SLIDE 1
J.C. Hardy
Cyclotron Institute Texas A&M University
Measuring |V | and testing CKM unitarity: past, present & - - PowerPoint PPT Presentation
Measuring |V | and testing CKM unitarity: past, present & - - PowerPoint PPT Presentation
J.C. Hardy Cyclotron Institute Texas A&M University Measuring |V | and testing CKM unitarity: past, present & future ud CURRENT STATUS OF V ud .9700 .9800 .9750 nuclear 0 0 + + neutron nuclear mirrors pion V ud V =
SLIDE 2
SLIDE 3
CURRENT STATUS OF V
ud .9700 .9800 .9750
nuclear 0 0 + + neutron nuclear mirrors pion
Vud
V = 0.97420 + 0.00021
ud
SLIDE 4
+ +
SUPERALLOWED 0 0 BETA DECAY
+
0 ,1
+
0 ,1
t1/2
QEC BR
BASIC WEAK-DECAY EQUATION
ft = K
2 2
G < >
V
f = statistical rate function: f (Z, ) QEC t = partial half-life: f ( , ) t BR
1/2
G = vector coupling constant
V
< > = Fermi matrix element
EXPERIMENT
SLIDE 5
+ +
SUPERALLOWED 0 0 BETA DECAY
+
0 ,1
+
0 ,1
t1/2
QEC BR
BASIC WEAK-DECAY EQUATION
ft = K
2 2
G < >
V
f = statistical rate function: f (Z, ) QEC t = partial half-life: f ( , ) t BR
1/2
G = vector coupling constant
V
< > = Fermi matrix element
EXPERIMENT INCLUDING RADIATIVE AND ISOSPIN-SYMMETRY-BREAKING CORRECTIONS
t = ft (1 + )[1 - (
- )] =
R C NS
K
2
2G (1 + )
V
R ,
SLIDE 6
+ +
SUPERALLOWED 0 0 BETA DECAY
+
0 ,1
+
0 ,1
t1/2
QEC BR
BASIC WEAK-DECAY EQUATION
ft = K
2 2
G < >
V
f = statistical rate function: f (Z, ) QEC t = partial half-life: f ( , ) t BR
1/2
G = vector coupling constant
V
< > = Fermi matrix element
EXPERIMENT INCLUDING RADIATIVE AND ISOSPIN-SYMMETRY-BREAKING CORRECTIONS
t = ft (1 + )[1 - (
- )] =
R C NS
K
2
2G (1 + )
V
R ,
~1.5%
f (Z, Q )
EC
0.3-1.5%
f (nuclear structure)
~2.4%
f (interaction)
SLIDE 7
+ +
SUPERALLOWED 0 0 BETA DECAY
+
0 ,1
+
0 ,1
t1/2
QEC BR
BASIC WEAK-DECAY EQUATION
ft = K
2 2
G < >
V
f = statistical rate function: f (Z, ) QEC t = partial half-life: f ( , ) t BR
1/2
G = vector coupling constant
V
< > = Fermi matrix element
EXPERIMENT INCLUDING RADIATIVE AND ISOSPIN-SYMMETRY-BREAKING CORRECTIONS
t = ft (1 + )[1 - (
- )] =
R C NS
K
2
2G (1 + )
V
R ,
~1.5%
f (Z, Q )
EC
0.3-1.5%
f (nuclear structure)
~2.4%
f (interaction)
THEORETICAL UNCERTAINTIES
0.05 – 0.10%
SLIDE 8
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
t values constant
Test for presence of a Scalar current
THE PATH TO Vud
SLIDE 9
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
t values constant
Test for presence of a Scalar current Validate the correction terms
THE PATH TO Vud
74Rb
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
10C
SLIDE 10
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
t values constant
Test for presence of a Scalar current Validate the correction terms
THE PATH TO Vud
74Rb
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
10C
5 10 15 20 25 30 35
Z of daughter
+2.5
- 0.5
+2.0 +1.5 +1.0 +0.5 +0.0
Correction terms (%)
R ’
SLIDE 11
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
t values constant
Test for presence of a Scalar current Validate the correction terms
THE PATH TO Vud
74Rb
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
10C
5 10 15 20 25 30 35
Z of daughter
+2.5
- 0.5
+2.0 +1.5 +1.0 +0.5 +0.0
Correction terms (%)
R ’ C
SLIDE 12
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
t values constant
Test for presence of a Scalar current Validate the correction terms
THE PATH TO Vud
74Rb
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
10C
5 10 15 20 25 30 35
Z of daughter
+2.5
- 0.5
+2.0 +1.5 +1.0 +0.5 +0.0
Correction terms (%)
R ’ NS C
SLIDE 13
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
t values constant
Test for presence of a Scalar current Validate the correction terms
THE PATH TO Vud
74Rb
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
10C
5 10 15 20 25 30 35
Z of daughter
+2.5
- 0.5
+2.0 +1.5 +1.0 +0.5 +0.0
Correction terms (%)
R R ’ NS C
SLIDE 14
FROM A SINGLE TRANSITION
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
t values constant
Validate the correction terms
THE PATH TO Vud
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
SLIDE 15
FROM A SINGLE TRANSITION
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
t values constant
Test for presence of a Scalar current Validate the correction terms
THE PATH TO Vud
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
SLIDE 16
FROM A SINGLE TRANSITION
Experimentally
2
determine G (1 + )
V R
V V V
ud us ub
V V V
cd cs cb
V V V
td ts tb
d' s' b' d s b =
WITH CVC VERIFIED
2
Obtain precise value of G (1 + )
V R
Determine Vud
2 2 2
V = G /G
ud V 2
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
t values constant
Test for presence of a Scalar current Validate the correction terms
weak eigenstates mass eigenstates Cabibbo Kobayashi Maskawa (CKM) matrix
THE PATH TO Vud
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
SLIDE 17
FROM A SINGLE TRANSITION
Experimentally
2
determine G (1 + )
V R
V V V
ud us ub
V V V
cd cs cb
V V V
td ts tb
d' s' b' d s b =
WITH CVC VERIFIED
2
Obtain precise value of G (1 + )
V R
Test CKM unitarity
V + V + V = 1
ud us ub
2 2 2
Determine Vud
2 2 2
V = G /G
ud V 2
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
t values constant
Test for presence of a Scalar current Validate the correction terms
weak eigenstates mass eigenstates Cabibbo Kobayashi Maskawa (CKM) matrix
THE PATH TO Vud
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
SLIDE 18
FROM A SINGLE TRANSITION
Experimentally
2
determine G (1 + )
V R
V V V
ud us ub
V V V
cd cs cb
V V V
td ts tb
d' s' b' d s b =
WITH CVC VERIFIED
2
Obtain precise value of G (1 + )
V R
Test CKM unitarity
V + V + V = 1
ud us ub
2 2 2
Determine Vud
2 2 2
V = G /G
ud V 2
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
t values constant
Test for presence of a Scalar current Validate the correction terms
weak eigenstates mass eigenstates Cabibbo Kobayashi Maskawa (CKM) matrix
THE PATH TO Vud
O N L Y P O S S I B L E I F P R I O R C O N D I T I O N S S A T I S F I E D
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
SLIDE 19
42Ti
t : data being analyzed
1/2
SUPERALLOWED-DECAY WORK INVOLVING TAMU GROUP
22Mg
t : BR: PRL 91, 082501 (2003)
1/2
Q : PRC 70, 042501(R) (2004)
EC 10C
t : PRC 77, 045501 (2008)
1/2
Q : PRC 83, 055501 (2011)
EC
BR: data being analyzed
34Ar
t ,: PRC 74, 055502 (2006)
1/2
Q : PRC 83, 055501 (2011)
EC
BR: to be published (2019)
38 m
K t : PRC 82. 045501 (2010)
1/2
Q : PRL 103, 252501 (2009)
EC 62Ga
t ,BR: PRC 68,
1/2
015501 (2003)
74Rb
t : PRL 86, 1454 (2001)
1/2
BR: PRC 67, 051305R (2003)
46V
t : PRC 85, 035501 (2012)
1/2
Q : PRL 95, 102501 (2005)
EC
PRL 97, 232501 (2006) PRC 83, 055501 (2011)
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
0 ,1 0 ,1
+ +
BR t1/2 QEC
26Si
t : PRC 82, 035502 (2010)
1/2
BR: to be published (2019)
50 54
Mn, Co Q : PRL 100, 132502 (2008)
EC 26 m
Al Q : PRL 97, 232501 (2006)
EC 14O
BR: PRC 72, 055501 (2005)
38Ca
t : PRC 84, 065502 (2011)
1/2
Q : PRC 83, 055501 (2011)
EC
BR: PRL 112, 102502 (2014) PRC 92. 015502 (2015)
34Cl
t : PRC 74, 055502 (2006)
1/2
Q : PRL 103, 252501 (2009)
EC
Theory/Reviews ( - ) calculations: PRC 77, 025501 (2008)
C NS
Recent critical survey: PRC 91, 025501 (2015) Measurement & interpretation of 0 0 : J. Phys G 41, 114004 (2014) Numerous reviews of CVC and CKM-unitarity tests Comparative tests of calculations: PRC 82, 065501 (2010)
C
Parameterization of f function: PRC 91, 015501 (2015)
+ +
42Sc
Q : PRC 95, 025501 (2017)
EC 30S
t : PRC 97,
1/2
035501 (2018)
SLIDE 20
WORLD DATA FOR 0 0 DECAY, 2019
+ +
9 cases with ft-values measured to ; 6 more cases <0.05% precision with . 0.05-0.23% precision ~220 individual measurements with compatible precision
Hardy & Towner PRC 91, 025501 (2015); updated to 2019
74Rb
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
0 ,1 0 ,1
+ +
BR t1/2 QEC
10C
SLIDE 21
WORLD DATA FOR 0 0 DECAY, 2019
+ +
t = ft
9 cases with ft-values measured to ; 6 more cases <0.05% precision with . 0.05-0.23% precision ~220 individual measurements with compatible precision
Hardy & Towner PRC 91, 025501 (2015); updated to 2019
Z of daughter
5 30 25 20 15 10 35 3090 3040 3050 3060 3070 3080 3140 3100 3110 3120 3130
10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca 26Si
74Rb
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
0 ,1 0 ,1
+ +
BR t1/2 QEC
10C
SLIDE 22
WORLD DATA FOR 0 0 DECAY, 2019
+ +
t = ft (1 + )
R
,
9 cases with ft-values measured to ; 6 more cases <0.05% precision with . 0.05-0.23% precision ~220 individual measurements with compatible precision
Hardy & Towner PRC 91, 025501 (2015); updated to 2019
Z of daughter
5 30 25 20 15 10 35 3090 3040 3050 3060 3070 3080 3140 3100 3110 3120 3130
10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca 26Si
74Rb
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
0 ,1 0 ,1
+ +
BR t1/2 QEC
10C
SLIDE 23
WORLD DATA FOR 0 0 DECAY, 2019
+ +
t = ft (1 + )[1 - ( - )]
R C NS
,
9 cases with ft-values measured to ; 6 more cases <0.05% precision with . 0.05-0.23% precision ~220 individual measurements with compatible precision
Hardy & Towner PRC 91, 025501 (2015); updated to 2019
Z of daughter
5 30 25 20 15 10 35 3090 3040 3050 3060 3070 3080 3140 3100 3110 3120 3130
10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca 26Si
74Rb
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
0 ,1 0 ,1
+ +
BR t1/2 QEC
10C
SLIDE 24
WORLD DATA FOR 0 0 DECAY, 2019
+ +
t = ft (1 + )[1 - ( - )]
R C NS
K
2
2G (1 + )
V R
,
9 cases with ft-values measured to ; 6 more cases <0.05% precision with . 0.05-0.23% precision ~220 individual measurements with compatible precision
Hardy & Towner PRC 91, 025501 (2015); updated to 2019
Z of daughter
5 30 25 20 15 10 35 3090 3040 3050 3060 3070 3080 3140 3100 3110 3120 3130
10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca 26Si
74Rb
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
0 ,1 0 ,1
+ +
BR t1/2 QEC
10C
=
SLIDE 25
WORLD DATA FOR 0 0 DECAY, 2019
+ +
t = ft (1 + )[1 - ( - )]
R C NS
K
2
2G (1 + )
V R
,
9 cases with ft-values measured to ; 6 more cases <0.05% precision with . 0.05-0.23% precision ~220 individual measurements with compatible precision
Hardy & Towner PRC 91, 025501 (2015); updated to 2019
Z of daughter
5 30 25 20 15 10 35 3090 3040 3050 3060 3070 3080 3140 3100 3110 3120 3130
10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca 26Si
74Rb
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10
0 ,1 0 ,1
+ +
BR t1/2 QEC
10C
=
Critical test passed: values consistent
2
/n = 0.6
t
SLIDE 26
CORRECTIONS USED IN THIS ANALYSIS
t = )] = ft (1 + )[1 - (
-
R C NS
K
2
2G (1 + )
V
R ,
SLIDE 27
- 1. Radiative corrections
CORRECTIONS USED IN THIS ANALYSIS
t = )] = ft (1 + )[1 - (
-
R C NS
K
2
2G (1 + )
V
R ,
R
, = [g(E ) + + + ... ]
m 2 3
2
One-photon brem. + low-energy W-box [Serlin]
SLIDE 28
- 1. Radiative corrections
= [4 ln(m /m ) + ln(m /m ) + 2C + ... ]
Z p p A Born
R
CORRECTIONS USED IN THIS ANALYSIS
t = )] = ft (1 + )[1 - (
-
R C NS
K
2
2G (1 + )
V
R ,
R
, = [g(E ) + + + ... ]
m 2 3
2 2
One-photon brem. + low-energy W-box High-energy W-box +ZW-box [Serlin] & Serlin] [Marciano
SLIDE 29
- 1. Radiative corrections
= [4 ln(m /m ) + ln(m /m ) + 2C + ... ]
Z p p A Born
R NS
Order- axial-vector photonic contributions
CORRECTIONS USED IN THIS ANALYSIS
t = )] = ft (1 + )[1 - (
-
R C NS
K
2
2G (1 + )
V
R ,
R
, = [g(E ) + + + ... ]
m 2 3
2 2
N N W
e+
One-photon brem. + low-energy W-box High-energy W-box +ZW-box universal [Serlin] [Towner] & Serlin] [Marciano
SLIDE 30
- 1. Radiative corrections
= [4 ln(m /m ) + ln(m /m ) + 2C + ... ]
Z p p A Born
R NS
Order- axial-vector photonic contributions
- 2. Isospin symmetry-breaking corrections
C
Charge-dependent mismatch between parent and daughter analog states (members of the same isospin triplet).
CORRECTIONS USED IN THIS ANALYSIS
t = )] = ft (1 + )[1 - (
-
R C NS
K
2
2G (1 + )
V
R ,
R
, = [g(E ) + + + ... ]
m 2 3
2 2
N N W
e+
One-photon brem. + low-energy W-box High-energy W-box +ZW-box universal [Serlin] [Towner] & Serlin] [Marciano [Towner & Hardy]
SLIDE 31
- 1. Radiative corrections
= [4 ln(m /m ) + ln(m /m ) + 2C + ... ]
Z p p A Born
R NS
Order- axial-vector photonic contributions
- 2. Isospin symmetry-breaking corrections
C
Charge-dependent mismatch between parent and daughter analog states (members of the same isospin triplet).
}
Dependent
- n nuclear
structure
CORRECTIONS USED IN THIS ANALYSIS
t = )] = ft (1 + )[1 - (
-
R C NS
K
2
2G (1 + )
V
R ,
R
, = [g(E ) + + + ... ]
m 2 3
2 2
N N W
e+
One-photon brem. + low-energy W-box High-energy W-box +ZW-box universal [Serlin] [Towner] & Serlin] [Marciano [Towner & Hardy]
SLIDE 32
WORLD DATA FOR 0 0 DECAY, 2008 ISOSPIN SYMMETRY BREAKING CORRECTIONS
= +
C
C1 C2
Full-parentage Saxon-Woods wave functions for parent and daughter. Matched to known binding energies and charge radii as obtained from electron scattering. Mismatch in radial wave function be- tween parent and daughter. Core states included based on measured spectroscopic factors. Difference in configuration mixing between parent and daughter. Shell-model calculation with well- established 2-body matrix elements. Charge dependence tuned to known single-particle energies and to meas- ured IMME coefficients. Results also adjusted to measured
+
non-analog 0 state energies.
SLIDE 33
WORLD DATA FOR 0 0 DECAY, 2008 ISOSPIN SYMMETRY BREAKING CORRECTIONS
5 10 15 20 25 30 35
Z of daughter Correction terms (%)
+2.5
- 0.5
+2.0 +1.5 +1.0 +0.5 +0.0
R R
’
NS C2 C1
= +
C
C1 C2
Full-parentage Saxon-Woods wave functions for parent and daughter. Matched to known binding energies and charge radii as obtained from electron scattering. Mismatch in radial wave function be- tween parent and daughter. Core states included based on measured spectroscopic factors. Difference in configuration mixing between parent and daughter. Shell-model calculation with well- established 2-body matrix elements. Charge dependence tuned to known single-particle energies and to meas- ured IMME coefficients. Results also adjusted to measured
+
non-analog 0 state energies.
SLIDE 34
WORLD DATA FOR 0 0 DECAY, 2008 ISOSPIN SYMMETRY BREAKING CORRECTIONS
5 10 15 20 25 30 35
Z of daughter Correction terms (%)
+2.5
- 0.5
+2.0 +1.5 +1.0 +0.5 +0.0
R R
’
NS C2 C1
= +
C
C1 C2
Full-parentage Saxon-Woods wave functions for parent and daughter. Matched to known binding energies and charge radii as obtained from electron scattering. Mismatch in radial wave function be- tween parent and daughter. Core states included based on measured spectroscopic factors. Difference in configuration mixing between parent and daughter. Shell-model calculation with well- established 2-body matrix elements. Charge dependence tuned to known single-particle energies and to meas- ured IMME coefficients. Results also adjusted to measured
+
non-analog 0 state energies.
0.02 0.04
Exp C
- NS
R ` R
V
- Frac. Uncertainty (%)
V Uncertainty Budget
ud
t = )] = ft (1 + )[1 - (
-
R C NS
K
2
2G (1 + )
V
R ,
SLIDE 35
WORLD DATA FOR 0 0 DECAY, 2008 ISOSPIN SYMMETRY BREAKING CORRECTIONS
5 10 15 20 25 30 35
Z of daughter Correction terms (%)
+2.5
- 0.5
+2.0 +1.5 +1.0 +0.5 +0.0
R R
’
NS C2 C1
= +
C
C1 C2
Full-parentage Saxon-Woods wave functions for parent and daughter. Matched to known binding energies and charge radii as obtained from electron scattering. Mismatch in radial wave function be- tween parent and daughter. Core states included based on measured spectroscopic factors. Difference in configuration mixing between parent and daughter. Shell-model calculation with well- established 2-body matrix elements. Charge dependence tuned to known single-particle energies and to meas- ured IMME coefficients. Results also adjusted to measured
+
non-analog 0 state energies.
0.02 0.04
Exp C
- NS
R ` R
V
- Frac. Uncertainty (%)
V Uncertainty Budget
ud
t = )] = ft (1 + )[1 - (
-
R C NS
K
2
2G (1 + )
V
R ,
-
C NS
Only can be tested experimentally.
SLIDE 36
TESTS OF ( - ) CALCULATIONS
C NS
- A. Test how well the transition-to-transition differences in - match the
C NS
data: i.e. do they lead to constant t values, in agreement with CVC?
- B. Measure the ratio of ft values for mirror 0 0 superallowed transitions
and compare the results with calculations.
+ +
SLIDE 37
TESTS OF ( - ) CALCULATIONS
C NS
10 40 30 20 Z of daughter
t
3050 3090 3080 3070 3060
Shell-model, Saxon-Woods radial functions
Towner & Hardy PRC 77, 025501 (2008)
2
t values have been calculated with different models for , then tested for consistency. No
C
theoretical uncertainties are included. Normalized
2
and confidence levels are shown.
2
Model CL(%) /N SM-SW 1.37 17
- A. Test how well the transition-to-transition differences in - match the
C NS
data: i.e. do they lead to constant t values, in agreement with CVC?
- B. Measure the ratio of ft values for mirror 0 0 superallowed transitions
and compare the results with calculations.
+ +
SLIDE 38
TESTS OF ( - ) CALCULATIONS
C NS
10 40 30 20 Z of daughter
t
3050 3090 3080 3070 3060
Shell-model, Saxon-Woods radial functions
Towner & Hardy PRC 77, 025501 (2008)
2
10 40 30 20 Z of daughter
t
3050 3090 3080 3070 3060
Shell-model, Hartree-Fock radial functions
Towner & Hardy PRC 79, 055502 (2009)
2
t values have been calculated with different models for , then tested for consistency. No
C
theoretical uncertainties are included. Normalized
2
and confidence levels are shown.
2
Model CL(%) /N SM-SW 1.37 17 SM-HF 6.38 0
- A. Test how well the transition-to-transition differences in - match the
C NS
data: i.e. do they lead to constant t values, in agreement with CVC?
- B. Measure the ratio of ft values for mirror 0 0 superallowed transitions
and compare the results with calculations.
+ +
SLIDE 39
TESTS OF ( - ) CALCULATIONS
C NS
10 40 30 20 Z of daughter
t
3050 3090 3080 3070 3060
Shell-model, Saxon-Woods radial functions
Towner & Hardy PRC 77, 025501 (2008)
2
10 40 30 20 Z of daughter
t
3050 3090 3080 3070 3060
Shell-model, Hartree-Fock radial functions
Towner & Hardy PRC 79, 055502 (2009)
2
t values have been calculated with different models for , then tested for consistency. No
C
theoretical uncertainties are included. Normalized
2
and confidence levels are shown.
2
Model CL(%) /N SM-SW 1.37 17 SM-HF 6.38 0 DFT 4.26 0
- A. Test how well the transition-to-transition differences in - match the
C NS
data: i.e. do they lead to constant t values, in agreement with CVC?
- B. Measure the ratio of ft values for mirror 0 0 superallowed transitions
and compare the results with calculations.
+ +
10 40 30 20
t
3050 3090 3080 3070 3060
Nuclear density functional theory
Satula et al. PRC 86, 054316 (2012)
2
Z of daughter
SLIDE 40
TESTS OF ( - ) CALCULATIONS
C NS
10 40 30 20 Z of daughter
t
3050 3090 3080 3070 3060
Shell-model, Saxon-Woods radial functions
Towner & Hardy PRC 77, 025501 (2008)
2
10 40 30 20 Z of daughter
t
3050 3090 3080 3070 3060
Shell-model, Hartree-Fock radial functions
Towner & Hardy PRC 79, 055502 (2009)
2
t values have been calculated with different models for , then tested for consistency. No
C
theoretical uncertainties are included. Normalized
2
and confidence levels are shown.
2
Model CL(%) /N SM-SW 1.37 17 SM-HF 6.38 0 DFT 4.26 0 RHF-RPA 4.91 0 RH-RPA 3.68 0
- A. Test how well the transition-to-transition differences in - match the
C NS
data: i.e. do they lead to constant t values, in agreement with CVC?
- B. Measure the ratio of ft values for mirror 0 0 superallowed transitions
and compare the results with calculations.
+ +
10 40 30 20
t
3050 3090 3080 3070 3060
Nuclear density functional theory
Satula et al. PRC 86, 054316 (2012)
2
Z of daughter
SLIDE 41
TESTS OF ( - ) CALCULATIONS
C NS
- A. Test how well the transition-to-transition differences in - match the
C NS
data: i.e. do they lead to constant t values, in agreement with CVC?
- B. Measure the ratio of ft values for mirror 0 0 superallowed transitions
and compare the results with calculations.
+ +
SLIDE 42
TESTS OF ( - ) CALCULATIONS
C NS
- A. Test how well the transition-to-transition differences in - match the
C NS
data: i.e. do they lead to constant t values, in agreement with CVC?
- B. Measure the ratio of ft values for mirror 0 0 superallowed transitions
and compare the results with calculations.
+ +
t = ft (1 + )[1 - ( - )]
R C NS
,
38Ar20 18
99.97% 0 ,1
+
38Ca18 20
0 ,1
+
444 ms
Q =
EC
6612
1 ,0
+
1 ,0
+
0 ,1
+
3 ,0
+
77.3% 2.8% 19.5% 924 ms
38K19 19
458 130 1698 1 ,0
+
0.3% 3341
Q =
EC
6044
A B
1 ,0
+
0.1% 3978
ftA ft B = (1 + )
R
(1 + )[1 - ( - )]
R C NS
A A A
[1 - ( - )]
C NS
B B B
, ,
= 1+ ( - ) + (
-
) - ( - )
R R NS NS C C
B B B A A A
, ,
SLIDE 43
TESTS OF ( - ) CALCULATIONS
C NS
- A. Test how well the transition-to-transition differences in - match the
C NS
data: i.e. do they lead to constant t values, in agreement with CVC?
- B. Measure the ratio of ft values for mirror 0 0 superallowed transitions
and compare the results with calculations.
+ +
t = ft (1 + )[1 - ( - )]
R C NS
,
38Ar20 18
99.97% 0 ,1
+
38Ca18 20
0 ,1
+
444 ms
Q =
EC
6612
1 ,0
+
1 ,0
+
0 ,1
+
3 ,0
+
77.3% 2.8% 19.5% 924 ms
38K19 19
458 130 1698 1 ,0
+
0.3% 3341
Q =
EC
6044
A B
1 ,0
+
0.1% 3978
ftA ft B = (1 + )
R
(1 + )[1 - ( - )]
R C NS
A A A
[1 - ( - )]
C NS
B B B
, ,
= 1+ ( - ) + (
-
) - ( - )
R R NS NS C C
B B B A A A
, ,
NUMBER OF PROTONS, Z
20 30 40 10
NUMBER OF NEUTRONS, N
20 30 40 50 60 10 10C 74Rb
0 ,1 0 ,1
+ +
BR t1/2 QEC
SLIDE 44
TESTS OF ( - ) CALCULATIONS
C NS
- A. Test how well the transition-to-transition differences in - match the
C NS
data: i.e. do they lead to constant t values, in agreement with CVC?
- B. Measure the ratio of ft values for mirror 0 0 superallowed transitions
and compare the results with calculations.
+ +
t = ft (1 + )[1 - ( - )]
R C NS
,
38Ar20 18
99.97% 0 ,1
+
38Ca18 20
0 ,1
+
444 ms
Q =
EC
6612
1 ,0
+
1 ,0
+
0 ,1
+
3 ,0
+
77.3% 2.8% 19.5% 924 ms
38K19 19
458 130 1698 1 ,0
+
0.3% 3341
Q =
EC
6044
A B
1 ,0
+
0.1% 3978
ftA ft B = (1 + )
R
(1 + )[1 - ( - )]
R C NS
A A A
[1 - ( - )]
C NS
B B B
, ,
= 1+ ( - ) + (
-
) - ( - )
R R NS NS C C
B B B A A A
, ,
26 42 38 34
A of mirror pairs ft / ft
+1
1.000 1.006 1.004 1.002
HF SW
SLIDE 45
TESTS OF ( - ) CALCULATIONS
C NS
- A. Test how well the transition-to-transition differences in - match the
C NS
data: i.e. do they lead to constant t values, in agreement with CVC?
- B. Measure the ratio of ft values for mirror 0 0 superallowed transitions
and compare the results with calculations.
+ +
t = ft (1 + )[1 - ( - )]
R C NS
,
38Ar20 18
99.97% 0 ,1
+
38Ca18 20
0 ,1
+
444 ms
Q =
EC
6612
1 ,0
+
1 ,0
+
0 ,1
+
3 ,0
+
77.3% 2.8% 19.5% 924 ms
38K19 19
458 130 1698 1 ,0
+
0.3% 3341
Q =
EC
6044
A B
1 ,0
+
0.1% 3978
ftA ft B = (1 + )
R
(1 + )[1 - ( - )]
R C NS
A A A
[1 - ( - )]
C NS
B B B
, ,
= 1+ ( - ) + (
-
) - ( - )
R R NS NS C C
B B B A A A
, ,
26 42 38 34
A of mirror pairs ft / ft
+1
1.000 1.006 1.004 1.002
HF SW
SLIDE 46
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
RESULTS FROM 0 0 DECAY
+ +
SLIDE 47
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC)
G constant to + 0.011%
V
- RESULTS FROM 0 0 DECAY
+ +
1/2 3
G (1+ ) /(hc)
V R
= 1.14962(13)
- 5
- 2
X10 GeV
x 100 50 40 30 20 10
Z OF DAUGHTER t-value (s)
6000 1000 2000 3000 4000 5000
Evaluated data
3070 3080 3090 3100 3060 5 30 25 20 15 10 35
t = 3072.1(7)
10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca 26Si
SLIDE 48
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC) Validate correction terms
G constant to + 0.011%
V
- RESULTS FROM 0 0 DECAY
+ +
SLIDE 49
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC) Validate correction terms
G constant to + 0.011%
V
- Z of daughter
5 30 25 20 15 10 35
t
3070 3080 3060 3090 3100
ft
3090 3040 3050 3060 3070 3080
RESULTS FROM 0 0 DECAY
+ +
10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca 26Si
SLIDE 50
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC) Validate correction terms
G constant to + 0.011%
V
-
Z of daughter
5 30 25 20 15 10 35
t
3070 3080 3060 3090 3100
ft
3090 3040 3050 3060 3070 3080
RESULTS FROM 0 0 DECAY
+ +
2
Model CL(%) /N SM-SW 1.37 17 SM-HF 6.38 0 DFT 4.26 0 RHF-RPA 4.91 0 RH-RPA 3.68 0
26 42 38 34
A of mirror pairs ft / ft
+1
1.000 1.006 1.004 1.002
SW HF SW HF
10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca 26Si
SLIDE 51
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC) Test for Scalar current Validate correction terms
G constant to + 0.011%
V
-
RESULTS FROM 0 0 DECAY
+ +
SLIDE 52
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC) Test for Scalar current Validate correction terms
G constant to + 0.011%
V
-
limit, C C = 0.0012 (10) = b/2
S V
/
RESULTS FROM 0 0 DECAY
+ +
Z of daughter
20 10 30 40
Ft (s)
3070 3080 3090 3060
C /C = + 0.002
S V
SLIDE 53
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC) Test for Scalar current Validate correction terms
G constant to + 0.011%
V
-
limit, C C = 0.0012 (10) = b/2
S V
/
RESULTS FROM 0 0 DECAY
+ +
0.1 0.2 0.3
- 0.1
- 0.2
0.1 0.2
- 0.1
- 0.2
0.3
C /C
S V
`
C /C
S V
38 m
a( K )
0+ 0+
Z of daughter
20 10 30 40
Ft (s)
3070 3080 3090 3060
C /C = + 0.002
S V
SLIDE 54
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC) Test for Scalar current Validate correction terms
V V V
ud us ub
V V V
cd cs cb
V V V
td ts tb
d' s' b' d s b =
weak eigenstates mass eigenstates
WITH CVC VERIFIED
2
Obtain precise value of G (1 + )
V R
Determine Vud
2
G constant to + 0.011%
V
-
limit, C C = 0.0012 (10) = b/2
S V
/
2 2
V = G /G = 0.94907 + 0.00041
ud V 2
- RESULTS FROM 0 0 DECAY
+ +
Cabibbo-Kobayashi-Maskawa matrix
SLIDE 55
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC) Test for Scalar current Validate correction terms
V V V
ud us ub
V V V
cd cs cb
V V V
td ts tb
d' s' b' d s b =
weak eigenstates mass eigenstates
WITH CVC VERIFIED
2
Obtain precise value of G (1 + )
V R
Determine Vud
2
G constant to + 0.011%
V
-
limit, C C = 0.0012 (10) = b/2
S V
/
2 2
V = G /G = 0.94907 + 0.00041
ud V 2
- RESULTS FROM 0 0 DECAY
+ +
Cabibbo-Kobayashi-Maskawa matrix
1990 2000 2010 0.975 0.974 0.973
Vud
SLIDE 56
FROM A SINGLE TRANSITION
t = ft (1 + )[1 - ( - )] =
R C NS
K
2
2G (1 + )
V R
,
Experimentally
2
determine G (1 + )
V R
FROM MANY TRANSITIONS
Test Conservation of the Vector current (CVC) Test for Scalar current Validate correction terms
V V V
ud us ub
V V V
cd cs cb
V V V
td ts tb
d' s' b' d s b =
weak eigenstates mass eigenstates
WITH CVC VERIFIED
2
Obtain precise value of G (1 + )
V R
Test CKM unitarity Determine Vud
2
G constant to + 0.011%
V
- V + V + V = 0.99939 + 0.00047
ud us ub
2 2 2
-
limit, C C = 0.0012 (10) = b/2
S V
/
2 2
V = G /G = 0.94907 + 0.00041
ud V 2
- RESULTS FROM 0 0 DECAY
+ +
Cabibbo-Kobayashi-Maskawa matrix
SLIDE 57
T=1/2 SUPERALLOWED BETA DECAY
t1/2
QEC BR
BASIC WEAK-DECAY EQUATION
f =
f(Z,
) t = partial half-life: f( , ) G = coupling constants
V,A
< > = Fermi, Gamow-Teller matrix elements statistical rate function: QEC t BR
1/2
EXPERIMENT
ft = K
2
G < >
V 2 2
G < >
A
- 2
+
J ,½
- J ,½
- +
asymmetry
SLIDE 58
T=1/2 SUPERALLOWED BETA DECAY
t1/2
QEC BR
BASIC WEAK-DECAY EQUATION
f =
f(Z,
) t = partial half-life: f( , ) G = coupling constants
V,A
< > = Fermi, Gamow-Teller matrix elements statistical rate function: QEC t BR
1/2
EXPERIMENT
ft = K
2
G < >
V 2 2
G < >
A
- 2
+
J ,½
- J ,½
- +
asymmetry
INCLUDING RADIATIVE CORRECTIONS
t = ft (1 + )[1 - (
- )] =
R C
- NS
K
2
G (1 + )
V
- R
, (1
2
- < > )
- +
- =
G /G
A V
2
SLIDE 59
T=1/2 SUPERALLOWED BETA DECAY
t1/2
QEC BR
BASIC WEAK-DECAY EQUATION
f =
f(Z,
) t = partial half-life: f( , ) G = coupling constants
V,A
< > = Fermi, Gamow-Teller matrix elements statistical rate function: QEC t BR
1/2
EXPERIMENT
ft = K
2
G < >
V 2 2
G < >
A
- 2
+
J ,½
- J ,½
- +
asymmetry
INCLUDING RADIATIVE CORRECTIONS
t = ft (1 + )[1 - (
- )] =
R C
- NS
K
2
G (1 + )
V
- R
, (1
2
- < > )
- +
Requires additional experiment: for example, asymmetry (A)
- =
G /G
A V
2
SLIDE 60
T=1/2 SUPERALLOWED BETA DECAY
t1/2
QEC BR
BASIC WEAK-DECAY EQUATION
f =
f(Z,
) t = partial half-life: f( , ) G = coupling constants
V,A
< > = Fermi, Gamow-Teller matrix elements statistical rate function: QEC t BR
1/2
EXPERIMENT
ft = K
2
G < >
V 2 2
G < >
A
- 2
+
J ,½
- J ,½
- +
asymmetry
INCLUDING RADIATIVE CORRECTIONS
t = ft (1 + )[1 - (
- )] =
R C
- NS
K
2
G (1 + )
V
- R
, (1
2
- < > )
- +
Requires additional experiment: for example, asymmetry (A)
- =
G /G
A V
2
NEUTRON DECAY
SLIDE 61
NEUTRON DECAY DATA 2019
Mean life:
= 879.7 + 0.8 s
880 900 1990 1995 2000 2005
Date of measurement Mean life
2010
- /N = 3.8
2
2015
SLIDE 62
NEUTRON DECAY DATA 2019
Mean life:
= 879.7 + 0.8 s
880 900 1990 1995 2000 2005
Date of measurement Mean life
2010
- /N = 3.8
2
2015 Beam Bottle
SLIDE 63
NEUTRON DECAY DATA 2019
Mean life:
= 879.7 + 0.8 s
880 900 1990 1995 2000 2005
Date of measurement Mean life
2010
- /N = 3.8
2
2015 Beam: 888.1 + 2.0 s Bottle: 879.4 + 0.6 s
- Beam
Bottle
SLIDE 64
NEUTRON DECAY DATA 2019
Mean life:
= 879.7 + 0.8 s
880 900 1990 1995 2000 2005
Date of measurement Mean life
- 1.28
- 1.27
- 1.26
1990 1995 2000 2005
Date of measurement = g /g
A V
asymmetry:
= -1.2756 + 0.0009 /N = 3.2
2
- 2010
- /N = 3.8
2
2010 2015 2015 Beam: 888.1 + 2.0 s Bottle: 879.4 + 0.6 s
- Beam
Bottle
SLIDE 65
NEUTRON DECAY DATA 2019
Mean life:
= 879.7 + 0.8 s
880 900 1990 1995 2000 2005
Date of measurement Mean life
- 1.28
- 1.27
- 1.26
1990 1995 2000 2005
Date of measurement = g /g
A V
asymmetry:
= -1.2756 + 0.0009 /N = 3.2
2
- 2010
- /N = 3.8
2
2010
V = 0.9740 + 0.0007
ud
- 2015
2015 Beam: 888.1 + 2.0 s Bottle: 879.4 + 0.6 s
- Beam
Bottle
SLIDE 66
NEUTRON DECAY DATA 2019
Mean life:
= 879.7 + 0.8 s
880 900 1990 1995 2000 2005
Date of measurement Mean life
- 1.28
- 1.27
- 1.26
1990 1995 2000 2005
Date of measurement = g /g
A V
asymmetry:
= -1.2756 + 0.0009 /N = 3.2
2
- 2010
- /N = 3.8
2
2010
V = 0.9740 + 0.0007
ud
- 2015
2015 Beam: 888.1 + 2.0 s Bottle: 879.4 + 0.6 s
- Beam
Bottle
0.9680 < V < 0.9750
ud -
Beam-bottle span
SLIDE 67
NEUTRON DECAY DATA 2019
Mean life:
= 879.7 + 0.8 s
880 900 1990 1995 2000 2005
Date of measurement Mean life
- 1.28
- 1.27
- 1.26
1990 1995 2000 2005
Date of measurement = g /g
A V
asymmetry:
= -1.2756 + 0.0009 /N = 3.2
2
- 2010
- /N = 3.8
2
2010
V = 0.9740 + 0.0007
ud
- V
= 0.9742 + 0.0002
ud
- nuclear 0 0
+ + 2015 2015 Beam: 888.1 + 2.0 s Bottle: 879.4 + 0.6 s
- Beam
Bottle
0.9680 < V < 0.9750
ud -
Beam-bottle span
SLIDE 68
NUCLEAR T=1/2 MIRROR DECAY DATA 2018
t = ft (1 + )[1 - (
- )] =
R C NS
K
2
G (1 + )
V
R , (1
2
< > )
+
SLIDE 69
NUCLEAR T=1/2 MIRROR DECAY DATA 2018
15 10 20 Z of daughter 6050 6250 6150
(1
2
< > )
+ t
19Ne 37K 35Ar 21Na
Naviliat-Cuncic & Severijns, PRL 102, 142302 (2009) + Fenker et al., PRL 120, 062502 (2018)
t = ft (1 + )[1 - (
- )] =
R C NS
K
2
G (1 + )
V
R , (1
2
< > )
+
SLIDE 70
NUCLEAR T=1/2 MIRROR DECAY DATA 2018
15 10 20 Z of daughter 6050 6250 6150
(1
2
< > )
+ t
19Ne 37K 35Ar 21Na
Naviliat-Cuncic & Severijns, PRL 102, 142302 (2009) + Fenker et al., PRL 120, 062502 (2018)
t = ft (1 + )[1 - (
- )] =
R C NS
K
2
G (1 + )
V
R , (1
2
< > )
+
V = 0.9727 + 0.0014
ud
SLIDE 71
NUCLEAR T=1/2 MIRROR DECAY DATA 2018
15 10 20 Z of daughter 6050 6250 6150
(1
2
< > )
+ t
19Ne 37K 35Ar 21Na
Naviliat-Cuncic & Severijns, PRL 102, 142302 (2009) + Fenker et al., PRL 120, 062502 (2018)
t = ft (1 + )[1 - (
- )] =
R C NS
K
2
G (1 + )
V
R , (1
2
< > )
+
V = 0.9742 + 0.0002
ud
- nuclear 0 0
+ +
V = 0.9727 + 0.0014
ud
SLIDE 72
PION BETA DECAY
Decay process:
- e
e
+ + 0 ,1 0 ,1
SLIDE 73
PION BETA DECAY
Decay process:
e e
+ + 0 ,1 0 ,1
- Experimental data:
= 2.6033+ 0.0005 x 10 s
- 8
- (PDG 2017)
BR = 1.036+ 0.007 x 10
- 8
- Pocanic et al,
PRL 93, 181803 (2004)
V = 0.9749 + 0.0026
ud
- Result:
SLIDE 74
PION BETA DECAY
Decay process:
e e
+ + 0 ,1 0 ,1
- Experimental data:
= 2.6033+ 0.0005 x 10 s
- 8
- (PDG 2017)
BR = 1.036+ 0.007 x 10
- 8
- Pocanic et al,
PRL 93, 181803 (2004)
V = 0.9749 + 0.0026
ud
- Result:
V = 0.9742 + 0.0002
ud
- nuclear 0 0
+ +
SLIDE 75
.001 .003 .002
Uncertainty
Experiment Radiative correction Nuclear correction
CURRENT STATUS OF V AND CKM UNITARITY
ud
.9700 .9800 .9750
nuclear 0 0 + + neutron nuclear mirrors pion
Vud
V = 0.97420 + 0.00021
ud
SLIDE 76
V + V + V = 0.99939 0.00047
ud us ub 2 2 2
+
- muon decay
nuclear decays
ud
V
0.94907 + 0.00041
- 2
0.05031 + 0.00022
- us
V PDG
kaon decays
2
B decays
0.00002
ub
V
2
.001 .003 .002
Uncertainty
Experiment Radiative correction Nuclear correction
CURRENT STATUS OF V AND CKM UNITARITY
ud
.9700 .9800 .9750
nuclear 0 0 + + neutron nuclear mirrors pion
Vud
V = 0.97420 + 0.00021
ud
SLIDE 77
V + V + V = 0.99939 0.00047
ud us ub 2 2 2
+
- muon decay
nuclear decays
ud
V
0.94907 + 0.00041
- 2
0.05031 + 0.00022
- us
V PDG
kaon decays
2
B decays
0.00002
ub
V
2
.001 .003 .002
Uncertainty
Experiment Radiative correction Nuclear correction
CURRENT STATUS OF V AND CKM UNITARITY
ud
.9700 .9800 .9750
nuclear 0 0 + + neutron nuclear mirrors pion
Vud
V = 0.97420 + 0.00021
ud
+
I f u n c e r t a i n t y
- n
r a d i a t i v e c
- r
r e c t i
- n
s c
- u
l d b e r e d u c e d b y a f a c t
- r
- f
5 : V u n c e r t a i n t y w
- u
l d d r
- p
t
- .
2 a n d t h e u n i t a r i t y
- s
u m u n c e r t a i n t y t
- .
3 .
u d 2
SLIDE 78
PROMISING FUTURE DIRECTIONS
SLIDE 79
PROMISING FUTURE DIRECTIONS
10
- 1. Improved ft value for C decay
Z of daughter
20 10 30 40
Ft (s)
3070 3080 3090 3060
C /C = + 0.002
S VTo limit or identify scalar current
SLIDE 80
PROMISING FUTURE DIRECTIONS
10
- 1. Improved ft value for C decay
Z of daughter
20 10 30 40
Ft (s)
3070 3080 3090 3060
C /C = + 0.002
S VTo limit or identify scalar current
- 2. Complete A = 42 mirror pair
To constrain correction terms
C
A of mirror pairs
26 42 38 34
ft / ft
+1
1.000 1.006 1.004 1.002
SW HF SW HF
SLIDE 81
PROMISING FUTURE DIRECTIONS
10
- 1. Improved ft value for C decay
Z of daughter
20 10 30 40
Ft (s)
3070 3080 3090 3060
C /C = + 0.002
S VTo limit or identify scalar current
- 2. Complete A = 42 mirror pair
To constrain correction terms
C
A of mirror pairs
26 42 38 34
ft / ft
+1
1.000 1.006 1.004 1.002
SW HF SW HF
- 3. Reduce uncertainty in calculated R
+
If uncertainty on radiative corrections could be reduced by a factor of 5: V uncertainty would drop to 0.00020 and the unitarity-sum uncertainty to 0.00030.
ud 2
To improve unitarity test
SLIDE 82
PROMISING FUTURE DIRECTIONS
10
- 1. Improved ft value for C decay
Z of daughter
20 10 30 40
Ft (s)
3070 3080 3090 3060
C /C = + 0.002
S VTo limit or identify scalar current
- 2. Complete A = 42 mirror pair
To constrain correction terms
C
A of mirror pairs
26 42 38 34
ft / ft
+1
1.000 1.006 1.004 1.002
SW HF SW HF
- 3. Reduce uncertainty in calculated R
+
If uncertainty on radiative corrections could be reduced by a factor of 5: V uncertainty would drop to 0.00020 and the unitarity-sum uncertainty to 0.00030.
ud 2
To improve unitarity test
- 4. Revisit all calculated corrections.
If transition-dependence is altered, improve all measured ft values to verify that CVC is preserved.
Z of daughter
5 30 25 20 15 10 35
t
3070 3080 3060 3090
SLIDE 83
SUMMARY AND OUTLOOK
- 3. The current value for V , when combined with the PDG
ud
values for V and V , satisfies CKM unitarity to +0.05%.
us ub
- 1. Analysis of superallowed 0 0 nuclear decay confirms
CVC to +0.011% and thus yields V = 0.97420(21).
ud
- 2. The three other experimental methods for determining V
ud
yield consistent results; the neutron-decay result is only a factor of 4 less precise and agrees completely.
+ +
SLIDE 84
SUMMARY AND OUTLOOK
- 3. The current value for V , when combined with the PDG
ud
values for V and V , satisfies CKM unitarity to +0.05%.
us ub
- 1. Analysis of superallowed 0 0 nuclear decay confirms
CVC to +0.011% and thus yields V = 0.97420(21).
ud
- 2. The three other experimental methods for determining V
ud
yield consistent results; the neutron-decay result is only a factor of 4 less precise and agrees completely.
+ +
- 5. Transition-dependent corrections have been tested by
requiring consistency among the 14 known transitions (CVC), and agreement with mirror-transition pairs.
- 4. The largest contribution to V uncertainty is from the
ud
inner radiative correction, . Very little reduction in V
R ud
uncertainty is possible without improved calculation of .
R
- 6. Improved and new correction terms are appearing. They
will need to be tested for compatibility with CVC.
SLIDE 85
SUMMARY AND OUTLOOK
- 3. The current value for V , when combined with the PDG
ud
values for V and V , satisfies CKM unitarity to +0.05%.
us ub
- 1. Analysis of superallowed 0 0 nuclear decay confirms
CVC to +0.011% and thus yields V = 0.97420(21).
ud
- 2. The three other experimental methods for determining V
ud
yield consistent results; the neutron-decay result is only a factor of 4 less precise and agrees completely.
+ +
- 5. Transition-dependent corrections have been tested by
requiring consistency among the 14 known transitions (CVC), and agreement with mirror-transition pairs.
- 4. The largest contribution to V uncertainty is from the
ud
inner radiative correction, . Very little reduction in V
R ud
uncertainty is possible without improved calculation of .
R
- 6. Improved and new correction terms are appearing. They
will need to be tested for compatibility with CVC.
It’s been a fun way to make a living
SLIDE 86
Victor Iacob Ninel Nica Hyo In Park Vladimir Horvat Lixin Chen Vladimir Golovko Maria Sanchez-Vega Peter Lipnik Russell Neilson John Goodwin Miguel Bencomo Livius Trache Brian Roeder Evgeny Tereshatov Dan Melconian Bob Tribble Carl Gagliardi
The people who helped make it fun (since 1997)
Ian Towner
Gordon Ball (TRIUMF) Dick Helmer (INEEL) Guy Savard (ANL) Subramanian Raman (ORNL) Malvina Trzhaskovskaya (St. Petersburg) Tommi Eronen (Jyvaskyla) Juha Aysto (Jyvaskyla) Maxime Brodeur (Notre Dame)
TAMU External