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

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

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%

CONTRIBUTION OF CORRECTION TERMS 20  NS Correction terms (%) +0.0 +0.5 +1.0 +1.5 +2.0 -0.5 +2.5 Z of daughter 35 30 25 15 t = 10 5 , R V 2G (1 +  ) 2 K NS C R ft (1 +  ) [ 1 - (  -  ) ] =  C

CONTRIBUTION OF CORRECTION TERMS 25  NS ’  R Correction terms (%) +0.0 +0.5 +1.0 +1.5 +2.0 -0.5 +2.5 Z of daughter 35 30 20 t = 15 10 5 , R V 2G (1 +  ) 2 K NS C R ft (1 +  ) [ 1 - (  -  ) ] =  C

CONTRIBUTION OF CORRECTION TERMS 30  NS ’  R  R Correction terms (%) +0.0 +0.5 +1.0 +1.5 +2.0 -0.5 +2.5 Z of daughter 35 25 t = 2 = ft (1 +  ) [ 1 - (  -  ) ] R C NS K 2G (1 +  ) 20 V R , 5 10 15  C

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 ; 6 more cases PRC 91, 025501 (2015) Hardy & Towner with compatible precision ~220 individual measurements 0.05-0.3% precision . with <0.05% precision to ft 8 cases with ft -values measured , R V 2G (1 +  ) 2 K NS C R updated to 2017 3090 = 50 Mn values consistent Critical test passed: 38 Ca 62 Ga 34 Ar 22 Mg 74 Rb 54 Co 46 V 3040 42 Sc 38m K 34 Cl 26m Al 14 O 10 C 3080 3070 3060 3050 ft (1 +  ) [ 1 - (  -  ) ] t = 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 ’ 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 ) +  +  + ... ]