Neutrino oscillations/mixing

1. Richard Kass The 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+n2sinqnm(t=0) º nm= -n1sinq+n2cosq Since 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: Neutrino oscillations/mixing 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)> |2 M&S 11.1.1

2. Richard Kass Neutrino Oscillations/Mixing If 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)> |2 • In order to have neutrino oscillations: • at least one neutrino must have mass • the neutrinos must mix • Since the oscillation depends on Dm2 the mass of the neutrinos • must be determined from “other” experiments: • n energy endpoint experiments • double b-decay experiments

3. Richard Kass Original purpose was to search for proton decay: p®e+p0 (baryon # violation). Found lepton number violation instead! The SuperKamiokande Experiment Use water as target and detector medium Need lots of protons to get neutrino interactions. Size: Cylinder of 41.4m (Height) x 39.3m (Diameter) Weight: 50,000 tons of pure water Need to identify e-’s and, m’s, p0’s (use Cerenkov radiation) Reject unwanted backgrounds (cosmic rays, natural radiation) 103m underground at the Mozumi mine of the Kamioka Mining&Smelting Co Kamioka-cho, Japan

4. Richard Kass Atmospheric neutrinos are the end product of high energy collisions of cosmic rays (mostly protons) with the nuclei in our upper atmosphere. Neutrinos are mostly the result of pion decay (and subsequent muon decay) but kaons also contribute to neutrino production. From the figure on the right we (naively) expect for the number of muon and electron induced interactions: Atmospheric Neutrinos The experiments cannot distinguish the charge of the lepton produced in the neutrino interaction. The efficiency for detecting muons is usually very different than the efficiency for detecting electrons so the measured R is not 2.

5. Richard Kass Atmospheric Neutrino Oscillation Results from SuperK Measure the number of ne and nm interactions in SuperK as a function of neutrino path length in the earth’s atmosphere. n Neutrinos are produced by cosmic ray interactions in earths atmosphere. superK Phys. Rev. Lett. 86(2001)5656-5660 earth Phys. Rev. Lett. 81 (1998)  1562-1567 atmosphere n The nm‘s are “disappearing”! 2002 Nobel Prize M. Koshiba

6. Richard Kass SuperK does not actually see an “oscillation”. For example use the solution with: Dm2 = 2.2x10-3 eV2 assume <En>=103 MeV losc = (p/1.27)(<En>/Dm2) = (p/1.27)(103/2.2x10-3) = 1.1x106 m (@620miles) SuperK 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/E depletion of muon neutrino interactions Vs. L/E Scenario #3: muon neutrino oscillates into tau neutrino (nm®nt) SuperK has low detection efficiency for nt interactions constant number of electron neutrino interactions Vs. L/E depletion of muon neutrino interactions Vs. L/E Scenario #4: muon neutrino oscillates into a neutrino (nm®nS) that doesn’t interact Scenario #5: Combination of 3&4 or something else?? Atmospheric Neutrino Oscillation Results from SuperK

7. Richard Kass The sun only produces electron neutrinos (ne)! M&S 11.1.2 The Solar Neutrino Problem • Since 1968 R.Davis and collaborators have been measuring the cross section of: ne + 37Cl ® e- + 37Ar Their measured rate is significantly lower than what is expected from the “standard solar model” Measured: 2.55±0.17±0.18 SNU Calculated: 7.3±2.3 SNU SNU=standard solar unit SNU=1 capture/s/1036 target atoms Data from the Homestake Gold Mine (South Dakota) 2002 Nobel Prize R. Davis There is a long list of other experiments have verified this “problem”. Too few neutrinos from the sun!

8. Richard Kass Figure by J. Bahcall The Solar Neutrino Energy Spectrum Homestake: Chlorine ne + 37Cl ® e- + 37Ar SAGE/GALLEX: Gallium ne + 71Ga ® e- + 71Ge SuperK: nX + e-® nX + e- nmt + e-® 1/6(ne + e-)

9. Richard Kass The Solar Neutrino Problem

10. Richard Kass Located in a mine in Sudbury Canada Uses “Heavy” water (D2O) Detects Cerenkov light like SuperK The SNO Detector SNO=Sudbury Neutrino Observatory Nucl. Inst. and Meth. A449, p172 (2000)

11. Richard Kass Charged Current interaction (CC): ne + d ® e- + p + p (ne + n ® e- + p ) Deuterium has neutrons! Only electron neutrinos can cause this reaction Neutral Current Interactions (NC): nemt+ d ®nemt+ n + p D2O has twice as many nucleons as H2O all neutrino flavors contribute equally energy threshold for NC reaction is 2.2 MeV Elastic Scattering interactions (ES): nemt + e-®nemt + e- mostly electron neutrinos (NC and CC) Why Use “Heavy” Water? Neutrons are captured by deuterium and produce 6.25 MeV g SuperK only has protons! SNO measures several quantities (fCC, fNC,fES) and from them calculates the flux of muon and tau neutrinos (fm+ft): The quantities can be compared with the standard solar model. They also measure the total 8B solar neutrino flux into NC events and compare it with the prediction of the SSM.

12. Richard Kass +1.01 Fssm = 5.05 -0.81 +0.44 +0.46 -0.43 -0.43 Results from SNO neutral current results: • Fsno = 5.09 Best fit to data gives: Flux of 8B solar neutrinos Fmt=0 if no oscillations. “SSM”=Standard Solar Model Strong 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”)

13. Richard Kass Neutrino oscillations can be enhanced by traveling through matter. Origin of enhancement is very similar to a “birefringent” medium where different polarizations of light have different indexes of refraction. When polarized light passes through a birefringent medium the relative phase of each polarization component evolves 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, electrons All 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 seen by muon and tau neutrinos. The MikheyevSmirnov Wolfenstein Effect The MSW effect gives for the probability of an electron neutrino produced at t=0 to be detected as a muon neutrino: The MSW effect is very similar to “K-short regeneration” M&S 10.2.4 Here Ne is the electron density. For travel through vacuum Ne=0 and the MSW result reduces to our previous result.

14. Richard Kass There are only a few allowed regions in (q, Dm2) space that are compatible with MSW effect: LMA= Large Mixing Angle region favored. The MSW Effect SNO Day and Night Energy Spectra Alone Combining All Experimental and Solar Model information From A. Hamer, APS Talk, 4/2002