Presented at the Seventh Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 20-24, 201

Arguelles, CA

Katori, T

Salvado, J

arXiv

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Test of Lorentz Violation with Astrophysical Neutrino FlavorKatori, T; Argüelles, CA; Salvado, J     arXiv file http://arxiv.org/abs/1607.08448  For additional information about this publication click this link.http://qmro.qmul.ac.uk/xmlui/handle/123456789/14412   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.ukProceedings of the Seventh Meeting on CPT and Lorentz Symmetry (CPT’16), Indiana University, Bloomington, June 20-24, 20161Test of Lorentz Violation with Astrophysical Neutrino FlavorTeppei Katori1 , Carlos A. Argu¨elles2,3,4, and Jordi Salvado2,3,51School of Physics and Astronomy, Queen Mary University of London, E1 4NS, UK2Department of Physics, University of Wisconsin, Madison, WI 53706, USA3Wisconsin IceCube Particle Astrophysics Center, Madison, WI 53706, USA4Physics Department, Massachusetts Institute of Technology, Cambridge, MA 02139,USA5Instituto de F´ısica Corpuscular (IFIC), CSIC-Universitat de Vale`ncia, E-46071Valencia, SpainThe high-energy astrophysical neutrinos recently discovered by IceCube openeda new way to test Lorentz and CPT violation through the astrophysical neu-trino mixing properties. The flavor ratio of astrophysical neutrinos is a verypowerful tool to investigate tiny effects caused by Lorentz and CPT violation1.There are 3 main findings; (1) current limits on Lorentz and CPT violationin neutrino sector are not tight and they allow for any flavor ratios, (2) how-ever, the observable flavor ratio on the Earth is tied with the flavor ratio atproduction, this means we can test both the presence of new physics and theastrophysical neutrino production mechanism simultaneously, and (3) the as-trophysical neutrino flavor ratio is one of the most stringent tests of Lorentzand CPT violation.1. Neutrino mixingThe propagation of neutrinos are eigenstates of Hamiltonian, however, theproduction and detection of neutrinos are flavor eigenstates. This is thesource of “neutrino oscillations”, which is the topic of the 2015 Nobel Prizeof Physics2,3, and the 2016 Breakthrough Prize in Fundamental Physics2–7.The flavor eigenstates |να〉 is written by the superposition of the prop-agation eigenstates |νi〉 with a unitary matrix V (E), which diagonalize theHamiltonian in the flavor basis,|να〉 =∑iVαi(E)|νi〉 , H(E) = V (E)†∆1(E) 0 00 ∆2(E) 00 0 ∆3(E)V (E),where ∆i(E) is the ith eigenvalue. Note through this article we assumethere are only 3 generations. Also we consider a simple case where thearXiv:1607.08448v1  [hep-ph]  28 Jul 2016Proceedings of the Seventh Meeting on CPT and Lorentz Symmetry (CPT’16), Indiana University, Bloomington, June 20-24, 20162Hamiltonian only depends on the neutrino energy. Given the Hamiltonianand solving the evolution of an initial flavor state |να〉 over a distance L,the probability of measuring a flavor state |νβ〉 is obtained,Pνα→νβ (L,E) = δαβ − 4∑i>jRe(V ∗αiVβiVαjV∗βj) sin2(∆i −∆j2L)+ · · ·However, not all experiments actually measure the neutrino as it “oscil-lates”, most notably solar neutrinos. When neutrinos propagate a signif-icantly longer distance than their oscillation lengths, coherent behavior iswashed out. Then, neutrinos do not oscillate, but “mix” incoherently. Inthis situation, Eq. 1 can be written only with mixing matrix elements,P¯να→νβ (E) =∑i|Vαi(E)|2 |Vβi(E)|2 . (1)This is the mixing probability of astrophysical neutrinos which propagatemostly in the vacuum. Any new physics in the vacuum, such as Lorentz andCPT violation, would induce anomalous neutrino mixings which may beimprinted in the astrophysical neutrino flavor ratio measured on the Earth.This is expected to be more sensitive than kinematic tests of Lorentz andCPT violation with astrophysical neutrinos8.2. Astrophysical Neutrino Flavor RatioDetails of this analysis are described in the published paper1. The astro-physical neutrino flux on the Earth’s surface, φ⊕β (E), can be obtained byconvoluting Eq. 1 with the astrophysical neutrino flux at the production,φpα, i.e., φ⊕β (E) =∑α P¯να→νβ (E)φpα(E). Then, an energy averaged flavorcomposition φ¯⊕β is obtained by integrating E−2 power law production fluxwithin ∆E =[10 TeV, 10 PeV] with 50 bins in log10. Since the absoluteflux of astrophysical neutrinos are not well known, we focus on the relativeflavor information, namely the flavor ratio, α⊕β = φ¯⊕β /∑γ φ¯⊕γ .We use following Hamiltonian to look for new physics.H =12EUM2U† +∑n(EΛn)nU˜nOnU˜†n = V†(E)∆V (E) , (2)here, the first term is the standard neutrino mass matrix9, and the restare the effective operators of new physics. For example, n = 0 and n =1 terms can be interpreted as the time component of the CPT-odd andCPT-even SME coefficients. This moment we do not take into account theProceedings of the Seventh Meeting on CPT and Lorentz Symmetry (CPT’16), Indiana University, Bloomington, June 20-24, 20163spatial components, mainly because of the lack of the spatial distributioninformation of astrophysical neutrinos.Figure 1 shows our results for the n = 1 case (CPT-even Lorentz vi-olation, or “c” coefficients in minimal SME). The result is obtained byusing the standard GSL library10 and the Armadillo C++ linear algebralibrary11. In our approach, we first set the “scale” of new physics, then wesample 100,000 points of the mixing matrix U˜n by the anarchy samplingscheme12. Neutrino parameters are also sampled by choosing symmetric er-rors9 from a Gaussian distribution, except δCP which is sampled from a flatdistribution. The results are all from the lower octanct (θ23 <pi2 ) and withnormal mass ordering, however, these choices only give minor effects. Here0.00.0 1.00.20.2 0.80.40.4 0.60.60.6 0.40.80.8 0.21.01.0 0.0(1 :2 :0)(1 :0 :0)(0 :1 :0)(0 :0 :1)α ⊕eα⊕τα ⊕µ0.00.0 1.00.20.2 0.80.40.4 0.60.60.6 0.40.80.8 0.21.01.0 0.0(1 :2 :0)(1 :0 :0)(0 :1 :0)(0 :0 :1)α ⊕eα⊕τα ⊕µ0.00.0 1.00.20.2 0.80.40.4 0.60.60.6 0.40.80.8 0.21.01.0 0.0(1 :2 :0)(1 :0 :0)(0 :1 :0)(0 :0 :1)α ⊕eα⊕τα ⊕µFig. 1. Allowed flavor ratio region using for the CPT-even SME coefficients1. Theleft plot corresponds roughly to the current limits (c = 1.0 × 10−27); the middle plotcorresponds to c = 1.0× 10−30, while the right plot corresponds to c = 3.2× 10−34.we show the result with 3 scales, the left plot of Fig. 1 is c = 1.0 × 10−27,this is around the current best limit for CPT-even SME coefficients in theneutrino sector by Super-K and IceCube atmospheric neutrino data13,14.As you see, whole flavor triangle is covered, this means by current limits ofLorentz violation we could expect any flavor ratio from observations.Next, we set the scale to be c = 1.0 × 10−30 and c = 3.2 × 10−34,these are the scale of CPT-even Lorentz violation terms when they becomecomparable to the neutrino mass term with E = 35 TeV and E = 2 PeV.The available phase space of flavor triangle shrinks, this means now thesize of new physics is getting smaller compared to the neutrino mass, andeventually the neutrino mass will dominate the flavor ratio. In fact, theright plot is almost identical to the standard flavor ratio with differentassumptions on neutrino production models1,15,16.Proceedings of the Seventh Meeting on CPT and Lorentz Symmetry (CPT’16), Indiana University, Bloomington, June 20-24, 20164There are four distinct regions, depending on different assumptions ofthe astrophysical neutrino production mechanism. However, regardless ofthe details of the production process, the predicted flavor ratio is alwaysaround the center (νe : νµ : ντ ∼ 1 : 1 : 1), and only by the presence of newphysics, will it deviate from the central area. Therefore, the exotic flavorratio may nail down both the presence of new physics, and the productionmechanism of astrophysical neutrinos.Finding the flavor ratio is experimentally challenging17, due especiallyto the separation of νe and ντ largely relying on the simulation input18. Themeasurements can be improved with current detectors, but future IceCube-Gen219 and KM3NeT20 will have a better chance of studying the astro-physical neutrino flavors from their superior detectors.AcknowledgmentsTK thanks to the organizers of CPT 2016 for their hospitality during mystay at Bloomington, Indiana, USA. We also thank Shivesh Mandalia forthe careful reading of this manuscript. This work is supported by Scienceand Technology Facilities Council, UK.References1. C. Argu¨elles, T. Katori, and J. Salvado, Phys. Rev. Lett. 115, 161303 (2015).2. Super-Kamiokande, Y. Fukuda et al., Phys. Rev. Lett. 81, 1562 (1998).3. SNO Collaboration, Q. R. Ahmad et al., Phys. Rev. Lett. 87, 071301 (2001).4. K2K Collaboration, M. H. Ahn et al., Phys. Rev. Lett. 90, 041801 (2003).5. T2K Collaboration, K. Abe et al., Phys. Rev. Lett. 107, 041801 (2011).6. KamLAND, K. Eguchi et al., Phys. Rev. Lett. 90, 021802 (2003).7. Daya Bay Collaboration, F. P. An et al., Phys. Rev. Lett. 108, 171803 (2012).8. J. S. Dı´az, V. A. Kostelecky´, and M. Mewes, Phys. Rev. D. 89, 043005 (2014).9. M. C. Gonzalez-Garcia et al., JHEP 1212, 123 (2012).10. http://www.gnu.org/software/gsl/11. http://arma.sourceforge.net/12. N. Haba and H. Murayama, Phys. Rev. D 63, 053010 (2001).13. Super-Kamiokande, K. Abe et al., Phys. Rev. D 91, 052003 (2015).14. IceCube Collaboration, M. G. Aartsen et al., Phys. Rev. D 82, 112003 (2010).15. M. Bustamante et al., Phys. Rev. Lett. 115, 161302 (2015).16. A. Palladino and F. Vissani, Eur. Phys. J. C 75 (2015) 433.17. IceCube Collaboration, M. G. Aartsen et al., Phys. Rev. Lett. 114, 171102(2015); Astrophys. J. 809, 98 (2015).18. S. Palomares-Ruiz et al., Phys. Rev. D 91, 103008 (2015).19. IceCube-Gen2 Collaboration, M. G. Aartsen et al., arXiv:1412.5106.20. KM3NeT, S. Adrian-Martinez et al., J. Phys. G 43, 084001 (2016).

Test of Lorentz Violation with Astrophysical Neutrino Flavor

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Test of Lorentz Violation with Astrophysical Neutrino Flavor

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