The Earth Matter Effect in the The Earth Matter Effect in the T2KK Experiment T2KK Experiment

Ken-ichi SendaGrad. Univ. for Adv. StudiesGrad. Univ. for Adv. Studies

Present status of neutrino oscillation parametersPresent status of neutrino oscillation parameters

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ToTokai-kai-toto--KaKamioka (T2K)mioka (T2K) 　　experimentexperiment

J-PARC (Tokai)Super – Kamiokande (SK)

•T2K will start at the beginning of 2009. 　

•The beam intensity for the T2K experiment

is about 100 times as the one for the K2K experiment.

(1021 Proton On Target / yr)

•Main purpose: observing the νμ→νe transition ( sin∝ 2

θrct) 　 　 　 　 　 　

Distance 295km

Off-axis beam & T2KK experiment

narrow0.5GeV ~ 0.7 GeV

２ ° ～３ °

wide More than

1.0 GeV

near the center

（～ 0.5° ）

Energy rangePeak energy

In order to observe the oscillation maxima at SK,

the neutrino energy should be 0.5GeV ~ 0.7 GeV

High energy neutrino produces a lot ot π0’s

⇒ Back Ground to the νe

appearance event

Korea

If we place the second detector in Korea, we can perform 2 detector Long baseline neutrino experiment, Tokai-to-Kamioka-and-Korea experiment!!

Matter effect, CP phase, and mass hierarchyMatter effect, CP phase, and mass hierarchy

The interaction with electrons in the earth affects the neutrino oscillation. → Matter effectMatter effect

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Matter effect Contribution of the solar parameter

The interaction between neutrino and the electron affects the neutrino oscillation !!

•The matter effect term in Ae

is sensitive to the sign of δm213

. In Korea (L ~1000km), this term produces the large difference between thenormal(δm2

13>0) and Inverted (δm2

13 <0) hierarchy.

•The correlated ambiguity beweenn sin2 θRCT

and δMNS

can be solved by the difference of the matter effect between Kamioka and Korea.

Determining the mass hierarchy in T2KKDetermining the mass hierarchy in T2KK

Input: Normal hierarchy

Fit: Inverted hierarchyInput sin2 2θRCT = 0.10 δMNS = 0

K.Hagiwara, N. Okamura, and KS (hep-ph/0607255)Detector size: SK 22.5kt Korea 100ktMatter density: SK 2.8 g/cm3 Korea 3.0 g/cm3

Exposure time: 5 yearsIncluding the expected constraint on θ

RCT from the future reactor experiment

Best location to dermine the hierarchy Capability of determining the mass hierarchy by Best combination

The hierarchy pattern can be constrained at more than 3σ level

if sin2 2θRCT

> 0,05.

Input: normal

Fit : normal

Inverted

δMNS is constrained ± 30° 　 at 1 sigma level.

Around small θRCT region, the allowed regions for the fake hierarchy remain.

Measurement of CP phase in T2KKMeasurement of CP phase in T2KK

Earth matter effect Earth matter effect

Previous studies, we assume that the matter density is constant along the baseline, and the average of the density is same for all Tokai-to-Korea baseline. However...

Matter density along the baseline is not constant.Neutrinos travel through various matters.

Neutrinos go through deeper region when the baseline length becomes longer. So the matter density distribution depends on the baseline length.

We need detail studies on the “earth matter effect ” to justify the potential of T2KK experiment.

Earth matter profile - average density-Earth matter profile - average density-

averaged density of the path (g/cm3)

base-line lengthdepth

of crust

3.003.002.992.872.79-2.0km

3.002.992.902.802.79 0.0 km

2.992.932.822.802.79+2.0km

1200km1150km1100km1050km1000km

Error : ±0.1 g/cm3

What is the effect of the local dependent matter What is the effect of the local dependent matter effect ?effect ?

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Only the cos modes affect the neutrino oscillation.The oscillation phase is not affected..δA term is sensitive to the hierarchy pattern.

Earth matter profile - fluctuation-Earth matter profile - fluctuation-

Previous ： ρ=3.0 g/cm3 New: Earth matter effect

•The significance to determine the hierarchy at the best point becomes lower. ←The averaged matter effect becomes small

　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 ρ=3.0g/cm3 → 2.8g/cm3

But… We can still confirm the mass hierarchy at more than 4 σ CL!!

Capability of the mass determination

SummarySummary The lower side of the T2K beam will appear in Korea. The matter effect in T2KK experiment is key to

determine the mass hierarchy pattern and CP phase. The mean value of the density along the Tokai-to-

Korea baselines are 2.8, 2.9, and 3.0 g/cm3 for L = 1000, 1100, 1150km, respectively. The only first Fourier mode and the average matter

density are important in T2KK experiment. The best combination (SK3.0deg + Korea 0.5 deg.)

keep the enough capability to determine the hierarchy, whenever we consider the earth matter distribution along each baseline length.

For Achivement

1st Workshop: November 2005

@ KIAS

2nd Workshop: July 2006

@Soul National Univ.

Topic:

The kind of detectors,

Candidate place for constructing the detector in Korea

Sensitivity to the new physics

How to solve the atomospheric-angle degeneracy

3rd Work shop: September 2007 in Tokyo

To Be Continued…….To Be Continued…….

Analysis methodAnalysis method•Detector size (fiducial volume) Super-Kamiokande : 22.5 kt The detector in Korea : 100 kt

•Exposure time 5 years ( time of T2K running) → 5 ×1021 Proton On Target •Matter density Tokai-to-Kamioka: 2.8 g/cm3

Tokai-to-Korea: 2.0 g/cm3

•Base line length and off-axis angle Kamioka: L = 295 km off-axis angle: 2.5°, 3.0° Korea: L = 1000km – 1200km off-axis angle: 0.5°- 3.0 °

•Signals Charged Current Quasi Elastic Events …We can reconstruct the neutrino energy and distinghish e events and μ events. bin width: 200MeV 0.4 – 5.0 GeV for -like (SK/Korea)

0.4 – 1.2 GeV for e-like (SK) 0.4 – 2.8 GeV for e-like (Korea) Background Secondary neutrino flux of the νμ 　 primary beam.

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Capability to determine the mass hierarchyCapability to determine the mass hierarchy

3σ: sin2 2θRCT > 0.045 (normal hierarchy) or 0.055 (inverted hierarchy)

The normal hierarchy can exclude the fake hierarchy more strongly than the inverted hierarchy. → statistical error.

Capability strongly depends on CP phase. ← Contribution of the phase shift !

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Fit CP phase and reactor angleFit CP phase and reactor angle

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Fitting CP phase is favored around 0 deg. in order to reduce the phase difference.

When the input hierarchy is normal (inverted), the fitting reactor angle is larger (smaller) than input reactor angle.

In this analysis, the statistical error is dominant. →Δχ2 is roughly proportional to detector size of the

beam flux.

•Δχ2 　 is proportional to the fudicial volume.

•Only Hyper?-Kamiokande can not determine the mass hierarchy.

•Constraint from the reactor experiment plays the same role of Kamioka.

•Constraint on CP phase by the Kamioka is useful.

•Optimal ratio is 1:11 ~ 2:4

Total fiducial volume: 600kt