Discovery of. Do we throw away the energy conservation?

Transkrypt

1 Discovery of s At end of 18 s radioactivity was discovered and three types identified: : an electron comes out of the radioactive nucleus. Energy conservation should have had a fixed energy But 1914 James Chadwick showed that the electron energy spectrum is continuous Do we throw away the energy conservation?

2 Discovery of s The idea of the neutrino came in 193 when W. Pauli tried a desperate saving operation of the energy conservation principle. In his letter addressed to the Liebe Radioaktive Damen und Herren (Dear Radioactive Ladies and Gentlemen the participants of a meeting in Tubingen. He put forward the hypothesis that a new particle exists as constituent of nuclei the neutron able to explain the continuous spectrum of nuclear beta decay The light (in Pauli s words: the mass of the is should be of the same order as the mass neutral and has spin 1 In order to distinguish them from heavy neutrons Fermi proposed to name them neutrinos.

3 First Detection of s In 1934 Hans Bethe and Rudolf Peierls showed that the cross section between matter should be so small that a and go through the Earth without deviation In 1953 Frederick Reines and Clyde Cowan place a neutrino detector near a nuclear plant 4 litters of water and cadmium chloride. annihilates of the surrounding material giving two simultaneous s. neutron captured by a cadmium nucleus with emission of s some 15 msec after The neutrino was there. Its tag was clearly visible

4 The Other Flavours because it is emitted together with an coming out of a nuclear reactor is Question: Is it different from the muon type neutrino that could be associated to the muon? Or is this difference a theoretical arbitrary convention? In 1959 M. Schwartz thought of producing an intense beam from s decay (produced when a proton beam of GeV energy hits matter Schwartz Lederman Steinberger and Gaillard built a spark chamber (a 1 tons of neon gas to detect They observe 4 If interactions: in 6 an equal numbers of and comes out and in 34 a comes out. Conclusion: is a different particle In 1977 Martin Perl discovers the particle tau the third lepton family. The was observed by DONUT experiment at FNAL in 1998 (officially indec..

5 Sources of s The Big Bang cm.4 ev SN1987 MeV The Sun p MeV cm s Human Body day Atmospheric cm s Nuclear Reactors few MeV Earth s radioactivity cm s Accelerators.3 3 GeV

6 .4.- % in the SM The SM is a gauge theory based on the symmetry group LEP tested this symmetry to 1% precission and the missing particles Notice there is no Accidental global symmetry: When SM was invented upper bounds on K (T mν Q T 1 " % 3 ( " 5-6 +* ( ( Neutrinos are conjured to be massless and left-handed "

7 had negative helicity helicity Neutrino Helicity The neutrino helicity was measured in 1957 in a experiment by Goldhaber et al. Using the electron capture reaction with +and Angular momentum conservation Nuclei are heavy So momentum conservation helicity= Goldhaber et al found has helicity Thus so far was a particle with (because for massless fermions helicity chirality... and left handed. +

8 Dirac versus Majorana Neutrinos In the SM neutral bosons can be of two type: Their own antiparticle such as... Different from their antiparticle such as... In the SM are the only neutral fermions OPEN QUESTION: are neutrino and antineutrino the same or different particles? ANSWER 1: different from anti- is a Dirac particle (like It is described by a Dirac field And the charged conjugate neutrino field the antineutrino field % " ( which contain two sets of creation annihilation operators These two fields can rewritten in terms of 4 chiral fields * + -.

9 same as anti- is a Majorana particle : and which verify Dirac versus Majorana Neutrinos ANSWER : So we can rewrite the field which contains only one set of creation annihilation operators A Majorana particle can be described with only independent chiral fields: In the SM the interaction term for neutrinos Only involves two chiral fields Weak interaction cannot distinguish if neutrinos are Dirac or Majorana The difference arises from the mass term and "

10 Mass Terms A fermion mass can be seen as at a Left-Right transition (this is not gauge invariant In the Standard Model mass comes from spontaneous symmetry breaking via Yukawa interaction of the left-handed doublet with the right-handed singlet : the scalar doublet After spontaneous symmetry breaking = Dirac mass matrix for charged leptons there is no dynamical reason for introducing How can we generate a mass for the neutrino? do not participate in QED or QCD and only s is relevant for weak interactions so

11 -. -. involves the four chiral fields =Dirac mass for neutrinos % % % % Mass Terms: Dirac Mass OPTION 1: One introduces Under spontaneous symmetry-breaking The eigenstates of are Dirac particles (same as quarks and charged leptons Total Lepton number is conserved by construction (not accidentally: which can couple to the lepton doublet by Yukawa interaction

12 Mass Terms: Majorana Mass OPTION : One does not introduce can write a Lorentz-invariant mass term but uses that the field is right-handed so that one =Majorana mass for neutrinos But under any symmetry But -. it can only appear for particles without electric charge Total Lepton Number is not conserved The eigenstates of are Majorana particles (verify gauge invariance is broken

13 % % % % % % % General invariant Mass Terms OPTION 3: Introduce ( and write all Lorentz and invariant mass term Under spontaneous symmetry-breaking with and In general if 3+m Majorana neutrino states (verify how many are light depends on hierarchy between Total Lepton Number is not conserved and

14 The See-Saw Mechanism A particular realization of OPTION 3: Assume Heavy s of mass 3 light neutrinos s of mass The heavier the lighter See-Saw Mechanism Arises in many extensions of the SM: SO(1 GUTS Left-right...

15 Mass from Non-Renormalizable Operator If SM is an effective low energy theory for The same particle content as the SM and same pattern of symmetry breaking But there can be non-renormalizable (dim operators First NP effect dim=5 operator There is only one which after symmetry breaking induces a Majorana mass breaks total lepton and lepton flavour numbers Implications: It is natural that mass is the first evidence of NP Naturally other fermions masses if see-saw with heavy neutrinos integrated out is a particular example of this

16 * - * - Lepton Mixing Charged current and mass for charged leptons basis neutrinos and. In weak Changing to mass basis by rotations Unitary matrices and The charged current in the mass basis Unitary matrix. matrix

17 Lepton Mixing For example for 3 Dirac s : 3 Mixing angles + 1 Dirac Phase For 3 Majorana s : 3 Mixing angles + 1 Dirac Phase + Majorana Phases

18 Effects of Mass Neutrino masses can have kinematic effects Also if neutrinos have a mass the charged current interactions of leptons are not diagonal (same as quarks 1 ( 1 W + νj _ l i SM gauge invariance does not imply W + u j _ d i symmetry Total lepton number can be or cannot be still a symmetry depending on whether neutrinos are Dirac or Majorana (

19 Neutrino Mass Scale: Tritium Decay Fermi proposed a kinematic search of mass from beta spectra in beta decay For allowed nuclear transitions the electron spectrum is given by phase space alone maximum kinetic energy (for beta decay KeV distortion from the straight-line at the end point of the spectrum K (T m ν Q T At present only a bound: Katrin proposed to improve present sensitivity to (at 95 % CL (Mainz Troisk experiments

20 ( Neutrino Mass Scale: Other Channels Muon neutrino mass From the two body decay at rest Energy momentum conservation: Measurement of plus the precise knowledge of and The present experimental result bound: Tau neutrino mass The much heavier is phase space Large for GeV difficult precision The best precision is obtained from hadronic final states with Lep I experiments obtain: mixing angles If are not negligible Best kinematic limit on Neutrino Mass Scale comes from Tritium Beta Decay

21 Dirac Majorana ( ( Neutrino Mass Scale: -less Double- Decay only for Majorana s Sensitive to Majorana CP phases Amplitude involves the product of two leptonic currents: If annihilates a neutrino and creates an antineutrino same state no Amplitude = If same state annihilates and creates a neutrino=antineutrino Amplitude Amplitude of -lessdecay is proportional to " Present bound: " % +theor. uncert. ((9% CL Several proposed experiments to reach " *

22 ( has effects on: Neutrino Mass Scale in Cosmology Cosmic Microwave Background Temperature Fluctuations Most recent from WMAP Large scale structure: Field Galaxy Redshift Survey (dfgrs Sloan Digital Sky Survey (SDSS Tegmark et. al astro-ph3173 Problem: 13 parameters to be determined limit on prior and data used to constraint other 1 parameters depends on

23 Effects of Mass: Flavour Transitions Flavour ( Interaction basis (production and detection: Mass basis (free propagation in space-time: In general interaction eigenstates and propagation eigenstates... and Flavour is not conserved during propagation different (or same flavour than produced can be detected with The probability of producing neutrino with flavour flavour has to depend on: and detecting with Misalignment between interaction and propagation states ( Difference between propagation eigenvalues Propagation distance

24 + % " ( * ( - ( Vacuum Oscillations A state mixture of neutrino species and or equivalently of and where and Evolution of is given by the Dirac Equations. Calling In the relativistic limit Under some approximations spinorial part factorizes out. Check Baltz and Wesener PRD37 ( where.

25 and % + " *. ( Defining ( Km After a distance If was produced with flavour it can be detected with flavour with probability the probability of flavour to appear after a distance is the probability of flavour to survive after a distance

26 and " " " - ( The probabilities oscillate in In real experiments neutrinos are not monochromatic Maximal sensitivity for No time to oscillate Averaged oscillations " " "

27 Distance - ( Vacuum Oscillations The oscillation probability for N neutrinos: Re Im ev KmGeV The first term Re equal for conserves CP ( The last piece Im opposite sign for violates CP depends on Theoretical Parameters and on Two Experimental Parameters: The mass differences The neutrino energy source to detector (and Dirac phases No information on mass scale nor Majorana phases The mixing angles

28 + " To allow observation of neutrino oscillations: Nature has to be good: Need the right set up ( right for Source E (GeV L (Km Solar (ev Atmospheric Reactor SBL: LBL: + Accelerator SBL: LBL:

29 Atmospheric atmosphere Atmospheric Neutrinos are produced by the interaction of cosmic rays (p He... with the _ π + ν µ ( π ν µ -+ ν ( ( e N π + _ µ +_ p He e +_ Nν+ µ R µe = N + ν e N ν νµ N ν e ~

30 Atmospheric Neutrinos: Data EVENT CLASSIFICATION Angular Distribution at SK [not to scale] down-going p He + π + K µ + L ~ 1-3 km e + atmosphere E ν ν eµ CONTAINED eµ Fully Contained µ ν µ Partially Contained UPGOING MUONS µ µ νµ ν µ Stopping Thru-going Muon Muon.1 - few GeV few GeV few 1 GeV few 1 GeV Total Rates for Contained Events in agreement with SM Number of Events Number of Events 45 Sub-GeV e-like cosθ.5 1 Multi-GeV e-like cosθ Number of Events Number of Events Sub-GeV µ-like cosθ 35 Multi-GeV µ-like + PC cosθ zenith angle detector L 1 4 km ν µ ν µ ν e L km up-going L 5 km Deficit grows with EARTH Flux(1-13 cm - s -1 sr Upward Through Going µ cosθ Upward Stopping µ cosθ Decreases with

31 For Atmospheric Oscillations: Parameter Estimate From Total Contained Event Rates: From Angular Distribution: L~ 13Km ~ 5Km ~ 15Km N events N events 4 1 SK sub-gev e-like No oscillation SK multi-gev e-like SK sub-gev µ-like SK multi-gev µ-like UP HORIZ DOWN cosθ 1 GeV deficit at Km ( ( + (

32 Atmospheric Oscillation Solution: Best fit: ev

33 Oscillations: Lab Searches at Short Distance In laboratory experiments source: Accelerator or Nuclear Reactor ν source α Appearance Experiment L Experiment ν detector CCFR 1 FNAL E531 5 FNAL Nomad 13 CERN Chorus 13 CERN E776.5 BNL Karmen.5 Rutherford LSND 3 Los Alamos β Searches for β diffα Disappearance Experiment να source ν ν α detector ν α detector L I Compares Φ I Φ α Ι α Ι L Experiment II and Φ α ΙΙ II Φ α ΙΙ to look for loss CDHSW 1.4 CERN BugeyIII.5 Reactor Chooz.5 Reactor

34 LSND The only short distance signal for oscillation: Used the proton beam of Los Alamos m with * " MeV * * * * observed probability with " which searched for the same signal and did not observe oscillations. in Fermilab is running to solve this.

35 + Summary of at Short Baseline Reactor disappearance experiments Lower E and longer L are more sensitive to lower Accelerator appearance experiments higher E shorter L more precision better limits on mixing To reach small ev very large L and intermediate E Long Baseline Experiments at Accelerators: To reach smaller ev Long Baseline Experiments at Reactors

36 ATM Test at Long Baseline Experiments KK MINOS OperaIcarus KK 4: spectral distortion Events. (GeV at KEK SK L=5 km at Fermilab Soundan L=735 km at CERN Gran Sasso L=74 km MINOS 6: spectral distortion rec E ν (GeV Confirmation of ATM oscillations Confirmation of ATM oscillations

37 Solar Neutrinos: Fluxes pp chain Sun shines by : * + Solar Standard Model Fluxes CNO cycle e + N 13 <E >=.77MeV He 4 C 1 C 13 p p p p N 15 N 14 He 4 O 15 O 16 e + <E >=.997MeV O17 p F 17 p e + <E >=.999MeV

38 " real time radiochemical Solar Neutrinos: Data Experiment Detection Flavour Homestake Cl Ar Sage + Gallex+GNO Ga Ge (MeV Kam SK ES SNO CC NC ES % % % All experiments measuring mostly deficit Deficit is energy dependent Deficit disappears in NC observed a (

39 Solar Neutrinos: Flavour Conversion Evidence SK and SNO measure ES CC NC in different reactions In the SSM with SM interaction all results should be equal If flavour conversion everything fits perfectly: SNO φ NC φ SSM φ e (1 cm s 6 (1 φ µτ cm - s -1 SNO φ ES SNO φ CC

40 Neutrinos in Matter:Effective Potentials In SM the characteristic -p interaction cross section + So if a beam of was aimed at the Earth only 1 would be deflected so it seems that for neutrinos matter does not matter But that cross section is for inelastic scattering Does not contain forward elastic coherent scattering In coherent interactions and medium remain unchanged Interference of scattered and unscattered waves

41 Neutrinos in Matter:Effective Potentials Coherence decoupling of evolution equation from equations of the medium. The effect of the medium is described by an effective potential depending on density and composition of matter For example for in medium with electron number density The effective potential has opposite sign for neutrinos y antineutrinos Other potentials for due to different particles in medium medium and and " " and Neutral %

42 9 : 9 6 > = " " ( % " " " % " " ( % " " " % Neutrinos in Matter: Evolution Equation Evolution Eq. for ( (a In vacuum in the mass basis: (b In vacuum in the weak basis (c In matter * + in weak basis (c (b because different flavours have different interactions For example : (opposite sign for 9 : ; : 9 <only : 9 9.

43 % 3 Effective masses and mixing are different than in vacuum If matter density varies along trajectory the effective masses and mixing vary too The effective masses: ( µ m m 1 AR ν ν ν 1 A ν 1 At resonant potential: Minimum % % The mixing angle in matter "At "At "At (vacuum

44 % The oscillation length in vacuum The oscillation length in matter presents a resonant behaviour At the resonant point L osc L osc The width of the resonance in potential: δar A R A The width of the resonance in distance:

45 and In terms of the mass eigenstates in matter: For constant potential are constant along evolution the evolution is determined by masses and mixing in matter as For varying potential: the evolution equation in flavour basis (removing diagonal part the evolution equation in instantaneous mass basis 9

46 The evolution equation in instantaneous mass basis " It is not diagonal Instantaneous mass eigenstates - eigenstates of evolution Transitions can occur Non adiabaticity For Slowly varying matter potent behave approximately as evolution eigenstates do not mix in the evolution This is the adiabatic transition approximation The adiabaticity condition % Many oscillations take place in the resonant region

47 Neutrinos in The Sun : MSW Effect Solar neutrinos are produced in the core ( of the Sun The solar matter density At core: The energy spectrum of solar For in vacuum % ev ev 1 MeV For ev ev can cross resonance condition in its way out of the Sun %

48 dramatically at resonance is mostly is mostly " " % % % % component " before and after resonance " For : In vacuum In Sun core % % is mostly is mostly If Adiabatic transition µ m m 1 This is the MSW effect ν µ ν e ν e ν µ ν ν 1 A A A A R R component If Non-Adiabatic transition till the resonance "At resonance the state can jump into (with probability µ m m 1 ν µ ν e ν e ν µ ν ν 1

49 Neutrinos in The Sun : MSW Effect does not cross resonance: Adiabacity breaking Effect of crosses resonance MSW effect Adiabatic MSW transition

50 Neutrinos from The Sun : The Full Story

51 Solar Neutrinos: Oscillation Solutions Allowed regions by Fit to Total Rates: Cl Ga SK and SNO CC LMA Different regimes can explain the Total Rates SMA 1-6 Need more observables to discriminate LOW -1 1 VAC

52 Energy Dependence of SMA for Different Solutions LMA LOW VAC

53 Real Time experiments can also give information on Energy and Direction of and can search for Energy and Time variations of the effect scome from the SUN No Energy Distorsion From SK Deficit indep MeV.5 (Confirmed Super-Kamiokande by SNO. Eventdayktonbin θ sun cos Θ Sun No Earth Matter Effect: Small Day-Night Asymmetry Seasonal Variation Nothing beyond

54 Solar Neutrinos: Oscillation Solutions RATES ONLY SK and SNO E and t dependence GLOBAL LMA SMA -7 1 LMA LOW SMA LOW VAC 1-1 VAC at ev (1

55 Terrestrial Test of LMA: KamLAND Search on at 18 L km reactors few MeV: : Deficit Oscillation Analysis NobsNexp ILL Savannah River Bugey Rovno Goesgen Krasnoyarsk Palo Verde Chooz KamLAND Distance to Reactor (m 4: Significant Energy Distortion (MeV delayed E no-oscillation Events.45 MeV 6 4 best-fit oscillation accidentals KamLAND data ev ( E (MeV Fri Jun 11 11:43:3 4 prompt

56 oscillation parameters compatible with. Solar + KamLAND : Sensible to assume CPT: ev (1

57 Two Neutrino Oscillations: Summary How to fit all this together? 3 oscillation signals in 3 different scales Mixing of Explain only two evidences: For example Solar + Atmos mass diff Theorists have tried hard to fit LSND in: Adding a fourth sterile neutrino Breaking CPT but nothing works well The Naked True: If Miniboone finds a signal we have no good theory of what to do Ergo I am going to ignore LSND

58 1 " % " " solar M Solar+Atmospheric+Reactor+LBL 3 Oscillations : 3 angles 1 CP-phase + ( Majorana phases Two mass schemes m m 1 3 m m 3 m atmos m 1 m NORMAL INVERTED m oscillation analysis Generic 3 mixing effects: Interference of two wavelength oscillations Effects due to Difference between Inverted and Normal CP violation due to phase In Present Data: 4But all these 3 effects within reach of planned experiments 1 3 * + -." ( ( % " ( solar

59 - 5 % % % % % % % % (.- (.- 67 " ( - ( ( - ( + ( - 34 " (* (.- + (* + ( (* + (.- ( ( - Global Analysis: Three Neutrino Oscillations 3 ranges: with structure very different from quark s (.- 34 ( - (.-

60 : : Different from ( * 5 ( " % ( " % ( + Summary 4In the SM: Accidental global symmetry: To include Need to extend SM adding different ways of to the SM breaking total lepton number ( conserving total lepton number Dirac Majorana Lepton Mixing breaking of oscillate in flavour 4Neutrino oscillation searches have shown us % 4 ev and % ev s are massive " % " % ( 34 " % " % 34

61 + + % Summary 4Still open questions Is? Is there CP violation in the leptons (is Is large or maximal?? Normal or Inverted mass ordering? Are neutrino masses: hierarchical:? degenerated:? Dirac or Majorana? what about the Majorana Phases?...

62 + Summary 4Majorana are more Natural: appear generically if SM is a LE effective theory If SM is an effective low energy theory for The same particle content as the SM and same pattern of symmetry breaking But there can be non-renormalizable (dim operators First NP effect dim=5 operator There is only one which after symmetry breaking induces amajorana mass breaks total lepton and lepton flavour numbers 5 3 ev ( % Implications: It is natural that mass is the first evidence of NP Naturally other fermions masses - GeV