Teilchenphysik – ohne Beschleuniger
und Kosmologie
Wiederholung zum 24.5.07Sommersemester 2007
Hartmut Abele, University of Heidelberg 2
Correlation measurements in -decay
Electron
Proton
Neutrino
Neutron SpinA
B
C Observables in neutron decay:
Lifetime SpinMomenta of decay particles
Observables in neutron decay:
Lifetime SpinMomenta of decay particles
n n p e p e eeaa
DD
RRNN
Hartmut Abele, University of Heidelberg 3
Coefficient A
Coefficient A and lifetime determine Vud and
Electron
Neutron Spin
ElectronNeutron SpinA
W()={1+v/cPAcos()}
231
)1(2
A 231
)1(2
A
on flipper spin with spectrum electron
off flipper spin with spectrum electron
:N
:N
on flipper spin with spectrum electron
off flipper spin with spectrum electron
:N
:N
PfAAc
vexp PfAA
c
vexp
= gA/gV= gA/gV
No coincidences !
)31(
sec249082
2
udV)31(
sec249082
2
udV
2 2
0 0
(1 cos )sinv
N P dA dc
NN
NNAexp
NN
NNAexp A
N N
N Nexp
A
N N
N Nexp
Hartmut Abele, University of Heidelberg 4
A as a function of gA and gV
Time reversal invariance, phase 180°
gAgV
Coefficient A and lifetime determine Vud and
2
( 1)2
1 3A
= gA/gV
)31(
sec249082
2
udV
Hartmut Abele, University of Heidelberg 5
Hartmut Abele, University of Heidelberg 6
Hartmut Abele, University of Heidelberg 7
Hartmut Abele, University of Heidelberg 8
3. Origin of nature’s lefthandedness
Standard Model: Elektroweak interaction 100% lefthanded
Grand unified theories:Universe was left-right symmetric at the beginningParity 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 9
• Parity violation: spontaneous symmetry breaking
• 2 bosons (W1, W2) in the „symmetric base“; W2 very heavy
SM: = 0, mW2 =
•
Why do we measure B?•
Manifest LeftRightSymmetric Models [eg: PRL 38, 22 (1977)]
22W
21W
2
1
iiR
L
m
mW
W
cosesine
sincos
W
W
Hartmut Abele, University of Heidelberg 10
Hartmut Abele, University of Heidelberg 11
Right handed current contributions
AVJ udh )1( 5
aJ el v)1( 5
, (2.4) v
5 5
1( (1 ) ) (1 )
2 2 2
1( )( ).
2 2
p nVint p n e
p
Fud
GL k
m
GV V A a
,
.
int v
v v
2
2
2
2
1( )( )
2 8
1( ( ))
2 8
gL V A a
m
gV Aa Va A
m
L v
v
int
1
2 8
1
2 8
2
12
2
22
g
mc V A s V A c v a s a
g
ms V A c V A s v a c a
[( ( ) ( )) ( ( ) ( ))]
[( ( ) ( )) ( ( ) ( ))]
Lefthanded 5
1: (1 )
2Le e
Righthanded 5
1: (1 )
2Re e
211
22 2
cos sin
sin cos
LW
i iR W
W W mW We e m
Hartmut Abele, University of Heidelberg 12
LG
V V a
A
intF
udVA VA
VAAA VA AA VA
AA VA
~{ [( ( )]
[( ( ]}
2
1
2
1
1
2
v - a) v +
v - a) + v + a)rV
VA
VA
1
1
rAAA VA
AA VA
λ2
ηη
2
G'g
2
η1
2
G'g
VAAAA
VAV
LVA
VAAA
V
A λλη-1
ηη
'g
'g
222
22
22
VA
2VA
2AA
2L2
F
2GT
2FF
2GTGT2
GT/F
λ1δε
δε
λη1
ηη
λr1
r1
M/P
M/Pλ
)r1('gM
)(r)(13
2
)(r)()(r)(2
1
3
1M'g
|ψ|P
)r1('gM
)(r)()(r)(2
11M'g
|ψ|P
2GT
2A
2GT
2GT
GTGT2
GT2
A
2GTGT
2F
2V
2F
2
FF2
F2
V
2FF
rAAA VA
AA VA
12
2
AA
1
)1(2
VA
Hartmut Abele, University of Heidelberg 13
)r1(λ3)r1(
)rλr(λr)1λ(λ2B
)r1(λ3)r1(
)rλr(λr)1λ(λ-2A
λ31
λ1
)r1(λ3)r1(
)r1(λ3)r1(a
2GT
2L
2F
FLGTLGTLL
2GT
2L
2F
FLGTLGTLL
2GT/F
2GT/F
2GT
2L
2F
2GT
2L
2F
2GT/F
2GT
2L
2F
2F
2GT
2A
2F
2V
2F
2V
00
n
λ31
2
)r1(λ3)r1(
)r(12R
)r1('g3)r1('g
)r1('g2
ft
ftR
Hartmut Abele, University of Heidelberg 14
Right Handed Currents?
Exclusion Plot
3 Observables A, B and
for 3 parameters, m1/m2, ,
B
A
SM
current situation (PDG 2004)
B=0.983(4) B=0.983(2)
Hartmut Abele, University of Heidelberg 15
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
- ...
(90% c.l.)2( ) 300 /RmW GeV c (90% c.l.)0.2 0.03 /S Vg g (90% c.l.)/ 0.08T Ag g
Hartmut Abele, University of Heidelberg 16
Herczeg, Gudkov
Hartmut Abele, University of Heidelberg 17
Decay into hydrogen and the origin of nature’s lefthandedness
n H+, BR 4 . 10-6
Examine hyperfine state population
wrong neutrino helicity state!wrong neutrino helicity state!
Hartmut Abele, University of Heidelberg 18
Find the Parameters…
e e n e ee e
e e e e n e e
d( ) 1
d d da
Wb A B
mG E
E ED
E E E E E E
p p σ p p p p
e n ee e
e n e
d ( ) 1EE
RW G
σ σ p
w5 5
{S,V,T,A,P}
1 12
i i i ii
i i
GH p n e p n eL R
O O O O
J.D. Jackson et al.: Phys. Rev. 106 (1957) 517
2 2 2 2 2 2 2 2
S T V S T A
* * * *S T S V A T
2 2 2 2* * * *T S T A V A T S T
* * * *S T S T V A
2 2 2 2 2 2 2 2
S T
V A
V A
A V A
V A
V V T AA S
1
2Re 3 3
2Re
2Im
3 3 3 3
a L L R R R R
b L L R R R R
A L L L
L L
L L
L L L
L L
L
R R R R R R
D L L R R R R
RLL L R R R
0b
2
12
1 3A
0D
2
2
1
1 3a
A
V
L
L
Surviving in the SM:
Slide from T. SoldnerSlide from T. Soldner
Hartmut Abele, University of Heidelberg 19
Find the Parameters…
e e n e ee e
e e e e n e e
d( ) 1
d d da
Wb A B
mG E
E ED
E E E E E E
p p σ p p p p
e n ee e
e n e
d ( ) 1EE
RW G
σ σ p
w5 5
{S,V,T,A,P}
1 12
i i i ii
i i
GH p n e p n eL R
O O O O
udVg
g,
V
A
or
T violation beyond SM
Test for righthanded currents
Slide from T. SoldnerSlide from T. Soldner