1. SOLAR ATMOSPHERE NEUTRINOS
TAUP 2007 – International Conference on Topics in Astroparticle and Underground Physics
Sendai, September 2007
SOLAR ATMOSPHERE NEUTRINOS
Alessandro MIRIZZI
(MPI, Munich, Germany)
Based on:
G.L. Fogli, E. Lisi, A.M., D. Montanino, P.D. Serpico, PRD 74, (2006) [hep-ph/ ].

2. OUTILNE Solar atmosphere neutrino (SAn) fluxes
Sun as high energy neutrino source
Solar atmosphere neutrino (SAn) fluxes
SAn oscillations in Sun and in vacuum
Event rate in HE neutrino telescopes
Conclusions
Alessandro Mirizzi TAUP Sendai, 13/09/2007

3. MeV SOLAR NEUTRINOS
Sun is a well-known source of low-energy O(MeV) ne, produced in its core by nuclear reactions
Solar neutrinos provide us with solid evidence for  mass & mixing, and with a beautiful synthesis of physics and astrophysics.
Alessandro Mirizzi TAUP Sendai, 13/09/2007

4. HIGH ENERGY SOLAR NEUTRINOS
Solar flares (E~ 50 MeV)
WIMP annihilation in the Sun (E~ GeV)
Alessandro Mirizzi TAUP Sendai, 13/09/2007

5. SOLAR ATMOSPHERE NEUTRINOS (SAn)
Cosmic rays hitting the solar atmosphere lead to the production of secondary particles via high-energy pp interaction, the decay of which produces a flux of ne and nm.
( )
( )
(at production)

6. SAn ORIGINAL FLUXES
[G.Ingelman & M.Thunman, hep-ph/ ]
SAn flux calculated basing on Montecarlo models (PHYTIA & JETSET) for high energy particle interactions at different impact parameter 0<b<R. . b
The original fluxes are almost b-independent below the TeV scale
Alessandro Mirizzi TAUP Sendai, 13/09/2007

7. SAn ATTENUATION IN THE SUN
While propagating in Sun, SAn are affected by
oscillations in matter
attenuations through weak interactions with nucleons of the solar medium.
Interaction cross sections approximatively the same: oscillations and absorptions can be factorized [V.Naumov, hep-ph/ ]
Absorptions taken into account multiplying the original n fluxes by an overall attenuation function A(E,b)
Attenuation function
For E~ GeV, a flux attenuation of O(10%) or less is expected only for case with b~0 (which have little geometrical weight)

8. UNOSCILLATED SAn FLUXES
The factorization of oscillations and absorptions allows to take as unoscillated input the attenuated fluxes, integrated over the solar disk.
For E<100 GeV, no simulation
We assume
as in [C.Hettlage, K.Mannheim, J. Learned, astro-ph/ ]
with 1.75<g<2.45 to take into account uncertainties related to heliomagnetic effects [D.Seckel, T.Stanev, T.K. Gaisser, Astrophys. J. 382, 652 (1991)]

9. The neutrino event rates above 1 TeV can be ignored in practice.
The rapid decrease of the SAn fluxes with energy is only partially compensated by the increase of the (charged current) neutrino cross sections s.
The neutrino event rates above 1 TeV can be ignored in practice.
Relatively low experimental threshold will be crucial for future SAn detection.
Alessandro Mirizzi TAUP Sendai, 13/09/2007

10. Dynamical MSW term (in matter) Kinematical mass-mixing term
SAn OSCILLATIONS
SAn fluxes are affected by oscillation effects in Sun and then in vacuum.
We have solved numerically MSW neutrino equations
considering the standard 3n oscillation framework
Dynamical MSW term (in matter)
Kinematical mass-mixing term
Alessandro Mirizzi TAUP Sendai, 13/09/2007

11. Mixing parameters: U = U (q12, q13, q23) as for CKM matrix
3n FRAMEWORK
Mixing parameters: U = U (q12, q13, q23) as for CKM matrix
M2 = , , ± Dm2
dm2 2
“solar”
“atmospheric”
Mass-gap parameters: n3
Dm2
dm ≈ (1±0.09)  eV2
sin2q12 ≈ ( )
Dm ≈ 2.6 ( )  eV2
sin2q23 ≈ 0.45( )
sin2q13 =  10-2
inverted hierarchy n1
dm2/2 n1
dm2/2 n2
-dm2/2 n2
-dm2/2 n3
-Dm2
normal hierarchy
[Fogli et al., hep-ph/ ]
In the following we will assume normal hierarchy
Alessandro Mirizzi TAUP Sendai, 13/09/2007

12. NEUTRINO POTENTIAL
Matter effects on n oscillations crucially depend on neutrino potential in Sun:
+ ( n ) ; - ( n )
Potentially large matter effects are expected at resonance when or
In normal hierarchy the resonance condition can be fulfilled only by n

13. OSCILLATED n FLUXES
SAn fluxes at Earth expressed in terms of the oscillation probabilities
appearence ! ….
But, challenging to be detected at E~ 102 GeV
Alessandro Mirizzi TAUP Sendai, 13/09/2007

14. VACUUM APPROXIMATION (V=0)
[C.Hettlage, K.Mannheim, J. Learned, astro-ph/ ]
(at the production)
VACUUM OSCILLATIONS
Many oscillation cycles in vacuum
+ n decoherence at Earth (energy resolution)
(at Earth)
[for q23=p/4]
Alessandro Mirizzi TAUP Sendai, 13/09/2007

15. MATTER EFFECTS Matter effects High energy vacuum limit (l»R)
Resonance condition never realized in n channel. Matter effects negligible.
Matter effects suppressed after averaging over n+n
Alessandro Mirizzi TAUP Sendai, 13/09/2007

16. AVERAGING OVER THE IMPACT PARAMETER
Given the limited angular resolution of the detector (dq>1°), one has to integrate over the solar disk (qsun~0.26°).
Matter effects strongly suppressed after the averaging.
Oscillation probabilities very similar to the phase-averaged vacuum case
Alessandro Mirizzi TAUP Sendai, 13/09/2007

17. VARIATIONS OF OSCILLATION PARAMETERS
The spread of the curves due to sin2q23 uncertainties amounts to about ±15%, while the variations due to sin2q13 and d are roughly a factor of three smaller.
The ± 2s errors on the other oscillations parameters (Dm2, dm2, sin2q12), as well as the change from normal to inverted hierarchy, would produce even smaller variations in these curves.
In practice, one can currently evaluate the effects of oscillation parameters uncertainties in terms of sin2q23 only.
Alessandro Mirizzi TAUP Sendai, 13/09/2007

18. OSCILLATED SAn FLUXES AT EARTH
Uncertainty associated to 2s range of q23
Uncertainty associated to the initial fluxes
OSCILLATIONS
Alessandro Mirizzi TAUP Sendai, 13/09/2007

19. SAn EVENT RATE
Events rate in a km3 detector (e.g., Icecube) [A= 1 km2]
SAn signal dominates over the atmospheric bkg in the solar angular bin.
Mismatch between the produced m and the original n: in the observable angular bin S/N ~ 1 for E > 100 GeV
Huge cosmic ray bkg: only upgoing n useful
~ 4 useful m events/year above 100 GeV
In ~10 years it would allow a “SAn check” of q23
Alessandro Mirizzi TAUP Sendai, 13/09/2007

20. CONCLUSIONS
The Sun is a valuable source of high-energy neutrinos, produced by cosmic ray interactions in solar atmosphere (“solar atmosphere neutrinos”, SAn)
We have performed a detailed study of SAn oscillations, including matter effects in the Sun:
SAn are affected by peculiar matter effects (in principle, sensitive to q13 and to mass hierarchy). However, (i) the averaging over the impact parameter; (ii) the indistinguishability between n and n strongly contribute to suppress them.
“Vacuum” approximation is accurate enough to characterize SAn oscillation effects.
The detection of SAn in large telescope detectors would:
test n vacuum oscillation at high energy scale
provide information on solar astrophysics
perhaps provide signature of new neutrino physics and eventually of dark matter
Alessandro Mirizzi TAUP Sendai, 13/09/2007