CONSTRAINING THE FLAVOR STRUCTURE OF LORENTZ VIOLATION HAMILTONIAN WITH THE MEASUREMENT OF ASTROPHYSICAL NEUTRINO FLAVOR COMPOSITIONS

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1 CONSTRINING THE FLVOR STRUCTURE OF LORENTZ VIOLTION HMILTONIN WITH THE MESUREMENT OF STROPHYSICL NEUTRINO FLVOR COMPOSITIONS Lai, Wei-Hao(NCTU) Lai, Kwang-Chang(CGU) Lin, Guey-Lin(NCTU) arxiv:

2 OUTLINE Introduction Lorentz violation effects to neutrino flavor transitions Lorentz violation and the current IceCube results on astrophysical neutrino flavor compositions IceCube-Gen2 and its potential of constraining Lorentz Violation Hamiltonian Summary

3 INTRODUCTION Flavor discrimination Probe the flavor transition, ex: ν oscillation, ν decay, Lorentz Violation(LV) Φ e :Φ μ :Φ τ Generate the source Φ e :Φ μ :Φ τ detected at the Earth (Φe:Φ μ :Φ τ )=P αβ (Φe :Φ μ :Φ τ )

4 INTRODUCTION There are two types of astrophysical sources in proton-proton collision and proton-γ collision: PP (π +,π -,π )+Χ Pγ Δ + nπ +! µ + µ µ! e + e + µ (νe,ν μ,ν τ )=( e, µ, ) (,2,). π source(/3,2/3,) 2. μ damped source(,,) (νe,ν μ,ν τ ) (,,) ( e, µ, ) (,,). π source(/3,2/3,) 2. μ damped source(,,) J. P. Rachen and P. Meszaros, 998 T. Kashti and E. Waxman, Phy. Rev. Lett. 25

5 We shall focus on pion source from pp collision (νe,ν μ,ν τ )=( e, µ, ) (/3,2/3,) Defining neutrino flavor fraction: f = ( )/( ( e )+ ( µ )+ ( )) total flux of neutrinos and anti-neutrinos at the source Hence (fe,fµ,f )=(/3, 2/3, )

6 f = ( )/( ( e )+ ( µ )+ ( )) total flux of neutrinos and anti-neutrinos at the terrestrial detector f = P f P = P (! ) with (f e,f µ,f )=(/3, 2/3, ) f e =/3+(P eµ P e )/3 f µ =/3+(P µµ P µ )/3 test of μτ symmetry breaking f =/3+(P µ P )/3

7 LV EFFECTS TO NEUTRINO FLVOR TRNSITION For neutrinos, the general form of LV Hamiltonian H LV = p E a ee a eµ a e aeµ a µµ a µ a e a µ a p p E c ee c eµ c e c eµ c µµ c µ c e c µ c For rotationally invariant LV effects H LV = H LV = a T ee a T eµ a T e a T eµ a T µµ a T µ a T e a T µ a T a T ee a T eµ a T e a T eµ a T µµ a T µ a T e a T µ a T Sun-centered celestial equatorial frame (T,X,Y,Z) Let us first focus on a T αβ Teppei Katori, V. lan Kostelecký, and Rex Tayloe, Phys. Rev. D 74, 59(26) V. lan Kostelecký and Matthew Mewes, Phys. Rev. D 69, 65(24) 4E 3 4E 3 c TT ee c TT eµ c TT e c TT eµ c TT µµ c TT µ c TT e c TT ee c TT µ c TT c TT eµ c TT e c TT eµ c TT µµ c TT µ c TT e c TT µ c TT

8 LORENTZ VIOLTIONS ND CURRENT ICECUBE RESULTS ON STROPHYSICL NEUTRINO FLVOR COMPOSITION E ν is between 25 TeV and 2.8 PeV HSM Δm 2 3/2E ν Hence HSM is between and 5 x -26 GeV 4.5 x -28 GeV Can Lorentz Violation play role in this data? M. G. artsen et al. (IceCube Collaboration), strophys.j. 89 (25) no., 98

9 CURRENT BOUNDS ON LORENTZ VIOLTION PRMETERS Super-K s result: K. be et al. (Super-Kamiokande Collaboration),Phys. Rev. D 9, 523(25) [] [] [2] [2] HSM< 5 x -26 GeV Significant room for HLV to play an important role V. lan Kostelecký and Neil Russell, Rev. Mod. Phys. 83, (26) []T. Katori(MiniBooNE Collaboration), Mod. Phys. Lett. 27, 2324(22) [2]T. Katori and J. Spitz, in CPT and Lorentz Symmetry VI(World scientific, Singapore, 24)

10 SIMPLE LORENTZ VIOLTION HMILTONIN H LV = a e a e P = /2 /2 /2 /2 Recall: (Φe:Φ μ :Φ τ )=P αβ (Φe :Φ μ :Φ τ ) (Peμ-Peτ)=(P μτ -P ττ )= -/2 (P μμ -P μτ )= Large breaking of μτ symmetry (fe,f μ,f τ )=(/6,2/3,/6)

11 SIMPLE LORENTZ VIOLTION HMILTONIN H LV = a T µµ a T P =, aμμτ a ττ Τ Recall: (Φe:Φ μ :Φ τ )=P αβ (Φe :Φ μ :Φ τ ) (Peμ-Peτ)= (P μμ -P μτ )= (P μτ -P ττ )= - (fe,f μ,f τ )=(/3,2/3,) Large breaking of μτ symmetry

12 COMPRISONS OF SPECIL CSES WITH RECENT ICECUBE MESUREMENT OF STROPHYSICL NEUTRINO FLVOR COMPOSITION RED: aeτ Τ, aeτ Τ * Yellow: a μμτ, a Τ ττ Purple: aeμ Τ, aeμ Τ * Black: a μττ, a Τ * μτ ll cases fall into 2σ region as other elements grow from zero

13 ICECUBE-GEN2 ND ITS POTENTIL OF CONSTRINING LORENTZ VIOLTION HMILTONIN IceCube Collaboration (M.G. artsen (delaide U.) et al.), arxiv:42.56 ~ km 3 instrumented volume ~25 m spacing of photo sensors possible IceCube-Gen2 configuration IceCube, in red, and the infill sub-detector DeepCore, in green. blue volume shows the full instrumented next-generation detector, with PINGU displayed in grey as a denser infill extension within DeepCore.

14 SENSITIVITIES OF ICECUBE-GEN2 ON STROPHYSICL NEUTRINO FLVOR COMPOSITIONS γ=2.2±.2 Φ=(5.±.8) x -8 GeV - cm -2 s - sr - Pion source from pp collision is assumed Eth= TeV years of exposure σ, 2σ, and 3σ regions I. M. Shoemaker and K. Murase, Phys. Rev. D (26) IceCube-Gen2 regions

15 SK 95% C.L. limits: Re(aeτ Τ )< 4.x -23 GeV Im(aeτ Τ )< 2.8x -23 GeV H LV = a e a e llow other elements to grow from zero and include the contribution from HSM The parameter ranges in the table predict the black region of flavor fraction disfavored at 3σ.

16 H LV = a T µµ a T llow other elements to grow from zero and include the contribution from HSM The parameter ranges in the table predict the black region of flavor fraction disfavored at 3σ.

17 H=HSM+HLV H LV = = M a T eµ a T e a T eµ a T µµ a T µ a T e a T µ a T cos e i sin e i cos e i sin e i M cos2 sin2 e i sin2 e i cos2 Increasing M until the predicted flavor fraction is out of the IceCube Gen2 3σ region.

18 Excluded at 3σ For most values of sin2α x sin2ρ, the energy scale M is constrained to be less than few times -26 GeV

19 Constraint on C αβ ΤΤ -4ΕC αβ ΤΤ /3 replaces a αβ Τ when the latter is turn off. if the constraint on M, which is made of a αβτ, is few times -26 GeV, the corresponding constraint on M (dimensionless quantity made of C αβ ΤΤ ) is about -3 with E chosen as TeV(Threshold energy). K. be et al. (Super-Kamiokande Collaboration),Phys. Rev. D 9, 523(25) [] [] [2] [2]

20 SUMMRY We have introduced Lorentz violation Hamiltonian in neutrino sector. Previous experimental search on Lorentz violation with neutrino is introduced. Previous best limit by Super-Kamiokande experiment is summarized. We have shown that Lorentz violating Hamiltonian with parameters in the above SK limits can change significantly the flavor transition probabilities of high energy astrophysical neutrinos in TeV to PeV energy range. For the pion source induced from pp collisions, Lorentz violating Hamiltonian with large μτ symmetry breaking effect is more stringently constrained. We show that IceCube-Gen2 can place stringent constraints on the Lorentz violating Hamiltonian.