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					Neutrino Mixing and Mass


2007 Yonsei-Saga Joint Workshop

Nov. 19-23, 2007 Yonsei University, Korea



           Sin Kyu Kang
     (Seoul National University
          of Technology)
   Introduction to Neutrino

  There were problems in the early days of b decay.

                    F. A. Scott, Phys. Rev. 48, 391
b spectra were                                        Instead of
  continuous                                           discrete




 Bohr: maybe energy/momentum not conserved in b decay?
     Wolfgang Pauli’s solution (1930)


                         In b-decay




Weakly interacting massless neutral fermion
         Discovery of Neutrino

“ the first detection of anti-neutrinos ``


 Cowan & Reines (1956)
•Neutrinos in the the Standard Model

                  • How neutrinos describe in
                    the SM ?
                              L DL
                         ( D     igG )

                  • Weak interaction exchanging
•Three kinds of neutrinos :   •Neutrinos must be massless

        e ,  ,           All neutrinos left-handed




                               Right-handed Neutrinos ?
                                    No observation
                                 can’t have a mass !!
 Why Neutrino Physics Important ?



 Neutrino Oscillation
            Window for New Physics :




        Origin of Our Universe
  The Physics of
Neutrino Oscillation
Neutrino Oscillation
•   Quantum mechanical effects when
             Flavor states                           Mass states
                     cos  sin     1                  m1
                    
                               cos  1                  2
                      sin         2                  m2
                                                       m1        m2
     |   , t  |  1  cos  (e    im1 t / 4 p
                                                     ) |  2  sin  ( e    im2 t / 4 p
                                         2                                      2
                                                                                            )


    Oscillation Probability
     :
                                       Neutrino trajectory




                                           Neutrino energy


     For two neutrino flavors in vacuum oscillations
       lead to the appearance of a new neutrino flavor
 With the corresponding disappearance of the
  original neutrino flavor



              Survival Probability :
                Psurvival  1  Pμ




                                      (E=1 GeV, sin2 2=1
                                      Dm2=310–3(eV)2 )
 These oscillations can be significantly modifed
  when the neutrinos pass through matter




   Matter Effects – the MSW effect
                       (Mikheyev, Smirnov, Wolfestein)
    MSW effect

                    d  e    e 
                   i    H 
                    dt  x   x 
In vacuum:
                Δm 2      Δm 2      
                4E cos2θ 4E sin2 θ 
             H                     
                Δm sin2 θ Δm cos2θ
                   2          2

                4E
                           4E       
                                     
       MSW effect

                     d  e    e 
                    i    H 
                     dt  x   x 
In matter:
              Δm 2                     Δm 2        
                  cos2θ  2G F N e         sin2 θ 
         H   4E                        4E         
                   Δm 2                Δm 2
                         sin2 θ              cos2θ 
             
                    4E                  4E         
                                                    

  x                     x     e                      e-

               Z0                             W

  e-                     e-     e-                      e
       MSW effect

                     d  e    e 
                    i    H 
                     dt  x   x 
In matter:
              Δm 2                     Δm 2        
                  cos2θ  2G F N e         sin2 θ 
         H   4E                        4E         
                   Δm 2                Δm 2
                         sin2 θ              cos2θ 
             
                    4E                  4E         
                                                    

  x                     x     e                      e-

               Z0                             W

  e-                     e-     e-                      e
MSW effect

              d  e    e 
             i    H 
              dt  x   x 

       Δm 2                      Δm 2        
           cos2θ  2G F N e          sin2 θ 
  H   4E                         4E         
            Δm 2                 Δm 2
                  sin2 θ               cos2θ 
      
             4E                   4E         
                                              

                         sin 2 2
     sin 2 2 m 
                  (  cos 2 )2  sin 2 2
            2 2GF N e E / Dm 2
        Three Neutrino Oscillations

Neutrino Mixing         U i  i
                    Weak         Mass
                    eigenstate   eigenstate
How can we detect Neutrinos?
How can we detect Neutrinos?

Neutrino detectors         Super Kamiokande

                                Use Water
                                    Cheap
                                 Transparent




                 We will detect about 1 solar neutrino
                  per day per 100 tons of detector
Water Cerenkov method:
                                      Detection via cherenkov light
   x + e-        x +e-              emitted by particles moving
                                           “faster” than light




 An F-18 Breaking the Sound Barrier
Evidence for Neutrino Oscillations
              Cosmic Ray

             p, K
              μ
                e
        
                  e




                    (+ )/(e+ e)
   
                  e

Neutrinos from the                      Super-Kamiokande
other side of the Earth.                 (50,000ton water
                                           Ch. Detector)
Atmospheric Neutrino Oscillation




     A half of  lost !!
   SK : L/E Dependence
                            SK Collab. hep-ex/0404034
          oscillation




                                        oscillation dip
   decoherence



           decay




• SK        observed an apparent oscillation dip.
• Rival hypotheses such as neutrino decay and
  decoherence        disfavored at 3.5 
 oscillation parameters
                                       90%CL

   MINOS (atmospheric)   Soudan-2
                                                   
                                    MACRO

                                               Super-K




                                                Also, consistent
                                                results from long
                                                baseline experiments
                                                (K2K & MINOS)
•How the Sun burns
       Solar Neutrino Anomaly




• νe flux: about a half of SSM prediction
       Effects of neutrino oscillation?
               SNO Experiment
                                1,000 tonnes of D2O.

8
    B   solar neutrino
        observation via


CC       e  d  p  p  e


NC       x  d  p  n  x

                          
ES       x  e  x  e
 •    SNO Pure D2O Results                              •        SNO Salt Fluxes
      (SNO Collab. PRL 89 (2002) )                           (SNO Collab. PRL92 (2004) )




               +0.06         +0.09                                      +0.07         +0.09
Fcc(e) = 1.76−0.05 (stat.)−0.09 (syst.) ×       106   Fcc(e) = 1.70 −0.07(stat.) −0.10(syst.) × 106
                                                                        +0.29         +0.15
               +0.24         +0.12
Fes(x) = 2.39−0.23 (stat.)−0.12 (syst.) ×       106   Fes(x) = 2.13       (stat.)       (syst.) × 106
                                                                        −0.28        −0.08
                                                       Fnc(x) = 4.90   +0.24(stat.) +0.29(syst.)   × 106
Fnc(x) = 5.09 +0.44         +0.46
                       (stat.)       (syst.) ×   106                    −0.24         −0.27
               −0.43         −0.43
                                          SSM(2004) : F( 8 B)  5.26(1  0.23)  106 cm 2s 1

                  Evidence for flux deficit of solar neutrino
                        MSW effects are important !
                           + p
                           e      e+ + n




Reactor Long Baseline Experiment
150 - 210 km
              ( Epr > 2.6 MeV )
R  0.686  0.044(stat)  0.045(sys)
Neutrino Oscillation parameter allowed regions




2.5 103 eV2



                                7 105 eV 2




45              Evidence for the existence of
                                                32
                neutrino masses and mixing
               What known and unknown
      Present: Study of dominant oscillation channels
      Future: Study of sub-dominant oscillations

                Known:                             Unknown:

 12, Dm122            23,             13            Sign of Dm232
     e            |Dm232|
3
                                                              or

2
1
      Solar,         Atmospheric     If 23 ≠p/4,                  (CP)
      KamLAND        Long baseline   is it >p/4 or <p/4 ?

                                         Future atmospheric exp’s
       Determination of                            13
   CHOOZ experiment :                e  p  e  n

• intense and nearly pure neutrino flavor composition    ( e )
              ( L 1km, E    3MeV)



                                          sin2 2  0.16
                                               for
                                          Dm 2  2  103 eV 2
• Solar and KamLAND provide
  information on  13
  independent of CHOOZ and
  atmospheric neutrino data

        13  7.5 7.5 (2 )
                  
                    4.8




• Global analysis of all available
  data (Malton et al.) :


        13  4.4 4.4 (2 )
                  
                    6.3
                                     • Allowed regions at 90%, 95%,
                                       99%, 3  from CHOOZ(lines),
                                       CHOOZ+solar+KamLand(colored)
                0.79     0.86     0.50          0.61    0.16 
                                                              0
                                                              
     U exp     0.24     0.52 0.44             0.69 0.63 0.79 
                0.26                           0.71 0.60 0.77 
                         0.52     0.47                        

             Why both mixings Large ?
• Bi-large mixing
• In the limit              | U e 3 | 1         atm   45
                                                             
                       cos          sin  s            0    
                             s                               
                        sin  s     cos  s             1    
              U                                             
                            2              2            2    
                                                             
                       sin  s     
                                        cos  s          1    
                                                             
                          2                 2           2    

• When           s      p /4               Bi-maximal mixing !!
                        (Barger et al., Georgi & Glashow)
Neutrino Masses
           Mass scale of neutrinos


•Atmospheric neutrino;           x : Dmatm  103 eV 2
                                           2




•Solar neutrino;  e   x : Dmsol  104 eV 2
                               2



•Sum of 3 Δm2 should be 0;        Dm12  Dm23  Dm31  0
                                    2      2      2



•Assume mass hierarchy;          m1  m2  m3


       Dmsol  Dm12  Dm23  Dm13  Dmatm
         2       2       2      2      2
 How small Neutrino Mass ?




                          :
• Cosmological Mass Limit WMAP
                       m
         h 2             0.0076
                     92.5eV

                 m  0.3(eV )
• Why Neutrino Masses so small ?

              •     Seesaw Mechanism

                     1          0 mD  L 
            Lmass    ( L R )
                               m        c.c.
                     2          D M  R 
                                       
                                   2
    Mass eigenvalues ~            mD
                                       : M
                                  M
                       2
                      mD
                    
                      M
                                          M

 To obtain O(eV) neutrino mass,         M  1010  1014 GeV
                   Leptonic CP violation

 Dirac CP violation : CKM-like phase                        in UPMNS
      measurable in neutrino oscillation if P(     b )  P(     b )
      using the hierarchy
                                                 Dm 2 L  2  Dm 2 L 
  ACP  [P(     b )  P(     b )]  8J     21
                                                          sin 
                                                                  31
                                                                      ,
                                                 2E           2E 
     1
  J  cos 13 sin 223 sin 213 sin 212 sin 
     8
       for the golden channel             e  

  Conditions for observing CPV effects
    Dm 2
       21  and 12 should be large
     13    should not be too small
     CPV phase  should be large
     the baseline should be long enough (typically 3000 or 7000km)
• In matter : matter effect violates CP & CPT

 (   P  Pb  P  Pb   &   P  Pb  Pb  P   )

     in matter with costant density :
                         ACP  J CP
                                 matt
        JHF
        Plan to start in 2007

          Kamioka ~1GeV  beam
                                     JAERI
Super-K: 22.5 kt                  (Tokaimura)
Hyper-K: 1000 kt                   0.77MW 50 GeV PS

                                   4MW 50 GeV PS
                                  ( conventional  beam)

              Phase-I (0.77MW + Super-Kamiokande)
              Phase-II (4MW+Hyper-K) ~ Phase-I  200
           The Big Questions
 What is the origin of neutrino mixing and mass ?

 Did neutrinos play a role in our existence ?

 Did neutrinos play a role in birth of the universe ?

 Are neutrinos Majorana particles?
 Are neutrinos telling us something about
  unification of matter and/or forces ?
                      Quark vs. Lepton

         Mixing       Quarks        Leptons
           1-2, 12      13o            33o          sol  C = 46 (2.4)o
           2-3, 23      2.3o           45o
           1-3, 13     ~ 0.5o          <10o         atm  23q = 45 (3) o

Hierarchy of masses:
 Neutrinos |m2 /m3| ~ 0.2
                                                                   2-3
 Charged |m /m| = 0.06
 leptons                                                    1-2
 Down      |ms /mb| ~ 0.02 - 0.03                                            1
                                                     1-3
 quarks
 Up-quarks |mc /mt| ~ 0.005
                                    0          0.2         0.4       0.6   0.8
                                                             |sin |
  Quark-Lepton complementarity?
                                                       A.Smirnov
                                                       M. Raidal
 Understand phenomenological relationships            H. Minakata
                                                       SK, Kim, Lee
 between quarks and leptons at deeper level
                                                   p
      Example:      solar   Cabibbo   atm 
                                                   4

 Deeper underlying reason or accidental?

 Note: CKM/MNS
   matrix is composited
   of two parts

 Important in future:
  parameter precision measurements!
  Unknown Fermion Structure ?

                     Symmetry
                   correspondence




Provide with all the           Give relations
ingredients necessary          between masses of
for seesaw mechanism           leptons and quarks
                 Summary

• The present neutrino experiments
  indicate the strong evidence for massive
  neutrinos
    new physics beyond SM

• Small but finite neutrino masses
    need drastic idea to understand it

• Neutrino era is just beginning and
  we have long way to go…..
Neutrino Oscillation
  • Quantum mechanical effects when
         Flavor states            Mass states
    e                  1      2         3
                             m1       m2        m3

				
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