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 = 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 Experimentally a Scalar current Test for presence of t values constant R V determine G (1 + ) 2 , t = ft (1 + ) [ 1 - ( - ) ] = R V 2G (1 + ) 2 K NS C R THE PATH TO V ud
FROM A SINGLE TRANSITION 40 Validate the correction terms THE PATH TO V ud 74 Rb NUMBER OF PROTONS, Z 20 30 10 Test for presence of NUMBER OF NEUTRONS, N 20 30 40 50 60 10 a Scalar current t values constant t = ft (1 + ) [ 1 - ( - ) ] = R R C NS K 2 2G (1 + ) V , the Vector current (CVC) Experimentally 2 determine G (1 + ) V R FROM MANY TRANSITIONS Test Conservation of 10 C
FROM A SINGLE TRANSITION 20 NUMBER OF NEUTRONS, N 20 30 40 50 60 10 10 C 5 10 15 25 40 30 35 Z of daughter +2.5 -0.5 +2.0 +1.5 +1.0 +0.5 +0.0 Correction terms (%) R 10 30 t = ft (1 + ) [ 1 - ( - ) ] = determine G (1 + ) R C NS K 2 2G (1 + ) V R , Experimentally 2 V 20 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 V ud 74 Rb NUMBER OF PROTONS, Z ’
FROM A SINGLE TRANSITION 25 20 30 40 50 60 10 10 C 5 10 15 20 30 10 35 Z of daughter +2.5 -0.5 +2.0 +1.5 +1.0 +0.5 +0.0 Correction terms (%) R ’ NUMBER OF NEUTRONS, N 40 t = ft (1 + ) [ 1 - ( - ) ] = V R C NS K 2 2G (1 + ) V R , Experimentally 2 determine G (1 + ) R 30 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 V ud 74 Rb NUMBER OF PROTONS, Z 20 C
FROM A SINGLE TRANSITION 30 20 30 40 50 60 10 10 C 5 10 15 20 25 35 10 Z of daughter +2.5 -0.5 +2.0 +1.5 +1.0 +0.5 +0.0 Correction terms (%) R ’ NS NUMBER OF NEUTRONS, N 40 t = ft (1 + ) [ 1 - ( - ) ] = V R C NS K 2 2G (1 + ) V R , Experimentally 2 determine G (1 + ) R 30 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 V ud 74 Rb NUMBER OF PROTONS, Z 20 C
FROM A SINGLE TRANSITION 35 30 40 50 60 10 10 C 5 10 15 20 25 30 Z of daughter NUMBER OF NEUTRONS, N +2.5 -0.5 +2.0 +1.5 +1.0 +0.5 +0.0 Correction terms (%) R R ’ NS 20 10 t = ft (1 + ) [ 1 - ( - ) ] = V R C NS K 2 2G (1 + ) V R , Experimentally 2 determine G (1 + ) R 40 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 V ud 74 Rb NUMBER OF PROTONS, Z 20 30 C
FROM A SINGLE TRANSITION THE PATH TO V ud R V 2G (1 + ) 2 K NS C R t = ft (1 + ) [ 1 - ( - ) ] = terms Experimentally Validate the correction t values constant the Vector current (CVC) Test Conservation of FROM MANY TRANSITIONS R V determine G (1 + ) 2 ,
FROM A SINGLE TRANSITION terms R V 2G (1 + ) 2 K NS C R t = ft (1 + ) [ 1 - ( - ) ] = THE PATH TO V ud Validate the correction Experimentally a Scalar current Test for presence of t values constant the Vector current (CVC) Test Conservation of FROM MANY TRANSITIONS R V determine G (1 + ) 2 ,
FROM A SINGLE TRANSITION weak 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 eigenstates 2 mass eigenstates Cabibbo Kobayashi Maskawa (CKM) matrix THE PATH TO V ud t = ft (1 + ) [ 1 - ( - ) ] = R C NS K 2 2G (1 + ) V R 2 2 Experimentally V V V 2 determine G (1 + ) V R V V V ud us ub V V V cd cs cb td Determine V ud ts tb d' s' b' d s b = WITH CVC VERIFIED 2 Obtain precise value of G (1 + ) V R ,
FROM A SINGLE TRANSITION Test for presence of t values constant the Vector current (CVC) Test Conservation of FROM MANY TRANSITIONS 2 V Validate the correction ud V = G /G 2 2 2 Determine V ud a Scalar current terms 2 C R V 2G (1 + ) 2 K NS R weak t = ft (1 + ) [ 1 - ( - ) ] = THE PATH TO V ud Maskawa (CKM) matrix Cabibbo Kobayashi eigenstates mass eigenstates 2 2 Experimentally ub V V V cb cs cd V V V us ts ud V V V R V determine G (1 + ) 2 td tb ub Obtain precise value of G (1 + ) us ud V + V + V = 1 Test CKM unitarity R V 2 d' WITH CVC VERIFIED = b s d b' s' ,
FROM A SINGLE TRANSITION Test for presence of t values constant the Vector current (CVC) Test Conservation of FROM MANY TRANSITIONS 2 V Validate the correction ud V = G /G 2 2 2 Determine V ud a Scalar current terms 2 C R V 2G (1 + ) 2 K NS R weak t = ft (1 + ) [ 1 - ( - ) ] = THE PATH TO V ud Maskawa (CKM) matrix Cabibbo Kobayashi eigenstates mass Experimentally 2 eigenstates 2 V V V V V V cb cs cd ub ub ts us ud V V V R V determine G (1 + ) 2 td , tb Test CKM unitarity = d' WITH CVC VERIFIED Obtain precise value of G (1 + ) V R 2 V + V + V = 1 ud us b s d s' b' 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
42 Ti EC t : PRC 84 , 065502 (2011) 38 Ca 055501 (2005) BR: PRC 72 , 14 O EC Q : PRL 97 , 232501 (2006) Al m 26 Q : PRL 100 , 132502 (2008) Q : PRC 83 , 055501 (2011) Mn, Co 54 50 BR: to be published (2019) 1/2 t : PRC 82 , 035502 (2010) 26 Si Q EC t 1/2 BR + 1/2 EC 0 ,1 Numerous reviews of CVC and CKM-unitarity tests 1/2 t : PRC 97 , 30 S EC Q : PRC 95 , 025501 (2017) 42 Sc + + Parameterization of f function: PRC 91 , 015501 (2015) C Comparative tests of calculations: PRC 82 , 065501 (2010) Measurement & interpretation of 0 0 : J. Phys G 41, 114004 (2014) BR: PRL 112 , 102502 (2014) Recent critical survey: PRC 91 , 025501 (2015) NS C ( - ) calculations: PRC 77 , 025501 (2008) Theory/Reviews EC Q : PRL 103 , 252501 (2009) 1/2 t : PRC 74 , 055502 (2006) 34 Cl PRC 92 . 015502 (2015) + 0 ,1 t : data being analyzed BR: data being analyzed 1/2 t : PRC 82 . 045501 (2010) K m 38 BR: to be published (2019) EC Q : PRC 83 , 055501 (2011) 1/2 t ,: PRC 74 , 055502 (2006) 34 Ar EC EC Q : PRC 83 , 055501 (2011) 1/2 t : PRC 77 , 045501 (2008) 10 C EC Q : PRC 70 , 042501(R) (2004) 1/2 t : BR: PRL 91 , 082501 (2003) 22 Mg SUPERALLOWED-DECAY WORK INVOLVING TAMU GROUP 1/2 Q : PRL 103 , 252501 (2009) 62 Ga 10 PRC 83 , 055501 (2011) 60 50 40 30 20 NUMBER OF NEUTRONS, N 10 40 30 20 NUMBER OF PROTONS, Z PRL 97 , 232501 (2006) t ,BR: PRC 68 , EC Q : PRL 95 , 102501 (2005) 1/2 t : PRC 85 , 035501 (2012) 46 V BR: PRC 67 , 051305R (2003) 1/2 t : PRL 86 , 1454 (2001) 74 Rb 015501 (2003) 1/2 035501 (2018)
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