Transcript n - IN2P3
Lectures on Neutrino Physics Fumihiko Suekane Research Center for Neutrino Science Tohoku University [email protected] http://www.awa.tohoku.ac.jp/~suekane France Asia Particle Physics School @Ecole de Physique Les Houchess 18-20/Oct./2011 111018 suekane@FAPPS 1 * This lecture is intended to give intuitive understanding of neutrino physics for students and young physicists of other field. * I will try to make this lecture to be a bridge between general text books and scientific papers. * 3 lectures are very short to mention about all the varieties of neutrino physics and only limited but important topics are mentioned. 111018 suekane@FAPPS Scientific Papers This lectures Introduction to Particle Physics text books 2 Contents * History * Neutrinos in the Standard Model * Neutrino Oscillations (Main) * Double Beta decays * Prospects 111018 suekane@FAPPS Day-1 Day-2 Day-3 3 What is known for neutrinos PDG2010 Only a few things are known about neutrinos. .... There is much room to study. 111018 suekane@FAPPS 4 Basic Fermion Strong Interaction NO YES Lepton Quark u,d,s,c,b,t YES Charged Lepton e, m, t EM Interaction NO Neutrino e , m , t We call Fermions which do not perform strong nor EM interaction, Neutrinos 111018 suekane@FAPPS 5 big bang Neutrinos in Nature e e in early universe. Most abundant next to photons (~100/cc) 6 Timeline (years are approximate) 1899 Discovery of b-decay [Rutherford] 1914 b-ray has continuous energy spectrum [Chadwick] 1930 Neutrino hypothesis [Pauli] 1956 1st Evidence of neutrino @ reactor [Reines & Cowan] 1961 Discovery of m [Shwartz, Ledermann, Steinberger] 1969~ Deficit of solar neutrino [Davis] 1977 Discovery of t lepton ( indirect evidence of t ) [Perl] 1985 Proposal of MSW effect [Mikheyev, Smirnov, Wolfenstein] 1987 Detection of neutrinos from SN1987A [Koshiba] 1989 N=3 by Z0 shape [LEP] 1995 Nobel prize to Reines (1996, 1997Claim of m->e oscillation [LSND]) 1998 1st evidence of neutrino oscillation by atmospheric [SuperKamiokande] 2000 Direct evidence of t [DONUT] (2001 Claim of neutrinoless bb decay [Klapdor]) 2002 Nobel prize to Davis & Koshiba 2002 Flavor transition [SNO] Reactor Neutrino Deficit [KamLAND] 2004 m disappearance @ Accelerator [K2K] 2010 mt [OPERA] 2011 Indication of e appearance @ Accelerator [T2K] 1st Indication of Neutrino (The 1st anomaly in neutrino which lead great discovery.) ~1914, an anomaly found g & decays The energy of the decay particle is unique M’ M m n M m M 2 T 2 T/g 2M However, for b-decays, it is continuous. Why?? 111018 suekane@FAPPS J.Chadwick, 1914 n T b 8 Neutrino Hypothesis * Energy conservation low is broken （N.Bohr, 1932） A’ A Eb EA EA b Wikipedia * b-decay is a 3 body reaction (W.Pauli, 1930) A B b ν M’ Wikipedia 111018 M m Eb EA EA E EA EA Neutrino Hypothesis suekane@FAPPS 9 4/Dec./1930 Letter from Pauli to participants of a conference. 111018 suekane@FAPPS 10 Expected properties of from b-decays (1) Q=0 charge conservation (2) s=1/2 spin conservation (3) mass is small if exists maximum energy of b-rays. (4) Interact very weakly lifetime of b-decays. 111018 suekane@FAPPS 11 How -N cross section was estimated in early days. Fermi's model p e- Dirac e e e2 M 2 q p Fermi Analogy n GF p e- e- M GF Various b -decays & Electron caputure GF~10-11/MeV2 2 G 2 20 Then, p e n F pCM ~ 10 b!! "I did something a physicist should never do. I predicted something which will never be observed experimentally..".（W.Pauli) "There is no practically possible way of observing the neutrino" suekane@FAPPS 12 (Bethe & Peierls, 1934) Then 30 years had passed .... 235 n 236 n e e Very strong sources are necessary, Chain reactions of nuclear fissions. U * U 94 140 Te n Rb e e- 94 140 I e - 140 Xe 94 Energy release: 200MeV/fission b-decays: ~ 6 /fission Sr e e Discovery of e- Y 1.9x1011/J e e e- 140 Cs 94 Zr e Reactor or Nuclear Explosion E~ MeV 111018 suekane@FAPPS 13 An early idea to detect (not realized) by Reines & Cowan Reines & Cowan Nuclear Explosion Vacuum shaft Neutrino Detector Free fall to prevent the shock wave. => Physicists make use of everything available While preparing the experiment, they realized nuclear reactor is more relevant to perform experiment. 111018 suekane@FAPPS 14 Then they moved to a Savannah River Reactor 200L Cd loaded water tanks 1400L liquid scintillator tanks P=700MW 1982 Wikipedia 111018 suekane@FAPPS 15 Principle of detection * flux: @15m from Savannah Liver P reactor core. (P=700MW) flux~5x1012/cm2/s * Detection Principle: e p e n e e 2g 0.5MeV n Cd Cd* Cd ng 9MeV n e+ ~10ms 111018 Delayed Coincidence Technique Still used in modern experiments suekane@FAPPS 16 2 examples of delayed coincidence LS tank ID http://library.lanl.gov/cgibin/getfile?00326606.pdf#search='delayed%20coincidence%20cadmium%20neutrino' 111018 suekane@FAPPS 17 An episode At the same time of Reines& Cowan, R.Davis and L.Alvarez performed neutrino experiment at a Savannah river reactor, too. Their detection principle was, Cl e Ar However, they failed to detect positive result. But this actually means the reactor neutrino (anti neutrino) dose not cause the reaction Cl / e Ar and neutrino and anti-neutrino are different particles (concept of that time) Later on, Davis also won Novel prize by detecting solar neutrinos with the same technique. Lessons : Negative result can be an important signature. : Hanging on is important for success. 18 111018 suekane@FAPPS Discovery of μ-neutrino * Neutrino Source: @ Brookhaven AGS p15GeV Be X m π decays with 21m decay space. e 10 4 m 99.99% of neutrinos are associated with muon production 111018 suekane@FAPPS 19 Detection of neutrino * Target: 90 x 2.5cmt Al slab m X Looked for Al e X spark chambers m signal => a single track e signal => EM shower They observed 34 single track μ events 22 μ+X 6 backgrounds (not like e ) The neutrinos from b-decay and decay are different particle 111018 suekane@FAPPS 20 t neutrino (2000 DONUT group) * Production of t neutrino FNAL TEVATRON pE 800GeV W DS m 1.97GeV X Then DS t m 1.78GeV t cos C DS s mDs mt Cabibbo favor t c Br ~ 4% W t E ~ 70GeV, ~ 0.05 m t e, 111018 suekane@FAPPS 21 Detection principle Look for the "kink" t A t X t decays after ct~87um, neutral(s) 85% for 1 prong mode t t e , m , , K 数百ミクロン 15% for 3 prongs mode. t 111018 suekane@FAPPS t 22 the Detector Nuclear Emulsion (~thick camera film) position resolution <1mm 111018 suekane@FAPPS 23 Results (2000) 3 prongs 1prong 4 0.44 t was observed in 1000 neutrino events. (9 significance) "We did R&D for t-neutrino detection around 1980 but once gave up because it seemed too difficult to success". K.Niwa 111018 suekane@FAPPS 24 111018 suekane@FAPPS 25 Direct neutrino mass detection electron neutrino Principle A B e e 2 m 2 2 N pe dpe pe E0 Ee 1 dpe E0 Ee EeMAX E0 E0 m Distortion of energy spectrum at the end point 111018 suekane@FAPPS 26 3 Source: Tritium H 3 He e e Q 18.6KeV , t E0=small good m sensitivity Lifetime reasonably short & long Z＝small small correction 12 12.3y ideal isotope to seek for mν * Strong Source * Large Acceptance * Energy measurement by Electric potential V Electric potential detector 27 me Results 111018 suekane@FAPPS K. Eitel (Neutrino04) 28 K. Eitel (Neutrino04) From current to future experiments Mainz: m2 = -1.2(-0.7) ± 2.2 ± 2.1 eV2 m < 2.2(2.3) eV (95%CL) Troitsk: m2 = -2.3 ± 2.5 ± 2.0 eV2 m < 2.1 eV (95%CL) C. Weinheimer, Nucl. Phys. B (Proc. Suppl.) 118 (2003) 279 C. Kraus, EPS HEP2003 (neighbour excitations self-consistent) V. Lobashev, private communication (allowing for a step function near endpoint) aim: improvement of m by one order of magnitude (2eV 0.2eV ) improvement of uncertainty on m2 by 100 (4eV2 0.04eV2) statistics: stronger Tritium source (>>1010 b´s/sec) longer measurement (~100 days ~1000 days) energy resolution: DE/E=Bmin/Bmax spectrometer with DE=1eV Ø 10m UHV vessel suekane@FAPPS 111018 29 111018 suekane@FAPPS 30 111018 suekane@FAPPS 31 A famous picture 111018 suekane@FAPPS 32 111018 suekane@FAPPS 33 K. Eitel (Neutrino04) KATRIN sensitivity & discovery potential expectation: after 3 full beam years syst ~ stat m = 0.35eV (5) 5 m = 0.3eV (3) discovery potential m < 0.2eV (90%CL) sensitivity 111018 suekane@FAPPS 34 m mass limit stop m m 111018 m mm pm m pm 2 2 2 2 suekane@FAPPS m 0.34m pm 1 0 pm 35 K.Assamagan et al. PRD53,6065(1996) A precise spectrometer @PSI 111018 suekane@FAPPS 36 K.Assamagan et al. PRD53,6065(1996) energy loss in the target pmmax 29.79200 0.00011MeV / c 0.1MeV/c pm m m 0.19MeV 90%CL (PDG average) 111018 suekane@FAPPS 37 m mass limit m 0.34m pm 1 0 pm 2 1 m m p m m 2 2 m m m ~ m mm 2 m p 1 m m m m ~ 0.15MeV 49MeV m 111018 pm pm ~ 0.1MeV δmπ limits the precision suekane@FAPPS 38 τ neutrino mass limit e e t t t t X LEP,CLEO 111018 suekane@FAPPS 39 t t X LEP,CLEO distribution of mX & Ex, d f m X , E X ; m dm X dE X obtain most likely m Better precision for smaller Q-value, but low statistics, t 5 t are used. PDG average； mt 18.2MeV 95%CL 111018 suekane@FAPPS 40 Quark-Lepton masses mass is very small t m Lower limit of heaviest neutrino mass is ~50meV oscillation 111018 suekane@FAPPS 41 Neutrinos in the Standard Model * Q=0, * No color * m=0, * s=1/2 * * only L exists (or L may exist but it does not interact at all) 111018 eL W+ e gW ~ 1.4e 2 sin W igW eRg L Wm m L L igZ Rgm L Z m0 Z0 e gZ ~ 1.2e sin 2W L 2 sin W~0.23 (Weinberg suekane@FAPPS angle) 42 R L e eL m eL R L m R eL R eL gw W+ WLepton number violation 111018 W+ Flavor violation suekane@FAPPS Z0 Z0 Flavor violation 43 'Helicity' Suppression of -decay e 1.2 10 4 m Experimental fact: How it is explained? R L e W+ u 111018 d eR L only LH and RH e. You may say W couple So that J(e=1, while pion spin=0 => violates spin conservation However, this decay exists if very small. And for m decay, the spin conservation seems to strongly violated. suekane@FAPPS 44 Helicity and Chirality Sometimes Helicity and Chirality are used in confuse. Here they are defined and their relations are discussed. Dirac equation in free space is, ig mm mx 0 General solution is, r r u i pr xr Et v i pr xr Et x r r e e u v r r u1 v1 p r2 2 , E p m , u , v Em u 2 v2 r Nowwe take initial condition as positive energy and p 0, 0, p u 0 z u 111018 suekane@FAPPS 45 Helicity is the spin component to the direction of the movement. r s rˆ p rˆ r ps If the movement is along the z-direction, helicity components are, 1 u 1 1 rˆ r R 1p 1 z u1 2 2 u 1 u 2 1 1 rˆ r 1 p 1 z u2 L 2 2 u 2 These helicity states show actual spin direction. Here after we call Right(Left) handed Helicity =RH (LH) 111018 suekane@FAPPS 46 What W couples to: Chirarity W couples to negative Chirality (NC) particle and positive Chirality (PC) state anti-particle. W Chirality components of is defined by, 1 1 1 1 u 1 z u 1 g 5 2 2 1 1 z u 2 u For m 0, 1 and 1 z u m0 1 z u R/ L 2 u 2 u For high energy, the helicity and chirality are same and sometimes they are confused. For low energy, NC has RH component. 111018 suekane@FAPPS 47 In e- decay, e- is NC state and is PC state. Then the The RH component of electron in the decay is, u 1 1 rˆ r R 1 p 1 z 2 4 u So that the probability which is RH is, R 1 † g 1 b 2 m E1 m 2 2 u1 2 u1 u 1 z u 2 2 8 g 1 2 4E This means the electron has right handed component with probability P me2 4Ee2 ~ 1.310 5 R This conserve spin eL muon case, m /E ~1 and the suppression is not strong. For m m 111018 suekane@FAPPS 48 e Taking into account the phase space the theoretical prediction is m m 2 m 2 m 2 4 e e 2 1.28 10 2 m m m m m 1.23x10-4 while observation is Likewise for K decay, K e K m m 2 m 2 m 2 5 e e K2 2.4 10 2 m m m m K m 2.5x10-5 while observation is 111018 suekane@FAPPS 49 neutrino flavor counting using Z0 e e Z 0 f f f e Z 0 igZ g eg igZ g f g g f cVf cVf g m q2 2E 2 Mz=91GeV f e 4M 111018 If M=1, =0.1 2 Z ge2 g 2f q MZ 2 2 Z2 4 suekane@FAPPS 50 The width of the Z0: is inverse of the lifetime of Z0: t The lifetime is proportional to inverse sum of decay width. 1 1 t Z Z uu Z dd L Z e e If the number of neutrino flavors is n, Z 6U 9D 3L n 8 32 2 4 8 2 2 1, L 1 4xw 8xw , U 1 xw xw , D 1 xw xw 3 9 3 9 xw sin w ~ 0.23 measurement Z 6U 9D 3L known n 111018 suekane@FAPPS 51 Z0 data ４ experiments at LEP (ALEPH, DELPHI, OPAL, L3) showed n 2.984 0.008 If 4th neutrino exists m4 > 45GeV or it does not couple to Z0, called sterile neutrino. 111018 suekane@FAPPS 52 Oscillation: An Introduction Neutrino oscillation is phenomena in which flavor of neutrino oscillatory changes as time passed by. e m e m e t If we start from e, the probability to find m at time t is expressed as: 2 2 m m 1 P e m t sin 2 2 sin 2 2 t 4E Where m2 and m1 are masses of energy-eigenstate neutrinos, is called mixing angle. st firm evidence beyond the standard model and oscillation is the 1 its studies are important to understand the nature. 111018 suekane@FAPPS 53 Phenomena of spin-1/2 for Oscillation The formalism of the oscillation is very similar to that of spin-1/2 under magnetic field. So let's review the spin motion as introduction. The spin motion under magnetic field is described by the Pauli equation: r r iÝ mB r Where B Bx , By , Bz is the magnetic field and m is magnetic dipole moment of the particle. This equation was 1stly introduced empirically by Pauli, and later on obtained by taking non relativistic limit of the Dirac equation with electro-magnetic interaction. 111018 suekane@FAPPS 54 Phenomena of spin-1/2 for Oscillation rr iÝ mB The wave function is a mixture of spin up and down states t t t b t b t Here, we think the case that magnetic field is along the x axis. r B B,0,0 z y r Then the Pauli equation becomes B Ý 0 1 Ý imB b 1 0 b x b 111018 suekane@FAPPS 55 Phenomena of spin-1/2 for Oscillation Ý imBb bÝ imB by taking the delivertive of the 1st equation, and replacing bÝ by the 2nd equation, 2 Ý Ý mB This is the harmonic oscillator and we know the general solution; t peimBt qeimBt imBt imBt b t pe qe Where p & q are integral constants to be determined by initial condition. 111018 suekane@FAPPS 56 Phenomena of spin-1/2 for Oscillation Then the general spin state is, t peimBt qeimBt peimBt qeimBt Now we assume that at t=0, the spin pointed upward. 0 z y r B Then we can determine p and q for this case, 0 p q p q 1 x 0 0 111018 pq suekane@FAPPS 1 2 57 Phenomena of spin-1/2 for Oscillation Then we get specific wave function; t cosmBt i sin mBt This means at later time, state is generated with oscillating probability z P t sin 2 mBt r B If we recall that the wave function of the spin, which is in z-y plane and polar angle is is mBt y mBt, 0 111018 cos i sin Physically it corresponds to the precession of the spin, caused by the torque by B and m. suekane@FAPPS 58 Phenomena of spin-1/2 for Oscillation Ý 0 1 Ý imB b 1 0 b Quantum Mechanically, this is understood as the effect that magnetic field causes transition between with amplitude mB. We will draw this kind of effect schematically as follows. mB The neutrino oscillation can be understood as exactly same manner. 111018 suekane@FAPPS 59 A simple case of Oscillation We assume 2 neutrino system; e & m The general state is; t t e b t m We assume something makes transition: em m e me Then there are correspondences to the spin case If the initial state is pure e state, like beta decay, e then 2 P t sin Amet e m m This is the very basic of neutrino oscillation. Ame mB 111018 suekane@FAPPS 60 A simple case of Oscillation However, we often see the neutrino oscillation probability as 2 2 m m 1 P m t sin 2 2 sin 2 2 L 4E 111018 Where does this come from? What is the analogy of spin motion? suekane@FAPPS 61 Still spin-1/2 for Oscillation In actual case, mass term has to be included in the Pauli equation rr iÝ m mB and the most general equation with arbitrary magnetic field is, m mBz Ý Ý i b mB z Spin transition amplitudes are r B 111018 y b mB ; B Bx iBy m mBz b x = mB mB mmBz suekane@FAPPS mmBz 62 Still spin-1/2 for Oscillation m mBz Ý Ý i b mB mB m mBz b This equation has the general form * Ý P Q , P, R Re al Ý i b Q R b Relation between Polar angle of the magnetic field and transition r amplitudes is, z B B 2Q tan Bz R P x,y 111018 suekane@FAPPS 63 Still spin-1/2 for Oscillation P Q* Ý , P, R Re al Ý i b Q R b Then the general solution can be expressed using as, t C1 cos 2eiE t C2 cos 2eiE t iE t iE t b t C sin 2 e C cos 2 e 1 2 where, 1 2 2 E P R P R 4 Q 2 E 1 P R P R2 4 Q 2 2 (Note: by definition, E+>E-) 111018 suekane@FAPPS 2Q R-P 2Q tan RP 64 Still spin-1/2 for Oscillation The general wave function is, t C1 cos 2eiE t C2 sin 2eiE t C1 sin 2eiE t C2 cos 2eiE t 2Q Again we start with 0 Then, the integral constants are determined. R-P 2Q tan RP C1 cos 2 C2 sin 2 1 C1 cos 2 C2 sin 2 C1 sin 2 C2 cos 2 0 111018 suekane@FAPPS 65 Still spin-1/2 for Oscillation In this case, the specific wave function is 1 2 iE t 2 iE t t cos 2e sin 2e sin eiE t eiE t 2 This state corresponds to spin precession within the plane perpendicular to the magnetic field. r B z y The time dependent probability of spin-down state is sin iE t iE t 2 2 P t e e sin sin mBt 2 corresponds to the angle between the precession plane and z axis. 2 x t bt t 111018 Difference of the energies in the energy eigenstate suekane@FAPPS 66 Still spin-1/2 for Oscillation Look for Energy eigenstate, Remember the general state t C1 cos 2eiE t C2 sin 2eiE t C1 sin 2eiE t C2 cos 2eiE t If we choose, C1=1, C2=0, t cos 2 sin 2 eiE t This means cos 2 sin 2 is energy eigenstate with energy E+. Similarly, if we choose, C1=0, C2=1, t sin 2 cos 2 eiE t eiE t 111018 suekane@FAPPS 67 Still spin-1/2 for Oscillation The spin states , itselvs are NOT energy eigenstate and do not have definite energy. (If you try to measure the energy of state, you will see 2 energies.) But the mixed state, cos 2 sin 2 sin 2 cos 2 ARE energy eigenstate and have definite energy. /2 is called mixing angle between energy eigenstate and spinr state. =The mixing angle corresponds to 1/2 of the polar angle of B. 111018 suekane@FAPPS 68