J.C. Hardy Cyclotron Institute Texas A&M University with I.S. Towner The current evaluation of |V | and the top-row test of CKM matrix unitarity ud
CURRENT STATUS OF V ud .9700 .9800 .9750 nuclear 0 0 + + neutron nuclear mirrors pion V ud V = 0.97420 + 0.00021 ud
+ < > = Fermi matrix element V G = vector coupling constant 1/2 BR t ) , t = partial half-life: f ( Q EC ) f = statistical rate function: f (Z, V + G < > 2 2 K ft = BASIC WEAK-DECAY EQUATION BR Q EC t 1/2 0 ,1 + 0 ,1 + SUPERALLOWED 0 0 BETA DECAY EXPERIMENT
+ V < > = Fermi matrix element EXPERIMENT INCLUDING RADIATIVE AND ISOSPIN-SYMMETRY-BREAKING CORRECTIONS t = ft (1 + ) [ 1 - ( - ) ] = 1/2 R C NS K 2 2G (1 + ) V R G = vector coupling constant BR + K SUPERALLOWED 0 0 BETA DECAY + 0 ,1 + 0 ,1 t 1/2 Q EC BR BASIC WEAK-DECAY EQUATION ft = 2 t 2 G < > V f = statistical rate function: f (Z, ) Q EC t = partial half-life: f ( , ) ,
+ NS INCLUDING RADIATIVE AND ISOSPIN-SYMMETRY-BREAKING CORRECTIONS t = ft (1 + ) [ 1 - ( - ) ] = R C K 2 2G (1 + ) V R , ~1.5% f (Z, Q ) EC 0.3-1.5% f (nuclear structure) ~2.4% EXPERIMENT < > = Fermi matrix element + 2 SUPERALLOWED 0 0 BETA DECAY + 0 ,1 + 0 ,1 t 1/2 Q EC BR BASIC WEAK-DECAY EQUATION ft = K 2 G < > V V f = statistical rate function: f (Z, ) Q EC t = partial half-life: f ( , ) t BR 1/2 G = vector coupling constant f (interaction)
+ 2 t = ft (1 + ) [ 1 - ( - ) ] = R C NS K 2G (1 + EXPERIMENT ) V R , ~1.5% f (Z, Q ) EC 0.3-1.5% f (nuclear structure) ~2.4% f (interaction) THEORETICAL UNCERTAINTIES INCLUDING RADIATIVE AND ISOSPIN-SYMMETRY-BREAKING CORRECTIONS + 2 SUPERALLOWED 0 0 BETA DECAY + 0 ,1 + 0 ,1 t 1/2 Q EC BR BASIC WEAK-DECAY EQUATION ft = K 2 G < > < > = Fermi matrix element V f = statistical rate function: f (Z, ) Q EC t = partial half-life: f ( , ) t BR 1/2 G = vector coupling constant V 0.05 – 0.10%
FROM A SINGLE TRANSITION R R V determine G (1 + ) 2 Experimentally , V t = ft (1 + ) [ 1 - ( - ) ] = 2G (1 + ) 2 K NS C R THE PATH TO V ud
FROM A SINGLE TRANSITION determine G (1 + ) terms Validate the correction a Scalar current Test for presence of t values constant the Vector current (CVC) Test Conservation of FROM MANY TRANSITIONS R V 2 t = ft (1 + ) [ 1 - ( - ) ] = Experimentally , R V 2G (1 + ) 2 K NS C R THE PATH TO V ud
FROM A SINGLE TRANSITION = WITH CVC VERIFIED 2 Obtain precise value of G (1 + ) V R Determine V ud 2 2 2 V = G /G ud V 2 s 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 b d t = ft (1 + ) [ 1 - ( - ) ] = R R C NS K 2 2G (1 + ) V R , Experimentally 2 determine G (1 + ) V V V V b' ud us ub V V V cd cs cb V V V td ts tb d' s' THE PATH TO V ud
FROM A SINGLE TRANSITION 2 2 2 2 Determine V ud 2 2 ub ud us ud V + V + V = 1 Test CKM unitarity R V V = G /G V 2 terms Maskawa (CKM) matrix Cabibbo Kobayashi eigenstates mass eigenstates weak Validate the correction a Scalar current Test for presence of t values constant the Vector current (CVC) Test Conservation of FROM MANY TRANSITIONS 2 Obtain precise value of G (1 + ) WITH CVC VERIFIED t = ft (1 + ) [ 1 - ( - ) ] = R R V determine G (1 + ) 2 Experimentally , V ud 2G (1 + ) 2 K NS C R V V V us = tb b s d b' s' d' ts ub td V V V cb cs cd V V V THE PATH TO V ud
FROM A SINGLE TRANSITION 2 V = G /G 2 2 2 Determine V ud 2 2 V ub us ud V + V + V = 1 Test CKM unitarity R ud Obtain precise value of G (1 + ) weak THE PATH TO V ud Maskawa (CKM) matrix Cabibbo Kobayashi eigenstates mass eigenstates terms t = ft (1 + ) [ 1 - ( - ) ] = Validate the correction a Scalar current Test for presence of t values constant the Vector current (CVC) Test Conservation of FROM MANY TRANSITIONS V 2 2 R R V determine G (1 + ) 2 Experimentally , V us 2G (1 + ) 2 K NS C R WITH CVC VERIFIED V V V ud ub tb = b s d b' s' d' ts td V V V cb cs cd V V V R O I R P D F E I I F E S L I B T I A S S S O S N P O Y L I T N I D O N O C
74 Rb 8 cases with ft -values measured C NS K 2 2G (1 + ) V R , to ft (1 + ) [ 1 - ( - ) ] ; 6 more cases <0.05% precision with . 0.05-0.3% precision ~220 individual measurements with compatible precision Hardy & Towner PRC 91, 025501 (2015) R = NUMBER OF PROTONS, Z 10 20 30 40 10 NUMBER OF NEUTRONS, N 20 30 40 50 60 0 ,1 t = 0 ,1 + + BR t 1/2 Q EC 10 C WORLD DATA FOR 0 0 DECAY, 2017 + + updated to 2017
74 Rb with compatible precision 3090 ft updated to 2017 PRC 91, 025501 (2015) Hardy & Towner ~220 individual measurements 3050 0.05-0.3% precision . with <0.05% precision ; 6 more cases to 3040 3060 , 46 V 62 Ga 34 Ar 22 Mg 74 Rb 54 Co 50 Mn 42 Sc 3070 38m K 34 Cl 26m Al 14 O 10 C 3080 8 cases with ft -values measured R NUMBER OF PROTONS, Z 40 + 0 ,1 0 ,1 10 60 50 30 BR 20 NUMBER OF NEUTRONS, N 10 40 30 20 + t 1/2 V ft (1 + ) [ 1 - ( - ) ] 2G (1 + ) 2 K NS C R = Q EC t = 3030 + + WORLD DATA FOR 0 0 DECAY, 2017 10 C 38 Ca
74 Rb with PRC 91, 025501 (2015) Hardy & Towner with compatible precision ~220 individual measurements 0.05-0.3% precision . <0.05% precision ft ; 6 more cases to 8 cases with ft -values measured , R V 2G (1 + ) updated to 2017 3090 K 42 Sc 62 Ga 34 Ar 22 Mg 74 Rb 54 Co 50 Mn 46 V 38m K 3040 34 Cl 26m Al 14 O 10 C 3080 3070 3060 3050 2 NS NUMBER OF PROTONS, Z 50 BR + + 0 ,1 0 ,1 10 60 40 Q EC 30 20 NUMBER OF NEUTRONS, N 10 40 30 20 t 1/2 10 C C 3090 R [ 1 - ( - ) ] ft (1 + ) = t = ’ R ft (1+ ) 3080 WORLD DATA FOR 0 0 DECAY, 2017 3130 3120 3110 3100 3140 3030 + + 38 Ca
74 Rb , with compatible precision ~220 individual measurements 0.05-0.3% precision . with <0.05% precision ; 6 more cases to 8 cases with ft -values measured R Hardy & Towner V 2G (1 + ) 2 K NS C R ft (1 + ) [ 1 - ( - ) ] = PRC 91, 025501 (2015) ’ 34 Cl 62 Ga 34 Ar 22 Mg 74 Rb 54 Co 50 Mn 46 V 42 Sc 38m K 26m Al updated to 2017 14 O 10 C 3080 3070 3060 3050 3040 3090 ft t = R NUMBER OF PROTONS, Z 10 WORLD DATA FOR 0 0 DECAY, 2017 10 C Q EC t 1/2 BR + + 0 ,1 0 ,1 60 + 50 40 30 20 NUMBER OF NEUTRONS, N 10 40 30 20 + Z of daughter ft (1+ ) 3030 3090 3080 3130 3120 3110 3100 3100 3090 3140 3060 5 3080 3070 t 35 10 15 20 25 30 38 Ca
74 Rb <0.05% precision updated to 2017 PRC 91, 025501 (2015) Hardy & Towner with compatible precision ~220 individual measurements 0.05-0.3% precision . with ; 6 more cases 3090 to 8 cases with ft -values measured , R V 2G (1 + ) 2 K NS C ft 3040 ft (1 + ) [ 1 - ( - ) ] 54 Co /n = 0.6 2 values consistent Critical test passed: 38 Ca 62 Ga 34 Ar 22 Mg 74 Rb 50 Mn 3050 46 V 42 Sc 38m K 34 Cl 26m Al 14 O 10 C 3080 3070 3060 R = NUMBER OF PROTONS, Z 0 ,1 + WORLD DATA FOR 0 0 DECAY, 2017 10 C Q EC t 1/2 BR + + 0 ,1 10 Z of daughter 60 50 40 30 20 NUMBER OF NEUTRONS, N 10 40 30 20 + 5 t = 3090 ’ R ft (1+ ) 3090 3080 3130 3120 3110 3100 3100 3140 30 3030 3060 3080 3070 t 35 10 15 20 25 t
1. Radiative corrections 2 R C NS K 2 2G (1 + ) V R , R m 3 2 2 N N W e + One-photon brem. + low-energy W -box High-energy W -box + ZW -box - Z NS R Born A p p + ... ] photonic contributions = [4 ln(m /m ) + ln(m /m ) + 2C Order- axial-vector 2. Isospin symmetry-breaking corrections ) [ 1 - ( structure ft (1 + ) ] = t = CALCULATED CORRECTIONS TO 0 0 DECAYS + + on nuclear Dependent } (members of the same isospin triplet). parent and daughter analog states Charge-dependent mismatch between C universal , = [g(E ) + + + ... ]
WORLD DATA FOR 0 0 DECAY, 2008 Core states included based on + Results also adjusted to measured ured IMME coefficients. single-particle energies and to meas- Charge dependence tuned to known established 2-body matrix elements. Shell-model calculation with well- between parent and daughter. Difference in configuration mixing measured spectroscopic factors. tween parent and daughter. ISOSPIN SYMMETRY BREAKING CORRECTIONS Mismatch in radial wave function be- C2 C1 C + = electron scattering. and charge radii as obtained from Matched to known binding energies functions for parent and daughter. Full-parentage Saxon-Woods wave non-analog 0 state energies.
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