Neutrino masses and 0νββ from neutrino oscillations
Michele Maltoni Instituto de Física Teórica UAM/CSIC
Mini Workshop: Particle theory of neutrinoless double-beta decay Online Virtual Seminar – July 15th, 2020
Instituto de Física Teórica UAM-CSIC Formalism 2
General three-neutrino oscillation framework
• Equation of motion: 6 parameters (including Dirac and neglecting Majorana phases): d~ν i = H ~ν; H = U · D · U† ± V ; dt vac vac vac mat
−iδcp iη1 Z 1 0 0 c13 0 s13 e c12 s12 0 eZ 0 0 νe Z · · − · Ziη2 Uvac = 0 c23 s23 0 1 0 s12 c12 0 0 eZ 0 , ~ν = νµ ; Z − − iδcp Z 0 s23 c23 s13 e 0 c13 0 0 1 0 0 1Z ντ h i √ 1 2 2 2Z Dvac = diag 0, ∆m21, ∆m31 + mZ1ZI ; Vmat = 2GF Ne diag 1, 0, 0 . 2Eν 6 parameters ⇐⇒ 6 types of experiments ( − solar experiments (mainly SNO) −→ θ • SOLAR sector: 12 − −→ 2 rector LBL (KamLAND) ∆m21 2 • REACT sector: − rector MBL (Double-Chooz, Daya-Bay, Reno) −→ θ13 [∆m ] 31 − atmospheric experiments (SK, DC) −→ θ23 • − → −→ 2 ATMOS sector: accelerator LBL-DIS νµ νµ (T2K, NOvA) ∆m31 [θ23] − accelerator LBL-APP νµ → νe (T2K, NOvA) −→ δcp
Michele Maltoni
Reactor neutrino disappearance and θ13
• Positive ν¯e disappearance signal in DOUBLE-CHOOZ[1], DAYA-BAY[2], RENO[3]; • experimental results are mutually consistent ⇒ it is now a firmly established fact that
θ13 , 0 ⇒ full 3ν oscillation phenomenology; • all these experiments have spectral capabilities and detector units placed at different baselines ⇒ uncertainties in the reactor flux predictions do not affect the results.
×103
140 105
4 [1] 120 10 [3]
103 100 102 80 2 4 6 8 10 12
60 Far site data
Events/MeV Weighted near site best fit Accidental 40 241Am-13C 9Li / 8He 13C(α,n)16O 20 [2] Fast neutrons
2 4 6 8 10 12
1
0.95
0.9
Far/Near(Weighted) 2 4 6 8 10 12 Eprompt[MeV]
[1] T. Bezerra [DOUBLE-CHOOZ], online talk at Neutrino 2020, Fermilab, USA, June 22–July 2, 2020. [2] D. Adey et al. [DAYA BAY], Phys. Rev. Lett. 121 (2018) 241805 [arXiv:1809.02261]. [3] J. Yoo [RENO], online talk presented at Neutrino 2020, Fermilab, USA, June 22–July 2, 2020. Michele Maltoni
Trouble with reactor fluxes [6] • Neutrino 2014: RENO[5] reported an ex- cess of events around 5 MeV; • excess (not deficit) & independent of L ⇒ flux feature, not neutrino oscillations; • seen by Daya-Bay[4], Dbl-Chooz[6], and many others (also old Chooz[7]); 1.2 2 Prompt Positron4 Energy (MeV)6 8 ⇒ reactor fluxes not properly understood. [4] 1.1 1 [5] Near Far 0.9 (Huber + Mueller)
Ratio to Prediction 0.8 2 4 6 8 Prompt Energy (MeV)
2
Ratio Measured 1.75 Positron spectrum ()Expected 1.5 [4] F. P. An et al. [Daya-Bay], CPC 41 (2017) [arXiv:1607.05378]. 1.25 1 [5] S.H Seo [RENO], talk at Neutrino 2014, Boston, USA, June 2-7, 2014. 0.75 0.5 [6] I.G. Botella [Double-Chooz], talk at EPS 2017, Venice, Italy. 0.25 [7] 0 0 2 4 6 8 [7] M. Apollonio et al. [Chooz], PLB 466 (1999) 415 [hep-ex/9907037]. MeV
Michele Maltoni
10 h2 Entries 0 10 2 Mean 0 χ RMS 0 ∆ 2 8 Measuring θ and ∆m from reactor data 8 13 6 31 6
44 • Spectral information from Double-Chooz, Daya-Bay 22 ∆χ2 2 4 6 8 10 0 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105
2.8 2.8 and Reno ⇒ oscillation pattern clearly visible ⇒ θ13 2 2.7 2.7 ] and ∆m31 accurately determined by reactor data; 2 2.6 2.6 eV -3
2.5 • FAR/NEAR spectral ratio ⇒ flux shape irrelevant; 10 2.5 × [ 2 ee 2.4 2.4 • → m accuracy from reactor νe νe comparable with LBL ∆
2.3 2.3 νµ → νµ, but oscillation channel is different ⇒ impor- [2] 2.2 2.2 tant complementary information available. 0.07 0.08 0.09 0.1 2 θ sin (2 13)
[8] [3] preliminary
[2] D. Adey et al. [DAYA-BAY], arXiv:1809.02261. [3] [3] J. Yoo [RENO], online talk at Neutrino 2020. [8] J.P. Ochoa-Ricoux [DAYA-BAY], talk at Neutrino 2018.
Michele Maltoni
2 Relevance of solar data in the determination of ∆m21 and θ12
2 √ 2 d~ν ∆m − cos 2θ12 sin 2θ12 c 0 νe • 4 4 21 ± 13 ; Pee = c13Peff + s13, i = 2GF Ne ~ν, ~ν = dt 4Eν sin 2θ12 cos 2θ12 0 0 νa • ν ≡ ν ⇒ no sensitivity to θ and δ ; 20 µ τ 23 cp Cl + Ga + BX-lo SK (1 + 2 + 3 + 4) 2 2 • ∆m ≈ ∞⇒ specific ∆m value irrelevant; 15
31 31 ] − 2 0.2%
2 eV
⇒ data only depend on ∆m , θ and θ ; -5 −0.5% 21 12 13 10 [10 −1% 2 21 ★ ★ θ dominated by SNO; m 12 ∆ −2% • param’s: 5 ★ ★ ∆m2 dominated by KamLAND; −4% 21 −8% • 0 solar region determined by high-E data, low- 20 2 SNO-full 0.45 SK + SNO sin θ = 0.022 E contribution marginal; 13 15 ]
• SNO-NC measure- 1 2 eV ment confirms SSM; 0.8 -5 10 [10
0.6 2 21 ★ ★ m • KamLAND precisely ∆ 0.4 5 ★ ★ Survival Probability 0.2 determines the os- 0.2 σ best-fit oscillationν3- Data - BG - Geo νe [3 ] 0 0 cillation pattern. 20 30 40 50 60 70 80 90 100 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.5 2 2 L0/Eν (km/MeV) sin θ sin θ e 12 12
Michele Maltoni
Tension between solar and KamLAND data
• A weak tension appears in the NuFIT 4.1 (2019) 14 12 2 2 determination of m from solar sin θ = 0.0224 GS98 w/o D/N from SK ∆ 21 13 12 10 GS98 and KamLAND data; AGSS09 10 KamLAND ]
2 8 • the choice of the assumed solar eV 8 5 −
★ 2 6
model (GS or AGSS) has little im- ∆χ [10 6 2 21
m ★ 4 pact on the issue; ∆ 4
• historically, it was noted that such 2 2 [10] tension was alleviated by a non- 0 0 0.2 0.25 0.3 0.35 0.4 2 4 6 8 10 zero θ13 value[9]; 2 2 −5 2 sin θ12 ∆m21 [10 eV ] • it is known that part of the problem arises from the large D/N asymmetry measured by 2 SK, which favor lower ∆m21 values that KamLAND; • another cause is the non-observation of a “turn-up” in SK and SNO lowest energy bins; ¿? troubles in the reactor spectrum ⇒ is KamLAND measurement reliable?
[9] G.L. Fogli et al., Phys. Rev. Lett. 101 (2008) 141801 [arXiv:0806.2649]. [10] I. Esteban et al., JHEP 01 (2019) 106 [arXiv:1811.05487] & NuFIT 4.1 [http://www.nu-fit.org]. Michele Maltoni
1.15 KamLAND and reactor ν spectrum 1.10
• KamLAND detects neutrinos from various reac- 1.05 tors, and has no near detector. Hence, spectral 1.00 distortions may be potentially relevant; Flux / Huber 0.95 • the effects of such distortions in KamLAND were 0.90 discussed briefly in[11], and more in detail Daya Bay 0.85 in[12]. In both cases the impact on ∆m2 was 2 3 4 5 6 7 8 21 Eν [MeV] found to be small; 8.50 2θ sin 13 = 0.023 • since 2017 we fix KamLAND reactor spectrum 8.25 to the measured Daya-Bay ν flux[4]; 8.00 ] 2 7.75
2 eV
⇒ the determination of ∆m is robust against reac- -5 ★ 21 7.50 [10
tor flux uncertainties, and does not help in rec- 2 21 m 7.25 ∆
onciling solar and KamLAND data. 7.00
[4] F.P. An et al. [DAYA-BAY], arXiv:1607.05378. 6.75 6.50 [11] M. Maltoni, A.Yu. Smirnov, arXiv:1507.05287. 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 2 sin θ [12] F. Capozzi et al., arXiv:1601.07777. 12
Michele Maltoni
Transition between vacuum and MSW regime in solar data − too much D/N asymmetry in SK, • Tension between solar and KamLAND related to: − non-observation of low-E turn-up; • new SK data[13]: D/N asymmetry reduced ( 3.6% → 2.1%) and “hints” of turn-up.
0.7 Super-K SNO Borexino (pp) 8 Borexino ( B) Borexino (pep) 7 0.6 Borexino ( Be) pp
0.5 > ee < P [13] 0.4
0.3 [1σ, 2σ, 3σ] Best fit (SOLAR only) 0.2 Best fit (SOLAR + KamLAND)
0.2 0.3 0.4 0.6 1 1.4 2 3 4 6 10 14
Eν [MeV]
[13] Y. Nakajima [SK], online talk at Neutrino 2020, Fermilab, USA, June 22–July 2, 2020. Michele Maltoni
2 Atmospheric oscillations: ∆m31 and θ23 • 2 → ∆m31 & θ23 dominated by LBL disappearance (νµ νµ) data; • 2 ∆m21 effects contribute only at subleading level; • reasonably good agreement between all experiments in the allowed regions, although some small differences are visible.
[14]
[16] [15]
[14] P. Dunne [T2K], online talk at Neutrino 2020, Fermilab, USA, June 22–July 2, 2020. [15] A. Himmel [NOvA], online talk at Neutrino 2020, Fermilab, USA, June 22–July 2, 2020. [16] T. Carroll [MINOS], online talk at Neutrino 2020, Fermilab, USA, June 22–July 2, 2020. Michele Maltoni
The contribution of IceCUBE/DeepCore
• Various analysis (DC16[17], DC17[18], DC19[19]) of IceCUBE/DeepCore data have been presented, all based on three years of data (but not the same years); • contribution to global fit still limited, but analysis with eight years is in progress[20].
NuFIT 4.1 (2019) [20] 15 [10] DC16 DC17 R+LBL R+LBL+DC16 10 R+LBL+DC17 2 ∆χ
5
0 -3 -2.8 -2.6 -2.4 -2.2 2.2 2.4 2.6 2.8 3 2 -3 2 2 -3 2 ∆m32 [10 eV ] ∆m31 [10 eV ]
[10] I. Esteban et al., JHEP 01 (2019) 106 [arXiv:1811.05487] & NuFIT 4.1 [http://www.nu-fit.org]. [17] M.G. Aartsen et al. [DEEPCORE], PRD 91 (2015) 072004 [arXiv:1410.7227], updated Oct. 2016. [18] M.G. Aartsen et al. [DEEPCORE], PRL 120 (2018) 071801 [arXiv:1707.07081]. [19] M.G. Aartsen et al. [DEEPCORE], PRD 99 (2019) 032007 [arXiv:1901.05366]. [20] S. Blot [DEEPCORE], online talk at Neutrino 2020, Fermilab, USA, June 22–July 2, 2020. Michele Maltoni
NuFIT 4.1 (2019) θ mixing and octant IO NO 23 15 [10] Minos NOvA • Disappearance data: T2K LBL-comb − T2K( ν & ν¯) and NOvA( ν) 10 2
data favor maximal mixing; ∆χ − NOvA( ν¯) still favors non- 5 maximal mixing, but signifi- cance is reduced since the 0 15 previous release (2018); R + Minos R + NOvA R + T2K − Minos shows strongest devi- R + LBL-comb 10 ation but lowest statistics; 2 ∆χ • appearance data: 5 − all experiments (except Mi- ◦ nos) slightly favor θ23 > 45 ; 0 0.3 0.4 0.5 0.6 0.7 0.3 0.4 0.5 0.6 0.7 • similar results for NO and IO. 2 2 sin θ23 sin θ23
[10] I. Esteban et al., JHEP 01 (2019) 106 [arXiv:1811.05487] & NuFIT 4.1 [http://www.nu-fit.org]. Michele Maltoni
∆m2 and mass ordering NuFIT 4.1 (2019) 31 15 • All the LBL experiments exhibit a small preference for NO over IO, 10 2
even when taken by themselves; ∆χ Reactors 5 Minos • such preference increases when NOvA T2K they are combined with reac- LBL-comb tors, due to better agreement in 0 15 2 the preferred ∆m31 range; • LBL preference for NO over IO: 10
− 1.8σ (only θ from reactors); 2
13 ∆χ Reactors − 2.4σ (full reactor info); 5 R + Minos R + NOvA • inclusion of Super-K atmo- R + T2K R + LBL-comb [10] 0 spheric data raises the signifi- -3 -2.8 -2.6 -2.4 -2.2 2.2 2.4 2.6 2.8 3 2 2 -3 2 2 -3 2 cance to 3.2σ (∆χ = 10.4). ∆m32 [10 eV ] ∆m31 [10 eV ]
[10] I. Esteban et al., JHEP 01 (2019) 106 [arXiv:1811.05487] & NuFIT 4.1 [http://www.nu-fit.org]. Michele Maltoni
NuFIT 4.1 (2019) Status of the CP phase IO NO 15 [10] Minos NOvA ν
• T2K data show a clear pref- NOvA ν
NOvA (ν & ν) 10 erence for maximal CP viola- T2K 2 LBL-comb tion (δcp ' −π/2), irrespective ∆χ of the mass ordering; 5 • NOvA data also favor such value for IO, but for NO it dis- 0 15 favors it at 1.5σ, preferering R + Minos R + NOvA ν
R + NOvA ν instead δ ' ±π (CP-cons); cp R + NOvA (ν & ν) 10 R + T2K • Minos has practically no sen- 2 R + LBL-comb ∆χ sitivity to δ ; cp 5 • combined LBL experiments
indicate δcp ' −3π/4, midway 0 0 90 180 270 360 0 90 180 270 360 between T2K and NOvA. δCP δCP
[10] I. Esteban et al., JHEP 01 (2019) 106 [arXiv:1811.05487] & NuFIT 4.1 [http://www.nu-fit.org]. Michele Maltoni
CP phase after Neutrino 2020 conference
• Small tension between T2K and NOvA still present[15].
[15]
[15] A. Himmel [NOvA], online talk at Neutrino 2020, Fermilab, USA, June 22–July 2, 2020. Michele Maltoni
http://www.nu-fit.org NuFIT 4.1 (2019) 2.8
Neutrino oscillations: where we are 2 31 2.6
m ★ ★ ∆ 2.4 ] • 2 Global 6-parameter fit (including δcp): eV 2.2 -3 -2.2 − Solar: Cl + Ga + SK(1–4) + SNO-full (I+II+III) + Bx; [10 -2.4 2 32 m − Atmospheric: DeepCore; ∆ -2.6 -2.8 − Reactor: KamLAND + Dbl-Chooz + Daya-Bay + Reno; 360
− Accelerator: Minos + T2K + NOvA; 270
★ ★
• CP 180 best-fit point and 1σ (3σ) ranges: δ θ = 33.82 +0.78 +2.45 , ∆m2 = 7.39 +0.21 +0.62 × 10−5 eV2, 12 −0.76 −2.21 21 −0.20 −0.60 90 (48.3 +1.1 +3.0 , (+2.523 +0.032 +0.095 × 10−3 eV2, −1.9 −7.5 2 −0.030 −0.091 θ23 = ∆m = 0 +1.1 +2.9 31 − +0.032 +0.093 × −3 2 0.3 0.4 0.5 0.6 0.7 48.6 −1.5 −7.6 , 2.509 −0.030 −0.094 10 eV , 2θ sin 23 +0.13 +0.38 +38 +148 θ13 = 8.61 −0.13 −0.39 , δCP = 222 −28 −81 ; 8 ] 2
eV 7.5 • neutrino mixing matrix: -5 ★ ★ [10
2 21 7 0.797 → 0.842 0.518 → 0.585 0.143 → 0.156 m ∆ | | 0.244 → 0.496 0.467 → 0.678 0.646 → 0.772 6.5 [10] U 3σ = . 0.287 → 0.525 0.488 → 0.693 0.618 → 0.749 0.2 0.25 0.3 0.35 0.4 0.015 0.02 0.025 0.03 2θ 2θ sin 12 sin 13 [10] I. Esteban et al., JHEP 01 (2019) 106 [arXiv:1811.05487] & NuFIT 4.1 [http://www.nu-fit.org]. Michele Maltoni
Absolute neutrino mass scale and 0νββ q P 2 2 P 2 • Quantities sensitive to absolute ν masses: mβ = i mi Uei and mββ = i mi Uei ; • these new quantities depend on:
− new parameters: lightest neutrino mass (m0) and Majorana phases (η1 and η2); − 2 2 oscillation parameters: mass-squared (∆m21, ∆m31) and mixings (θ12, θ13, δcp); • notice that:
− θ23 does not appear in Uei ⇒ irrelevant for mβ and mββ;
− only combinations (δcp + ηi) enter mββ ⇒ specific δcp value is not relevant; • 2 2 hence, phenomenological picture only affected by (θ13, θ12, ∆m21, ∆m31). 2 2 2 2 2 2 m3 = m1 +∆ m31 m2 = m3 + ∆m32 mββ 2 2 2 δ cp m = m − ∆m i 1 2 21 2 NO: IO: − m2 = m2 +∆ m2 2 e 2 1 21 T ≡ m |U | 3 i i ei T 2 2 2 2 T m = m m = m 1 e 2i η 1 0 3 0 1 2i η2 T2e
Michele Maltoni
NuFIT 4.1 (2019) Status of mβ and mββ
10-1 • Results of the global fit of oscil-
lation data can be projected onto -2 10 [eV]
mβ and mββ as a function of light- ββ P m est ν mass m0 (or mi); 10-3 • no neutrino ordering assumed: -4 both cases considered on equal 10 footing ⇒ IO region disfavored at ∆χ2 = 6.2 by oscillation data 2 (growing to ∆χ = 10.4 if Super-K 10-1
atmospheric data also included); [eV] β m • extension of mββ regions domi- 2 nated by unknown ηi ⇒ flat χ val- 10-2 ley closed by steep walls ⇒ 1σ, -3 -2 -1 0 -1 0 2σ, 3σ, . . . ranges very similar. 10 10 10 10 10 10 m0 [eV] Σmi [eV]
Michele Maltoni
2 σ[∆m ] = 0 -1 Impact of osc. parameters ji 10 IO 10-1 -2 IO 10
2 2 [eV] [eV] β
• Uncertainty on ∆m and ∆m has ββ
21 31 m m negligible impact on the extension of 10-3 NO 10-2 NO the mβ and mββ regions; 10-4
• uncertainty on θ13 marginally affect mβ, & σ[θ ] = 0 -1 13 10 IO and is irrelevant for mββ; 10-1 -2 IO 10 [eV] [eV] β • the only oscillation parameter whose ββ m m -3 precision has a visible (albeit small) im- 10 -2 NO NO 10 -4 pact on mβ and mββ ranges is θ12; 10
⇒ & σ[θ12] = 0 -1 the present phenomenological picture 10 IO will not be significantly affected by fu- 10-1 -2 IO 10 [eV] [eV] β ture improvements in the determina- ββ m m -3 tion of the oscillation parameters, ex- 10 NO 10-2 NO cept for what concerns the neutrino 10-4 [3σ] -1 -1 mass ordering. 10-3 10-2 10 10-3 10-2 10 100 m0 [eV] m0 [eV]
Michele Maltoni
NO, IO (w/o SK-atm) NuFIT 4.1 (2019) • Most of the present data from solar, atmospheric, NO, IO (with SK-atm) 15 reactor and accelerator experiments are well ex- 10
plained by the 3ν oscillation hypothesis. The 2 ∆χ three-neutrino scenario is robust; 5
0 • some interesting “hints” seem to be emerging for 0.2 0.25 0.3 0.35 0.4 6.5 7 7.5 8 8.5 2 2 -5 2 sin θ ∆m [10 eV ] what concerns the mass ordering, with NO fa- 12 21 15 vored over IO at the 2.4σ ÷ 3.2σ level (depending 10
on the included data sets); 2 ∆χ
5 • the discovery of large θ13 opened the road to
0 searches for CP violation. However, results on 0.4 0.45 0.5 0.55 0.6 0.65 -2.6 -2.5 -2.4 2.4 2.5 2.6 2 2 -3 2 2 sin θ ∆m [10 eV ] ∆m this topic need further clarifications; 23 32 31 15 • deviation from maximal θ mixing is also still an 23 10
◦ 2 open issue. θ23 > 45 seems slightly preferred; ∆χ 5 • sinergies between different experiments will be [10] 0 0.018 0.02 0.022 0.024 0.026 0 90 180 270 360 crucial to increase the sensitivity. 2 δ sin θ13 CP
[10] I. Esteban et al., JHEP 01 (2019) 106 [arXiv:1811.05487] & NuFIT 4.1 [http://www.nu-fit.org]. Michele Maltoni