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

2. March 6-9, 2007XII Neutrino Telescope Exploring the unknowns; 1-3 sector and mass hierarchy <= solar + reactor Atm + accel  =>  =U  i i SK atm solar+KamLAND

3. March 6-9, 2007XII Neutrino Telescope Invitation to the question I want to address

4. March 6-9, 2007XII Neutrino Telescope We have proposed T2KK to resolve CP and the mass hierarchy => lifting all the 8-fold parameter degeneracy =>Kajita-san’s talk for more about T2KK

5. March 6-9, 2007XII Neutrino Telescope Good sensitivities robust to systematic errors 0.27 Mton fid. mass each, 4 years + 4 years anti-, 5% systematic E 3  (thick) 2  (thin) Mass hierarchy CP violation (sin  ≠0) hep-ph/0504026  23 degeneracy

6. March 6-9, 2007XII Neutrino Telescope We heavily rely on spectrum analysis CP & mass hierarchy  23 degeneracy

7. March 6-9, 2007XII Neutrino Telescope 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

8. March 6-9, 2007XII Neutrino Telescope We have assumed MSW theory for propagation in matter e e νeνe νeνe W charged current interaction with electron MSW effect electron number density charged current

9. March 6-9, 2007XII Neutrino Telescope 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 …

10. March 6-9, 2007XII Neutrino Telescope 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

11. March 6-9, 2007XII Neutrino Telescope Evidence for the MSW effect (?) Gianluigi Fogli, Eligio Lisi “Evidence for the MSW effect” New J.Phys.6:139,2004. a MSW =1 for standard a factor of ∼ 2 uncertainty (at 2σ)

12. March 6-9, 2007XII Neutrino Telescope Can one measure accurately solar matter density by neutrinos ? Yes, in principle, but we are trying to go to The reason is:

13. March 6-9, 2007XII Neutrino Telescope 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 ``K L ->2  ’’ in lepton CPV

14. March 6-9, 2007XII Neutrino Telescope 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

15. March 6-9, 2007XII Neutrino Telescope What should we do? #2 Verify MSW theory, and/or In situ measurement of matter density or MSW coefficient ``a=G F Ne’’ In principle I have to start from T2KK, but …. My favorite choice

16. March 6-9, 2007XII Neutrino Telescope Let us start from the most difficult case

17. March 6-9, 2007XII Neutrino Telescope In factory the problem is severer Matter effect dominant in factory MNjhep01==>

18. March 6-9, 2007XII Neutrino Telescope How matter density uncertainty affects CP sensitivity; opinion varies Koike-Ota-Sato 02  all the parameters are assumed be uncertain by 10%

19. March 6-9, 2007XII Neutrino Telescope How matter density uncertainty affects CP sensitivity; opinion varies Huber at al. 06  2%  5%

20. March 6-9, 2007XII Neutrino Telescope Why don’t we try alternative way? In situ measurement

21. March 6-9, 2007XII Neutrino Telescope 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)

22. March 6-9, 2007XII Neutrino Telescope Let us continue; which 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) Point most sensitive to matter density variation; the magic baseline S. Uchinami, Mr. thesis HM-Uchinami, hep-ph/0612002

23. March 6-9, 2007XII Neutrino Telescope ’s pass through the mantle region

24. March 6-9, 2007XII Neutrino Telescope Constant matter density is a good approximation Effective  higher than the naïve average (Gandhi-Winter06)

25. March 6-9, 2007XII Neutrino Telescope How can we go beyond “golden people”?

26. March 6-9, 2007XII Neutrino Telescope Response to matter density change depends upon energy low energy ⇔ high energy opposite response of density change 4.3g/cm 3 4.4g/cm 3 4.2g/cm 3 energy [GeV] high density → event down↓high density → event up↑

27. March 6-9, 2007XII Neutrino Telescope （ low E : event few & high E : event large ） → low density → high density Response to density change; opposite in and anti- energy [GeV] neutrinoanti-neutrino 4.3g/cm 3 4.4g/cm 3 4.2g/cm 3 → high density → low density （ low E : event few & high E : event large ） （ low E : event large & high E : event few ） low-high energy 2 bin analysis

28. March 6-9, 2007XII Neutrino Telescope Assumption of our analysis Assume flux of 3x10 21 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 E  =50 GeV

29. March 6-9, 2007XII Neutrino Telescope Sensitivity to matter density; robust to varying systematic error Upper panel: 2% Lower panel: 4%  fixed

30. March 6-9, 2007XII Neutrino Telescope Accurate measurement of matter density possible !  true =0  true =3  /4 For sin 2 2  13 =0.1,  =1% at 3  ! Even for sin 2 2  13 =0.001,  <3% at 1  !

31. March 6-9, 2007XII Neutrino Telescope Unfortunately, it is NOT the end of the story; strong  dependence of  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 Sin 2 2  13 =0.001 Sin 2 2  13 =0.0001

32. March 6-9, 2007XII Neutrino Telescope 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

33. March 6-9, 2007XII Neutrino Telescope Problem of  dependence has not been solved by near-far combination 4000+7500 km,  =0, normal hierarchy Gandhi-Winter 06  =0.24%(2%) at sin 2 2  13 =0.1(0.001) 1313 1313

34. March 6-9, 2007XII Neutrino Telescope Self-consistent in situ determination of  13, , and matter density These results open the possibility that ``matter density’’ or MSW refraction coefficient a=G F N e 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 ?

35. March 6-9, 2007XII Neutrino Telescope 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

36. March 6-9, 2007XII Neutrino Telescope 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

37. March 6-9, 2007XII Neutrino Telescope Supplementary slides

38. March 6-9, 2007XII Neutrino Telescope 7000-9000 km is in fact the best baseline  fixed  marginalized

39. March 6-9, 2007XII Neutrino Telescope 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 Warning !

40. March 6-9, 2007XII Neutrino Telescope 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