Measuring Earth Matter Density and Testing MSW

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


Invitation to the question I want to ad

dress


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


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


We heavily rely on spectrum analysis

CP & mass hierarchyCP & mass hierarchy 23 degeneracy23 degeneracy


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


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


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 …


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


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)


Can one measure accurately solar matter density by neutrinos ?

• Yes, in principle, but we are trying to go to • The reason is:


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


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


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


Let us start from the most d

ifficult case


In factory the problem is severer

Matter effect dominant in factory MNjhep01==>

Matter effect dominant in factory MNjhep01==>


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%


How matter density uncertainty affects CP sensitivity; opinion varies

Huber at al. 06Huber at al. 06

2%2%

5%5%


Why don’t we try

alternative way? In situ measureme

nt


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)


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


’s pass through the mantle region


Constant matter density is a good approximation

Effective higher than the naïve average (Gandhi-Winter06) Effective higher than the naïve average (Gandhi-Winter06)


How can we go

beyond “golden people”?


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↑


（ 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


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


Sensitivity to matter density; robust

to varying systematic error

Upper panel: 2% Lower panel: 4%

Upper panel: 2% Lower panel: 4%

fixed fixed


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 !


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


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


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


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 ?


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


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


Supplementary slides


7000-9000 km is in fact the best baseline

fixed fixed

marginalized marginalized


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 !


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

Documents

Measuring Earth Matter Density and Testing MSW