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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


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


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





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


• 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



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


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


)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


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)


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


Herczeg, Gudkov


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!


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


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