measuring earth matter density and testing msw
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Measuring Earth Matter Density and Testing MSW. Hisakazu Minakata Tokyo Metropolitan University. n a =U a i n i. Exploring the unknowns; 1-3 sector and mass hierarchy. Atm + accel n =>.TRANSCRIPT
Measuring Earth Matter Density and Testing MSW
Hisakazu Minakata
Tokyo Metropolitan University
March 6-9, 2007 XII Neutrino Telescope
Exploring the unknowns; 1-3 sector and mass hierarchy
<= solar + reactor
<= solar + reactor
Atm + accel =>
Atm + accel =>
=Ui i=Ui i
SK atmSK atm
solar+KamLANDsolar+KamLAND
March 6-9, 2007 XII Neutrino Telescope
Invitation to the question I want to ad
dress
March 6-9, 2007 XII Neutrino Telescope
We have proposed T2KK to resolve CP and the mass hierarchy => lifting all t
he 8-fold parameter degeneracy
=>Kajita-san’s talk for more about T2KK=>Kajita-san’s talk for more about T2KK
March 6-9, 2007 XII Neutrino Telescope
Good sensitivities robust to systematic errors Good sensitivities robust to systematic errors 0.27 Mton fid. mass each, 4 years + 4 years anti-, 5% systematic E0.27 Mton fid. mass each, 4 years + 4 years anti-, 5% systematic E
3 (thick)3 (thick) 2 (thin)2 (thin)
Mass hierarchyMass hierarchy CP violation (sin≠0)CP violation (sin≠0)
hep-ph/0504026
23 degeneracy23 degeneracy
March 6-9, 2007 XII Neutrino Telescope
We heavily rely on spectrum analysis
CP & mass hierarchyCP & mass hierarchy 23 degeneracy23 degeneracy
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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
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We have assumed MSW theory for propagation in matter
e
e
νe
νe
W
charged current interaction with electron
MSW effect
electron number density
charged current
March 6-9, 2007 XII 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 …Most probably, we are in trouble …
March 6-9, 2007 XII Neutrino Telescope
Is MSW theory verified by solar ?
• Yes and No• Yes because some matter effects are ne
eded 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
March 6-9, 2007 XII Neutrino Telescope
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)
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Can one measure accurately solar matter density by neutrinos ?
• Yes, in principle, but we are trying to go to • The reason is:
March 6-9, 2007 XII 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 ``KL->2’’ in lepton CPV There is no ``KL->2’’ in lepton CPV
March 6-9, 2007 XII 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
I prefer this option because of mass hierarchy
March 6-9, 2007 XII Neutrino Telescope
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 choiceMy favorite choice
March 6-9, 2007 XII Neutrino Telescope
Let us start from the most d
ifficult case
March 6-9, 2007 XII Neutrino Telescope
In factory the problem is severer
Matter effect dominant in factory MNjhep01==>
Matter effect dominant in factory MNjhep01==>
March 6-9, 2007 XII Neutrino Telescope
How matter density uncertainty affects CP sensitivity; opinion varies
Koike-Ota-Sato 02Koike-Ota-Sato 02
all the parameters are assumed be uncertain by 10%
all the parameters are assumed be uncertain by 10%
March 6-9, 2007 XII Neutrino Telescope
How matter density uncertainty affects CP sensitivity; opinion varies
Huber at al. 06Huber at al. 06
2%2%
5%5%
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Why don’t we try
alternative way? In situ measureme
nt
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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)
~10% level sensitivity obtained (SMA assumed)
March 6-9, 2007 XII 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
Point most sensitive to matter density variation; the magic baseline
S. Uchinami, Mr. thesisS. Uchinami, Mr. thesisHM-Uchinami, hep-ph/0612002HM-Uchinami, hep-ph/0612002
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’s pass through the mantle region
March 6-9, 2007 XII Neutrino Telescope
Constant matter density is a good approximation
Effective higher than the naïve average (Gandhi-Winter06) Effective higher than the naïve average (Gandhi-Winter06)
March 6-9, 2007 XII Neutrino Telescope
How can we go
beyond “golden people”?
March 6-9, 2007 XII Neutrino Telescope
Response to matter density change depends upon energy
low energy ⇔ high energy opposite response of density change
4.3g/cm3
4.4g/cm3
4.2g/cm3
energy [GeV]
high density → event down↓high density → event up↑
March 6-9, 2007 XII Neutrino Telescope
( low E : event few & high E : event large)→low density
→high density
Response to density change; opposite in and anti-
energy [GeV]
neutrino anti-neutrino
4.3g/cm3
4.4g/cm3
4.2g/cm3
→high density
→low density( low E : event few & high E : event large)
( low E : event large & high E : event few )
( low E : event large & high E : event few )
low-high energy 2 bin analysis
March 6-9, 2007 XII Neutrino Telescope
Assumption of our analysis
• 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. Nufact06Cervera et al. Nufact06
E=50 GeVE=50 GeV
March 6-9, 2007 XII Neutrino Telescope
Sensitivity to matter density; robust
to varying systematic error
Upper panel: 2% Lower panel: 4%
Upper panel: 2% Lower panel: 4%
fixed fixed
March 6-9, 2007 XII Neutrino Telescope
Accurate measurement of matter density possible !
true=0true=0 true =3/4true =3/4
For sin2213=0.1,=1% at 3 ! Even for sin2213=0.001,<3% at 1 !
For sin2213=0.1,=1% at 3 ! Even for sin2213=0.001,<3% at 1 !
March 6-9, 2007 XII 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
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
Sin2213=0.001Sin2213=0.001Sin2213=0.0001Sin2213=0.0001
March 6-9, 2007 XII 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
March 6-9, 2007 XII Neutrino Telescope
Problem of dependence has not been solved by near-far combination
4000+7500 km, =0, normal hierarchy Gandhi-Winter 06
4000+7500 km, =0, normal hierarchy Gandhi-Winter 06
=0.24%(2%) at sin2213=0.1(0.001) =0.24%(2%) at sin2213=0.1(0.001)
1 31 3
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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 ?
March 6-9, 2007 XII Neutrino Telescope
Conclusion • If such self-consistent procedure is formulat
ed, 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
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Conclusion (continued) • If the matter density can be measured by n
eutrino experiments it will give us a way of doing geophysics by an independent means from seismological study
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Supplementary slides
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7000-9000 km is in fact the best baseline
fixed fixed
marginalized marginalized
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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 !Warning !
March 6-9, 2007 XII 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