Reactor anomaly - Neutrino anomalies - Development of the oscillation analysis framework for th

1.4 Neutrino anomalies

1.4.3 Reactor anomaly

In nuclear reactor experiments, the ν_e’s coming from the reactor can be used to study oscillations by measuring the survival probability P_ν_e_→_ν_e, which can be derived from the PMNS matrix and formula 1.17 [44]:

P_ν_e_→_ν_e =1−^cos⁴(θ₁₃) sin²(2θ₁₂) sin² ∆m²₂₁L 4E

− ^sin²(2θ₁₃) sin² ∆m²₃₂L 4E

. (1.19)

18 CHAPTER 1. NEUTRINOS: FROM STANDARD TO STERILE

The Gallium neutrino (a) and reactor antineutrino (b) anomalies. The data error bars represent the uncorrelated experimental uncertainties. The horizontal solid green line and the surrounding shadowed band show the average ratio R and its uncertainty calculated taking into account the experimental uncertainties, their correlations and, in panel (b), the theoretical uncertainty of the Huber-Mueller antineutrino fluxes.

The LSND anomaly has been explored in the MiniBooNE experiment that is operating at Fermilab since 2002. In this experiment the neutrinos are produced by the 8 GeV protons from the Fermilab booster hitting a beryllium target and producing a beam of pions. The sign of the pions that are focused towards the detector is determined by the polarity of a focusing horn. The detector, placed at a distance of 541 m from the target, consists of a tank filled with 818 tons of pure mineral oil (CH

) viewed by 1520 phototubes that detect the Cherenkov light and isotropic scintillation produced by charged particles.

Since in MiniBooNE the neutrino energy ranges from 200 MeV to 3 GeV the range of L/E, from 0.18 to 2.7 m/MeV, covers the LSND range of L/E (from 0.5 to 1.5 m/MeV).

However, since in LSND L/E is smaller than 1.5 m/MeV, the LSND signal should be seen in MiniBooNE for E & 360 MeV.

Initially the MiniBooNE experiment operated in “neutrino mode” with a focused beam of ⇡

⁺

that decayed in a decay tunnel producing an almost pure beam or ⌫

’s. In the first article (35) the MiniBooNE collaboration considered the data with E > 475 MeV, arguing that this threshold “greatly reduced a number of backgrounds with little impact on the fit’s sensitivity to oscillations”. No excess over background was observed, leading to a 98%

exclusion of neutrino oscillation as the explanation of the LSND anomaly. However an excess of ⌫

-like events was observed below the 475 MeV analysis threshold. This low-energy excess was confirmed in the following years, in both neutrino (6, 36) and antineutrino (37) modes, whereas the data above 475 MeV continued to show little or no excess over the backgrounds.

Since most of the energy range below 475 MeV correspond to values of L/E outside the LSND range, the low-energy excess is an e↵ect di↵erent from the LSND anomaly, and it has been considered as the “MiniBooNE low-energy anomaly”. A possible explanation of this anomaly is that the low-energy excess is produced by photons, that cannot be distinguished from

⁽

⌫

e⁾

-like events in the MiniBooNE detector (single photon events are generated by neutral-current ⌫

-induced ⇡

⁰

decays in which only one of the two decay photons is visible).

This possibility is going to be investigated in the MicroBooNE experiment at Fermilab (38), with a large Liquid Argon Time Projection Chamber (LArTPC) in which electrons and photons can be distinguished.

12 C. Giunti and T. Lasserre

Figure 1.8: The calibration of the GALLEX and SAGE experiments resulted in an unexpectedly low average ratio Rof detected-over-calculated neutrino events. The result is known as the gallium anomaly. [43]

Figure 1.9 plots the survival probability as a function of the detector distance L, together with data points of different experiments.

From the figure, we see that experiments with a baselineLof the order of 1 km are sensitive to the shorter wavelength oscillation, that is governed by

∆m²₃₂. For these distances and a neutrino energy of the order 3 MeV, the term in ∆m²₂₁becomes negligible, and formula 1.19 simplifies to

P_ν_e_→_ν_e ≈¹− ^sin²(2θ₁₃) sin² ∆m²₃₂L 4E

. (1.20)

This implies that these experiments are most sensitive to measure the θ₁₃ mixing angle. Examples of such short baseline experiments are Daya Bay [45, 46], Double Chooz [47] and RENO [48, 49].

For experiments with L > 100 km, the rapid oscillations due to ∆m²₃₂ average out:

1.4. NEUTRINO ANOMALIES 19

Figure 1.9: Oscillation curve for a 3 MeV reactor antineutrino in the 3-flavour neu-trino model. The relativeν_e fluxes, measured by various experiments are indicated.

Adapted from [16].

and the dominant oscillation becomes the one determined by∆m²₂₁: P_ν_e_→_ν_e ≈¹−¹₂ ^sin²(2θ₁₃) −^cos⁴(θ₁₃) sin²(2θ₁₂) sin² ∆m²₂₁L

(1.22)

≈^cos⁴(θ₁₃) +sin⁴(θ₁₃) −^cos⁴(θ₁₃) sin²(2θ₁₂) sin² ∆m²₂₁L 4E

(1.23)

≈^cos⁴(θ₁₃)

1−^sin²(2θ₁₂)sin² ∆m²₂₁L 4E

, (1.24)

where we have applied some trigonometric identities to go from eq. 1.22 to eq. 1.23 and have neglected the very small term sin⁴(θ₁₃)to come to eq. 1.24.

This type of search was conducted by the long baseline experiment Kam-LAND, that found results consistent with the solar neutrino measurements [50].

A third type of experiments, also depicted in figure 1.9, are the ones mea-suring at very short baselines, ranging from 10 to 100 meters: Bugey [51],

20 CHAPTER 1. NEUTRINOS: FROM STANDARD TO STERILE Goesgen [52], ILL-Grenoble [53], Rovno [54], ... . For such small source-to-detector distances, we expectP_ν_e_→_ν_e ≈1 and thus also a ratio,R, of expected-to-predictedν_e-flux compatible with 1.

For some time, the combined data of a range of very short baseline exper-iments indeed resulted in a value R = 0.980±0.024, consistent with unity.

However, in 2011, a new set of theoretical reactor antineutrino spectra were published, based on a novel calculation method.⁵ This updated prediction model resulted in an increase of the predicted reactor flux by about 3%, mov-ing the expected-to-observed ν_e ratio down to R = 0.927±0.023, see figure 1.10. This 2.9σdeficit is known as thereactor antineutrino anomaly(RAA) [55].

R=NexpNcal 0.650.750.850.951.051.15