1.5 Origin of Lepton Mixing and Neutrino Oscillation
1.5.1 Neutrino Oscillation Parameters
As mentioned earlier, from enormous number of experiments around the globe it is now confirmed that neutrinos oscillate and we now have strong constraints on the oscillation parameters. For three flavor neutrino oscillation the involved parameters are2:
2Here, two Majorana phases appearing in the neutrino mixing matrix (Eq. 1.44), however have no consequence in the oscillation probabilities.
• Three mixing angles (θ12,θ23 and θ13).
• Dirac CP phase (δ).
• Two mass-squared differences, namely solar mass-squared difference (∆m2) and atmospheric mass-squared difference (∆m2atm).
Figure 1.3: Schematic diagram form neutrino mass hierarchies. Left-panel represents normal hierarchy whereas right panel represents inverted hierarchy [68].
It turns out that scale associated with the two mass-squared differences are distinct and differs almost by two orders of magnitude. The ‘small’ mass-squared difference,
∆m2 = ∆m221=m22−m21is involved in solar neutrino oscillation whereas the ‘large’ mass- squared difference, ∆m2atm= ∆m232=m23−m22 ( or ∆m231) is involved in the atmospheric neutrino oscillation. From the present data the sign of ∆m2atm is still unknown to us and this leads to two very different arrangement of the neutrino mass spectrum as shown in Fig. (1.3)3. Conventionally for ∆m2atm ≈ ∆m232 > 0 it as called normal hierarchy (NH) and the the mass ordering is m1 < m2 < m3. On the other hand for ∆m2atm ≈
∆m231<0 it is known as inverted hierarchy (IH) and the mass ordering follows the pattern m3 < m1 < m2. Over the years neutrino oscillation parameters are being measured and we are now moving towards the precision measurement era of these parameters. The Super-Kamiokande experiment with atmospheric neutrinos first hinted a large mixing, close to maximal value (θ23 ' 45◦) and the atmospheric mass-squared difference to be
3In addition to this, quasi-degenerate spectrum of neutrino masses is possible with m1 ' m2 ≈ m3
withm21,2,3>>∆m2atm.
∆m2atm ' O(10−3 eV2) [69] providing a solution to the atmospheric neutrino problem stated earlier. Subsequently, SNO [62], KamLAND [64] suggested that sin2θ12'1/3 and solar mass-squared difference to be ∆m2 ' O(10−5 eV2) and solved the solar neutrino puzzle. Thus neutrino oscillation was confirmed by several oscillation experiments and the two mixing (θ12 and θ23) angle were measured and found to be large. Afterwards several atmospheric and solar, neutrino oscillation experiments gathered plenty of data to achieve commendable precision. However the experiments aiming to measure the reactor mixing angle θ13 were sill in their evolutionary stage and prior to 2012 it was suggested that this mixing angle is small (sin2θ13= 0.01+0.016−0.011, best-fit vale with 1σ error)[9].
Now for complete understanding of neutrino mixing matrix it is essential to measure the third mixing angle θ13 as it can play an important role in theoretical model building of neutrino mass matrices. In addition to this, precise measurement of θ13 is extremely important for the design of the experiments aiming to measure the CP-violating phase δ. Further, neutrino mass hierarchy can be determined incorporating matter effect in neutrino oscillation which also depends on the magnitude of θ13. Keeping this in mind several experiments were commissioned and in last ten years significant improvement have been made in measuring the size ofθ13. Earlier, the CHOOZ experiment [70–72] in France and Palo Verde experiment [73] in Arizona, USA both made attempts to measureθ13. In each of these experiments the detector was placed roughly at a distance of 1 kilometer to study electron antineutrinos emitted (through inverse beta decay: ¯νe+p→e++n) from nuclear reactors. However these two reactor experiments did not observe any positive hint for the mixing angleθ13and was speculated to be very small. Upto 2003, these experiments only set an upper limit on θ13 and it is sin22θ13<0.14 at 90% CL. Subsequently, several experiments started taking data to improve the measurement ofθ13with higher sensitivity.
In this regards three reactor experiment were set up to observe short baseline neutrino oscillation. These experiments are Double Chooz (in France), Daya Bay (in China) and RENO (in South Korea). By construction these experiments are very similar having both near and far detectors to measure un-oscillated and oscillated neutrino flux. Below we briefly discuss about these three short baseline experiments.
Double Chooz: This experiment is located at the same site of the earlier CHOOZ experiment in The Chooz Nuclear Power Plant, France. It is an upgraded version of CHOOZ with better statistical and systematic uncertainties. Also some development were made in the detection technique and material (the core target is made of transparent
acrylic and holds Gadolinium-doped liquid scintillator). In this experiment, the near detector is placed at 400 meter away from the core for renormalization of the neutrino flux and to measure oscillation with any effect of θ13. The far detector is placed at a distance of 1050 meter to study the oscillation. Comparing the data accumulated by both of these detectors an estimation for sin22θ13 is made. In 2012 this experiment reported the best fit value of θ13 with 1σ error as [74]
sin22θ13= 0.109±0.030(stat.)±0.025(syst.), (1.46) with ∆m231= 2.32×10−3eV2and discarded no oscillation assumption at 99.8% CL (2.9σ).
After the announcement of first positive hint [75] on θ13 in 2011 by Double Chooz, two independent collaborations Daya Bay and RENO also started publishing their result.
Daya Bay: This experiment is situated at the Daya Bay Nuclear Plant in southern China.
In this experiment six cores (two from Daya Bay Nuclear Plant and six from nearing LingAo Nuclear Plant) are used to study the antineutrino flux and relies on the basic principle of Double Chooz experiment. For Daya Bay reactor the near and far detectors are placed at a distance 350 meter and 2000 meter respectively. Whereas for LingAo reactor near and far detectors are located at a distance of 480 meter and 1600 meter respectively. Here the acrylic vessel filled with Gadolinium-doped liquid scintillators are used as detector. In 2012 Day Bay published its first result with positive hint of nonzero θ13 as [76]
sin22θ13= 0.089±0.010(stat.)±0.005(syst.) (1.47) at 5.2σ. Afterwards more data was accumulated and a precise measurement was made in 2013 [77].
RENO: The RENO experiment [78] is located at the Hanbit Nuclear Power Plant (for- merly Yeonggwang Nuclear Power Plant), Jeollanam-do province, South Korea. This experiment is also governed by Double Chooz concept. Two identical 16-ton Gadolinium- doped liquid scintillator detectors are placed roughly 294 meter (near detector) and 1383 meter (far detector) from the center of the six core reactor array. This experiment started taking data with both the detectors in August 2011 and after 229 day data-taking it reported
sin22θ13= 0.113±0.013(stat.)±0.019(syst.) (1.48) at 4.9σ.
Apart from these short baseline experiments, few next generation long baseline exper- iments were built with an aim to measure θ13 using the same multiple detector concept.
In these experiments θ13 is estimated from appearance of electron neutrino in a muon electron beam. In addition, these experiments aims to measure Dirac CP phaseδ as well as the mass hierarchy considering matter effect. T2K (in Japan), MINOS and NOνA (both in USA) are examples of such long baseline experiments and typical baseline in these experiments ranges within few hundred kilometers.
Considering data obtained from various experiments a global analysis can be done to estimate the parameters appearing in the neutrino mass matrix as well as the mass squared differences [5]. In Table 1.2 we have summarized the neutrino oscillation parameters form a recent global analysis by Foreroet al. Other similar analysis can be found in [79, 80].
Oscillation parameters best fit 1σrange 3σrange
∆m221 [10−5eV2] 7.60 7.42–7.79 7.11–8.18
|∆m231|[10−3eV2] 2.48 (NH) 2.38 (IH)
2.41−2.53 2.32−2.43
2.30−2.65 2.20−2.54
sin2θ12 0.323 0.307–0.339 0.278–0.375
sin2θ23 0.567 (NH) 0.573 (IH)
0.439–0.599 0.530–0.598
0.392–0.643 0.403–0.640 sin2θ13 0.0234 (NH)
0.0240 (IH)
0.0214–0.0254 0.0221–0.0259
0.0177–0.0294 0.0183–0.0297
Table 1.2: Summary of neutrino oscillation parameters for normal and inverted neu- trino mass hierarchies from the analysis of [5].
Currently the goal of present and future neutrino oscillation experiments involve de- termination of (i) octant of θ23, i.e. whether θ23 <45◦ or θ23 >45◦. (ii) sign of ∆m2atm, which will determine the hierarchy of neutrino masses and (iii) magnitude of Dirac CP violating phaseδ. Any theoretical model which have potential to address these issues can by verified by the upcoming experiments.