Transcript Particle Physics with Neutrons

Teilchenphysik –
ohne Beschleuniger
und Kosmologie
Wiederholung zum 24.5.07
Sommersemester 2007
Correlation measurements in -decay
Neutron Spin
A
a
Electron
n  p e e
B
D
R
C
Proton
N
Neutrino
Observables in neutron decay:
Lifetime 
Spin
Momenta of decay particles
Hartmut Abele, University of Heidelberg
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Coefficient A
W(J)={1+v/cPAcos(J)}

N 
Neutron Spin
J
Electron
A
Electron
Neutron Spin
2 2

0
v
(1

0 c P A cos J) sin J dJd
Coefficient A and lifetime 
determine Vud and l
Aexp 



N N
N  N
Aexp

N N
 
N  N
A  2
N : electron spectrum with spin flipper off
N  : electron spectrum with spin flipper on
Aexp
v
 A Pf
c
Vud
2
l (l  1)
1  3l
2
l= gA/gV
4908  2 sec

  (1  3l2 )
No coincidences !
Hartmut Abele, University of Heidelberg
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gV
l= gA/gV
gA
A as a function of gA and gV
l ( l  1)
A  2
1  3l 2
Time reversal invariance, phase 180°
Coefficient A and lifetime 
determine V
and l
Hartmut Abele, University of Heidelberg
Vud
2
4908  2 sec

2
  (1  3l )
4
Hartmut Abele, University of Heidelberg
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Hartmut Abele, University of Heidelberg
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Hartmut Abele, University of Heidelberg
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3. Origin of nature’s lefthandedness
Standard Model:
Elektroweak interaction 100% lefthanded
Grand unified theories:
Universe was left-right symmetric at the beginning
Parity violation = 'emergent' Order parameter <100%
Neutron decay: Correlation B + A:
Mass right handed W-Boson: mR > 280 GeV/c2
Phase:
-0.20 <  < 0.07
Hartmut Abele, University of Heidelberg
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Why do we measure B?
•
Manifest LeftRightSymmetric Models [eg: PRL 38, 22 (1977)]
• Parity violation: spontaneous symmetry breaking
• 2 bosons (W1, W2) in the „symmetric base“; W2 very heavy
 sin    W1 
 WL   cos 
    i
  
i
 WR   e sin  e cos    W2 
•
Hartmut Abele, University of Heidelberg
m2W1
d 2
mW 2
SM: d = 0, mW2 = 
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Hartmut Abele, University of Heidelberg
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Right handed current contributions
J h  d  (1   5)u  V   A
J l  e (1   5)  v   a 
Lint 
,
,
  n
1 GV
  p (  (1  l 5 )  p
  k  )n  e   (1   5 )
2 2
2m p
1 GF
 (2.4)
V ud  (V   lA  )( v   a  ).
2 2
.
Lint 

L int
1 g2

 (V  l A )( v  a )
2 8m 2
1 g2

(V v  lA a  (V a  lA v))
2 8m 2
1
Righthanded : R e  (1   5 )e
2
1
Lefthanded : Le  (1   5 )e
2
 sin   W 1 
W L   cos 
 
    i
W R  e sin  e i cos   W 2 
  
 
mW2 1
d 2
mW 2
2
1 g
 
 [(c  (V  lA)  s  (V  lA))  (c  (v  a )  s  ( v  a ))]
2 8m12
2
1 g
 
 [( s  (V  lA)  c  (V  lA))  ( s  (v  a )  c  ( v  a ))]
2 8m2 2
Hartmut Abele, University of Heidelberg
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 2 d
 AA  2
 d 1
~
GF
1  VA
1  VA

Vud {V 
[( v - a) 
( v + a )]
2
1  VA
2
  VA
  VA
 l  A  AA
[( v - a) + AA
( v + a)]}
2
 AA  VA
Lint
G 1  η VA

2
2
G η AA  η VA
gA '

λ
2
2
gV '
VA 
rV 
1  VA
1  VA
  (1  d )
 2d  1
 
rA  AA VA
 AA  VA
 
rA  AA VA
 AA  VA
g A ' η AA  η VA

 λ  λL
gV '
1 - η VA
PF | ψ F | 2
 g V ' M F
2
λ GT/F
2


PGT / M GT
PF / M F
1  rGT
1  rF
2

2
 λL
η AA  η VA
1  η VA
PGT | ψ GT | 2
2
 g A ' 2 M GT   
2
2
ε δ
 λ2
2 2
ε δ 1
2

2
2
2
2


1


  1
 (    )  rF  (    )  (    )  rF  (    ) 
2


 M F  g V ' 2 (1  rF )
2
2
2
2
 λ2

2
2
3
1
3


1
2

 (    )  rGT  (    )  (    )  rGT  (    )
 1  (    )  rGT  (    )


2
 M GT  g A ' (1  rGT )
2
2
2
Hartmut Abele, University of Heidelberg
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2  g V ' 2 (1  rF )
ft n
R  0 0 
2
2
ft
g V ' 2 (1  rF )  3  g A ' 2 (1  rGT )
2
2  (1  rF )
2
R
(1  rF )  3  λ L  (1  rGT )
2
2
(1  rF )  3  λ L  (1  rGT )
2
a
2

2
A  -2 
B  2 
1  3  λ GT/F
2
(1  rF )  3  λ L  (1  rGT )
2
2
2
2

2
1  λ GT/F
2
1  3  λ GT/F
2
λ L  (λ L  1)  rGT  λ L  (rGT  λ L  rF )
(1  rF )  3  λ L  (1  rGT )
2
2
2
λ L  (λ L  1)  rGT  λ L  (rGT  λ L  rF )
(1  rF )  3  λ L  (1  rGT )
2
Hartmut Abele, University of Heidelberg
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2
13
Right Handed Currents?
B=0.983(4)
B=0.983(2)
Exclusion Plot
3 Observables A, B and 
for 3 parameters, m1/m2, , l
A
B
SM
current situation (PDG 2004)
Hartmut Abele, University of Heidelberg
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weitere Größen: jenseits des SM
- Masse für ein „rechtshändiges“
W-Boson
- Mischungswinkel
- rechts links
- skalare schwache Kopplung
- tensorielle schwache Kopplung
- Fiertz-Interferenzamplitude
- Second Class Currents
- Neutrinohelizität < 1
- ...
2
gS /c.l.)
gc.l.)
m (WgTR ) /g300
GeV
/
c
(90%

0.08
(90%
Vc.l.)
0.2



0.03
(90%
A
Hartmut Abele, University of Heidelberg
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Herczeg, Gudkov
Hartmut Abele, University of Heidelberg
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Decay into hydrogen and the origin of
nature’s lefthandedness
n H+, BR 4 . 10-6
Examine hyperfine
state population
wrong neutrino helicity state!
Hartmut Abele, University of Heidelberg
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Find the Parameters…
Gw
H
Li pOi n eOi 1   5   Ri pOi n eOi 1   5  


2 i{S,V,T,A,P}

dW
pp
m σ  p
p
p p
 Ge ( Ee )  1  a e   b e  n  A e  B   D e 
dEeded
Ee E
Ee  n  Ee
E
Ee E

J.D. Jackson et al.: Phys. Rev. 106 (1957) 517
Surviving in the SM:
1 l2
a
1  3l 2
b0
A  2
D0
l
LA
LV
l  l  1
1  3l 2
 

 


1
2
2
2
2
2
2
2
2
LV  LS  LT  LA  RV  RS  RT  RA

2
b  Re  LS LV*  3LA LT*  RS RV*  3RA RT* 

2
2
2
2
2
A
Re LA  LV LA*  LT  LS LT*  RA  RV RA*  RT  RS RT*

2
D  Im  LS LT*  LV LA*  RS RT *  RV RA* 

a

  LV  LS  3 LT  3 LA
2
2
2
2

σe σn  pe 
dW  Ge ( Ee )  1   R 



E
e
n e 

Hartmut Abele, University of Heidelberg
 RV  RS  3 RT  3 RA
2
2
2

2
Slide from T. Soldner
18
Find the Parameters…
Gw
H
Li pOi n eOi 1   5   Ri pOi n eOi 1   5  


2 i{S,V,T,A,P}

dW
pp
m σ  p
p
p p
 Ge ( Ee )  1  a e   b e  n  A e  B   D e 
dEeded
Ee E
Ee  n  Ee
E
Ee E

 

 
or
gA
, Vud
gV
Test for right
handed currents
T violation beyond SM


σe σn  pe 
dW  Ge ( Ee )  1   R 



E
e
n e 

Hartmut Abele, University of Heidelberg
Slide from T. Soldner
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