1. Menu Isospin mixing in nuclei Isospin symmetry breaking Hadrons Nuclei
Witold Nazarewicz (FRIB/MSU)
Top Row CKM Unitarity Workshop
January , Texas A&M University, College Station, Texas
Menu
Isospin symmetry breaking
Hadrons
Nuclei
Isospin mixing in nuclei
Isospin mixing corrections to superallowed beta decays
Conclusions
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

2. radiative corrections experiment
Superallowed 0+ → 0+ Fermi beta decays
radiative corrections
experiment
Isospin breaking correction
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

3. Isospin symmetry
The isospin symmetry, introduced by Heisenberg (1932) and Wigner (1937), is largely preserved by strong interactions; a small violation of isospin on the hadronic level is due to the difference in the masses of the up and down quarks and via quark electromagnetic effects. In atomic nuclei, the main source of isospin breaking is the electromagnetic interaction.
Isospin invariance, charge independence
charge symmetry
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4. Isospin and quarks
PDG, 2018
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5. Isospin Splittings in the Light-Baryon Octet from Lattice QCD and QED
(ab initio calculation of the neutron-proton mass difference)
Science 347, 1452 (2015)
Neutron =  MeV
Proton =  MeV
Electron =  MeV
mp=195 MeV
“The neutron–proton mass difference, one of the most consequential parameters of physics, has now been calculated from fundamental theories. This landmark calculation portends revolutionary progress in nuclear physics.” Wilczek, Nature 520, 303 (2015)
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

6. Isospin breaking is good for you!
Science 347, 1452 (2015)
charge
symmetry
Isospin breaking is good for you!
“The result of the neutron-proton mass splitting as a function of quark-mass difference and electromagnetic coupling. In combination with astrophysical and cosmological arguments, this figure can be used to determine how different values of these parameters would change the content of the universe. This in turn provides an indication of the extent to which these constants of nature must be fine-tuned to yield a universe that resembles ours.”
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

7. Isospin symmetry breaking
and exchanges
All realistic NN interactions contain charge dependent (CD) and charge symmetry breaking (CSB) components
All nuclear models are phenomenological but at different resolution
1S0
Many realistic effective interactions used in CI and DFT studies contain isovector and isotensor CD and CSB components, in addition to Coulomb
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

8. Class-I isoscalar forces are invariant under any rotation in the isospin space
Class-II isotensor forces break the charge independence but preserve the charge symmetry
Class-III isovector forces break both the charge independence and the charge symmetry, and are symmetric under interchange of two interacting particles
Class-IV forces break both symmetries and are antisymmetric under the interchange of two particles
Ann.Rev.Nucl.Part.Sci.56, 253 (2006)
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

9. The main effect of Coulomb force in nuclei is to exert a long-range overall polarization effect on nuclear states whose detailed structure is dictated by the short-ranged strong force. The net effect of such a polarization is a result of two competing trends:
the nuclear force is strongly attractive in the isoscalar neutron-proton channel
the Coulomb force acts against this attraction by making neutron and proton states different.
The situation becomes dramatic in superheavy nuclei and in the neutron star crust, where not only the binding but also spectra are strongly impacted by the Coulomb frustration effects resulting from a self-consistent, non-perturbative feedback between strong and electromagnetic parts of the nuclear Hamiltonian.
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

10. Mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets; recent DFT analysis [PLB 778, 178 (2018)]:
Class-III
ISB forces
Class-II
ISB forces LO
(2 LECC)
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

11. Inclusion of gradient ISB terms
NLO
(2+4 LECC)
P. Bączyk et al., J. Phys. G(L), accepted
The root-mean-square deviations between the DFT and experimental values of MDEs and TDEs (in keV)
See also
PRC 97, (R) (2018)
PRL 120, (2018)
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

12. PRC 96, 024323 (2017) PRC 94, 054311 (2016) Coulomb CSB
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13. What is the origin of ISB effects in nuclei?
Electromagnetic effects
Coulomb term (direct, exchange, spin-orbit, nucleon finite size corrections, vacuum polarization)
Coulomb correlations beyond mean field (including pairing effects)
Continuum effects (Coulomb-related)
Thomas-Ehrman–related correlations
Hadronic ISB effects
Isovector kinetic energy term
Charge symmetry breaking forces
Charge independence breaking forces
PRL 120, (2018)
"It does not seem reasonable to expect that low-energy nuclear experimental data would allow for disentangling these distinct sources of the ISB in finite nuclei." PLB 778, 178 (2018)
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

14. Isospin Mixing in Atomic Nuclei
within the nuclear density functional theory
W. Satuła et al., PRL 103, (2009)
Within the nuclear DFT, the presence of the neutron or proton excess automatically yields isovector mean fields, i.e., different HF potentials for protons and neutrons.
The Giant Monopole Resonance appreciably influences the radial mismatch between the proton and neutron wave functions.
DFT is nonperturbative: it fully takes into account long-range polarization effects associated with the Coulomb force and neutron excess. The nuclear Hamiltonian, including the full Coulomb interaction, is diagonalized in a good-isospin basis obtained by isospin projection from self-consistent HF states.
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

15. We expend the mean-field wave function in a good-isospin basis:
To assess the true isospin mixing, the total Hamiltonian (strong interaction plus the Coulomb interaction with the physical charge) is rediagonalized in the space spanned by the good-isospin wave functions:
n=1 corresponds to the isospin-mixed ground state. In practice,
AR (after rediagonalization):
BR (before rediagonalization):
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

16. Spurious mixing due to the neutron excess
No Coulomb
Full Coulomb
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

17. giant-dipole-resonance decay studies in 80Zr
isospin-forbidden E1 decay in 64Ge AR BR
Stars mark empirical values in 64Ge (only the lower bound is known in this case) and 80Zr. From arXiv:
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

18. The AR isospin-mixing parameter for even-even nuclei
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

19. There is a clear correlation of the BR values of ac with the differences between the proton and neutron rms radii. Indeed, the monopole polarization does impact the proton and neutron radii, and their difference.
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

20. Mean-field configurations in an odd-odd N=Z nucleus
W. Satuła et al., PRC 86, (2012); Phys. Scripta 91, (2016)
J>0
J=0
T=1, J=0+ states in odd-odd nuclei are not representable by a single MF configuration
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

21. No-core-configuration-interaction (NCCI)
Phys. Rev. C94, (2016)
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

22. Superallowed Jp=0+,T=1 → Jp=0+,T=1 Fermi beta decays
W. Satuła et al., PRC 86, (2012); Phys. Scripta 91, (2016)
DFT HT
RMF
PRC 77, (2008)
PRC 79, (2009)
Differences between the ISB corrections to the 12 accurately measured superallowed β transitions (excluding A = 38) calculated with SV and those of HT
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

23. W. Satuła et al., PRC 86, (2012)
For the no-core-configuration-interaction (NCCI) results, see Phys. Rev. C94, (2016)
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

24. PRELIMINARY ISB corrections in 78≤A ≤98 nuclei
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

25. Ground-state beta-transitions in T=1/2 mirror nuclei
The T=1/2 mirror nuclei offer an alternative way to test the CVC hypothesis. These nuclei decay via the mixed Fermi and Gamow-Teller transitions. Hence, the extraction of Vud also requires measuring another observable, such as the β-neutrino correlation coefficient, β asymmetry, or the neutrino-asymmetry parameter.
PRC 78, (2008)
For NCCI results, see PRC 93, (R) (2016)
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

26. Preliminary valence-space in-medium similarity renormalization group results
arXiv:
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

27. Conclusions
We demonstrated that no-core and self-consistency aspects of nuclear DFT are essential for our quantitative understanding of isospin breaking. The approximate nature of isospin poses many theoretical challenges as the underlying symmetry is broken both explicitly and spontaneously, and the isospin mixing is highly non- perturbative due to a mismatch between the ranges of electrostatic and strong forces. To handle this situation theoretically, one needs to go beyond the usual single- reference DFT formalism. The proposed multi-reference DFT framework, based on isospin- and angular-momentum projected wave functions, provides a very satisfactory description of isospin breaking effects in beta decay.
The future developments will utilize the newly developed isospin-invariant density functional framework. The pn-mixed DFT formalism needs to be extended to the particle-particle channel by including pairing interaction of both isoscalar and isovector types. This will enable us to study the importance of the isoscalar pairing densities and fields on the structure of N~Z nuclei and the impact of pn-mixing on beta decays. Here, the AJT projection is essential: arXiv:
In quantitative calculations, quality input is crucial. A development of a realistic Hamiltonian-based DFT is among the most important needs. This will not only improve the predictive power of the model but will also help addressing the burning question pertaining to the role of ISB interaction components.
Collaborators: Wojtek Satuła, Jacek Dobaczewski, Paweł Bączyk, Maciek Konieczka
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

28. The measurements were far from simple
The measurements were far from simple. The radioactive isotopes necessary for the decay studies had to be produced by a particle accelerator, and most of them lived for at most a few seconds, during which time measurements with a precision of a few hundredths of a percent had to be completed.
The first important advance came when the results of combined nuclear measurements showed that a key part of the weak force is the same within 1 part in 10 thousand for the 13 different nuclear decays studied. This precise result made it possible to enlarge the scope to test Kobayashi and Maskawa’s prediction that the universality of the weak force extends beyond nuclei to all subatomic particles. The outcome confirms their 35‑yearold prediction to unprecedented accuracy, a stunning success for both experiment and theory!
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018

29. Congratulations John! The best is yet to come!
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30. Backup
W. Nazarewicz, Top Row CKM Unitarity Workshop 2018