Understanding Earth Matter Effect in Neutrino Oscillation Base

Understanding Earth Matter Effect in Neutrino Oscillation 廖玮 华东理 大学近代物理所 Base on PRD 77, 053002(2008) ar. Xiv: 0802. 2642 Nucl. Phys. B 702, 307(2004)

Contents 1) Neutrino oscillation & Earth matter effect 2) Oscillation of low energy neutrinos 3) Oscillation of high energy neutrinos 4) Non-standard matter effect in oscillation 5) Conclusion

Earth Density Profile 1) is complicated 2) was not known how to formulate 3) gives problem in precision measurement in future experiments We are going to 1) describe neutrino oscillation using perturbation theories 2) answer how to simplify physics picture and data analysis For solar neutrinos, supernovae neutrinos (E < 50 Me. V), atmospheric neutrinos, extra-galactic neutrinos(E> 500 Me. V)

For solar neutrinos, supernovae neutrinos E < 50 Me. V, 3 -3 analysis reduced to 2 -2 analysis

de Holanda, Liao, Smirnov, 2004 For Solar Neutrino E <20 Me. V L 31 ～ 10 km, L 21 ～ 100 km L 21, 31 << h Neutrino events can see the structure of the Earth Oscillation pattern can be perfectly described by an adiabatic perturbation theory expanded using 2 E Ve /Δm 221

For solar neutrino The thoery tells us 1) averaging over energy greatly simplify the oscillation pattern 2) main uncertainty is in events of neutrinos coming horizontally to detectors

For atmospheric neutrinos, extra-galactic neutrinos, and so on E> 500 Me. V, we do 3 -3 analysis

E > 10 Ge. V L 21 , L 31 > h Neutrino 1) can not see the structure of the Earth 2) see an average potential in matter The analytic result is computed using average potential in neutrino trajectory A very nice hint!

Conclusion We have shown that neutrino oscillation in the Earth can be perfectly described by perturbation theories in energy range with broad interests. 1) These theories tell us how to simplify the physical pictures; more importantly they tell us how to simplify data analysis. 2) Core crossing neutrino events are interesting when non-standard matter effect is present. They can provide independent probe to NC interaction to neutron and the chemical composition in the Earth.