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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.
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