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Neutrini da reattore: la misura di θ13

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Gli esperimenti fino al 2003

I nuovi esperimenti

Impact of the CHOOZ (1998) experiment on the mixing matrix

νe disappearance probability: 22

)()(1 LLee νννν τµ −−=P

Evolution of a neutrino produced as ne at distance L from source:

LiEe

LiEe

LiEe eUeUeUL 321

332211)( −−− ++= νννν

( )LEEie

LEEiee

LiE eUUeUUUUeL )(33

)(2211

13121)( −−−−− ++= µµµµ νν

Remember: for E >> m EmmEE ki

ki 2

22 −≈−

Ignoring the overall phase exp(–iE1L) :

LE

i

e

LE

i

ee eUUeUUUUL 233

22211

1312

)(Δ−Δ−

++= µµµµ νν

( )LEEie

LEEiee

LiE eUUeUUUUeL )(33

)(2211

13121)( −−−−− ++= ττττ νν

LE

i

e

LE

i

ee eUUeUUUUL 233

22211

1312

)(Δ−Δ−

++= ττττ νν

In the CHOOZ experiment <E> ≈ 3 MeV , L ≈ 1000 m

1(m)(MeV)

)(eV534.22

21212 <<Δ=Δ LE

LE

oscillation effects associated with Δ12 are negligible

03.013

12 ≈ΔΔ=αDefine:

CHOOZ limit: Pee < 0.11 for |Δ13| ≈ 2.5 x 10-3 eV2 (90% conf. level)

θ13 < 11.5°

Series expansion of three – flavour νe (and νe) disappearance probability (E.K. Akhmedov et al., JHEP 04 (2004) 078):

⎟⎠⎞⎜

⎝⎛ Δ−−=−−=

ELLLee 13

213

212

2222

267.1sinsin42sin1)()(1 θθανννν τµP

( ) ( )( ) ( )( ) ( ) ⎥

⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

00

00

00

2/12/34cos2/34sin2/12/34cos2/34sin034sin34cos

ννν

ννν

τ

µ e < 0.2

CHOOZ limit

Three – neutrino mixing matrix consistent with all measured oscillation parameters:

L’ esperimento RENO (Reactor Exp. for Neutrino Oscillations)

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Il detector

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Flusso di neutrino e meccanismo di rivelazione

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Selezione eventi

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Fondi

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Risultati

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Analisi Dati

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Errori sistematici

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Double Chooz

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Comparazione risultati

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AGGIORNAMENTO 2013

G.Battistoni 2014

sin2(2θ13) = 0.092±0.017 tan2(θ12) = 0.457+0.040−0.029. Questo corrisponde a θ12 ≡ θsol = 34.06+1.16−0.84° sin2(2θ23) > 0.92 at 90% confidence level, corrispondente a θ23 ≡ θatm = 45±7.1° Δm221 ≡ Δm2sol = 7.59+0.20−0.21×10−5 eV2 |Δm2

31| ≈ |Δm232| ≡ Δm2

atm = 2.43+0.13−0.13×10−3 eV2 δ, α1, α2, e il segno di Δm2

32 non sono attualmente noti

This effect is only possible for m2 > m1

=> Information on mass hierarchy in the m2 m1 system

21

Aggiornamento 2015

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This is the first measurement obtained with the completed Daya Bay detector configuration consisting of eight modular antineutrino detectors, providing a total target mass of 160 tonnes. Four detectors located around 300 to 500 m from the reactors measure the initial νe rate from the reactors, while four detectors at around 1.6 km from the reactors observe the subsequent disappearance. The analysis found sin2(2θ13) = 0.084±0.005 from the amplitude of anti-νe disappearance, while the energy dependence of this disappearance provided a measurement of oscillation frequency expressed in terms of the effective mass-squared difference |Δm2

ee| = (2.42±0.11) × 10–3 eV2 This is actually related to the two almost-equal neutrino mass-squared differences |Δm2

32| and |Δm231| = |Δm2

32 + Δm221|.

If the mass hierarchy is normal, then |Δm2

32| = (2.37±0.11) × 10–3 eV2, while if it is inverted, |Δm2

32| = (2.47±0.11) × 10–3 eV2.