Tests of ab-initio nuclear theory via the isobaric multiplet
mass equation in T = 1 superallowed beta decay systems
Matthew S. Martin1, K.G. Leach1, J.D. Holt2, S.R. Stroberg3
1Department of Physics, Colorado School of Mines 2Theory Division, TRIUMF, Canada 3Department of Physics, University of Washington
The CKM Matrix
The mass eigenstates and weak-interaction eigenstates of the quarks are not equal
In the Standard Model, the Cabbibo-Kobayashi-Maskawa (CKM) matrix provides a unitary transformation between these eigenstates
d0 s0 b0 = Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb d s b
If CKM unitarity does not hold, it implies that there is physics outside the Standard Model
Experimental Allowed f t Value
0 10 20 30 40 50 60 70 80 Z of Daughter 2000 2500 3000 3500 4000 4500 5000 ft V alu e ( s )ft Values for Allowed β Decay Transitions
Allowed Superallowed
Experimental Superallowed f t Value
0 10 20 30 40 50 60 70 80 Z of Daughter 3030 3040 3050 3060 3070 3080 3090 ft V alu e ( s )Experimental Superallowed F t Value
F t = f t(1 − δR)(1 − δC) =
K 2GV2(1 + ∆R)
F t = corrected f t value
δR = transition-dependent radiative correction
δC = isospin symmetry breaking correction
K = constants
GV2 = vector coupling constant
Experimental Superallowed F t Value
0 10 20 30 40 50 60 70 80 Z of Daughter 3055 3060 3065 3070 3075 3080 3085 3090 F t V alu e ( s )Isobaric Analogue States
Superallowed β decay chain is a T = 1 isobaric analogue triplet
E
Tz=1 Tz=0 Tz=-1
T=1
Isobaric Multiplet Mass Equation
M = Nmn+ Zmp− Ebind − A
Testing the validity of theoretical methods for use in calculating isospin symmetry breaking corrections for superallowed decay Using the Isobaric Multiplet Mass Equation
M(Tz) = a + bTz+ cTz2
IMME derived from first order perturbation of Coulomb potential12
b and c coefficients very sensitive to isospin symmetry breaking
1J.M. Dong et al., Physical Review C 99, 014319 (2019) 2
M(T
z) = a + b T
z+ cT
z2Seem to converge well Similar for all A ∈ {14 : 74}
2 4 6 8 10 12 14 emax ( ω) 4000 3950 3900 3850 3800 3750 IM M E b C oe ffi ci en t ( ke V )
VS-IMSRG
IMME B Coefficients for A = 22
EM1.8/2.0 N2LOsat Experiment USD Phenom.
M(T
z) = a + b T
z+ cT
z2General trend of uniform sphere Slight peak at A = 14, 38
10 20 30 40 50 60 70 80 A 14000 12000 10000 8000 6000 4000 2000 b C oe ffi ci en t ( ke V )
VS-IMSRG
IMME b Coefficients Uniform Sphere EM1.8/2.0 N2LOsat EM1.8/2.0 0ω-shell N2LOsat 0ω-shell ExperimentM(T
z) = a + b T
z+ cT
z2Same peaks can be seen sd -shell VS reduces error
10 20 30 40 50 60 70 80 A 1400 1500 1600 1700 1800 1900 2000 2100 2200 b C oe ffi ci en t U ni fo rm S ph er e (k eV )
VS-IMSRG
Shifted IMME b Coefficients
EM1.8/2.0 N2LOsat EM1.8/2.0 0ω-shell
N2LOsat 0ω-shell
VS-IMSRG
0¯hω-shell Valence Space sd-shell Valence Space
ν π 38Ca cor e sd-shell high er ν π 38Ca cor e sd-shell high er
M(T
z) = a + bT
z+ c T
z2Converging? Similar for all A ∈ {14 : 70}
2 4 6 8 10 12 14 emax (ω) 300 350 400 450 500 550
IMME C Coefficient (keV)
VS-IMSRG
IMME c Coefficients for A = 22
EM1.8/2.0 N2LOsat Experiment USD Phenom.
M(T
z) = a + bT
z+ c T
z2A = 14, 38 peaks larger Fixed by sd -shell VS
10 20 30 40 50 60 70 80 A 500 0 500 1000 1500 2000 2500 3000 3500 c C oe ffi ci en t ( ke V )
VS-IMSRG
IMME c Coefficients Uniform Sphere EM1.8/2.0 N2LOsat EM1.8/2.0 0ω-shell N2LOsat 0ω-shell ExperimentVS-IMSRG
0¯hω-shell Valence Space sd-shell Valence Space
ν π 38Ca cor e sd-shell high er ν π 38Ca cor e sd-shell high er
Summary
IMME coefficients converge well with emax
b coefficients converging
c coefficients not changing much wtih emax Need to check emax = 14 to see further
Both coefficients follow trend predicted by uniform charged sphere
IMME seems to remove systematic theoretical and many-body errors
Significant error/deviation at shell closures
Fixed by forcing valence space to be same in IAT Currently running the rest of these cases
