1. Phenomenology of weak decays 2. Parity violation and neutrino helicity 3. V-A theory 4. Neutral currents

The weak interaction was and is a topic with a lot of surprises: Past: Flavor violation, P and CP violation. Today: Weak decays used as probes for new physics

1 1. Phenomenology of weak decays

All particles (except and gluons) participate in the weak interaction. At small q2 weak interaction can be shadowed by strong and electro-magnetic effects. • Observation of weak effects only possible if strong/electro-magnetic processes are forbidden by conservation laws. • Today’s picture for charge current interaction is the exchange of massive W-bosons coupling only to left-handed currents

      e e  

 e    2.6 106 s

 e

Electromagnetic decay   e forbidden by lepton number conservation 2 Application of Feynman-rules for massive W boson and LH coupling:

 gw   e

 e

 q q    g      M 2 M  (ig )2 u   (1 5 )u  W  u   (1 5 )v  w    q 2  M 2  e  P  W  L  

2 “weakness” result of (1/Mw) suppression

Calculation is straight forward ... (everything known!) 3 Today’s picture of the -decay

• Nucleons are composed of quarks, which are the fundamental . Fundamental couple to the the quarks .

Using the the “quark level” decay one can describe weak hadron decays (treating the quarks which are not weakly interacting as spectators)

u   n  pe  e d   p Currents: u  V-A structure u   d Transition matrix: n  d g w    qq   e W   g  2  I3  1 2   MW   M  (igw ) Jquark 2 2 Jlepton gw  e  q  M   w    4 Strong I3 not conserved. All other quark flavor numbers also violated. Motivation of massive boson exchange:

• Long range electromagnetic mediated by massless :

e2 Potential: V (r )  infinite range Coulomb 4 r

• Replace massless photon by massive W boson for weak interaction:

2 g Yukawa potential: V (r )  eMw r Yukawa 4 r Screened Coulomb potential

Can be verified by using Fourier transform of propagtor (Greens Funktion of Klein-Gordon Eq.)  g 2   4  V (r )  eikr dk Yukawa 3  2 2 2  q MW g 2  For Mw   : VYukawa(r )   (r ) point-coupling 4 r 5 or Mw  |q| Non local current – current coupling Point-like 4-fermion interaction

GF 2    e

 e Fermi , dimension = (1/M)2 G M  F u  u u   (1 5 )v  2  ,L  ,L e,L  ,L

• 4-fermion theory is an effective theory valid for small q2. Gives reliable results for most low energy problems.

• Conceptual problems in the high-energy limit (see later)

• Introduced by Fermi in 1933 to explain nuclear  decay. 6  Fermi’s treatment of nuclear -Decay: n  p e e Fermi’s explanation (1933/34) of the nuclear -decay:

J Two fermionic vector currents coupled by a weak n N p coupling const. at single point (4-fermion interact.)

Apply “Feynman Rules”

G  G M  F  J  J   F  u  u  u  v  2 N, e 2 p  n e   e  e  J

-5 -2 Weak coupling constant GF is a very small number ~10 GeV . Explains the “weakness” of the force.

Fermi’s ansatz was inspired by the structure of the electromagnetic interaction and the fact that there is essentially no energy dependence observed.

Problem: Ansatz cannot explain parity violation (was no a problem in 1933) 7 Universality of weak coupling constant:       e e    e

GF  e d,s Vud   u,c         d  W       u 

G V u  c  GF Vud F ud         G V d  s F  cs   GF Vus K     s GF Vus  K GF Vcd

If one considers the quark mixing the weak coupling constant GF is universal. 8 2. Parity violation

Parity transformations (P) = space inversion

  P transformation properties: P : r  r t  t   p  p       r  p   Axial/pseudo vector

    s  p P s  p e.g.: Helicity operator H      (pseudo- scalar) p p

H=+1/2 P H=-1/2

Experimentally:  mirroring at plane + rotation around axis perpendicular to plane  To test parity it is sufficient to study the process in the “mirrored system”: physics invariant under rotation 9 2.1 Historical / puzzle (1956)

Until 1956 parity conservation as well as T and C symmetry was a “dogma”:  very little experimental tests done In 1956 Lee and Yang proposed parity violation in weak processes. Historical names Starting point: Observation of two particles + and + with exactly equal mass, charge and strangeness but with different parity:      0 w / P(  )  P( )2 (1)  J P (  )  0 P()=-1        P(  )  P( )3(1)2  J P (  )  0,2 Lee + Yang: + and + same particle, but decay violates parity

 today, particle is called K+:

K  (0 )    0 P is violated K  (0 )      P is conserved

To search for possible P violation, a number of experimental tests of parity conservation in weak decays has been proposed: 1957 Observation of P violation in nuclear  decays by Chien-Shiung Wu et al. 10 2.2 Observation of parity violation, C.S. Wu et al. 1957

Idea: Measurement of the angular distribution of the emitted e- in the decay of polarized 60Co nuclei

60Co  60Ni   e  e 60Co 60Co  pe  P  J J  

J=5 J=4  pe Gamov-Teller Transition J=1     - Jp Observable: J pe e

If P is conserved, the angular distribution must be symmetric     in  (symmetric to dashed line): transition rates for J  p e and - Jpe are identical. Experiment: Invert Co polarization and compare the rates at the same position . 11 NaJ detector to measure e rate Result: Electron rate opposite to Co e polarization is higher than along   the 60Co polarization: J - J parity violation “freeze” Co 60Co Polarization Qualitative explanation: 

e J=5 J=4

Warm-up (polarization lost) Today we know: Consequence of existence of only left-handed (LH) neutrinos (RH anti-neutrinos)

Electron 1 v polarization He   in  decays 122 c 2.3 Determination of the neutrino helicity Goldhaber et al., 1958

Indirect measurement of the neutrino helicity in a K capture reaction:

P  152Eu J  0 K capture 152Eu  e  152Sm  152  P - e Sm  e J  1

E  950KeV  (960 keV) 152 Sm JP  0 Idea of the experiment:

1. Electron capture and  emission RH 2  possibilities  LH e 152  Sm  e JP  1-

Sm undergoes a small recoil (precoil =950 KeV). Because of angular * momentum conservation Spin J=1 of Sm is opposite to neutrino spin. 13 Important: neutrino helicity is transferred to the Sm nucleous. 2.  emission: 152Sm(JP  1 )152Sm(JP  0 )  

Configuration 152 152Sm Sm   RH  or RH LH

LH or

P LH RH JP  1- J  0

Photons along the Sm recoil direction carry the polarization of the Sm* nucleus

• How to select photons along the recoil direction ?  3 • How to determine the polarization of these photons ?  4

14 3. Resonant photon scattering:  152Sm152Sm152Sm 

152Sm152Sm  Resonant scattering: To compensate the nuclear recoil, the photon energy must be slightly larger than 960 keV. This is the case for photons which have been emitted in the direction of the EuSm recoil (Doppler-effect).

 152 Sm152 Sm 152 Sm   Resonant scattering only possible for “forward” emitted photons, which carry the polarization of the Sm* and thus the polarization of the neutrinos.

15 4. Determination of the photon polarization Exploit that the transmission index through magnetized iron is polarization dependent: Compton scattering in magnetized iron   LH RH   B B

Polarization of electrons in iron Polarization of (to minimize pot. energy) electrons in iron

Absorption leads to spin flip

LH photons cannot be absorbed: RH photons undergo Compton scattering: Bad transmission Good transmission

Photons w/ polarization anti-parallel to magnetization undergo less absorption16 Experiment

Sm* emitted photons pass through the magnetized iron. Resonant scattering allows the photon detection by a NaJ scintillation counter. The counting rate difference for the two possible magnetizations measures the polarization of the photons and thus the helicity of the neutrinos.

Results: P  0.66  0.14

 photons from Sm* are left-handed. The measured photon polarization is compatible with a neutrino helicity of H=1/2. From a calculation with 100% photon polarization one expects a

measurable value P~0.75. Reason is the finite angular acceptance.  Also not exactly forward-going ’s can lead to resonant scattering.

e- e+   Summary: Lepton polarization in  decays 1 H=  - v/c +v/c -1 +1 2 17 3. “V-A Theory” for charged current weak interactions

3.1 Lorentz structure of the weak currents

 Fermi: M  CV JN,  Je  CV up un  ue v 

Cannot explain the parity violation in beta decays. (Treats LH and RH current components the same).

More general ansatz: M  Ci upiun  ueiv  (proposed by Gamov i & Teller) i  S, P, V, A, T

up i un bilinear Lorentz covariants:  (4  4) 18 S : upun scalar 5 pseudo-scalar P : up un up i un   V : up un vector 5  A : up  un pseudo-vector  i     T : u  u tensor         p n 2

 5  i  0 1 2 3

 I 0   0  i  0 I  0 i   5             0  I   i 0   I 0

2  5   1  5     5  0

Remark: Pure P or A couplings do not lead to observable parity violation! 19 Mixtures like (15) or  (15) do violate parity. 3.2 Chirality

1 5 PL  (1  ) are projection operators: Operators 2 2 1 5 P  P , P  P  1, P P  0 P  (1  )  i  i L R L R R 2 (properties of 5)

working on the fermion spinors they result in the left / right handed chirality components:

1 5 Not observable! uL  (1  )u 2   1 5 In contrary to helicity, 1   p u  (1  )u  R 2 which is an observable: 2 p

20 Dirac spinors Eigenvectors of helicity operator 1 1 solution spin  i.e. helicity    solution spin  i.e. helicity    2 2  1   0       0   1   pz   px  ipy  u1(p)  E  m  u2(p)  E  m   E  m   E  m   p  ip    spinors  p  x y   z   E  m   E  m    p along z p along z

of Dirac Dirac of  1   0      Specific representation representation Specific  0   1  u (p)  E  m  u (p)  E  m  1  p (E  m) 2  0       0   p (E  m)

1 k pk 1  3 0  1 1 k pk 1  3 0  1  u   u  u  u1   u1   u2 1  3  1 1  3  2 p 2  0   2 2 p 2  0   2 21 Dirac spinors and chirality projection operators:

Positive helicity:  1    1  5 1  p   0  u1  E  m  1     2 2  E  m  1  0 for E  m    0   0 for E  m

Negative helicity:  0    1  5 1  p   1  u2  E  m  1     2 2  E  m  0  u2 for E  m   1  E for E  m

In the relativistic limit helicity states are also eigenstates of the chirality operators. 22 Polarization for particles with finite mass

5 Left handed spinor component 1  Not uL  (u1  u2) of unpolarized electron: 2 normalized unpolarized u1,u2  uL,uR

Helicity polarization of left handed chirality state uL :

2 2 P(   1 2)  P(  1 2) u1 uL  u2 uL Pol   P(   1 2)  P(  1 2) 2 2 u1 uL  u2 uL 1 p (E  m)2  1 p (E  m)2 p v      1 p (E  m)2  1 p (E  m)2 E c

i.e. the LH spinor component for a particle with finite mass is not fully in the helicity state “spin down” (=-½) . For massive particles of a given chirality there is a finite probability to observe the “wrong” helicity state: P = [1- (p/E)]/2 23 Neutrino-Electron Vertex

1  5    Only left-handed neutrinos are observed in beta decays: u   u  2 

1  5  This leads to the following electron-neutrino vertex    ue  u (assuming vector coupling between LH neutrino and e):  2 

5 If one further exploits that Pl= 1/2(1 -  ) is a projection operator one finds:

2 1  5  1  5  1  5  1  5  u    u  u     u  u    0   u  u   u e    e    e       e L   L  2   2   2   2 

The left-handed neutrino thus couples only to left-handed electrons (vector current).

1  5  1      5 V-A structure: ue  u  ue     u  2  2 V - A (vector – axial-vector) 24