Presentation on theme: "Neutrino oscillations/mixing"— Presentation transcript:
1Neutrino oscillations/mixing P Spring 2003 L15Neutrino oscillations/mixingRichard KassThe derivation of neutrino oscillations is very similar to the derivation of “strangeness” oscillations (Lec. 7) and B meson oscillations.To make the derivation “simple” assume that CP is conserved, there are only 2 types of neutrinos and both neutrinos are stable (t1 = t2 = ¥).At t=0 we have an electron (ne) and muon (nm) neutrino which are both mixtures of n1 and n2.ne(t=0) º ne= n1cosq+n2sinq nm(t=0) º nm= -n1sinq+n2cosqSince we don’t know (beforehand) how “mixed” the neutrinos are we use q to describe the mixture. Note: for the kaon case we assumed equal amounts of K1 and K2 or q=45 degrees.The mass eigenstates (n1 and n2) propagate through space with energy E1 and E2 according to:We are interested in the case where the neutrinos are relativistic (E>>m) and therefore:Assuming the same energy (and E= p) for both neutrino components we can write:The probability of observing a ne at x (=ct) given that a nm was produced at t=0 is:P(nm® ne)=|< ne|nm(t)> |2M&S
2Neutrino Oscillations/Mixing P Spring 2003 L15Richard KassNeutrino Oscillations/MixingIf we measure mass in eV, x in meters, and E in MeV we can write the above as:The probability of observing a nm at x given that a nm was produced at t=0 is:P(nm® nm)=|< nm|nm(t)> |2In order to have neutrino oscillations:at least one neutrino must have massthe neutrinos must mixSince the oscillation depends on Dm2 the mass of the neutrinosmust be determined from “other” experiments:n energy endpoint experimentsdouble b-decay experiments
3The SuperKamiokande Experiment P Spring 2003 L15The SuperKamiokande ExperimentRichard KassOriginal purpose was to search for proton decay: p®e+p0 (baryon # violation).Found lepton number violation instead!Use water as target and detector mediumNeed lots of protons to get neutrino interactions.Size: Cylinder of 41.4m (Height) x 39.3m (Diameter)Weight: 50,000 tons of pure waterNeed to identify e-’s and, m’s, p0’s (use Cerenkov radiation)Reject unwanted backgrounds (cosmic rays, natural radiation)103m underground at the Mozumi mineof the Kamioka Mining&Smelting Co Kamioka-cho, Japan
4Atmospheric Neutrinos P Spring 2003 L15Atmospheric NeutrinosRichard KassAtmospheric neutrinos are the endproduct of high energy collisions ofcosmic rays (mostly protons) withthe nuclei in our upper atmosphere.Neutrinos are mostly the result ofpion decay (and subsequent muondecay) but kaons also contribute toneutrino production.From the figure on the right we (naively) expect for the number of muon and electron induced interactions:The experiments cannot distinguishthe charge of the lepton produced in theneutrino interaction.The efficiency for detecting muons is usually very different than the efficiency fordetecting electrons so the measured R is not 2.
5Atmospheric Neutrino Oscillation Results from SuperK P Spring 2003 L15Richard KassAtmospheric Neutrino Oscillation Results from SuperKMeasure the number of ne and nm interactions in SuperK as a function of neutrino path length in the earth’s atmosphere.nNeutrinos are produced bycosmic ray interactions inearths atmosphere.superKPhys. Rev. Lett. 86(2001)earthPhys. Rev. Lett. 81 (1998) atmospherenThe nm‘s are“disappearing”!2002 Nobel PrizeM. Koshiba
6Atmospheric Neutrino Oscillation Results from SuperK P Spring 2003 L15Richard KassAtmospheric Neutrino Oscillation Results from SuperKSuperK does not actually see an “oscillation”.For example use the solution with:Dm2 = 2.2x10-3 eV2 assume <En>=103 MeVlosc = (p/1.27)(<En>/Dm2) = (p/1.27)(103/2.2x10-3) = 1.1x106 mSuperK sees too few muon neutrinos.The number of expected muon neutrino interactions is calculated using a detailed simulation of the detector and takes into account detection efficiency as a function of energy and angle (atmospheric path length and detector path length).Scenario #1: No oscillations (or equal muon and electron neutrino oscillations neÛnm)number of muon and electron neutrino interactions independent of L/E.Scenario #2: muon neutrino oscillates into electron neutrino (nm®ne)excess number of electron neutrino interactions Vs. L/Edepletion of muon neutrino interactions Vs. L/EScenario #3: muon neutrino oscillates into tau neutrino (nm®nt)SuperK has low detection efficiency for nt interactionsconstant number of electron neutrino interactions Vs. L/EScenario #4: muon neutrino oscillates into a neutrino (nm®nS) that doesn’t interactScenario #5: Combination of 3&4 or something else??
7The Solar Neutrino Problem P Spring 2003 L15The Solar Neutrino ProblemRichard KassThe sun only produces electron neutrinos (ne)!M&SSince 1968 R.Davis and collaborators have been measuring the cross section of:ne + 37Cl ® e- + 37ArTheir measured rate is significantly lower than what is expected from the“standard solar model”Measured: 2.55±0.17±0.18 SNUCalculated: 7.3±2.3 SNUSNU=standard solar unitSNU=1 capture/s/1036 target atomsData from theHomestake GoldMine (South Dakota)2002 Nobel PrizeR. DavisThere is a long list of other experiments have verified this “problem”.Too few neutrinos from the sun!
8The Solar Neutrino Energy Spectrum P Spring 2003 L15Richard KassThe Solar Neutrino Energy SpectrumFigure by J. BahcallHomestake:Chlorinene + 37Cl ® e- + 37ArSAGE/GALLEX:Galliumne + 71Ga ® e- + 71GeSuperK:nX + e- ® nX + e-nmt + e- ® 1/6(ne + e-)
9The Solar Neutrino Problem P Spring 2003 L15Richard KassThe Solar Neutrino Problem
10The SNO Detector Located in a mine in Sudbury Canada P Spring 2003 L15The SNO DetectorRichard KassLocated in a mine in Sudbury CanadaUses “Heavy” water (D2O)Detects Cerenkov light like SuperKSNO=Sudbury Neutrino ObservatoryNucl. Inst. and Meth. A449, p172 (2000)
11Why Use “Heavy” Water? The quantities can be compared with the P Spring 2003 L15Why Use “Heavy” Water?Richard KassCharged Current interaction (CC): ne + d ® e- + p + p (ne + n ® e- + p )Deuterium has neutrons!Only electron neutrinos can cause this reactionNeutral Current Interactions (NC): nemt + d ® nemt+ n + pD2O has twice as many nucleons as H2Oall neutrino flavors contribute equallyenergy threshold for NC reaction is 2.2 MeVElastic Scattering interactions (ES): nemt + e- ® nemt + e-mostly electron neutrinos (NC and CC)Neutrons are captured by deuterium and produce 6.25 MeV gSuperK onlyhas protons!SNO measures several quantities (fCC, fNC, fES) and fromthem calculates the flux of muon and tau neutrinos (fm+ft):The quantities canbe compared with thestandard solar model.They also measure the total 8B solar neutrino fluxinto NC events and compare it with the prediction of the SSM.
12Results from SNO neutral current results: Fssm = 5.05 Fsno = 5.09 P Spring 2003 L15Results from SNORichard Kassneutral current results:Fssm = 5.05+1.01-0.81+0.44-0.43+0.46-0.43Fsno = 5.09Best fit to data gives:Flux of 8B solar neutrinosFmt=0 if no oscillations.“SSM”=Standard Solar ModelStrong evidence for Neutrino Flavor Mixing at 5.3s (5.5s if include SuperK).Total active neutrino flux agrees with standard solar model predictions.Believe that the mixing occurs in the sun (“MSW effect”)
13The Mikheyev Smirnov Wolfenstein Effect P Spring 2003 L15Richard KassThe Mikheyev Smirnov Wolfenstein EffectNeutrino oscillations can be enhanced by traveling through matter.Origin of enhancement is very similar to a “birefringent” medium where differentpolarizations of light have different indexes of refraction. When polarized light passesthrough a birefringent medium the relative phase of each polarization componentevolves differently and the plane of polarization rotates.The neutrino “index of refraction” depends on its scattering amplitude with matter:sun is made of protons, neutrons, electrons ®up/down quarks, electronsAll neutrinos can interact through neutral currents equally.Only electron neutrino can interact through CC scattering: ne+ e- ® ne + e-The “refractive index” seen by electron neutrinos is different than the one seenby muon and tau neutrinos.The MSW effect gives for the probability of an electron neutrino produced at t=0to be detected as a muon neutrino:The MSW effect isvery similar to“K-short regeneration”M&SHere Ne is the electron density.For travel through vacuum Ne=0 and the MSW result reduces to our previous result.
14P Spring 2003 L15The MSW EffectRichard KassThere are only a few allowed regions in (q, Dm2) space that are compatible withMSW effect:LMA= Large Mixing Angle region favored.SNO Day and Night Energy Spectra AloneCombining All Experimentaland Solar Model informationFrom A. Hamer, APS Talk, 4/2002