Weak Interactions in the Nucleus II

Weak Interactions in the Nucleus II

Summer School, Tennessee

June 2003

Recoil effects in E&M

e-

e-p

p

Recoil effects

pV p p g g q g q pE M V WM S&

Has to be zero to allowconservation of charge:

V g q g q q g q q g qE M V WM S S& 2 0

Anomalous magnetic moment

Hadrons exchange gluons so need to include most general

Lorentz-invariant terms in interaction

Recoil effects in Weak decays

e+e

d

W

u

pV n p g g q g q nV WM S

pA n p g g q g q nA T PS

5 5 5

Recoil effects

gS and gWM: Conservation of the Vector Current: I=1 form factors in VE&M are identical to form factors in VWEAK

gPS: Partial Conservation of the Axial Current

(plus pion-pole dominance):

gi m g

q mPS

p A

22 2

gT: Second Class Currents:

breaking of G-parity

Conservation of the Vector Current: I=1 form factors in VE&M are identical to form factors in VWEAK

14O

14C14N

I=1,J=0+

I=1,J=0+

I=1,J=0+

Shape of beta spectrum,, determines <gWM>

for WEAK

Width of M1 and (e,e’)cross-section

determine <gWM>for E&M

A. Garcia and B.A. Brown,Phys Rev. C 52, 3416 (1995).

Potential for checking CVCat fraction of % level

gPS: Partial Conservation of the Axial Current

(plus pion-pole dominance):

g m g m gP PS A ( . ) ( . . )0 8 8 6 7 0 22

gi m g

q mPS

p A

22 2

Measure intensity of + p = + n

Approximation should hold very well : u and d quarks are very lightchiral symmetry: V. Bernard et al. Phys. Rev. D 50, 6899 (1994).

g gP A/

1 0

2 0

5

0

54 0 8 06 0

op m s( / )1

Radiative capture

Ordinary capture

1sS 0

S 1

L 0

L 1 op

p p

p

gT: Second Class Currents:breaking of G-parity

In 1970’s evidence that (ft)+/(ft)- changed linearly with end-point energy

From R. D. McKeown, et al.Phys. Rev. C 22, 738-749 (1980)

From Minamisono et al.Phys. Rev. Lett. 80, 4132(1998).

Angular momentum and Rotations

x R xRz ( )

( ) ( ) x xR R

Rzx U x( ) ( ) ( )

Invariance:

Rotating the coordinate system:

( ) ( )1

R x

( ) ( ) ( )1

x xR U z ( ) ( )

1

For any rotation: U eni J .n

( ) /

Invariance under rotations imply conservation of J

IsospinNotice n+n, n+p, p+p hadronic interactions are very similar.

Use spin formalism to take into account Pauli exclusion principle etc.

p n

I n p I p n

I n n I p pz z

1

0

0

1

1

2

1

2

;

; ;

; ;

( ) .q e I z 1

2

Weak Decays of QuarksOnce upon a time: u d s

Weak interactions needed neutral component to render g sin= e.

s

d

Z0

But the process KL

0+- could not be observed.

Why not??

Weak Decays of Quarksu

d s

c

s dco s sin co s sin

The neutral weak currents go like:

d s J d s

d s J d s

d J d s J s

nc

nc

nc nc

co s sin | | co s sin


| | | |

No strangeness-changingNeutral Currents

G.I.M. proposed

Weak Decays of Quarksu

d s

c

s dco s sin co s sin

The neutral weak currents go like:

The process KL

0+- actually goes through

this diagram

sd

W

W

d s J d s

d s J d s

d J d s J s

nc

nc

nc nc



| | | |

u c

G.I.M. proposed

Finding J/Psi confirmed the existence of the c quark and gave validity to the G.I.M. hypothesis

Weak decays in the Standard Model

d

s

b

Vud Vus Vub

Vcd Vcs Vcb

V td V ts V tb

d

s

b

'

'

'

e

e

u

d

c

s

t

b' ' '

From nuclear 0.974

Ke3 0.220 b u l 0.080

d

u

e+

e+

e

e

W

Q

0

-1

+2/3

-1/3

CKM matrix: Is it really Unitary?

I

1/2

1/2

In order to measure Vud we compare intensities for semi-leptonic to purely leptonic decays d

u

e+

e+

e

e

Fermi’s Golden rule:-1 α |<f H i>|2 f(E)

Then:|<f I i>|2 Vud

2 f /fquarks

I I I I I I I I Iz z z z, | | , ( ) ( ) 1 1

Example: decay of 14O

I=1 Iz=1, J=0+

14O (t1/2=70.6 s)

I=1 Iz=0, J=0+

14N

branch <1%

Additional branches so small that beta intensity can almost be obtaineddirectly from 14O half-life

14O easy to produceand half-life convenient

for separating from otherradioactivity.

Level density not highso Isospin config. mixing very small.

Many features contributeto allowing a precisedetermination of ft

Nuclear weak decays are driven by two currents : V and AV is conserved (in the same sense that the electromagnetic current is conserved).

Initially most precise results came from decays for which only V can contribute:

J(Initial nucleus)=0+ J(Final nucleus)=0+

From Hardy et al, Nucl. Phys. A509, 429 (1990).

Note thisrange isonly 0.5%

Nuclear 0+ 0+ decays:

0014.09968.0|||||| 222 VubVusVud

2.3 away from 1

Complication: Isospin symmetry breakingNuclei do have charge and I I I Iz z, ,1

To understand it we can separate it into effects at two different levels:

1) decaying proton and new-born neutron sample different mean fields.

2) shell-model configurations are mixed

n p

E

From Hardy et al, Nucl. Phys. A509, 429 (1990).

Radiative and isospin breaking corrections have to be taken into account.

The complication of isospin-breaking correctionscan be circumvented by looking at: 1) +0 e+ 2) n p e-

+0 e+ has a very small branch (10-

8);2) n p e- is a mixed transition (V and Acontribute.

Determinnig Vud from neutron decay Disadvantage: V and A contribute to this

J=1/2+ 1/2+ decay. Consequently need to measure 2 quantities with precision.

Advantage: Simplest nuclear decay. No isospin-breaking corrections.

Neutron already well known: need to determine asymmetry (e- angular distribution) from polarized neutrons.

Weak Coupling Constants

-1.81

-1.8

-1.79

-1.78

-1.77

-1.76

-1.75

1.4 1.405 1.41 1.415 1.42 1.425 1.43 1.435 1.44

gv x 1062 (J m 3)

PNPI

PERKEO

ILL - TPC

n = 885.4 0.9 sAbele 1999

Ft (0+->0+) = 3072.3 ± 2.0 sHardy (1999)

PERKEO II

A0

-0.1146±0.0019 (PERKEO, 1986)-0.1135±0.0014 (PNPI, Corrected-1998)-0.1160±0.0015 (ILL- TPC, 1995)-0.1189±0.0008 (PERKEO II, 1998)

CKM Unitarity

REH 3/16/00

Weak Coupling Constants

-1.81

-1.8

-1.79

-1.78

-1.77

-1.76

-1.75

1.4 1.405 1.41 1.415 1.42 1.425 1.43 1.435 1.44

gv x 1062 (J m 3)

PNPI

PERKEO

ILL - TPC

n = 885.4 0.9 sAbele 1999

Ft (0+->0+) = 3072.3 ± 2.0 sHardy (1999)

PERKEO II

A0

-0.1146±0.0019 (PERKEO, 1986)-0.1135±0.0014 (PNPI, Corrected-1998)-0.1160±0.0015 (ILL- TPC, 1995)-0.1189±0.0008 (PERKEO II, 1998)

CKM Unitarity

REH 3/16/00

Cold-Neutron Decay

CONTRIBUTIONS TO V UNCERTAINTYud

10

12

Un

cert

ain

ty x

10

4

Neutron

V = 0.9740 0.0013ud+-

Exp

R

R

Pion beta decay

V = 0.9760 0.0161ud+-

Exp

161 (24 future)

R

R

Nuclear 0 0

V = 0.9740 0.0005ud+-

+ +

Exp

R

R

C

2

4

6

8

NS

J.C. Hardy, 2003

neutronmomentum

Beta asymmetry with beam of Cold Neutrons (v 500 m/s)

e-

neutronspin

vacuum beam pipe

B field decreases todecrease transverse

component of momentumwhich lowers

backscatteringAbele et al.

Phys. Rev. Lett. 88, 211801 (2002).

Ultra-Cold Neutron Source Layout(LANL)

Liquid N2

Be reflector

Solid D2

77 K poly

Tungsten Target

58Ni coated stainless guide

UCN Detector

Flappervalve

LHe

SS UCN Bottle

A. Saunders, 2003C. Morris et al, PRL 89, 272501

Line C MeasurementsUCN

DetectorCold Neutron

Detector

ProtonBeam

0

20

40

60

80

100

0 100 2 10-3 4 10-3 6 10-3 8 10-3 1 10-2

cn_spec

100 cm3

200 cm3

400 cm3

800 cm3

Col

d N

eutr

ons/

109 p

roto

ns

Time (s)

0

5

10

15

20

25

30

0 0.1 0.2 0.3 0.4 0.5

0 cm3 Solid Deuterium



VC

N+

UC

N/1

012

pro

tons

/bin

Time (s)

• Line C results show reduced ( 100) UCN production.• D2 frost on guide windows and walls.• Gravity+Aluminum detector window


Solid D2 in a “windowless” container

Grown from a gas phase at 50 mbar Cooled through the triple point


Neutrons in Magnetic Field

dM

dtM B

M J

In a frame rotating with freq.

dM

dt

M

tM

M

tM B ( )

B Be

M

B 0

Neutrons in Magnetic Field

dM

dtM B

M J

In a frame rotating with freq.

dM

dt

M

tM

M

tM B ( )

B k B i Be ( )

0 1

B k ie ( )

0 1

M

B 0

Field B1 rotating with freq. around B0 .

B k B B 0 1

strength of B0

freq. of B1

strength of B1

Neutrons in Magnetic Field B e

B

ae

0

2

1

2

B k ie ( )

0 1 B 0

tan

1

0

In S’ motion is precession around Be with angular velocity a = -Be

co s co s sin co s( ) 2 2 a t

B B B0 0 00 ( , sin , co s )

M M at M at M ( sin sin( ) , sin co s( ) , co s )

co s

B M

B M0

0

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Weak Interactions in the Nucleus II