Measuring Earth Matter Density and Testing MSW

1. Measuring Earth Matter Density and Testing MSW Hisakazu Minakata Tokyo Metropolitan University

2. na=Uaini Exploring the unknowns; 1-3 sector and  mass hierarchy Atm + accel n => <= solar + reactor n SK atm solar+KamLAND XII Neutrino Telescope

3. Invitation to the question I want to address XII Neutrino Telescope

4. We have proposed T2KK to resolve CP and the  mass hierarchy =>lifting all the 8-fold parameter degeneracy XII Neutrino Telescope =>Kajita-san’s talk for more about T2KK

5. 0.27 Mton fid. mass each, 4 years  + 4 years anti-, 5% systematic E Good sensitivities robust to systematic errors hep-ph/0504026 Mass hierarchy CP violation (sind≠0) 23 degeneracy 3 s (thick) 2 s (thin) XII Neutrino Telescope

6. We heavily rely on spectrum analysis CP & mass hierarchy 23 degeneracy XII Neutrino Telescope

7. Question • Does this way of uncovering CP violation give a robust evidence for CPV? • This talk is meant to raise the questions, not answering them XII Neutrino Telescope

8. We have assumed MSW theory for  propagation in matter e νe charged current W MSW effect νe e charged current interaction with electron electron number density XII Neutrino Telescope

9. Then the question is: • What happens if the MSW theory is in error • You may say that it was verified by bunch of the solar  experiments • In what sense and to what accuracy? Most probably, we are in trouble … XII Neutrino Telescope

10. Is MSW theory verified by solar ? • Yes and No • Yes because some matter effects are needed to explain the solar  data in consistent with KamLAND • No because there is no confirmation of characteristic feature of LMA solution: day-night variation, spectrum upturn • The accuracy neutrinos can measure matter density by MSW is still limited, currently only ~factor of 2 XII Neutrino Telescope

11. Evidence for the MSW effect (?) Gianluigi Fogli, Eligio Lisi “Evidence for the MSW effect” New J.Phys.6:139,2004. aMSW=1 for standard a factor of ∼2 uncertainty (at 2σ) XII Neutrino Telescope

12. Can one measure accurately solar matter density by neutrinos ? • Yes, in principle, but we are trying to go to • The reason is: XII Neutrino Telescope

13. The problem I want to address ultimately • Demonstrate leptonic CPV under any variation of MSW theory that are allowed by the current (or available at that time) experimental constraints There is no ``KL->2’’ in lepton CPV XII Neutrino Telescope

14. What should we do? #1 • Invent robust way of uncovering CPV;namely, verify CPV in a manner independent of the current uncertainty in ``matter effect’’ in  propagation in matter • Or, carry out vacuum effect dominated CP measurement => MEMPHYS (or T2K II) I prefer this option because of mass hierarchy XII Neutrino Telescope

15. What should we do? #2 • Verify MSW theory,and/or • In situ measurement of matter density or MSW coefficient ``a=GFNe’’ • In principle I have to start from T2KK, but …. My favorite choice XII Neutrino Telescope

16. Let us start from the most difficult case XII Neutrino Telescope

17. In  factory the problem is severer Matter effect dominant in  factory MNjhep01==> XII Neutrino Telescope

18. How matter density uncertainty affects CP sensitivity; opinion varies  all the parameters are assumed be uncertain by 10% Koike-Ota-Sato 02 XII Neutrino Telescope

19. How matter density uncertainty affects CP sensitivity; opinion varies 2% 5% Huber at al. 06 XII Neutrino Telescope

20. Why don’t we try alternative way? In situ measurement XII Neutrino Telescope

21. In situ measurement of the matter density in Nufact • In situ measurement of the matter density in fact has been tried by Cervera et al. ``Golden measurement paper 00’’ ~10% level sensitivity obtained (SMA assumed) XII Neutrino Telescope

22. Let us continue; which baseline? Point most sensitive to matter density variation; the magic baseline • Matter effect / vacuum effect depends upon  energy E • So we examined ``energy scan’’ • In high energy expansion aL= results analytically (another derivation of magic baseline) HM-Uchinami, hep-ph/0612002 S. Uchinami, Mr. thesis XII Neutrino Telescope

23. ’s pass through the mantle region XII Neutrino Telescope

24. Constant matter density is a good approximation Effective  higher than the naïve average (Gandhi-Winter06) XII Neutrino Telescope

25. How can we go beyond “golden people”? XII Neutrino Telescope

26. Response to matter density change depends upon  energy high density → event up↑ high density → event down↓ 4.3g/cm3 4.4g/cm3 4.2g/cm3 energy [GeV] low energy　⇔　high energy opposite response of density change XII Neutrino Telescope

27. Response to density change; opposite in  and anti- neutrino anti-neutrino 4.3g/cm3 4.4g/cm3 4.2g/cm3 energy [GeV] （low E : event few & high E : event large） （low E : event large & high E : event few） →low density →high density （low E : event few & high E : event large） （low E : event large & high E : event few） →high density →low density low-high energy 2 bin analysis XII Neutrino Telescope

28. Assumption of our analysis E=50 GeV • Assume  flux of 3x1021 useful muon decays for each polarity (Blondel et al. 06) • Assume 40 kton magnetized iron detector at L=7500 km from the  source • Detection efficiency of 80% in E=5-50 GeV • near (3000-4000) km detector modeled as gaussian 2 (width 20 deg.) Cervera et al. Nufact06 XII Neutrino Telescope

29. Sensitivity to matter density; robust to varying systematic error  fixed Upper panel: 2% Lower panel: 4% XII Neutrino Telescope

30. Accurate measurement of matter density possible ! true=0 true =3/4 For sin2213=0.1,=1% at 3 !Even for sin2213=0.001,<3% at 1 ! XII Neutrino Telescope

31. Unfortunately, it is NOT the end of the story; strong  dependence of  Sin2213=0.0001 Sin2213=0.001 At very small 13, atm and interference terms are of the same order in size; No -dependence at the magic baseline is merely a folklore XII Neutrino Telescope

32. The way out • Clearly the way out of the problem is to combine measurement at (1) L=3000 - 4000 km from which most of the CP sensitivity come but still have some sensitivities to  (2) L=7500 km from which most of the sensitivity to  come • (3000-4000)+7500 km the ``standard setting’’ in Nufact XII Neutrino Telescope

33. Problem of  dependence has not been solved by near-far combination 4000+7500 km, =0, normal hierarchy Gandhi-Winter 06 1 3 =0.24%(2%) at sin2213=0.1(0.001) XII Neutrino Telescope

34. Self-consistent in situ determination of 13, , and matter density • These results open the possibility that ``matter density’’ or MSW refraction coefficient a=GFNe can be determined in situ in nufact experiments • Global strategy yet to be formulated; e.g., (1)Three unknown parameters to be determined2 analysis with 3 DOF? (2) Iterative analysis ? XII Neutrino Telescope

35. Conclusion • If such self-consistent procedure is formulated, nufact can determine in situ all the relevant parameters without relying on geophysical earth models • My original problem, demonstrating CPV in a robust way (which survives even with current experimental uncertainty of MSW theory), prevails • I want to come back soon to this issue with T2KK XII Neutrino Telescope

36. Conclusion (continued) • If the matter density can be measured by neutrino experiments it will give us a way of doing geophysics by an independent means from seismological study XII Neutrino Telescope

37. Supplementary slides XII Neutrino Telescope

38. 7000-9000 km is in fact the best baseline  fixed  marginalized XII Neutrino Telescope

39. Warning ! The problem I want to address ultimately • Though I said ``Demonstrate leptonic CPV under any variation of MSW theory that are allowed by the current (or available at that time) experimental constraints’’ the variation cannot be too general • We may not be able to deal with generic case such as XII Neutrino Telescope

40. What do you mean exactly by ``testing MSW’’? • Measuring the matter density is NOT the only way to test MSW theory But, it is certainly one of the consistency check • ``Mass eigenstate in matter’’ will be tested by solar day-night effect XII Neutrino Telescope