Slide 1

Experimental Neutrino PhysicsSusan CartwrightUniversity of Sheffield

Introduction: Massive neutrinos in the Standard ModelDirac and Majorana massesThe mixing matrix and neutrino oscillations Massive neutrinos in the Standard ModelIn the original Standard Model, neutrinos are two-component spinors with mass exactly zerodisproved by existence of neutrino oscillationssee laterThere are two ways to add a neutrino mass term to the SM LagrangianDirac: exactly like other fermion massesMajorana:where c = CT = C0*different chiral states need not have same mass in this case neutrino and antineutrino same particle, different chirality

Seesaw mechanismGeneral mass term has both Dirac and Majorana components:

If , we can diagonalise matrix to get eigenstates

with masses

naturally small mass for LH state

Neutrino oscillationsIf neutrinos have mass, then they can be described in terms of mass eigenstates as well as weak (flavour) eigenstatesno reason why these should align (and they dont), so we have a 33 unitary mixing matrix (the PMNS matrix) U:

mass eigenstates propagate according to

if c = 1 and v c (and hence L t)therefore even if |(0) is a pure flavour state, |(L) is not

Neutrino oscillationsProbability of observing neutrinos of flavour ' at distance L (in vacuo) from a beam of initial flavour :

For two-flavour case we have

giving

therefore key variable for experiments is L/Ecant measure absolute masses

Matter effectse interact with electrons via W exchange; , do notThis leads to an increased effective mass for a e-dominated state in dense matteras propagates out through decreasing density, effective mass drops, eventually crossing another eigenvalueresulting resonant conversion can greatly enhance oscillationcritical for solar neutrinos, significant for long baseline terrestrial tooMSW effectsees sign of M2

Theory SummaryNon-zero neutrino masses implyneutrino oscillation (change of effective flavour)hence, non-conservation of lepton family numberthis is experimentally establishedalso, if 33 mixing, non-conservation of CPimaginary phase in PMNS matrixnot established yetif non-zero Majorana mass, = hence, non-conservation of global lepton numbernot establishedExperimental tasksdetermine oscillation parameters (m2, , )measure neutrino massesNeutrino oscillationsPrinciples of oscillation measurementsSolar neutrinos, 12Atmospheric neutrinos, 23New measurements of 13Principles of oscillation measurementsRelevant physical properties are m2ij and ijExperiment parameters are L, E and initial flavour e, but physical parameter is L/E, so result is conversion probability P(L/E), giving contour on m2 sin2 2 planeTwo distinct experimental techniquesdisappearance experiments look for reduction in flux of original flavouronly possibility for very low-energy neutrinos (reactor e, solar e)appearance experiments look for converted flavoure.g. e events from a beamThe PMNS matrix

atmosphericneutrinos solar neutrinos e Xreactor & accel. neutrinos eneed all three mixing angles to be non-zero for CP violation to be possibleSolar neutrinosProduced as by-product of hydrogen fusion4 1H 4He + 2e+ + 2ereaction goes by many paths which produceneutrinos of differentenergiesinitial flavour state eas too little energy toproduce , Detected by inverse decay, elastic scattering,or dissociation of 2H

http://www.kip.uni-heidelberg.de/tt_detektoren/neutrinos.php?lang=enSolar neutrinos: 12, m212 requires L/E ~ 30 km/MeV in vacuumexperimental approaches: solar neutrinos: e X disappearanceresonant conversion via MSW effect in solar interiorexpected flux calculated from models of solar luminosity (John Bahcall et al.)experimental normalisation via NC reactions (SNO)reactor neutrinos: e X disappearancerequires long-baseline experiment owing to small m2expected flux from known reactor power output

Solar neutrinos: 12, m212

NC: d + X p + n + XCC: d + e p + p + eES: e + X e + X

Solar neutrinos: 12, m2123-flavour analysis of SNO+KamLAND data gives

(arXiv 1109.0763)

Solar neutrinos: new resultsMeasurement of 7Be and pep flux by Borexinoline fluxes, therefore potentially more informative about energy dependenceAlso no day-night asymmetryexcludes low m2 region of planethis exclusion previouslydepended on reactordata ()

16Atmospheric neutrinos: 23, m223Initially studied using neutrinos produced in cosmic-ray showersincident proton or heavier nucleus produces pions which decay to + some of the muons then also decay (to e + e + )if they all do so then :e ratio ~ 2Also addressed by accelerator-generated neutrino beamsessentially identical process: collide proton beam from accelerator with target, collimate produced pions with magnetic horns, allow to decay in flightmagnets select charge of pion, hence either or beamAtmospheric and accelerator s

1 0 +1 1 0 +1cos(zenith angle)

Atmospheric neutrinos: 23, m223MINOS combined fit

3-flavour global fit

first time that best fit 23 45!

Third mixing angle 13

Absence of signal in e shows that atmospheric mixing is measurements of appearance in OPERA and Super-K are statistics-limitedbut in qualitative agreement with this Therefore 3rd mixing angle 13 involves ecan be seen in e appearance in beam ore disappearance from reactorsbecause m213 = m223 m212 and m212 m223, disappearance always dominated by 23

e appearance:

Off-axis geometry produces lower-energy, much more monochromatic beamT2K beam is 2.5 off-axisoptimised for oscillation measurementT2K analysisSuper-Kamiokande measures Cherenkov radiation from e/ produced in interactioncan distinguish the two based on ring morphology

sharp muon ring

fuzzy electron ring

11 events observed3.220.43 expected3.2 effect

e disappearance: Multiple detectors associated with extended reactor complexe detected via inverse decayin Gd-loaded liquid scintillator

23Daya Bay analysisLarge difference between m213 and m212 means that L/E can be tuned for 13no ambiguitysimple 2-flavour systemnear and far detectorsidentical to minimise systematicsfar/near ratio R = 0.940 0.011 0.0045.2 effect

e disappearance: Detector design and analysis very similar to Daya BayResults very similar too:R = 0.920 0.009 0.0144.9 effect

Results for 13T2K :Daya Bay: sin2 213 = 0.092 0.016 0.005Reno: sin2 213 = 0.113 0.013 0.019Global fit (Fogli et al. arXiv 1205.5254):

measurement of m2 still best done bycombining solar & atmospheric m2

Open questionsWe know the e-dominated state m1 is lighter than m2 (from MSW effect), but we still dont know if m3 > m2 (normal hierarchy) or vice versa (inverted hierarchy)longer baseline experiments, e.g. NOA, should be able to sort this out via matter effects in EarthConstraints on phase are very weakcan be constrained by antineutrino running and/or matter effects (NOA again)

Effect on modelsTri-bimaximal mixing predicts

and hence 13 = 0, which it clearly isnt.Theorists are of course trying to rescue this with perturbations of various kinds The current hint that 23 45 is also inconsistent with tri-bimaximal predictions

Neutrino massesTritium beta-decayNeutrinoless double beta decayAstrophysical constraintsNeutrino mass: decayBasic principle: observe electron spectrum of -decay very close to endpointpresence of mc2 term for neutrino will affect thisunfortunately not by much!!

tritium (3H) favoured because of combination of low Q-value (18.57 keV) and shortish half-life (12.3 y) decay status and prospectsBest efforts so far by Mainz and Troitsk experiments of late 90s:

Two experiments in pipeline should do much betterKATRINtritium decay experiment with planned sensitivity ~0.2 eVMARErhenium-187 experiment, similar reach187Re has very low Q-value but extremely long half-lifeMARE uses single-crystal bolometers to get good energy resolution and measure differential spectrumVery hard experiments: dont expect results for ~5 years

Neutrinoless double- decayEven-even isobars are lighter than odd-odd (pairing term)can be energetically permitted for nucleus (Z, A) to decay to (Z2, A) but not (Z1, A)these decays do happen through conventional 2 mode, albeit at very low ratelifetime age of universeif neutrino is Majorana particle, can also happen with no neutrino emission, 0

Key featuresViolates lepton number by 2 unitspossible relevance to baryogenesisSensitive to PMNS matrix multiplied by diag(1, ei, ei) introducing two additional phases Rate for SM, amplitude mi/q2 where m ~ 0.5 eV and q ~ 108 eVsmall!nuclear matrix element M is a major systematic errortheoretical calculations disagree by factors of 2 or more

Relation of mee to lightest m

hep-ph/1206.2560Experimental issuesSignature: (A, Z) (A, Z+2) + 2e, soE(e) = Q/2 spike at energy endpointp(e1) = p(e2) electrons are back to back Two experimental approachessource = detectorcalorimetric; energy signaturetarget isotope fixedsource detectortracker; topological signaturetarget isotope variableMost isotopes are only ~10% of natural element.Enrichment is often needed.

232Th60CoExperimental resultsBest results probe down to mee ~ 0.2-0.6 eV not yet quite in rangeof interesting limitsNext few years: improvement of ~ 10EXO-1000, CUORE,KamLAND-ZEN,GERDA/MAJORANAall hoping for ~0.02-0.06 eVEffect on modelsSensitivity to hierarchy: IHimplies accessible minimummass ( m213)within reach of next generationNon-observation possible even with Majorana neutrinosin NH masses and phases can conspire to cancel effect Conversely, 0 decays can be driven by mechanisms other than Majorana mass (e.g. LR symmetry) such mechanisms do imply that the neutrino has a Majorana mass, but it can be very small

Astrophysical constraints on mNumber density of relic neutrinos from early universe (CB) is 112 per species per cm3these are hot dark matter and will affect structure formationhence leave astrophysical signaturesSensitive to m, which is bounded below by oscillations m223 ~ 0.0024 eV2 means m 0.05 eVbounds are within factorof 10 and will improve soon(e.g. Planck)Model dependenceQuoted constraints assumeflat geometryexactly 3 neutrino species with T = (4/11)1/3 TCMBdark energy is a cosmological constantThere are correlations between m and other parameters

WMAP5Comparing different measures0CosmologyyesnoyesnoKATRINyesQD+MQD+DQDN-S CnoN-S Ilow IH/NH/Dm < 0.1 eV/N-S CNH0yes(IH/QD)+MN-S C/Inolow IH/(QD+D)NHD = Dirac; M = Majorana; QD = quasi-degenerate; NH/IH = normal/inverted;N-S C = non-standard cosmology; N-S I = non-standard interpretation of 0Assumes sensitivities of m = 0.2 eV, mee = 0.02 eV, m = 0.1 eVW. Rodejohann, hep-ph/1206.2560Conclusion: it does help to have multiple approaches.41Important things I dont have time to discuss!

Non-standard interpretations of 0Light sterile neutrinosNeutrino astrophysics and cosmology

Summary and ConclusionAll 3 neutrino mixing angles are definitely non-zeronave tri-bimaximal mixing ruled outConstraints on and determination of hierarchy should be possible with next generation of oscillation experimentsExperimental limits on neutrino mass do not currently compete with cosmological constraints, but next decade should see complementarity developingPhysics of massive neutrinos is a rich and interesting field!Backups

Solar neutrinos

Double beta decay

Hot dark matter

Hannestad et al., astro-ph/1004.0695WMAP7 + halo power spectrumWMAP7 + HPS + H0

Giusarma et al., astro-ph/1102.4774Sterile neutrinos and axions can also contribute to hot dark matter