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Comments on: Flavor Mix and Fluxes of High Energy Astrophysical Neutrinos

Sandip Pakvasa University of Hawaii Honolulu
XVI Lomonosov conf., Lomonosov Moscow, 26 august,2013


Existence of High Energy Gammas suggests that High energy accelerators in space EXIST P+P and P+ collisions produce 0`s and + `s 0 `s observed.....(?) + `s.......hence high energy `s must exist! At detectable, useful fluxes? We know now that the answer is yes....


Possible neutrino sources: (i) GRB's as suggested by Waxman and Bahcall (ii) AGN's
Recent revival of 1991 model for AGN neutrinos, F. Stecker(2013) Neutrino flux has a broad peak at about 1 PeV.Basic process: P+gamma -> delata+ -> n +pi_0

06/28/13


FLAVORS at the Source: The variety of initial flavor mixes
Conventional: P +P + X, + , + e hence: e / = 1/2 Same for P + , except no anti-e. Damped muon sources: if does not decay or loses energy: No e `s, and hence e / = 0/1 Pure Neutron Decay or Beta-Beam sources: n antie, hence e/ = 1/0 Prompt sources, when 's absorbed and only heavy flavors contribute and e/ = 1, such a flavor mix also occurs in muon damped sources at lower energies from decays. (Winter et al,2010) In general, flavor mix will be energy dependent...... See for example papers by Walter Winter et al.......


Neutrinos from "GZK" process: BZ neutrinos:
Berezinsky and Zatsepin pointed out the existence/inevitability of neutrinos from : PCR + CMB + n + + Flavor Mix: below 10 Pev: (n decays)pure BetaBeam: e:: = 1:0:0 Above 10 PeV: conventional( decays) :e:: =1:2:0 (due to Engel et al. PRD64,(2001), also Stanev(2009))


This is for Primaries being Primarily protons.


Current Knowledge of Neutrino Mixing and Masses
e
=

UMNSP

1 2 3

m322 ~ 2.5 .10-3 eV2, m212 ~ 8 .10-5 eV2 UMNSP~ UTBM = 2/3 1/3 -1/6 1/3 1/2 -1/6 1/3 -1/2

( ~ 0.15:DB,RENO,DC(2012)) Unkown: Mass Pattern: Normal or Inverted:, phase 3 _______
2_________ 1_________

2_______ 1 _______
3________


Effects of oscillations on the flavor mix are very simple: m2 > 10-5 eV2 , hence (m2 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 (m2L/4E) averages to Ѕ survival and transition probablities depend only on mixing angles: P = i Ui4 P = i Ui2Ui2


In this tri-bi-maximal approximation, the propagation matrix P is:
P = 1/18 10 4 4 4 7 7 4 7 7

e
source

=
earth

P

e


Using the most recent best fit from e.g. Schwetz et al, the propagation matrix P becomes
0.5543 0.28/0.186 0.164/0.219 0.28/0.186 0.346/0.41 0.164/0.22 0.378/0.371

0.3775/0.3713 0.47/0.4325

(the two values correspond to = 0 or )


Flavor Mix at Earth (using Tri-BiMax mixing):
Beam type Initial Final 1:1:1 Conventional (pp,p) 1:2:0 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!


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.


Discriminating flavors
The ratios used to distinguish various flavor mixes are e.g. fe (e/(e++) and R(/[e+]) Source type fe R Pionic 0.33 0.5 Damped- 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 , and Betabeam can be distinguished but probably not the prompt
(Beacom et al. PRD69(2003).{Esmaili(2009).Choubey(2009).}


Can small deviations from TBM be measured in the flavor mixes? Corrections due to /13 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!


Some examples of exceptions:
1. Pseudo-Dirac Neutrinos, where the Mixing angle is maximal, but m^2 Is very small: < 10^-12 eV^2 2. Mixing angle with sterile enhanced over some range of E and L due to a MSW-like resonant effect (e.g. Sterile taking short-cut in bulk a la the model of Paes et al).


In addition, sources are never "pure" meaning:
Conventional/pp: after including polarization and effects due to K, D etc decays, the mix changes from1:2:0 to approx. 1:1.85:, ( < 0.01) Damped sources do not have exactly 0:1:0 but probably more like :1:0 with 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)


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.


Current Icecube bounds on GRB 's correspond to a limit on flux of 's to about a factor of 4(3.7) below the somewhat conservative Waxman-Bahcall bound. (the bound is for each flavor assuming 1:1:1 mix) R. Abbasi et al. Nature, 484,351(2012) Also there has been no hints yet of a signal from AGNS or other sources of high energy neutrinos in form of µ events......... Caveat: Recent modified versions of WB can accommodate lower fluxes..... e.g. P. Hummer et al., Z. Li(2012). If we take the two PeV shower events at face value(and one shower event at 2 PeV) assuming they are CC _e events then e's are NOT depleted.....but _'s maybe? BTW decay length for a 2 PeV is 100m....


Large deviations:


How many ways can the flavor mix deviate significantly from 1:1:1 ?
1.

Initial flux different from canonical: e.g. the damped muon scenario. In this case the flavor mix will be: 4:7:7 (But this is unlikely at ALL energies.) similarly for the beta beam source, the flavor mix will be: 5:2:2 instead of 1:1:1

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


What do we know?
Radiative decays: i j + : m.e.: j(C + D5)µ i Fµ SM: 1/ = (9/16)(/)GF2/{1283}(mij2)3/mi m2/mW2(UiUj*) 2 SM > 1045 s
(Petcov, Marciano-Sanda)(1977)

Exptl. Bounds on = e/mi[ C+ D 2]1/2 = 0B From e + e e + ': 0 < 10-10 (PDG2010), this corresponds to: > 1018 s. Bounds for other flavors somewhat weaker but still too strong for radiative decay to be Of practical interest. {Caveat: the two processes are at very different momentum transfers}


Invisible Decays:
i j + +: Exptl Bounds: F < GF, < O(1), from invisible width of Z
> iL jL + : gij jL jL d If isospin conserved: invisible decays of charged leptons governed by the same gij, and bounds on e + , and /e + yield bounds such as: > 1024 s.
{Jodidio et al. (1986), PDG(1996)} Bilenky and Santamaria(1999): 1034 s


Conclusion: Only "fast" decays are Majoron type

g CjRiL : I(isospin) can be a mixture of 0 and 1(GR, CMP) The final state can be mixture of flavor/sterile states......... Bounds on g from & K decays
Barger,Keung,SP(1982),Lessa,Peres(2007), g2 < 5.10-6 SN energy loss bounds: Farzan(2003): g < 5.10-7

invisible couplings

g2 < 5.10-6 corresp. to > 10-8 s/eV g < 5. 10-7 corresp. to > 0.1 s/ev


Current experimental limits on i:
1/m1 > 105 s/eV SN 1987A B. o. E. Careful analysis. 2/m2 > 10-4 s/eV (Solar) 10-4-10-2s/eV
Beacom-Bell(2003),KamLand(2004) 3/m3 > 3.10-11s/eV (Atm) Gonzalez-Garcia-Maltoni(2008)

9.10-11 s/eV

Cosmology: WMAP/PLANCK free-streaming 's > 1010 s/eV at least for one ...
Hannestad-Raffelt(2005), Bell et al.(2005)

( With L/E of TeV/Mpsc or PeV/1000Mpsc, can reach of 104 s/eV)

These bounds depend crucially on free-streaming and whether one or all neutrinos are free-streaming.


When i decays, Ui gets multiplied by the factor exp(-L/c) and goes to 0 for sufficiently long L. For normal hierarchy, only 1 survives, and the final flavor mix is simply (SP 1981):

e:: = Ue12:U12:U12 ~ 4:1: 1 or even 10:1:1 with the new best fits... These flavor mixes are drastically different from canonical 1:1:1 and easily distinguishable. Some sensitivity to cos()... {Inverted hierarchy leads to strong depletion of electorn neutrino flux}
Beacom et al(2003)


Effects on absolute fluxes in decay scenarios:
In normal hierarchy, if only 1 survives: µ flux can go down by as much as a factor of 0.1 from the original flux at the source. . e 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). (As pointed out by Weinberg(2013), a Goldstone boson also would give the same factor of 4/7 modified by the factor depending on the time of decoupling)


But if the decay is into a sterile neutrino then (NH)........
3 and 2 simply disappear and only 1 survives but at a smaller flux. The final fluxes are then: e : 2/3 of the original flux µ : 1/6 of the original flux Other implications: -counting in early universe modified by 3 -> 4+4/7, this is in some conflict with PLANCK + BBN.




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 KobayashiLim(2001). These arise when there are sub-dominant Majorana mass terms present along with dominant Dirac mass terms.


The three m2's will be different, in general. Deltam^2 has to be smaller than 10^-12 eV^2 so as not to disturb solar nu fits.





In principle, there is some sensitivity to cosmolgical parameters:
The oscillation phase at great distances depends on the redshift z, the Hubble constant H etc.. and may not average out ... And if there are enuf data points, one can measure the redshift in neutrinos, rather than photons!


Implications for absolute fluxes:
In particular, if the separation for the m21 is much smaller than for the other two, '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 1/2 and the flavor mix returns to the canonical 1:1:1


6. Effects of Magnetic Fields
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 at the maximum allowed values of about 10-14B and B of order of a Gauss
In this case, large conversion from flavor to sterile state can occur, and reduce absolute fluxes by a factor of 2 or more.....

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


Flavor Signatures in IceCube ...
1013 eV (10 TeV) 6x1015 eV (6 PeV) Multi-PeV
B10


+N+... ± (300 m!) +hadrons

signature of



signature of


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 Ѕ: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 13 and ....
If a is <<1, then decays with inverted hierachy may be occuring.. Can probe v.v. small m2 beyond reach of neutrinoless double beta decay.... Anisotropy can be due to flavor violating gravity?


As for the absolute fluxes of flavor neutrinos .........
There are two new physics scenarios can account for the suppression of fluxes of µ `s without affecting e very much: (i) Neutrino Decay and (ii) pseudo-Dirac neutrinos
In both cases there are other implications of the proposals which render them testable in principle ............e.g. the neutrino counting in early universe being 3+4/7 for decay and lack of observable neutrinoless double beta decay for pseudo-Dirac case.(Joshipura,Mohanty and SP PRL,110,171802(2013). Same thing can be done for suppression of electron neutrinos...