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Neutrino History and properties

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					    Neutrino History and properties
       Neutrinos they are very small.
       They have no charge and have no mass
       And do not interact at all.
       The earth is just a silly ball
       To them, through which they simply pass,
       Like dustmaids down a dusty hall....


                         ”Cosmic gall”,
                         John Updike,
                         Telephone Poles and other Poems,
                         1963
                                
                                              PX435 –  Physics
     
        PX435 –  Physics
    CRISIS
        
           PX435 –  Physics
    Energy conservation violated!




      m1   M    m2            2     2    2
                             M m 2−m 1
                      E 2=
                                  2M
                   
                                  PX435 –  Physics
    Pauli's Desperate Remedy




                
                       PX435 –  Physics
         The birth of the neutrino
    4th December 1930
    Dear Radioactive Ladies and Gentlemen,
    As the bearer of these lines, to whom I graciously ask you to listen, will explain to
    you in more detail, how because of the ”wrong” statistics of the N and 6Li nuclei
    and the continuous beta spectrum, I have hit upon a desperate remedy to save the
    ”exchange theorem” of statistics and the law of conservation of energy. Namely,
    the possibility that there could exist in the nuclei electrically neutral particles, that I
    wish to call neutrons, which have spin and obey the exclusion principle and which
    further differ from light quanta in that they do not travel with the velocity of light.
    The mass of the neutrons should be of the same order of magnitude as the electron
    mass (and in any event not larger than 0.01 proton masses). The continuous beta
    spectrum would then become understandable by the assumption that in beta
    decay a neutron is emitted in addition to the electron such that the sum of the
    energies of the neutron and the electron is constant...
    From now on, every solution to the issue must be discussed. Thus, dear radioactive
    people, look and judge. Unfortunately I will not be able to appear in Tubingen
    personally, because I am indispensible here due to a ball which will take place in
    Zurich during the night from December 6 to 7...


    Your humble servant,
    W. Pauli
                                              
                                                                     PX435 –  Physics
                   Oh the pain


    “I have done something very bad today by proposing a
        particle that cannot be detected. It is something
                 that no theorist should ever do.”


                                        Pauli, 1930




                              
                                         PX435 –  Physics
                Fermi Theory (1926)
       p                             p

     e-                               e-
          2
          p x  p x][ e x e x]
    L=e [                   

       n                             p

                                     e-
                                               Enrico Fermi
    L=G F [  p x n x][e x  x]
                            

                                             
                    NB Vector                      PX435 –  Physics
    Fermi Theory (1926-34)


              Initial paper rejected by
              Nature because:

              “it contains speculations
              to remote from reality
              to be of interest to the
              reader”



               
                           PX435 –  Physics
                      But where is it?
Still no neutrino observed experimentally? Why?
Bethe-Peierls (1934) provided some of the answer.

    Early theory predicted
                                          ~ 10-44 cm2 for 2 MeV 
    cross section for  p

                  1                            1
       lead ~          =
                                23                   2                2
                 NA       6.10 nuc / g×7.9 g /cm ×10   −44
                                                                   cm 
                        lead ≈ 22 light years

            Need large detectors and huge fluxes
                                      
                                                    PX435 –  Physics
    Detection of the Neutrino
    1950 – Reines and Cowan set out to detect 




                         
                                    PX435 –  Physics
    Project Poltergeist - 1951




                 
                         PX435 –  Physics
    Project Poltergeist - 1951




                 
                         PX435 –  Physics
    Project Poltergeist - 1951

                              I. Explode bomb
                              II.At same time let
                              detector fall in
                              vacuum tank
                              III. Detect neutrinos
                              IV. Collect Nobel
                              prize




    OK – but repeatability is a bit of a problem
                         
                                     PX435 –  Physics
        Idea Number 2 - 1956
      A nuclear reactor is the next best thing
    Fission of U235 produces a chain of  decays
           Reactor on – Reactor off = 2.88 +/- 0.22 hr-1
                    = (11 +/- 2.6) x 10-44 cm2
                  (Pred) = (5 +/- 1) x 10-44 cm2


                             Liquid scintillator

                    e
                                                     H20+
                                                 2
                             1                       CdCl2   10 s


                              511 KeV


                              e+p  e+ + n
                                    
                              2. Neutron capture      PX435 –  Physics
                                  on Cd
Finally – 26 years after being proposed the neutrino is
discovered

Telegram to Pauli : “We are happy to inform you that we
have definitely detected neutrinos” - Pauli and friends
put away an entire crate of Champagne.




    In 1995 Reines received the Noble Prize for this
    work - 40 years after doing so.
                             
                                         PX435 –  Physics
                  More than one?
    Muons were detected in 1930's, prompting one theorist
    (Isidor Ravi) to proclaim loudly at a major conference :
    “Who ordered that?”

    Muon decay seemed to show the familiar 3 body spectrum.
    Noone had seen the otherwise allowed decay

            e             so        e              ?




                                   
                                               PX435 –  Physics
           Lederman,Schwarz and
                Steinberger
    In 1962, Schwartz, Steinberger and Lederman presented
    evidence for the muon neutrino and built the very first
    neutrino beam!


                                            + → + + 


                                        + n →  + p OK

                                        + n → e + p OK
Bits of the
USS Missouri
                                
                                              PX435 –  Physics
     
        PX435 –  Physics
        The State of Play 1962




    ?
                   
                          PX435 –  Physics
               Aside - resonance
    Very short-lived compound states. These barely last long
    enough to traverse a nucleus.In the region of a resonance,
    the cross section for an interaction increases


          e             e           e              e
                                            J
          e             e           e              e


                            Shorter the lifetime, the larger the
      E  t≤ℏ              uncertainty in the mass of the
                            resonance state
                                 
                                               PX435 –  Physics
    Aside - Resonances




                               K
                N W =         2    2
                          W −M   /4

                Mass of        Width of
                resonance      resonance


             
                              PX435 –  Physics
    M
        Decay Widths

    
           =∑ all decay modes  i
                1        Decay time
            i=          for decay mode, i
                i



                 
                             PX435 –  Physics
                                            0
                Decay of the Z




             ee  f   f   More neutrinos would make the
    f f∝                  cross section for visible particles
               Z          decrease.


             Z = e e   q qN   
                                
                                                PX435 –  Physics
    LEP




      
          PX435 –  Physics
    The Number of light neutrinos




             N =2.98 41 0.008 3
                       ±

                     
                                   PX435 –  Physics
There's just got
to be something
here



                    
                       PX435 –  Physics
              The Tau Neutrino
       was finally discovered by DONUT in 2000.

    800 GeV protons on
    Tungsten produce
    Ds (=cs) mesons


      Ds  
      N X
        

                            
                                       PX435 –  Physics
    The Tau Neutrino




            
                   PX435 –  Physics
           Neutrino Properties
     Electrically neutral and interact only via the weak
    interaction.
     (Anti)neutrinos are chirally (right)left-handed.
     Exist in (at least) 3 active flavours
     Are almost massless
     Are the most common fermions in the universe

     Is a neutrino it's own anti-particle (Majorana
    particle)?
     Are there sterile neutrinos?
     What is the absolute neutrino mass?
     Is there CP violation in the neutrino sector?
     Does the neutrino have a magnetic moment?
     Are they stable?
                              
                                            PX435 –  Physics
           Neutrino Properties
     Electrically neutral and interact only via the weak
    interaction.
     (Anti)neutrinos are chirally (right)left-handed
     Exist in (at least) 3 active flavours
     Are almost massless
     Are the most common fermions in the universe

    Is a neutrino it's own anti-particle (Majorana particle)?
    Are there sterile neutrinos?
    What is the absolute neutrino mass?
    Is there CP violation in the neutrino sector?
    Does the neutrino have a magnetic moment?
    Are they stable?
    How do they interact with matter?
                              
                                            PX435 –  Physics
    A neutrino can interact with...


         An electron in an atomic orbit
         A nucleus as a whole
         A proton (free or bound)
         A quark in a nucleon

    Which happens depends on neutrino energy
                        2
    Larger E  Larger q  smaller wavelength
     can see smaller things.
                             
                                      PX435 –  Physics
            Kinematic Variables
                                  p = (E,p) –  4-momentum
                                  p = (E',p') –  4-momentum
                                  q=(,q) – W 4-momentum

                                  Eh = Hadronic energy
                                  P = Momentum of target



                                   4-momentum transfer
Momentum                           Q2=-q2 = (p - p)2
of proton

            Hadronic energy
                               
                                             PX435 –  Physics
                    W as a probe
 Very low Q2,  >rp, and scattering      
is off a “point-like” particle
 Low Q2,  ~rp, scattering is off an         
extended object

 High Q2,  <rp, can resolve quark           
in the nucleon


                                             
     Very High Q ,  <<rp, can resolve
                2


    sea of quarks and gluons in
    nucleon                          1           1
                                    = ~
                                 
                                      p  Q
                                           2
                                                    PX435 –  Physics
    Types of Interactions




               
                      PX435 –  Physics
    Neutrino Cross Sections




                
                       PX435 –  Physics
    Neutrino Cross Sections
        Quasielastic




                  
                       PX435 –  Physics
    Neutrino Cross Sections
      Resonance




                   
                       PX435 –  Physics
    Neutrino Cross Sections
            Deep Inelastic
            Scattering




                 
                             PX435 –  Physics
              Problems with QE
    The CC QE process is the best known neutrino process
    occurring at a few GeV




                                 −38
                                            E         2
               QE ~0.975×10                       cm
                                                      PX435 –  Physics
                                           1 GeV
          Resonance Region Data
               The data is impressively imprecise




           −                     −                             
      p   p             p   n           p   n 
    Added complication that the final state pions can (i) scatter
    (ii) be absorbed (iii) charge exchange within the nucleus
    before being observed (iv) nucleons rescatter producing 
                                    
                +
                n  p
                        0                        PX435 –  Physics
    World Data for Antineutrinos




                  
                         PX435 –  Physics
                      Summary
    Neutrino Interactions cover a broad energy range, from
    2 MeV to hundreds of GeV

    Broadly categorised into quasielastic, resonance
    and DIS events as Q2 increases (also inverse beta decay
    and elastic scattering)

    Unfortunately many neutrino interaction cross sections
    are not well known.

    A topic of research right now is to go back and measure
    the cross sections with today's technology, techniques
    and high intensity beams.

                               
                                             PX435 –  Physics
    Quasielastic Scattering
         GF cos C                               2         2
    M=               [ 1−5  ][ p   F V Q F A Q  5 n ]
            2
    Standard V-A                         Vector and Axial-vector
                                         “form factors”

                                   Form factors are corrections
                                   for target structure.

                                   Essentially they are the Fourier
                                   Transform of the charge
                                   spatial distribution (see handout)

                                   Must be measured!

                                      
                                                           PX435 –  Physics
                   What use is it?
          Experimentally we have a bit of a problem.

       Number of events E  = E ×E  × E  

        Can measure     Want to know            Damn!
                        the cross
                        section    Can estimate
                                   efficiency

    We never “see” neutrinos so we never have a measurement
    of the flux. We can only estimate it – badly – errors of 25%
    to 50% are not uncommon.
                                 
                                               PX435 –  Physics
                         What use is it
    Measurement of  has large errors. But suppose we have
    another process we know the cross section of reasonably
    well?

        N  E           E  E   E             E   E 
                   =                                 =
        G E          g  E g  E   E         g E  g  E  

    Can get ratio of cross sections with much better accuracy
    than we can measure the absolute number. Quasielastic
    scattering is the best known process at these energies to
    normalise off.


                                         
                                                               PX435 –  Physics
    ID&Energy Measurement
               ­
      n   p       Two-body interaction

                                              Outoing
                          Incoming            proton
                          neutrino
                                              

                            target          Outgoing
      p                     neutron         lepton (El,pl)
                            at rest


                                        2     2      2
                               m n E l m −m −m /2
                                        p     n      l
          -
                        E =
                                  mn− El  p l cos 

                     
                                      PX435 –  Physics
    Neutrino-Electron Scattering




                  
                         PX435 –  Physics
    Neutrino-Electron Scattering




                  
                         PX435 –  Physics
            Kinematic Variables
                                  p = (E,p) –  4-momentum
                                  p = (E',p') –  4-momentum
                                  q=(,q) – W 4-momentum

                                  Eh = Hadronic energy
                                  P = Momentum of target

                                   Inelasticity
                                           Ptarg⋅q          
Momentum                             y=                   =
of proton                                  P targ⋅p        E
            Hadronic energy
                               
                                                  PX435 –  Physics
    Charged Current Scattering

                    GF             5                         5
               M=        [ 1−   ][ e  1−  e]
                    2
                          2
               d        GF s             −41
                                                     E            2
                    =           =1.7×10                     cm
               dy                                  1 GeV

               Cross section linear with E
               Classic behaviour for point-
               point with no structure
               Completely calculable

                 
                                        PX435 –  Physics
    Neutral Current Scattering
                    GF                 5                           5
             M=          [ 1− ][e  g V −g A   e ]
                    2                                     mixture
                     g L e  1−5 eg R e   15  e
                         Left handed                Right handed
                1                −1                        1
                                            2
            g L =  gV g A = sin W ; g R =  gV −g A =sin 2 W
                 2            2               2
                                  2             2
             d  NC  e       G s
                                  F
                                            m   Z
                             =                       [ g2 g2 1− y2 ]
                                                        L   R
                    dy             q 2−m 2
                                          Z
                                  2             2
             d  NC  e       GF s       mZ
                             =                       [ g2 1−y 2g 2 ]
                                                        L           R
                    dy             q 2−m 2
                                          Z         PX435 –  Physics
                              So what?
                                      2
                 2    1cos 
        1−y  =                              In the COM frame
                              2
                                                  2     2
      d  NC  e       d  NC   e      G s g
                                                  F   1cos  2 2
                                                        L
                      ⇒                     =              gR
            dy                d cos            2      2

                                                      J=0
    Before                                                           e

                                                                      

    After

                                                      J=0
                          e                  
                                                            PX435 –  Physics
                        So what?
                                  2
                    1cos 
        1−y 2=                        In the COM frame
                       2
      d  NC  e d  NC   e  G2 s g 2 1cos  2 2
                                     F     L
                   ⇒               =              gR
           dy         d cos          2       2

                                             J=-1
    Before                                                    e


                 e                           J=-1               
    After
                                            J=+1               e
                                       
                                                     PX435 –  Physics
                        So what?
                                  2
                    1cos                In the COM frame
        1−y 2=             
                       2
      d  NC  e d  NC   e  G2 s g 2 1cos  2 2
                                     F     L
                   ⇒               =              gR
           dy         d cos          2       2

                                             J=-1
    Before                                                    e




    After
                 e
                                             
                                             J=-1               



 
                 
                                       
                                             
                                             J=+1               e

                                                     PX435 –  Physics
         Summary for electrons
     Cross section for -e scattering rises linearly with
    energy – general feature of point-like scattering
    Cross section is completely calculable (but small)
     Neutral currents interactions can probe both left-
    and right-handed chiral currents, and the cross
    section reflects this.

     Anytime you see a (1-y)2 in a cross section
    itmeans that there is some helicity mismatch
    going on. Integrated over y yields a factor of 1/3.


                              
                                            PX435 –  Physics
    Kinematic Variables
                 Center of mass energy
                 S = (p + Ptarg)2

                 4-momentum transfer
                 Q2=-q2 = (p - p)2

                 Inelasticity
                 y = (Ptarg ·.• q)/(pn • Ptarg)

                 Bjorken-x, xBj
                 xBj = q2 / 2 Ptarg• q

                 Invariant hadronic mass
                 W2 = (q + Ptarg)2
              
                             PX435 –  Physics
    Kinematic Variables
                          Center of mass energy
                          S = (p + Ptarg)2

                          4-momentum transfer
                          Q2=-q2 = (p - p)2

                          Inelasticity
                          y = (Ptarg ·.• q)/(pn • Ptarg)

                          Bjorken-x, xBj
                          xBj = Q2 / 2 Ptarg• q

                          Invariant hadronic mass
                          W2 = (q + Ptarg)2
    “Scaling variables”
                       
                                      PX435 –  Physics
              What do these mean?
                   2     2           2                               2
s = p Ptarg  = pP targ2 p⋅P targ=0M 2 E  M − p⋅P targ
                                                                 2
    In the lab frame : Ptarg = (M,0)                       s =M 2 E M

              Ptarg⋅q              M          
      y=                     =               =            (in lab frame)       0≤ y≤1
              P targ⋅p        M E            E

         2                       2       2       2                         2     2
      W = qPtarg  =q P                       targ
                                                         2 q⋅Ptarg =−Q M 2M 


             Effectively the mass of the hadronic system

                                                      
                                                                         PX435 –  Physics
               Neutral Currents
    The electroweak theory of Glashow, Weinberg and
    Salam predicted two types of weak interactions
    rather than just one, as predicted by V-A Fermi
    theory
    Charged current :    l X lX '      (l-, )(l+,)
    Neutral current :    l X  l X '   Flavour blind

    Interpreted as the exchange of two IVBs : W±, Z0

    Discovery by Gargamelle bubble chamber in 1970
    very controversial at the time. It was to take
    another year before the claims were verified
                              
                                             PX435 –  Physics
    e
            e




         e + e  e + e-
                -
                  
                        PX435 –  Physics
    The second neutrino




              
                    PX435 –  Physics
     
        PX435 –  Physics
    The First Neutrino




             
                    PX435 –  Physics
    Nuclear Emulsion




            
                   PX435 –  Physics
    First 




        
               PX435 –  Physics

				
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