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Bonn, May 12, 2014

Comments on: Flavor Mix and Fluxes of High Energy Astrophysical Neutrinos. Sandip Pakvasa University of Hawaii Honolulu. Bonn, May 12, 2014. Existence of High Energy Gammas suggests that High energy accelerators in space EXIST P+P and P+ γ collisions produce π 0 ‘s and π + ‘s

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Bonn, May 12, 2014

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  1. Comments on: Flavor Mix and Fluxesof High Energy AstrophysicalNeutrinos Sandip Pakvasa University of Hawaii Honolulu Bonn, May 12, 2014

  2. Existence of High Energy Gammas suggests that High energy accelerators in space EXIST • P+P and P+γ collisions produce π0‘s and π+ ‘s • π0 → γ ‘s → observed…..upto 100s of TeV • π+ → ν ‘s…….hence high energy ν ‘s must exist! • At detectable, useful fluxes?(used to be the question) • Now we have seen them at Icecube!

  3. Candidates for Neutrino Sources:(i)AGNs(ii)GRBs (iii) GZK/BZ in all three the likely processes are: γ+p -> π + n and p+p->π + X

  4. GRB: The estimate Of the prompt flux due to charm Decay has some major Uncertainties. See Recent summary by Lipari.

  5. Expected energy Spectrum from GRB’s The spectrum Peaks at 1 PeV and dies out after about 10 PeV.

  6. Expected Energy Spectrum from AGN’s I In this case the Spectrum lasts from 1 PeV to about 100 PeV

  7. In the last year, IC has reported 29 very high energy neutrino events lying between 100 TeV and 2 PeV. Atmospheric BG dies out at 100 TeV.The observed energies are given as follows:22 shower events from 28 TeV to 1.2 PeV(one additional one at 2 PeV) and 7 muon track events from 32 TeV to 350 TeV.Most probably NOT prompt atmospheric ( can be from charm decays, with large uncertainties)and most probably extra-galactic….According to IC the flavor mix is consistent withthe canonical expected mix of 1:1:1….. But probably with large statistical errors... Icecube data at Moriond 2014(Kopper talk): the gap between 300 teV and 1 PeV has disappeared with more data!

  8. FLAVORS at the Source: The variety of initial flavor mixes • Conventional: P +P → π + X, π → νμ+ μ, μ → νμ+ νe hence: νe / νμ = 1/2 • Same for P + γ, except no anti-νe. • Damped muon sources: if μ does not decay or loses energy: No νe ‘s, and hence νe / νμ= 0/1 • Pure Neutron Decay or Beta-Beam sources: n → anti-νe, hence νe/νμ= 1/0 • Prompt sources, when π’s absorbed and only heavy flavors contribute and νe/νμ= 1, such a flavor mix also occurs in muon damped sources at lower energies from μ decays. (Winter et al,arXiv:1007.0006) • In general, flavor mix will be energy dependent……(e.g. can go from conventional to muon damped at higher energies as emphasized in the paper above)

  9. Neutrinos from “GZK” process: BZ neutrinos: • Berezinsky and Zatsepin pointed out the existence/inevitability of neutrinos acompanying GZK cutoff from : • PCR + γCMB → Δ+ → n + π+ • Flavor Mix: below 10 Pev: (n decays)pure Beta-Beam: e:μ:τ = 1:0:0 • Above 10 PeV: conventional(π decays) :e:μ:τ =1:2:0 (due to Engel et al. PRD64,(2001), also Stanev(2009))

  10. This is for Primaries being Primarily protons.

  11. Current Knowledge of Neutrino Mixing and Masses νe ν1 νμ = UMNSP ν2 ντν3 δm322 ~ 2.5 .10-3 eV2, δm212 ~ 8 .10-5 eV2 √2/3√1/3ε UMNSP~ UTBM = -√1/6 √1/3 √1/2 -√1/6 √1/3 -√1/2 (ε ~ 0.15:DB,RENO,DC(2012)) Unkown: Mass Pattern: Normal or Inverted:, phase δ 3 _______ 2_______ 1 _______ 2_________ 1_________ 3________

  12. Effects of oscillations on the flavor mix are very simple: • δm2 > 10-5 eV2 , hence (δm2 L)/4E >> 1 for all relevant L/E, e.g. in one light day, already this osc argument even for E~(PeV) is >>1 and • → sin2 (δm2L/4E) averages to ½ • survival and transition probablities depend only on mixing angles: • Pαα= i Uαi4 • Pαβ = i Uαi2Uβi2

  13. In this tri-bi-maximal approximation, the propagation matrix P is: 10 4 4 P = 1/18 4 7 7 4 7 7 νeνe νμ = Pνμ ντ earth ντ source

  14. Using the most recent best fit from e.g. Schwetz et al, the propagation matrix P becomes 0.5543 0.28/0.186 0.164/0.22 0.28/0.186 0.346/0.41 0.378/0.371 0.164/0.219 0.3775/0.3713 0.47/0.4325 (Again the two values correspond to δ = 0 or π)

  15. Flavor Mix at Earth (using Tri-Bi-Max mixing): Beam type Initial Final Conventional (pp,pγ) 1:2:0 1:1:1 Damped Muon 0:1:0 4:7:7 Beta Beam(n decay) 1:0:0 5:2:2 Prompt 1:1:0 1.2:1:1 Damped Muon produces a pure muon decay beam at lower energies with same flavor mix as the Prompt beam!

  16. Using the mixing from most recent best fits(e.g. Schwetz et al): • 1:1:1 can become 1:0.86:0.86 to 1.0:1.05:1.01 These numbers include the “known” corrections to the standard 1:2:0 due to muon polarization effects, K’s etc.

  17. Discriminating flavors • The ratios used to distinguish various flavor mixes are e.g. fe (e/(e+μ+τ) and R(μ/[e+τ]) • Source type fe R • Pionic 0.33 0.5 • Damped-μ 0.22 0.64 • Beta-beam 0.55 0.29 • Prompt 0.39 0.44 • It has been shown that R and/or fe can be determined upto 0.07 in an ice-cube type detector. Hence pionic, damped μ, and Beta-beam can be distinguished but probably not the prompt • (Beacom et al. PRD69(2003).{Esmaili(2009).Choubey(2009).} • Since showers count equally e+μ+τ with CC interactions and e+τ CC interactions; it is not possible to disentangle uniquely the true flavor ratios e/μ/τ but only test a given hypothesis, e.g. 1/1/1......

  18. It should be stressed that the initial flavor mix will, in general be energy dependent. E.g. a typical example is when the mix starts out as pionic, i.e. a flavor mix of 1:2:0 and at a higher energy changes into a muon damped beam with a mix of 0:1:0.See e.g. Mehta and Winter, arXiv:1101.2673,Hummer et al.,arXiv:1007.0006Incidentally, a damped muon flux is accompanied at lower eneries by a “prompt” flux with the mix of 1:1:0 due to contribution from muon decay. This makes it important to measure flavor mix over a reasonably broad energy range.

  19. Can small deviations from TBM be measured in the flavor mixes? Corrections due to ε/θ13 are rather small(<10%) and we will neglect them with a few exceptions… Measuring such small deviations remains impractical for the foreseeable future By the same token the corrections due to a small mixing with a light sterile neutrino are also rather small and we will neglect those as well again with some exceptions!

  20. In addition, sources are never “pure” meaning: • Conventional/pp: after including μ polarization and effects due to K, D etc decays, the mix changes from1:2:0 to approx. 1:1.85:ε, (ε < 0.01) • Damped μ sources do not have exactly 0:1:0 but probably more like δ:1:0 with δ of a few %.......and similarly for Beta-beam. • For our present purposes, we will neglect such corrections as well. Lipari et al(2007), Rodejohann, Weiler, SP(2008)

  21. To summarise, small deviations in flavor content NOT easy to measure in near future. But it should be possible to measure LARGE deviations from the canonical flavor mix. For our purposes here, let us agree to use the conventional flavor mix as canonical. In this case the initial mix of 1:2:0 is expected to become 1:1:1 at earth. So we look for large deviations from this.

  22. Large deviations:

  23. How many ways can the flavor mix deviate significantly from 1:1:1 ? • Initial flux different from canonical: e.g. the damped muon scenario. In this case the flavor mix will be: 4:7:7 similarly for the beta beam source, the flavor mix will be: 5:2:2 instead of 1:1:1

  24. 2. Neutrino Decay: Do neutrinos decay? Since δm’s ≠ 0, and flavor is not conserved, in general ν’s will decay. The only question is whether the lifetimes are short enuf to be interesting and what are the dominant decay modes.

  25. What do we know? • Radiative decays: νi → νj + γ: m.e.: Ψj(C + Dγ5)σµνΨi Fµν SM: 1/τ = (9/16)(α/π)GF2/{128π3}(δmij2)3/mi ‌ Σαm2α/mW2(UiαUjα*)‌ 2τSM > 1045 s (Petcov, Marciano-Sanda)(1977) Exptl. Bounds on κ = e/mi[ ‌C‌+ ‌D‌ 2]1/2 = κ0μB From νe + e → e + ν’: κ0 < 10-10 (PDG2010), this corresponds to: τ > 1018 s. Bounds for other flavors somewhat weaker but still too strong for radiative decay to be Of practical interest.

  26. Invisible Decays: • νi → νj + ν +ν: Exptl Bounds: F < εGF, ε < O(1), from invisible width of Z Bilenky and Santamaria(1999): τ > 1034 s νiL → νjL + φ: gij ΨjL γμΨjL dμφ If isospin conserved: invisible decays of charged leptons governed by the same gij, and bounds on μ→ e + φ, and τ → μ/e + φ yield bounds such as: τ > 1024 s. {Jodidio et al. (1986), PDG(1996)}

  27. Conclusion: Only “fast” invisible decays are Majoron typecouplings • g νCjRνiL χ : • I(isospin) can be a mixture of 0 and 1(G-R, CMP) • The final state ν can be mixture of flavor/sterile states……… • Bounds on g from π & K decays • Barger,Keung,SP(1982),Lessa,Peres(2007), g2 < 5.10-6 • SN energy loss bounds: Farzan(2003): g < 5.10-7 • g2 < 5.10-6 corresp. to τ > 10-8 s/eV • g < 5. 10-7 corresp. to τ > 0.1 s/ev

  28. Current experimental limits on τi: • τ1/m1 > 105 s/eV SN 1987A B. o. E. Careful analysis. • τ2/m2 >10-4 s/eV (Solar) 10-4-10-2s/eV Beacom-Bell(2003),KamLand(2004) τ3/m3 > 3.10-11s/eV(Atm) 9.10-11 s/eV Gonzalez-Garcia-Maltoni(2008) Cosmology: WMAP/PLANCKfree-streaming ν’s τ > 1010 s/eV at least for one ν… Hannestad-Raffelt(2005), Bell et al.(2005) ( With L/E of TeV/Mpsc or PeV/1000Mpsc, can reach τ of 104 s/eV) These bounds depend crucially on free-streaming and whether one or all neutrinos are free-streaming. We ignore these strong bounds.....

  29. When νi decays, Uαi2 gets multiplied bythe factor exp(-L/γcτ) and goes to 0 for sufficiently long L. For normal hierarchy, only ν1 survives,and the final flavor mix is simply (SP 1981):e:μ:τ = Ue12:Uμ12:Uτ12~ 4:1: 1or even 10:1:1 with the new best fits… These flavor mixes are drastically different from canonical 1:1:1 and easily distinguishable. Beacom et al(2003)

  30. Effects on absolute fluxes in decay scenarios: • In normal hierarchy, if only ν1 survives: νµ flux can go down by as much as a factor of 0.1 from the original flux at the source. . νe flux is enhanced from the original by a factor of 2. Early Universe neutrino count is modified to 3+4/7(this is allowed by PLANCK and BBN)

  31. But if the decay is into a sterileneutrino then (NH).……. ν3 and ν2 simply disappear and only ν1 survives but at a smaller flux. The final fluxes are then: νe : 2/3 of the original flux νµ : 1/6 of the original flux Other implications: ν-counting in early universe modified by 3 -> 4+4/7, this is in some conflict with PLANCK + BBN(?)

  32. The so-called Learned Plot The Learned Plot

  33. 4. Pseudo-Dirac Neutrinos:(Sometimes called Quasi-Dirac) If no positive results are found in neutrino-less double-beta-decay experiments, it behooves us to consider the possibility that neutrinos are Dirac or Pseudo-Dirac Idea of pseudo-Dirac neutrinos goes back to Wolfenstein, Petcov and Bilenky - Pontecorvo (1981-2). Also a recent clear discussion in Kobayashi-Lim(2001). These arise when there are sub-dominant Majorana mass terms present along with dominant Dirac mass terms.

  34. The three δm2’s willbe different, in general.

  35. Implications for absolute fluxes: • In particular, if the separation for the δm21 is much smaller than for the other two, νμ’s get depleted almost by a factor of 2. And in a model with mirror matter one can get a further factor of 2, yielding a net suppression of factor 4. • Eventually, when L/E gets large enuf all flavors get suppressed by the factor of and trhe flavor mix returns to the canonical 1:1:1

  36. 6. Effects of Magnetic Fields • Can change the spectra in GRB/AGN model predictions….. • In regions with large magnetic fields, neutrino magnetic transitions can modify the flavor mix. • However, for Majorana neutrinos, the magnetic moment matrix is antisymmetric and hence, a flavor mix of 1:1:1 remains 1:1:1 ! • For Dirac case, possible interesting effects via RSFP (Akhmedov and Lim-Marciano) for μνat the maximum allowed values of about 10-14μB and B of order of a Gauss In this case also, large conversion from flavor to sterile state can occur, and reduce absolute fluxes by a factor of 2 or more…..

  37. Other possibilities • 7. Lorentz Invariance Violation • 8. CPT Violation • 9. Decoherence • 10. Mass varying Neutrinos • 11. etc…..

  38. Lorentz Invariance Violation See later....... • Discussed esp. by Coleman-Glashow(1997-8), Kostelcky(1997 on..) etc • Many possible manifestations: can lead to many fascinating possibilties-e.g. Mass depending on velocity. E.g. if mν depends on velocity, it can make the decay of π into μ+ν forbidden above some energy and hence no ν’s are emitted above that energy leading to a cut-off in the highest possible energy-can this be the reason for no events(yet) above 2 PeV? • In another scenario with phenomenology identical to Violation of Equivalence Principle (Halprin,Leung,Pantaleone,Glashow(1998)……..

  39. Flavor Signatures in IceCube … 1013 eV (10 TeV) 6x1015 eV (6 PeV) Multi-PeV  B10 +N+... ± (300 m!) +hadrons signature of  signature of

  40. Conclusions/summary • Neutrino Telescopes MUST measure flavors, and need to be v.v.large(Multi-KM), just OBSERVING neutrinos NOT enuf…… • If the flavor mix is found to be 1:1:1, it is BORING and confirms CW, even so can lead to many constraints. • If it is approx ½:1:1, we have damped muon sources. • If the mix is a:1:1, then a>1 may mean decays with normal hierarchy and can give info about θ13 and δ….. • If a is <<1, then decays with inverted hierachy may be occuring.. • Can probe v.v. small δm2 beyond reach of neutrinoless double beta decay…. • Anisotropy can be due to flavor violating gravity?

  41. Some idle thoughts:Is it possible that the lack of events above 2 PeV indicates a cut-off in neutrino energies?E.g. Glashow resonance would lead to not only a shower at 6.3 PeV(due to W->hadrons) but also events at ½ (6.3) PeV and 1/4(6.3)PeV due to the events in which W -> e+nu or W->tau+nu.No such events have been seen….One can speculate about the origins of such a cut-off…It of course can be due to simply petering out at the production, or e.g. just the effect of a steep energy spectrum or maybe Something more interesting involving exotic new physics?

  42. Possible High Energy Cutoff? Based on the fact that no events due to the Glashow Resonance are seen, either at 6.3 PeV or at 1/2 and 1/4 the energy.(3.15 and 1.58 PeV)(due to W->h, W->eν and W->τν; rates go as 66%, 9% and 11% resp.) So maybe there is a cutoff? Let us ignore the simplest possibility which does not involve any new physics, namely that the production mechanism simply peters out and the spectrum ends. We search for possible new physics scenarios which can give rise to such a cutoff: People involved in this search: Anchordoqui,Barger, Marfatia, Learned,SP,Weiler, Goldberg et al........

  43. Any scenario which gives rise to such a cutoff has to be LIV..... One possibility is a la the scenarios due to Coleman-Glashow (1997-8). In these there is a limiting velocity for each particle such that v_m is a MAV (maximum attainable velocity), as long as this v_m < c, causality is OK. v_m is different for each particle species. For example, one possibility is that neutrino mass depends on velocity such That it increases to be larger than pion mass – muon mass and at energies Beyond that the decay of pi into mu+nu is forbidden and hence there is an Upper bound on neutrino energy. Another possibility is that at some very high energy, in the plasma, there is restoration of Chiral symmetry, leading to pion mass going to zero, in which case pion Cannot decay into mu+nu, again leading to a high energy cutoff in neutrino Energy. (BTW, even then pizero CAN decay into two gammas!) Then also no neutrinos result..

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