Weak Interactions in the Nucleus II
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Weak Interactions in the Nucleus II
Summer School, Tennessee
June 2003
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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
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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
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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
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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
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gT: Second Class Currents:breaking of G-parity
In 1970’s evidence that (ft)+/(ft)- changed linearly with end-point energy
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From R. D. McKeown, et al.Phys. Rev. C 22, 738-749 (1980)
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From Minamisono et al.Phys. Rev. Lett. 80, 4132(1998).
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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
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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
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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??
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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
co s sin | | co s sin
| | | |
No strangeness-changingNeutral Currents
G.I.M. proposed
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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
co s sin | | co s sin
co s sin | | co s sin
| | | |
u c
G.I.M. proposed
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Finding J/Psi confirmed the existence of the c quark and gave validity to the G.I.M. hypothesis
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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
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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
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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
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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+
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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
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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
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From Hardy et al, Nucl. Phys. A509, 429 (1990).
Radiative and isospin breaking corrections have to be taken into account.
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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.
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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.
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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
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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
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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
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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).
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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
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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
400 cm3 Solid Deuterium
800 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
A. Saunders, 2003C. Morris et al, PRL 89, 272501
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Solid D2 in a “windowless” container
Grown from a gas phase at 50 mbar Cooled through the triple point
A. Saunders, 2003C. Morris et al, PRL 89, 272501
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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
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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
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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