[PPT] - The current evaluation of |V | and the role played by radiative PowerPoint Presentation

SLIDE 1

SLIDE 2

J.C. Hardy

Cyclotron Institute Texas A&M University

with I.S. Towner

The current evaluation of |V | and the role played by radiative corrections

ud

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

CONTRIBUTION OF CORRECTION TERMS

t = = ft (1 +  )[1 - ( -  )]

R C NS

K

2

2G (1 +  )

V R

,

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 (%)

NS C

SLIDE 9

CONTRIBUTION OF CORRECTION TERMS

t = = ft (1 +  )[1 - ( -  )]

R C NS

K

2

2G (1 +  )

V R

,

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 10

CONTRIBUTION OF CORRECTION TERMS

t = = ft (1 +  )[1 - ( -  )]

R C NS

K

2

2G (1 +  )

V R

,

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 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

THE PATH TO Vud

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

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

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

SLIDE 14

FROM A SINGLE TRANSITION

t = ft (1 +  )[1 - ( -  )] =

R C NS

K

2

2G (1 +  )

V R

,

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

SLIDE 15

FROM A SINGLE TRANSITION

t = ft (1 +  )[1 - ( -  )] =

R C NS

K

2

2G (1 +  )

V R

,

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

SLIDE 16

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

WORLD DATA FOR 0 0 DECAY, 2017

+ + t = = ft (1 +  )[1 - ( -  )]

R C NS

K

2

2G (1 +  )

V R

,

8 cases with ft-values measured to ; 6 more cases <0.05% precision with . 0.05-0.3% precision ~220 individual measurements with compatible precision

Hardy & Towner PRC 91, 025501 (2015) updated to 2017

SLIDE 17

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

WORLD DATA FOR 0 0 DECAY, 2017

+ +

3030

t = = ft (1 +  )[1 - ( -  )]

R C NS

K

2

2G (1 +  )

V R

,

8 cases with ft-values measured to ; 6 more cases <0.05% precision with . 0.05-0.3% precision ~220 individual measurements with compatible precision

Hardy & Towner PRC 91, 025501 (2015) updated to 2017

ft

3090 3040 3050 3060 3070 3080

10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca

SLIDE 18

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

WORLD DATA FOR 0 0 DECAY, 2017

+ +

3030 3140 3100 3110 3120 3130 3080 3090

ft (1+ )

R

’

t = = ft (1 +  )

R [1 - ( -  )] C NS

K

2

2G (1 +  )

V R

,

8 cases with ft-values measured to ; 6 more cases <0.05% precision with . 0.05-0.3% precision ~220 individual measurements with compatible precision

Hardy & Towner PRC 91, 025501 (2015) updated to 2017

ft

3090 3040 3050 3060 3070 3080

10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca

SLIDE 19

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

WORLD DATA FOR 0 0 DECAY, 2017

+ +

Z of daughter

5 30 25 20 15 10 35

t

3070 3080 3060 3030 3140 3090 3100 3100 3110 3120 3130 3080 3090

ft (1+ )

R

’

t = = ft (1 +  )[1 - ( -  )]

R C NS

K

2

2G (1 +  )

V R

,

8 cases with ft-values measured to ; 6 more cases <0.05% precision with . 0.05-0.3% precision ~220 individual measurements with compatible precision

Hardy & Towner PRC 91, 025501 (2015) updated to 2017

ft

3090 3040 3050 3060 3070 3080

10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca

SLIDE 20

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

WORLD DATA FOR 0 0 DECAY, 2017

+ +

Z of daughter

5 30 25 20 15 10 35

t

3070 3080 3060 3030 3140 3090 3100 3100 3110 3120 3130 3080 3090

ft (1+ )

R

’

t = = ft (1 +  )[1 - ( -  )]

R C NS

K

2

2G (1 +  )

V R

,

8 cases with ft-values measured to ; 6 more cases <0.05% precision with . 0.05-0.3% precision ~220 individual measurements with compatible precision

Hardy & Towner PRC 91, 025501 (2015) updated to 2017

ft

3090 3040 3050 3060 3070 3080

10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca

Critical test passed: values consistent

t

SLIDE 21

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

+ +

CALCULATED CORRECTIONS TO 0 0 DECAYS

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

SLIDE 22

WORLD DATA FOR 0 0 DECAY, 2008 ISOSPIN SYMMETRY BREAKING CORRECTIONS

Full-parentage Saxon-Woods wave functions for parent and daughter. Matched to known binding energies and charge radii as obtained from electron scattering.

 = +

C

C1 C2

Mismatch in radial wave function between 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 measured IMME coefficients. Results also adjusted to measured

+

non-analog 0 state energies.

SLIDE 23

WORLD DATA FOR 0 0 DECAY, 2008 ISOSPIN SYMMETRY BREAKING CORRECTIONS

Full-parentage Saxon-Woods wave functions for parent and daughter. Matched to known binding energies and charge radii as obtained from electron scattering.

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 C2 C1

 = +

C

C1 C2

Mismatch in radial wave function between 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 measured IMME coefficients. Results also adjusted to measured

+

non-analog 0 state energies.

SLIDE 24

WORLD DATA FOR 0 0 DECAY, 2008 TESTS OF STRUCTURE-DEPENDENT CORRECTION TERMS

5 10 15 20 25 30 35

Z of daughter

+2.5 +2.0 +1.5 +1.0 +0.5 +0.0

Correction terms (%)

R R

’

C NS

t =

= ft (1 +  )[1 - ( -  )]

R C NS

K

2

2G (1 +  )

V R

,

SLIDE 25

WORLD DATA FOR 0 0 DECAY, 2008 TESTS OF STRUCTURE-DEPENDENT CORRECTION TERMS

5 10 15 20 25 30 35

Z of daughter

+2.5 +2.0 +1.5 +1.0 +0.5 +0.0

Correction terms (%)

R R

’

C NS

t =

= ft (1 +  )[1 - ( -  )]

R C NS

K

2

2G (1 +  )

V R

,

Only  - can

C NS

be tested experimentally!

SLIDE 26

WORLD DATA FOR 0 0 DECAY, 2008 TESTS OF STRUCTURE-DEPENDENT CORRECTION TERMS

5 10 15 20 25 30 35

Z of daughter

+2.5 +2.0 +1.5 +1.0 +0.5 +0.0

Correction terms (%)

R R

’

C NS

t =

= ft (1 +  )[1 - ( -  )]

R C NS

K

2

2G (1 +  )

V R

,

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.

+ +

Only  - can

C NS

be tested experimentally!

SLIDE 27

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 

A. Agreement with CVC:

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

SLIDE 28

TESTS OF ( - ) CALCULATIONS

C NS

10 40 30 20 Z of daughter

t

3050 3090 3080 3070 3060 10 40 30 20 Z of daughter

t

3050 3090 3080 3070 3060

Shell-model, Saxon-Woods radial functions Shell-model, Hartree-Fock radial functions

Towner & Hardy PRC 77, 025501 (2008) Towner & Hardy PRC 79, 055502 (2009)



2 



2 

A. Agreement with CVC:

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

SLIDE 29

TESTS OF ( - ) CALCULATIONS

C NS

10 40 30 20 Z of daughter

t

3050 3090 3080 3070 3060 10 40 30 20 Z of daughter

t

3050 3090 3080 3070 3060 10 40 30 20 Z of daughter

t

3050 3090 3080 3070 3060

Shell-model, Saxon-Woods radial functions Shell-model, Hartree-Fock radial functions Nuclear density functional theory

Towner & Hardy PRC 77, 025501 (2008) Towner & Hardy PRC 79, 055502 (2009) Satula et al. PRC 86, 054316 (2012)



2 



2 



2 

A. Agreement with CVC:

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

SLIDE 30

TESTS OF ( - ) CALCULATIONS

C NS

10 40 30 20 Z of daughter

t

3050 3090 3080 3070 3060 10 40 30 20 Z of daughter

t

3050 3090 3080 3070 3060 10 40 30 20 Z of daughter

t

3050 3090 3080 3070 3060

Shell-model, Saxon-Woods radial functions Shell-model, Hartree-Fock radial functions Nuclear density functional theory

Towner & Hardy PRC 77, 025501 (2008) Towner & Hardy PRC 79, 055502 (2009) Satula et al. PRC 86, 054316 (2012)



2 



2 



2 

A. Agreement with CVC:

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

SLIDE 31

B. Measurements of mirror superallowed transitions:

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

TESTS OF ( - ) CALCULATIONS

C NS

SLIDE 32

B. Measurements of mirror superallowed transitions:

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

, , TESTS OF ( - ) CALCULATIONS

C NS

SLIDE 33

B. Measurements of mirror superallowed transitions:

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

, , TESTS OF ( - ) CALCULATIONS

C NS

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 34

B. Measurements of mirror superallowed transitions:

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

, , TESTS OF ( - ) CALCULATIONS

C NS

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 35

B. Measurements of mirror superallowed transitions:

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

SW HF

TESTS OF ( - ) CALCULATIONS

C NS

SLIDE 36

B. Measurements of mirror superallowed transitions:

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

SW HF

ft 38Ca ft 38mK

H.I. Park et al. PRL 112, 102502 (2014) PRC 92, 015502 (2015)

TESTS OF ( - ) CALCULATIONS

C NS

SLIDE 37

B. Measurements of mirror superallowed transitions:

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

SW HF

Preliminary

TESTS OF ( - ) CALCULATIONS

C NS

SLIDE 38

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 39

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 34Cl 38mK 46V 54Co 74Rb 22Mg 14O 26mAl 42Sc 50Mn 34Ar 62Ga 38Ca

SLIDE 40

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 41

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

10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca

RESULTS FROM 0 0 DECAY

+ +

SLIDE 42

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

10C 14O 26mAl 34Cl 38mK 42Sc 46V 50Mn 54Co 74Rb 22Mg 34Ar 62Ga 38Ca

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

ft 38Ca ft 38mK

SLIDE 43

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 44

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)

S V

/

Z of daughter

20 10 30 40

Ft (s)

3070 3080 3090 3060

C /C = + 0.002

S V

RESULTS FROM 0 0 DECAY

+ +

SLIDE 45

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)

S V

/

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

RESULTS FROM 0 0 DECAY

+ +

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) Test for Scalar current Validate correction terms

WITH CVC VERIFIED

2

Obtain precise value of G (1 +  )

V R

Determine Vud

2 2 2

V = G /G = 0.94907 + 0.00041

ud V  2

G constant to + 0.011%

V



limit, C C = 0.0012 (10)

S V

/

RESULTS FROM 0 0 DECAY

+ +

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 Cabibbo-Kobayashi-Maskawa matrix

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) Test for Scalar current Validate correction terms

WITH CVC VERIFIED

2

Obtain precise value of G (1 +  )

V R

Determine Vud

2 2 2

V = G /G = 0.94907 + 0.00041

ud V  2

G constant to + 0.011%

V



limit, C C = 0.0012 (10)

S V

/

RESULTS FROM 0 0 DECAY

+ +

1990 2000 2010 0.975 0.974 0.973

Vud

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 Cabibbo-Kobayashi-Maskawa matrix

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) 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 = 0.99962 + 0.00049

ud us ub

2 2 2



limit, C C = 0.0012 (10)

S V

/

2 2

V = G /G = 0.94907 + 0.00041

ud V  2

RESULTS FROM 0 0 DECAY

+ +

Cabibbo-Kobayashi-Maskawa matrix

SLIDE 49

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 50

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 51

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 52

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 53

NEUTRON DECAY DATA 2017

Mean life:

 = 879.4 + 0.9 s

880 900 1990 1995 2000 2005

Date of measurement Mean life

2010

/N = 4.2

2

2015

SLIDE 54

NEUTRON DECAY DATA 2017

Mean life:

 = 879.4 + 0.9 s

880 900 1990 1995 2000 2005

Date of measurement Mean life

2010

/N = 4.2

2

2015 Beam Bottle

SLIDE 55

NEUTRON DECAY DATA 2017

Mean life:

 = 879.4 + 0.9 s

880 900 1990 1995 2000 2005

Date of measurement Mean life

2010

/N = 4.2

2

2015 Beam: 888.1 + 2.0 s Bottle: 878.9 + 0.6 s

Beam

Bottle

SLIDE 56

NEUTRON DECAY DATA 2017

Mean life:

 = 879.4 + 0.9 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:

 = -1.2725 + 0.0020 /N = 4.1

2

2010
/N = 4.2

2

2010 2015 2015 Beam: 888.1 + 2.0 s Bottle: 878.9 + 0.6 s

Beam

Bottle

SLIDE 57

NEUTRON DECAY DATA 2017

Mean life:

 = 879.4 + 0.9 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:

 = -1.2725 + 0.0020 /N = 4.1

2

2010
/N = 4.2

2

2010

V = 0.9762 + 0.0014

ud

2015

2015 Beam: 888.1 + 2.0 s Bottle: 878.9 + 0.6 s

Beam

Bottle

SLIDE 58

NEUTRON DECAY DATA 2017

Mean life:

 = 879.4 + 0.9 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:

 = -1.2725 + 0.0020 /N = 4.1

2

2010
/N = 4.2

2

2010

V = 0.9762 + 0.0014

ud

2015

2015 Beam: 888.1 + 2.0 s Bottle: 878.9 + 0.6 s

Beam

Bottle

0.9700 < V < 0.9770

ud -

Beam-bottle span

SLIDE 59

NEUTRON DECAY DATA 2017

Mean life:

 = 879.4 + 0.9 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:

 = -1.2725 + 0.0020 /N = 4.1

2

2010
/N = 4.2

2

2010

V = 0.9762 + 0.0014

ud

V

= 0.9742 + 0.0002

ud

nuclear 0 0

+ + 2015 2015 Beam: 888.1 + 2.0 s Bottle: 878.9 + 0.6 s

Beam

Bottle

0.9700 < V < 0.9770

ud -

Beam-bottle span

SLIDE 60

NUCLEAR T=1/2 MIRROR DECAY DATA 2009

15 10 20 Z of daughter 6000 7000 6500

(1

2

< > )



+ t

19Ne 37K 35Ar 29P 21Na

Naviliat-Cuncic & Severijns PRL 102, 142302 (2009) + B. Fenker, Phd Thesis TAMU

t = ft (1 + )[1 - (

)] =

  

R C NS

K

2

G (1 + )

V

R , (1

 2

 < > )



+

SLIDE 61

NUCLEAR T=1/2 MIRROR DECAY DATA 2009

15 10 20 Z of daughter 6000 7000 6500

(1

2

< > )



+ t

19Ne 37K 35Ar 29P 21Na

Naviliat-Cuncic & Severijns PRL 102, 142302 (2009) + B. Fenker, Phd Thesis TAMU

t = ft (1 + )[1 - (

)] =

  

R C NS

K

2

G (1 + )

V

R , (1

 2

 < > )



+

V = 0.9730 + 0.0014

ud

SLIDE 62

NUCLEAR T=1/2 MIRROR DECAY DATA 2009

15 10 20 Z of daughter 6000 7000 6500

(1

2

< > )



+ t

19Ne 37K 35Ar 29P 21Na

Naviliat-Cuncic & Severijns PRL 102, 142302 (2009) + B. Fenker, Phd Thesis TAMU

t = ft (1 + )[1 - (

)] =

  

R C NS

K

2

G (1 + )

V

R , (1

 2

 < > )



+

V = 0.9730 + 0.0014

ud

V

= 0.9742 + 0.0002

ud

nuclear 0 0

+ +

SLIDE 63

PION BETA DECAY

Decay process:

e

e

+ + 0 ,1 0 ,1

SLIDE 64

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 65

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 66

.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

t = = ft (1 +  )[1 - ( -  )]

R C NS

K

2

2G (1 +  )

V R

,

SLIDE 67

V + V + V = 0.99962 0.00049

ud us ub 2 2 2

+

muon decay

nuclear decays

ud

V

0.94906 + 0.00041

2

0.05054 + 0.00027

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 68

V + V + V = 0.99962 0.00049

ud us ub 2 2 2

+

muon decay

nuclear decays

ud

V

0.94906 + 0.00041

2

0.05054 + 0.00027

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 4 .

u d 2

SLIDE 69

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, but are less precise by a factor

f 7 or more.

+ +

SLIDE 70

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, but are less precise by a factor

f 7 or more.

+ +

5. Isospin symmetry-breaking correction,  , has been tested

C

by requiring consistency among the 14 known transitions (CVC), and agreement with mirror-transition pairs. It contributes much less to V uncertainty than does .

ud

R

4. The largest contribution to V uncertainty is from the

ud

inner radiative correction, . Very little reduction in V

ud

R uncertainty is possible without improved calculation of . R

6. With significant improvement in  uncertainty alone, the

R

V uncertainty could be reduced by factor of 2!

ud

SLIDE 71

Supplementary slides

SLIDE 72

FINAL REMARK ON V

us

Kaon decay yields two independent determinations of V :

us

1) Semi-leptonic K  l  decay (K ) yields |V |.

us

l l3

2) Pure leptonic decays K   and    together yield |V | / |V |.

us ud

+ +  + +

Both require lattice calculations of form factors to obtain their result. Until March 2014 these gave highly consistent results for |V |.

us

SLIDE 73

FINAL REMARK ON V

us

Kaon decay yields two independent determinations of V :

us

1) Semi-leptonic K  l  decay (K ) yields |V |.

us

l l3

2) Pure leptonic decays K   and    together yield |V | / |V |.

us ud

+ +  + +

Both require lattice calculations of form factors to obtain their result. Until March 2014 these gave highly consistent results for |V |.

us

BUT, Bazavov et al. [PRL 112, 112001 (2014)] produced a new lattice calculation of the form factor used for K decays.

l3

Their new result for |V | is inconsistent with the |V |/|V | result

us us ud

Stay tuned ... and, when combined with the superallowed result for |V |, leads to

ud

a unitarity sum over two standard deviations below 1.