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1 March 30, 01 Lecture 5 of ORICL Philosophical Society Yuri Kamyshkov/ University of Tennessee kamyshkov@utk.edu 1. Concept/misconception of mass in Special Relativity (March,9). and n Oscillations: a Window to Parallel World? (March 16, 3, 30, April 13) All lectures are posted at

2 Two-flavor reactor antineutrino oscillations from KamLAND experiment Hitoshi Murayama

3 e3 e e1 e U U U U U U U U U Maki-Nakagawa-Sakata- Pontecorvo (MNSP) neutrino mixing matrix: ( ) etc. e e e e t U U U n n n n = + + ν e,μ,τ born by weak interaction in weak (flavor) states are the superpositions of mass eigenstates ν 1,,3 that develop in time : 3

4 PMNS neutrino mixing matrix æ id n ö æ - c c s c s e öæ n ö e 1 id id n s c c s s e c c s s s e s c n m = ç ç id id ç nt s s c c s e c s s c s e c c n ç ç ç 3 è ø è øè ø Neutrino mixing matrix is described by 3 Euler angles 1, 3, 13 and one complex phase. The latter determines CP-symmetry violation between neutrinos and antineutrinos. 1 and 3 previously have been measured by Super-Kamiokande, SNO, KamLAND, TK, MINOS and other experiments together with values of m 1 and m 3. Time dependence of all appearance and disappearance probabilities can be calculated from PMNS mixing matrix. Probability depend on both mixing angles that determine amplitudes of mixing and m s that determine frequencies of oscillations. e.g. Dm m -m 1 1 With 3 different masses only two independent mass differences can be constructed. Last mixing angle 13 has been recently measured by our experiment Double Chooz in France and Daya-Bay experiment in China. CP violating parameter will be measured by NOA at Fermilab, TK in Japan, and hopefully by LBNE in Homestake mine, SD. 4

5 Survival probability of reactor antineutrinos in case of three flavor oscillations: P m L m L e e 1 sin 13 sin cos 13 sin 1 sin 4E 4E Was determined recently by our Double Chooz experiment in France: sin ( q ) = ( stat) 0.030( syst) 13 Phys.Rev.Lett. 108, , 30 March 01 D m» D m 31 3 "atmospheric" " solar " Dm1 seen by KamLAND L/E(km/MeV) 5

6 Recent neutrino oscillation results from Double Chooz experiment can be learned from CBS presentation Episode: The Speckerman Recurrence, Images Copyright CBS 6

7 7

8 A sterile neutrino is a neutral lepton with no ordinary weak interactions except those induced by mixing. They are present in most extensions of the Standard Model, and in principle can have any mass. Very heavy sterile neutrinos are utilized in the See-saw model and play a pivotal role in leptogenesis (explanation of matter-antimatter asymmetry). Much attention is given also to relatively light sterile neutrinos that mix significantly with ordinary neutrinos and thus can be relevant to neutrino oscillations, mirror matter, dark matter, astrophysics, etc. 8

9 LSND experiment at LANL; MiniBooNE experiment at Fermilab; Reactor Antineutrino Flux Anomaly oscillation experiments with detectors at m; 51 Cr and 37 Ar sources used to test solar detectors; In cosmology: Big Bang Nucleosynthesis and Cosmic Microwave Background anisotropies count the effective number of relativistic degrees of freedom (i.e. different neutrino species), N eff 4-5 (3, 6) Individual hints are not convincing, but together provide some tension with 3-flavor mixing New 011 9

10 1. The Reactor Antineutrino Anomaly, G. Mention et al. (Saclay) Improved Predictions of Reactor Antineutrino Spectra, Th. A. Mueller et al. (Saclay) 3. Light Sterile Neutrinos: A White Paper. Contains almost 700 references 4. More from Fermilab Future Short-Baseline Neutrino Experiments Workshop, March 1,

11 New flux predictions Old flux predictions Short baseline reactor antineutrino anomaly. The experimental results are compared to the prediction without oscillation. The mean averaged ratio including possible correlations is 0.97±0.03. As an illustration, the red line shows a 3 active neutrino mixing solution fitting Double Chooz data. The blue line displays a solution 3+1 (fit) including a new neutrino mass state with D m > ev new There is a space for one or more oscillation effects into additional neutrino species 11

12 ~ amplitude 1 ~ frequency

13 Measurement of number of active species at LEP in ~ 1991 LEP data n = 3 Average = ± 0.03 ( =19.6/19) 13

14 Let s see first how Dirac mass of electron works in theory: L v g (mass term) eh = mee= mee v m eh e e e L R Mass term mixes left and right components of fermion particle. Mass of fermion particles arises due to interaction of initially massless particle with the Higgs field - - = g Dirac mass e æe ö R = ç e è L ø is "vacuum expectation value" of Higgs field (= 46 GeV) is relative strength of electron interaction with Higgs field e L m e e R 14

15 m n Dirac mass of neutrino would mean that besides being R - H, the antineutrino has some other properties that make it different from L - H neutrino: i.e. n e ¹ n e æe ö L in SM the pair is an isospin doublet ç n è L ø interacting with W; e, n - isospin singlets Dirac masses of neutrino leave one problem unresolved: why neutrinos are many orders of magnitude lighter than other fermions? R R 15

16 SM /3 quarks 1/3 quarks Ch. leptons why so much difference? Neutrinos Why neutrinos are much different in mass from all other particles? 16

17 See-saw neutrino mass mechanism f v H N M R N v H C M N N R R R f æe ö L ç n è L ø and e, n + R R R v g H l 1 L ( lf)( lf) ( lf) 5 M M R R Heavy Majorana neutrino N with mass M (and with D L = ) R N R = N m m M l R Including heavy Majorana neutrino makes observable neutrino very light (see-saw mechanism) 17

18 L violation in ordinary (O) and mirror (M) matter Berezhiani, Mohapatra (1995) O: 1 L5 M lf D L = ~ ( ) ( ) m ~ v M n 1 M: L l L 5 M ~ ( f ) ( D = ) m ~ v M n mix 5 L ~ 1 ( lf)( l f ) mix 5 M ( D L = 1, D L = 1) n sterile n disappearance If L = L-L is conserved i.e. L and L are forbidden; 5 5 then L yields light Dirac neutrinos with n R = n c L 18

19 B violation in ordinary (O) and mirror (M) matter Berezhiani, Bento (006) O: L 9 1 ( udd ) 5 M n n B ( D = ) M: L 1 ( udd ) 9 5 M n n ( D B = ) L mix ( udd )( u d d ) M ( D B = 1, D B = 1) n mirror n disappearance S is a color-triplet scalar with mass M S (can be discovered at LHC) N additional gauge singlet fermion (like heavy Majorana neutrino) If B = B -B is conserved L and L are suppressed; 9 9 mix L provides fast n «n ; however n n is also possible 9 due to higher order corrections ; that is why it can be less probable than n «n 19