Physics of Neutrino Oscillation Experiments. in the near future

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1 Physics of Neutrino Oscillation Experiments in the near future September 23, 212 International Symposium on Neutrino Physics and Beyond in Shenzhen, China Kaoru Hagiwara (KEK, Sokendai)

2 On March 8 this year, we heard a great news of discovery of sin 2 2θ 13.1 from DayaBay, which was confirmed in less than a month by RENO. The discovery advanced our knowledge on lepton flavor physics significantly, and we now have a realistic hope that the lepton flavor sector will soon be measured as accurately as the quark flavor sector with quark masses and the CKM mixing matrix. Let me stay in this talk within the 3 neutrino model, as the most conservative framework in which effects from sterile neutrinos and additional interactions can be recognized as anomalies.

3 Three neutrino model has 9 parameters: 3 masses m 1, m 2, m 3 3 angles θ 23, θ 12, θ 13 3 phases δ MNS, α 1, α 2 Neutrino oscillation experiments can measure 6 out of the 9 parameters: 2 mass-squared differences m 2 2 m2 1, m2 3 m2 1 3 angles θ 23, θ 12, θ 13 1 phase δ MNS Both mass-squared differences and ALL 3 angles have been measured. The tasks of the future neutrino oscillation experiments are to determine: the mass hierarchy m 2 3 m2 1 > or m2 3 m2 1 < the CP phase δ MNS the octant degeneracy sin 2 θ 23 >.5 or sin 2 θ 23 <.5 besides sharpening of the existing measurements and search for new physics.

4 Late in April, Yifang Wang told me about this symposium in Shenzhen near DayaBay. Shortly after I accepted his invitation, I proposed my colleagues to study the following three subjects, which are all boosted by the discovery of relatively large θ 13 : Reactor anti-neutrino oscillation experiments at medium baseline length, 1 km< L <1 km at 1 MeV< E <8 MeV. Accelerator neutrino oscillation experiments at two long baselines, T2K (L =295 km) + Tokai-to-Oki (L =653 km) at.5 GeV< E <2 GeV. Atmospheric neutrino oscillation experments with a huge detector such as PINGU in IceCube, 2 km< L <13 km at 2 GeV< E <2 GeV.

5 This talk is based on the following recent studies with my collaborators: Determination of mass hierarchy with intermediate baseline reactor anti-neutrino experiments by Shao-Feng Ge, KH, Naotoshi Okamura, Yoshitaro Takaesu arxiv:121.xxxx[hep-ph] Physics potential of neutrino oscillation experiment with a far detector in Oki Island along the T2K baseline by KH, Takayuki Kiwanami, Naotoshi Okamura, Ken-ichi Senda arxiv: [hep-ph]

6 RAPID COMMUNICATIONS PHYSICAL REVIEW D 78, 11113(R) (28) Determination of the neutrino mass hierarchy at an intermediate baseline Liang Zhan, Yifang Wang, Jun Cao, and Liangjian Wen Institute of High Energy Physics, Beijing, P.R. China 149 (Received 21 July 28; revised manuscript received 24 October 28; published 1 December 28) It is generally believed that neutrino mass hierarchy can be determined at a long baseline experiment, often using accelerator neutrino beams. Reactor neutrino experiments at an intermediate baseline have the capability to distinguish normal or inverted hierarchy. Recently, it has been demonstrated that the mass hierarchy could possibly be identified using Fourier transform to the L=E spectrum if the mixing angle sin 2 ð2 13 Þ > :2. In this study, a more sensitive Fourier analysis is introduced. We found that an ideal detector at an intermediate baseline ( 6 km) could identify the mass hierarchy for a mixing angle sin 2 ð2 13 Þ > :5, without requirements on accurate information of reactor neutrino spectra and the value of m DOI: 1.113/PhysRevD PACS numbers: g, 14.6.Lm, 14.6.Pq

7 LIANG ZHAN, YIFANG WANG, JUN CAO, AND LIANGJIAN WEN PHYSICAL REVIEW D 78, 11113(R) (28) ðeþ ¼:58 expð:87 :16E :91E 2.6 Þ No oscillation þ :3 expð:896 :239E :981E 2 Þ.5 1-P 21 oscillation þ :7 expð:976 :162E :79E 2 Þ.4 P ee for NH þ :5 expð:793 :8E :185E 2 Þ; (2) P ee for where four exponential terms are contributions from isotopes U, 239 Pu, 238 U, and 241 Pu in the reactor fuel, respectively. The leading-order expression for the cross section [17] of inverse- decay ( e þ p! e þ þ n) is ðþ ¼ : cm 2 ðe ðþ e p ðþ e =1 MeV 2 Þ; (3) ¼ E ðm n M p Þ is the positron energy when neutron recoil energy is neglected, and pe ðþ is the where E ðþ e positron momentum. The survival probability of e can be expressed as [18] P ee ðl=eþ ¼1 P 21 P 31 P 32 P 21 ¼ cos 4 ð 13 Þsin 2 ð2 12 Þsin 2 ð 21 Þ P 31 ¼ cos 2 ð 12 Þsin 2 ð2 13 Þsin 2 ð 31 Þ P 32 ¼ sin 2 ð 12 Þsin 2 ð2 13 Þsin 2 ð 32 Þ; where ij ¼ 1:27m 2 ij L=E, m2 ij is the neutrino masssquared difference (m 2 i m2 j )inev2, ij is the neutrino mixing angle, L is the baseline from reactor to e detector in meters, and E is the e energy in MeV. P ðl=eþ has three oscillation components P P (4) RAPID COMMUNICATIONS L/E (km/mev) FIG. 1. Reactor neutrino spectra at a baseline of 6 km in L=E space for no oscillation (dashed-dotted line), 1 P 21 oscillation (dotted line) and P ee oscillation in the cases of NH and, assuming sin 2 ð2 13 Þ¼:1. on the neutrino energy spectra and much smaller binning than the energy resolution, is difficult for the mass hierarchy study. Since neutrino masses all appear in the frequency domain as shown in Eq. (4), a Fourier transform of FðL=EÞ shall enhance the sensitivity to the mass hierarchy. The frequency spectrum can be obtained by the following Fourier sine transform (FST) and Fourier cosine transform (FCT):

9 GW th, 5kton, 5 years, E vis /E vis = %/ E vis 3 km NH dn / de [1/MeV] 14 4 km NH km NH 6 km NH E [MeV]

10 GW th, 5kton, 5 years, E vis /E vis = 1.5%/ E vis 3 km NH dn / de [1/MeV] 14 4 km NH km NH E [MeV] 6 km NH

11 GW th, 5kton, 5 years, E vis /E vis = 3%/ E vis 3 km NH dn / de [1/MeV] 14 4 km NH km NH E [MeV] 6 km NH

12 GW th, 5kton, 5 years, E vis /E vis = 6%/ E vis 3 km NH dn / de [1/MeV] 14 4 km NH km NH E [MeV] 6 km NH

13 4 3 2 NH Best Fit to NH data E vis /E vis = %/ E vis L=3 km dn / de [1/MeV] E vis /E vis = 6%/ E vis E [MeV]

14 6 5 NH Best Fit to NH data L=5 km dn / de [1/MeV] E vis /E vis = %/ E vis E vis /E vis = 6%/ E vis E [MeV]

15 % NH 3% NH 6% NH L [km]

16 .5 sin % NH sin % NH 6% NH pull factor m 2 12 m 2 13 f sys L [km]

17 Statistical Error %: NH sin ev ev 2 4 sin m 2 12 m %: NH 6%: NH L [km]

18 KEK-TH-1568 Physics potential of neutrino oscillation experiment with a far detector in Oki Island along the T2K baseline [hep-ph] 13 Sep 212 Kaoru Hagiwara 1,2, Takayuki Kiwanami 2, Naotoshi Okamura 3, and Ken-ichi Senda 1 1 KEK Theory Center, Tsukuba, 35-81, Japan 2 Sokendai, (The Graduate University for Advanced Studies), Tsukuba, 35-81, Japan 3 Faculty of Engineering, University of Yamanashi, Kofu, Yamanashi, , Japan Abstract

19 Some of these experiments observe the survival probability of ν μ and ν μ which are generated in the atmosphere by the cosmic ray [2]. Accelerator based long baseline experiments [3, 4, 5] also measure the ν μ survival probability. From the combined results of these experiments [2]-[5], the mass-squared difference and the mixing angle are obtained as sin 2 2θ ATM >.9 (9%C.L.), (1a) δm 2 ATM = ( ) ev 2. (1b) The sign of the mass-squared difference, eq. (1b), cannot be determined from these experiments. The SK collaboration also reported that the atmospheric neutrino oscillates into the active neutrinos [6]. The combined results of the solar neutrino observations [7, 8], which measure the survival probability of ν e from the sun, and the KamLAND experiment [9], which measure the ν e flux from the reactors at distances of a few 1 km, find sin 2 2θ SOL = , (2a) δm 2 SOL = ( 7.5.2) ev 2, (2b) where the sign of mass-squared difference has been determined by the matter effect inside the sun [13]. The SNO experiment determined that ν e from the sun changes into the active neutrinos [8].

20 Recently another new reactor experiment, the DayaBay experiment [17], announced that they have measured the neutrino mixing angle as sin 2 2θ RCT =.92 ±.16 (stat.) ±.5 (syst.), (7) which is more than 5σ away from zero. The RENO collaboration, which also measure the reactor ν e survival probability, shows the evidence of the non-zero mixing angle; sin 2 2θ RCT =.113 ±.13 (stat.) ±.19 (syst.), (8) from a rate-only analysis, which is 4.9σ away from zero. Since the MiniBooNE experiment [12] did not confirm the LSND observation of rapid ν μ ν e oscillation [18], there is no clear indication of experimental data which suggests more than three neutrinos. Therefore the ν μ ν e appearance analysis of T2K [14] and MINOS[15] presented above assume the 3 neutrino model, with the 3 3 flavor mixing, the MNS (Maki-Nakagawa-Sakata) matrix [19] ν e U e1 U e2 U e3 ν 1 ν μ = U μ1 U μ2 U μ3 ν 2, (9) ν τ U τ1 U τ2 U τ3 ν 3

21 Figure 1: The surface map of the T2K, T2KO, and T2KK experiment. The yellow blobs show the center of the neutrino beam for the T2K experiment at the sea level, where the number in the white box is the off-axis angle at SK.

22 Figure 2: The cross section view of the T2K, T2KO, and T2KK experiments along the baselines, which are shown by the three curves. The horizontal scale gives the distance from J-PARC along the arc of the earth surface and the vertical scale measures the depth of the baseline below the sea level. The numbers in the white boxes are the average matter density in units of g/cm 3 [35]-[42].

23 Under the same conditions that give eq. (17) for the ν μ survival probability, the ν e appearance probability can be approximated as [3] { ( ) } P νμ ν e = 4sin 2 θ ATM sin 2 θ RCT (1 + A e )sin 2 Δ13 + Be 2 2 sin Δ 13 + C e, (22) where we retain both linear and quadratic terms of Δ 12 and a. The analytic expressions for the correction terms A e, B e and C e are found in Ref.[3]. For our semi-quantitative discussion below, the following numerical estimates [3] for sin 2 2θ ATM =1andsin 2 2θ SOL =.852 suffice: ( ) A e ρ L π.37 3g/cm 3 1 sin2 2θ RCT 1km Δ 13 2 [ ].29 Δ 13.1 ρ L π π sin θ RCT 3g/cm 3 sin δ MNS, (23a) 1km Δ 13 ( ) B e ρ L.58 3g/cm 3 1 sin2 2θ RCT 1km 2 [ ][ ] +.3 Δ 13.1 ρ L π π sin 2 cos δ MNS θ RCT 3g/cm 3. (23b) 1km Δ 13

24 The first term in A e in eq. (23a) is sensitive not only to the matter effect but also to the mass hierarchy pattern, since Δ 13 π ( π) for the normal (inverted) hierarchy around the oscillation maximum Δ 13 π. For the normal (inverted) hierarchy, the magnitude of the ν μ ν e transition probability is enhanced (suppressed) by about 1% at Kamioka, 24% at Oki Island, and 37% at L 1 km in Korea, around the first oscillation maximum, Δ 13 π. When L/E ν is fixed at Δ 13 π, the difference between the two hierarchy cases grows with L, because the matter effect grows with E ν. Within the allowed range of the model parameters, the difference of the A e between SK and a far detector at Oki or Korea becomes A e peak(l = 653km) A e peak(l = 295km) ±.13, (24a) A e peak(l 1km) A e peak(l = 295km) ±.26, (24b) where the upper sign corresponds to the normal, and the lower sign for the inverted hierarchy. The hierarchy pattern can hence be determined by comparing P νμ ν e near the oscillation maximum Δ 13 π at two vastly different baseline lengths [26]-[3], independently of the sign and magnitude of sin δ MNS. In eq. (23b), it is also found that the first term in B e, which shifts the oscillation phase from Δ 13 to Δ 13 + B e = Δ 13 ±B e, is also sensitive to the mass hierarchy pattern. As in the case for A e, the difference in B e between SK and a far detectors is found Bpeak(L e = 653km) Bpeak(L e = 295km).1, (25a) Bpeak(L e 1km) Bpeak(L e = 295km).2, (25b)

25 18 (a) m 2 3 -m2 1 > 18 (b) m 2 3 -m2 1 < input δ MNS input sin 2 2θ RCT input sin 2 2θ RCT Figure 1: The Δχ 2 min contour plot for the T2KO experiment to exclude the wrong mass hierarchy in the plane of sin 2 2θ RCT and δ MNS. The left figure is for the normal hierarchy and the right one is for the inverted hierarchy. The OAB combination for both figures is 3. at SK and 1.4 at Oki Island with POT for both ν μ and ν μ focusing beams. Contours for Δχ 2 min = 4, 9, 16, 25, 36, 49 are shown. All the input parameters other than sin 2 2θ RCT and δ MNS are shown in eqs. (28) and (29).

26 18 (a) m 2 3 -m2 1 > 18 (b) m 2 3 -m2 1 < input δ MNS input sin 2 2θ RCT input sin 2 2θ RCT Figure 11: The same as Fig. 1, but for T2KK experiment with the optimum OAB combination, 3. OAB at SK and.5 OAB at L = 1km. Δχ 2 min values are given along the contours.

Figure 12: The Δχ 2 contour plot for the T2KO experiment in the plane of sin 2 2θ RCT and δ MNS when the mass hierarchy is assumed to be normal (left) or inverted (right).

27 Figure 12: The Δχ 2 contour plot for the T2KO experiment in the plane of sin 2 2θ RCT and δ MNS when the mass hierarchy is assumed to be normal (left) or inverted (right). Allowed regions in the plane of sin 2 2θ RCT and δ MNS are shown for the combination of 3. OAB at SK and 1.4 at Oki Island with POT each for ν μ and ν μ focusing beams. The input values of sin 2 2θ RCT is.4,.8, and.12 and δ MNS is,9, 18, and 27. The other input parameters are given in eqs. (28) and (29). The dotted-lines, dashed-lines, and solid-lines show Δχ 2 min = 1, 4, and 9 respectively. The blue shaded region has mirror solutions for the wrong mass hierarchy giving Δχ 2 min < 9.

28 Figure 13: OAB at L = 1km. The same as Fig. 12, but for T2KK experiment with 3. OAB at SK and.5

29 18 (a) 18 (b) δ MNS (c) 18 (d) δ MNS sin 2 2θ RCT sin 2 2θ RCT Figure 14: The Δχ 2 min contour plot for the T2K 122 experiment in the plane of sin 2 2θ RCT and δ MNS when the mass hierarchy is assumed to be normal (m 2 3 m2 1 > ). Allowed regions in the plane of sin 2 2θ RCT and δ MNS are shown for experiments with POT each for ν μ and ν μ focusing beam at 3. off-axis angle. The input values of sin 2 2θ RCT are.4,.8, and.12 and δ MNS are (a), 9 (b), 18 (c), and 27 (d). The other input parameters are listed in eqs. (29) and (28). The red dotted-lines, dashed-lines, and solid-lines show Δχ 2 min = 1, 4, and 9 contours, respectively, when the right mass hierarchy is assumed in the fit, whereas the blue contours give Δχ 2 min measured from the local minimum value (shown besides the symbol) at the cross point when the wrong hierarchy is assumed in the fit. -18

30 18 (a) 18 (b) 9 9 δ MNS (c) 18 (d) δ MNS sin 2 2θ RCT sin 2 2θ RCT Figure 15: The same as Fig. 14, but for the inverted mass hierarchy (m 2 3 m2 1 < ).

31 Summary Intermediate baseline reactor anti-neutrino oscillation experiments like Dayabay2 and RENO2 can (1) determine the mass hierarchy (2) measure sin 2 θ 12 and m 2 2 m2 1 very accurately with very fine energy resolution de/e <.3/ E/MeV. T2K+Korea and/or Oki is a very cost effective one-beam twodetector LBL neutrino oscillation experiment, which can (1) determine the mass hierarchy (2) measure δ MNS (3) determine sin 2 θ 23 >.5 or sin 2 θ 23 <.5

Revisiting T2KK and T2KO physics potential and ν µ ν µ beam ratio

NuFact1 - Rio de Janeiro, Brazil - August 1 Revisiting T2KK and T2KO physics potential and ν µ ν µ beam ratio Kaoru Hagiwara Theory Center, KEK, 1-1 Oho, Tuskuba, Ibaraki -81, Japan and Department of Accelerator