(sin2 2θ +R2n sin2 2ξ + 2Rn sin 2θ sin 2ξ cos η), (6)R =√1 +R2n + 2Rn(cos 2θ cos 2ξ + sin 2θ sin 2ξ cos η), (7)withRn =√δ2µµ +Re(δµτ )2 + Im(δµτ )24En+1∆m2, (8)tan η =Im(δµτ )Re(δµτ ), tan 2ξ =|δµτ |δµµ. (9)In Fig. 1 we show the effect on νµ disappearance for two values of c; resultswith a-terms have similar features.Fig. 1. The left (right) figure shows the νµ survival probability calculated according toEq. (5) for Re(cµµ) = 10−25(10−26).Proceedings of the Seventh Meeting on CPT and Lorentz Symmetry (CPT’16), Indiana University, Bloomington, June 20-24, 20164In summary, we start from a general parametrization of new neutrinooscillation physics, as introduced, e.g., in Argu¨elles et al.,1 and relate thethe terms that arise from Lorentz violation. Then, we explicitly calcu-late the oscillation probabilities in the νµ-ντ sector. The next step of thiswork requires modelling the event expectation for experiments that mea-sure the high energy atmospheric neutrino component, such as IceCube andANTARES. We then need to proceed to include systematic errors associ-ated with the atmospheric neutrino fluxes, as considered in Ref. 8. Then,we will proceed to search for the existence of Lorentz violation in highenergy νµ data.AcknowledgmentsC.A. and G.C. thank the organizers of the CPT’16 conference for theirhospitality during their stay in Bloomington. G.C., C.A., and J.C. aresupported by NSF grants 1505858 and 1505855. T.K. is supported by theScience and Technology Facilities Council, UK. A.K. was supported in partby the NSF under grants 0937462 and 1306958 and by the University ofWisconsin Research Committee.References1. C.A. Argu¨elles, T. Katori, and J. Salvado, Phys. Rev. Lett. 115, 161303(2015).2. T. Katori, C.A. Argu¨elles, and J. Salvado, arXiv:1607.08448.3. M. Bustamante, J.F. Beacom, and W. Winter, Phys. Rev. Lett. 115, 161302(2015).4. J.S. Dı´az, V.A. Kostelecky´, and M. Mewes, Phys. Rev. D 89, 043005 (2014).5. V.A. Kostelecky´ and M. Mewes, Phys. Rev. D 69, 016005 (2004).6. J.S. Dı´az and V.A. Kostelecky´, Phys. Rev. D 85, 016013 (2012).7. M.C. Gonzalez-Garcia, F. Halzen and M. Maltoni, Phys. Rev. D 71, 093010(2005).8. M.G. Aartsen et al., arXiv:1605.01990.

Search for Lorentz Violation in km(3)-Scale Neutrino Telescopes

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Search for Lorentz Violation in km(3)-Scale Neutrino Telescopes

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