Neutrino mass hierarchy Theory and phenomenology Walter Winter

Neutrino mass hierarchy: Theory and phenomenology. Walter Winter DESY, Zeuthen Neutrino 2014, Boston, MA, USA June 4, 2014

Contents > Why would one like to know the mass ordering? > How to measure the mass ordering? > Technological approaches to measure the mass ordering Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 2

Neutrino masses: Ordering versus Hierarchy > The (atmospheric) mass ordering is unknown (normal or inverted) 8 > The absolute neutrino mass scale is unknown (< e. V). Often parameterized by lightest neutrino mass: m 1 or m 3 8 > In theory: three cases Normal Inverted § Normal hierarchy: m 1 < (Dm 212)0. 5 (ordering: normal) § Inverted hierarchy: m 3 << |Dm 312|0. 5 (ordering: inverted) § (Quasi-)Degenerate: m 1 ~ m 2 ~ m 3 >> |Dm 312|0. 5 (ordering: normal or inverted) [plus some recently growing interest in the transition regime: m 1 (for NO) ~ |Dm 312| ] > Lower bound on neutrino masses from Dm 312 ~ 0. 0024 e. V 2: Normal hierarchy: m 3 ~ 0. 05 e. V Inverted hierarchy: m 1, m 2 ~ 0. 1 e. V Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 3

Why would one like to know the mass ordering? Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 4

Origin of neutrino mass (simple example: effective Majorana mass, charged leptons diagonal) > Neutrino masses read, roughly (e: hierarchy parameter) 1 Hierarchy: normal Degenerate case Hierarchy: inverted > Neutrino mixings, roughly (limit q 13 ~ 0) Tri- bi- maximal > Consequences for Hierarchy: normal (to leading order) Hierarchy: inverted Degenerate case > Very different structure of neutrino mass matrix! Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 5

Mass hierarchy as texture and model discriminator > Typically re-covered in more complicated cases, e. g. including charged lepton mixings, q 13>0 etc: Hierarchy: normal vs. Hierarchy: inverted (example from hep-ph/0612169) > Translates into flavor symmetry models (Albright, Chen, hep-ph/0608137) See also: talk by Morimitsu Tanimoto > Neutrino mass ordering is the prime model discriminator! Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 6

Neutrinoless double beta decay > If neutrinos are Majorana neutrinos, they will mediate 0 nbb. > The 0 nbb rate depends on the hierarchy in degenerate regime: (line corresponds to solid 0. 3 e. V bound) ~ 0 nbb rate Inverted ordering guarantees lower limit for 0 nbb rate! Future measurements? Hierarchical Degenerate Transition (from: Lindner, Merle, Rodejohann, hep-ph/0512143; see talk by Martin Hirsch) Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 7

Impact of direct mass ordering (MO) measurement MO Normal 0 nbb? Inverted No Yes Degenerate Majorana neutrinos or new physics Dirac neutrinos or strong hierarchy Majorana neutrinos or new physics Dirac neutrinos Cosm. ? Yes No Majorana neutrinos Yes No Dirac neutrinos New physics? Yes Majorana neutrinos Strong hierarchy 0 nbb? No No Yes New physics? No Hierarchical case Mass measured Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 8

How to measure the mass ordering? Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 9

Current status and perspectives for existing equipment > Indication for d. CP, no evidence for mass hierarchy Capozzi et al, ar. Xiv: 1312. 2878; see also Forero, Tortola, Valle, ar. Xiv: 1405. 7540 and www. nu-fit. sorg Main difference: NOv. A data! > Potential of existing equipment T 2 K, NOv. A, Double Chooz, Daya Bay; 5 years each CP cons. NH simulated High CL determination requires new equipment Huber, Lindner, Schwetz, Winter, JHEP 0911 (2009) 044 IH simulated Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 10

Method 1: Matter effects in neutrino oscillations > Ordinary matter: electrons, but no m, t (Wolfenstein, 1978; Mikheyev, Smirnov, 1985) > Coherent forward scattering in matter: Net effect on electron flavor > Hamiltonian in matter (matrix form, flavor space): Y: electron fraction ~ 0. 5 (electrons per nucleon) Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 11

Parameter mapping … for two flavors, constant matter density Oscillation probabilities in vacuum: matter: 8 8 Enhancement condition Normal Dm 312 >0 Inverted Dm 312 <0 Normal Inverted Neutrinos Resonance Suppression Antineutrinos Suppression Resonance Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 12

Long baseline experiments (up to first vacuum osc. maximum) Best-fit values from ar. Xiv: 1312. 2878 (first octant) Matter effect L=1300 km ~ sin 22 q 13 sin 2 q 23 + d. CP modulation Vacuum oscillation maximum Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 13

Matter profile of the Earth … as seen by a neutrino Resonance energy (from ): (Preliminary Reference Earth Model) Core For nm appearance, Dm 312: - r ~ 4. 7 g/cm 3 (Earth’s mantle): Eres ~ 6. 4 Ge. V - r ~ 10. 8 g/cm 3 (Earth’s outer core): Eres ~ 2. 8 Ge. V Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 14

Mantle-core-mantle profile (Parametric enhancement: Akhmedov, 1998; Akhmedov, Lipari, Smirnov, 1998; Petcov, 1998) > Probability for L=11810 km Best-fit values from ar. Xiv: 1312. 2878 (first octant) ! Oscillation length ~ mantle-core-mantle structure Parametric enhancement. Core resonance energy Mantle resonance energy Naive L/E scaling does not apply! Threshold effects expected at: 2 Ge. V 4 -5 Ge. V Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 15

Method 2: Disappearance probabilities > Works in vacuum, and even for q 13=0 > Just flipping the sign of Dm 2 is not sufficient > Example: Reactor experiment, L=53 km Probabilities apparently different (unphysical effect!) Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 16

Method 2: Disappearance probabilities > The disappearance Dm 2 depends on the channel. Consequence e. g. de Gouvea, Jenkins, Kayser, hep-ph/0503079; Nunokawa, Parke, Zukanovich, hep-ph/0503283 > Now first oscillation maxima match. Discrimination by higher osc. Maxima. Need energy resolution! Zoom-in 3% (E/Me. V)0. 5 Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 17

Technologies to measure the mass ordering Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 18

The “classics”: Long-baseline experiments > Mass ordering wants long baselines >> 500 km and energies ~ few Ge. V LBNE > LBNE optimal for mass hierarchy Nu. MI decay tunnel See talks this afternoon … (Barger, Huber, Marfatia, Winter, hep-ph/0703029; see also LBNE, ar. Xiv: 1311. 0212) New decay tunnel Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 19

Emerging technologies: Atmospheric ns > Example: PINGU (“Precision Ice. Cube Next Generation Upgrade“) > 40 additional strings, 60 optical modules each Talks by M. de Jong, D. Grant, D. Indumathi > Lower threshold, few Mtons at a few Ge. V > ORCA, INO: similar methods Mantle resonance energy (PINGU LOI, ar. Xiv: 1401. 2046) Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 20

Emerging technologies 2: Reactor experiments > Jiangmen Underground Neutrino Observatory (JUNO) [formerly Daya Bay-II] > L=53 km > Excellent energy resoluton (3% (E/Me. V)0. 5) requires O(100%) PMT coverage See talk by Liangian Wen Talk by Liangian Wen Posters? Yu-Feng Li, ar. Xiv: 1402. 6143 3% (E/Me. V)0. 5 Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 21

Time evolution, risks? True NO Bands: > Beam experiments: d. CP > PINGU, INO: q 23 > JUNO: Energy resolution (3%-3. 5%) (E/Me. V)0. 5 Caveats: > LBNE sensitivity scales with (true) q 23 as well (dashed curve) see e. g. Fig. 9 in ar. Xiv: 1305. 5539 (version from PINGU LOI, ar. Xiv: 1401. 2046; based on Blennow, Coloma, Huber, Schwetz, ar. Xiv: 1311. 1822 v 1; LBNE dashed curve from ar. Xiv: 1311. 1822 v 2) > Energy resolution, directional resolution etc major challenges for PINGU/INO as well WW, ar. Xiv: 1305. 5539 Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 22

Benefits of having different techniques (PINGU m tracks only, NO, q 23=50 o) > Complementarity different impact of d. CP (true) WW, ar. Xiv: 1305. 5539; see also (for INO): Ghosh, Thakore, Choubey, ar. Xiv: 1212. 1305 > Synergy by combination of different parameter space topologies Blennow, Schwetz, ar. Xiv: 1306. 3988 Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 23

Summary and conclusions > The mass ordering is one of the prime indicators of flavor models > Meaningful statements on neutrino mass schemes and nature of neutrino mass require direct measurent of neutrino mass ordering, as well as 0 nbb and cosmology/direct neutrino mass bounds > There are currently three approaches to the mass ordering measurement: Long baseline Atmospheric beam (e. g. LBNE) (e. g. PINGU) Reactor long baseline Benefit Robust, clean signal Predictable timescale/cost Independent technology Risk (osc. params. ) d. CP, q 23 - Challenges Timescale Energy res. , directional res. , particle ID Energy resolution!!! > Having all three approaches will guarantee high-CL determination and independent confirmation Walter Winter | Neutrino 2014 | 04. 06. 2014 | Page 24