地球の物質密度測定を使ったMSW理論のテスト“Testing MSW theory by Determination of Earth Matter Density”
Shoichi Uchinami(Tokyo Metropolitan University)
hep-ph/0612002

with Hisakazu Minakata

第２０回「宇宙ニュートリノ」研究会
2007年2月20日 ＠ 宇宙線研究所

研究会テーマ

ニュートリノで探る
non-standard physics

“standard physics” is standard ?

neutrino oscillationin vacuum

standard interaction theory
νeeMikheev-Smirnov-Wolfensteincharged currentWνe

MSW effectecharged current interaction with electron

neutrino oscillations are modified

in matterelectron number density

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)Testing MSW theory
in neutrino factory
more precisionOriginal Motivation
We want to determine the Earth Matter Density
in Neutrino FactoryEffect of matter density uncertainties
on sin22θ13on CP δ

Tommy Ohlsson , Walter Winter“The role of matter density uncertainties in the analysis of future neutrino factory experiments”

Phys.Rev.D68:073007,2003

Effect of matter density uncertainties
on sensitivity to CP violation

P. Huber , M. Lindner , M. Rolinec , W. Winter“Optimization of a neutrino factory oscillation experiment ”

Phys.Rev.D74:073003,2006

Determination of Earth Matter Density(highly precise)

Test of MSW theory(compare with geographic data)

Earth Structure by Geophysics
Seismic waves tell us about Earth
Mohorovičić discontinuity

travel-time curve

Core-Mantle boundary

mantleTime

corePathDensity Profile
seismic +free vibration by massive earthquake & inertia moment etc.

isotropic PREM
A. M. Dziewonski , D. L. Anderson“Preliminary reference Earth model”
Phys.Earth. Planet. Inter. 25, 4, 297, (1981)

accuracy 5%** Robert Geller , Tatsuhiko Hara
“Geophysical aspects of very long baseline neutrino experiments”
Nucl.Instrum.Meth.A503:187-191,2001

focus on

Neutrino Factory
NF have potential for determination of density(very long baseline & νe→νμ channel)

νe→νμ( appearance ) in matterDirect test of MSW in neutrino factory

MSW effect≠0(5σ)

Walter Winter“Direct test of the MSW effect by the solar appearance term in beam experiments”
Phys.Lett.B613:67-73,2005.

neutrino factory
e+μ+ decay
50 GeVoscillation

several thousand km

Large
Magnetized
IronCalorimeterdetectFirst Step (Which distance is better?)tune a muon energy

μ+ decay
50 GeV → 45 GeV
2 years

2 years(energy scan)
New Information
variation of event number

Energy Scana∝ρ（matter density）

aL=π large gradient→strong response to density change

Good determination

aL =π(a = const×matter density)

special distance(Magic Baseline)
L=7500 km

Magic Baseline（aL=π）
L=7500 km

vanish at aL=π→ measure θ13 independently of CP δof course matter density!

analysis
at Magic BL

event number scale depending on θ13↓

note energy spectraanalysishigh 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critical energy
response of density change
aL = π → π+ε

critical energy EC
normal hierarchy
neutrino channel

δP > 0 (E < EC)
δP < 0 (E > EC)response of density change
neutrinoanti-neutrino

4.3g/cm3
4.4g/cm34.2g/cm3

energy [GeV]（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 E : event few & high E : event large）→low density→high density→high density→low density

low-high energy 2 bin analysis

analysischi-square test

N1：event number of low energy bin
N2：event number of high energy bin
σ：systematic error
σcorr=σa=σi=2% , σai=1%

fit θ13 and ρresult
accuracy of matter density △ρ／ρ1σ(68%) C.L.
2σ(95%) C.L.
3σ(99.7%) C.L.
(1 DOF)a few (<5) ％ (1 σ)

1％ ! (3 σ)Magic Baseline（aL=π）
L=7500 km→It was independently of CP δBut…

δ dependence

sin22θ13=10-1
sin22θ13=10-2
sin22θ13=3×10-3
sin22θ13=10-3
sin22θ13=10-4
１σ(1DOF)if θ13 is small (sin22θ13<10-3),
accuracy of matter density get worse depending on δδ dependence（small θ１３）

sin22θ１３=10-3

δ= 0

δ= 7π/6

oscillation probability change is smallδ dependence
response of density change
aL = π → π+εIf θ13 is small
canceled out!
poor response to density change↓
enlarged error in Δρ/ρsummary► very precise determination of ρ at Magic BL→ 1 % (3σ)► small θ13 → < 5 % （1σ）
► large θ13

MSW theory 200 % (2σ) accuracy → 10 % ?
in future…
► Analysis with density profile► New Physics search !