1. 1 S1242 High Precision Mass Measurements of Superallowed T=2 Nuclear Beta Decay Emitters

2. 2 Quarks in the SM Coupling to Higgs field Φ T =(Φ 1 Φ 2 ): after symmetry breaking: mass term  weak ≠ mass eigenstates: interaction Lagrangian quarks - W + and W - Yukawa coupling Cabibbo–Kobayashi –Maskawa matrix:  - decay

3. 3 V ud measurements J. Hardy, CIPANP 2009  superallowed 0 + → 0 + decays most precise way to extract V ud due to  J =  T =  L =  S = 0: pure Fermi decay (only vector part) transition between isobaric analog states only total Isospin Ladder Operator T ± alters wave-function  for T = 1:

4. 4 ft- values, corrected Ft-value and V ud Combination to ft-values (T=1): corrected Ft value:  V R … transition indep.  R and  NS …. transition dep.  c … isospin symmetry breaking (tans. dep.) Corrections: small ( about a few %), BUT dominating uncertainty f … phase space integral (dep. on Q-value) t … „partial halflife“ (dep on. BR and T ½ ) K … numerical constant Experimental Input } radiative corrections

5. 5 Tests of Fundamental Symmetries I J. Hardy & I.S. Towner W. J. Marciano et al. 1)CVC2) Scalar Currents 3) |V ud | 2  /  = 0.28 J. Hardy & I.S. Towner, Phys. Rev. C 79, 055502 (2009)

6. 6 5) Coupling Universality: G F (|V ud | 2 + |V us | 2 + |V ub | 2 ) = G  = G  e.g. Z  boson in SO(10) implies: M(Z  )> 750 GeV at 95% CL Tests of Fundamental Symmetries II 4) CKM: basis transformation weak ↔ mass eigenstates  Unitarity test of 1 st row: |V ud | 2 + |V us | 2 + |V ub | 2 = 1SM = 0.99995(61) Experiment J. Hardy & I.S. Towner, Phys. Rev. C 79, 055502 (2009) 0.9491(4)0.0508(4) B. Tschirhart, CIPANP 2009

7. 7 T&H’s  c : use W + -spin, not isospin  + new  c – calculations (including core orbitals) I.S. Towner & J. C. Hardy, Phys. Rev. C77, 025501 (2008) Developments for  c J.C. Hardy and I.S. Towner, Phys. Rev. C66, 035501 (2002 ) Phys. Rev. C71, 055501 (2005) W. E. Ormond and B. A. Brown, Phys. Rev. C52, 2455 (1995) Nucl. Phys. A 440, 274 (1985) G.A. Miller & A. Schwenk, Phys. Rev. C 78, 035501 (2008) N. Auerbach, Phys. Rev. C 79, 035502 (2009) J. C. Hardy & I.S. Towner, Phys. Rev. C 79, 055502 (2009) New approach to  c (Coulomb force treated by perturbation theory) results lower than T&H New Hartree-Fock (same model space as Woods-Saxon with core orbitals) H. Liang et al., Phys. Rev. C, 064316 (2009)  c accessed via self-consistent RPA in relativistic framework  /  = 1.0-1.1 implementeddifferently

8. 8  c : comparisons between models T&H (2005) ↔ O&B T&H (2008) ↔ Perturbation theoryT&H (2008) ↔ RPA T&H: WS (2008) ↔ HF (2009)

9. 9 Status of  c T&H: currently best calculations –Wood Saxon & Hartree-Fock –same model space –good agreement with each other and CVC 4 other descriptions –3 with numerical results –disagree with T&H (all lower  c ) –but all need improvements  benchmark models / check  c –assume CVC –use –compare with experiment –new cases or/and cases with large  c T z = - 1 T z = 0 |V ud | 2 } superallowed T=2 cases

10. 10 new system → wider range for tests of  c T=2 allows systematic check of  c  c expected to be larger: example: 32 Ar → 32 Cl calculation based on HF (B.A. Brown)  c cm = 0.6 %  c ro = 1.4 % configuration mixing with other 0 + radial overlap radial wavefn altered by Coulomb enhanced near proton drip line T=1 T=2 Superallowed T=2 Decays M. Bhattacharya et al.,Phys. Rev. C 77, 065503 (2008)

11. 11 Exp. Challenges for T = 2 short half-lives ( down to 40 ms ) challenge for high precision mass measurements  -delayed proton emission M. Bhattacharya et al.,Phys. Rev. C 77, 065503 (2008) → feasible with HCI at TITAN → feasible: 32 Ar BR=22.71(11)(11)  ft ( 32 Ar)=1552(12)  c (exp)= 2.1 ± 0.8 %  c (th. )= 2.0 ± 0.4 % Note: used m.e.( 31 S) + their S p measurement: m.e.( 32 Cl)=-13337.0 ± 1.6 keV

12. 12 Proposed Measurements IsotopeHalf-life Present  m [keV]  m TITAN (A + ) [keV]q TITANHCI  m [keV]  E* [keV] comment Mg-2090 ms 271.86510He-like0.186 request stage 2 Na-20448 ms 6.661.8649He-like0.207 13request stage 2 Si-24140 ms 19.472.23712He-like0.186 ? Al-242.053 s 2.782.23611He-like0.203 6proposal S1191 S-28 125 ms1602.60914He-like0.186 requires development P-28 270 ms3.322.60713He-like0.20121 requires development Ar-3298 ms 1.82.98116He-like0.186 requires development Cl-32298 ms 6.592.97915He-like0.199 0.4requires development Ca-36102 ms 403.35310Ne-like0.335 feasible, request stage 2 K-36342 ms 0.393.3529Ne-like0.3728 request stage 2 Ti-40 53 ms1603.72512Ne-like0.310 requires development Sc-40 182 ms2.833.72411Ne-like0.339 8requires development Cr-4453 ms504.09714Ne-like0.293 requires development V-44111 ms1214.09613Ne-like0.315 ?? Ti-43509 ms6.904.00212Ne-like0.334 requires development Fe-4844 ms704.46916Ne-like0.279 requires development Mn-48158 ms1124.46815Ne-like0.298 0.9requires development Ni-5238 ms844.84218Ne-like0.269 requires development Co-52115 ms654.84017Ne-like0.285 30requires development IsotopeTargetSourceYield [ions / sec] Mg-20SiCTRILIS240 Na-20SiCRe surface1.7 ▪ 10 8 IsotopeTargetSourceYield [ions / sec] Ca-36TiCTRILISfeasible (M. Dombsky) K-36TiCRe surface2.9 ▪ 10 5 Request for each pair: 1 shift setup + calibration 5 shifts measurement

13. 13 Impact of Measurements BR measurements are planned require >10 ions/sec contributions to uncertainty of ft-value:

14. 14 Test of IMME Quintets C. Yazidjian et al., Phys. Rev. C 76, 024308 (2007)A. Gade et al., 76, 024317 (2007) A = 20A = 36 20 MgM.E. [keV]E* [keV] 0+0+ 17570(27) 2+2+ 19168(29)1598(10) Check for cubic term:

15. 15 Summary V ud most precisely determined via superallowed 0 + → 0 + nuclear  decays CKM unitarity test: σ ud ≈ σ us isospin symmetry breaking corrections  c –current calculations (T&H) in great agreement with CVC –many new theoretical descriptions (in development) –systematic discrepancies between models –experimental data to benchmark models (extreme cases i.p. T=2) T=2 cases in experimental reach: NEW NUCLEONIC SYSTEM –BR measurements feasible ( 32 Ar done + other in preparation) –masses: HCI on short lived isotopes with TITAN  propose high precision mass measurements on superallowed emitters: 20 Mg, 24 Si, 28 S, 32 Ar, 36 Ca, 40 Ti, 44 Cr, 48 Fe, and 52 Ni request 1 shift setup + 5 shifts measurement for each case  measurements also important for tests of IMME (i.p. 20 Mg, 36 Ca)

16. 16 S1242 collaboration TRIUMF: M. Brodeur, T. Brunner, S. Ettenauer, A. Gallant, A. Lapierre, S. Triambak, P.P.J. Delheij, J. Dilling University of Washington: A. Garcia, C. Wrede Texas A&M University: D.G. Melconian University of Manitoba: G. Gwinner NSCL: R. Ringle TITAN collaboration

17. 17 Details on new  c descriptions

18. 18 isospin operator  +  c T&H: W-spin operator M&S: W-spin formalism loses SM isospin commutation relations radial quantum numbers not necessarily the same separation model dependent correct SM  + complete formalism developed to calculate  c because proton and neutron states are not the same but assumes radial quantum numbers are the same G.A. Miller & A. Schwenk, Phys. Rev. C 78, 035501 (2008)

19. 19 Wood-Saxon ↔ Hartree Fock nucleus with Z+1 protons Coulomb term in proton wavefunction: Wood Saxon: Hartree Fock : J. C. Hardy & I.S. Towner, Phys. Rev. C 79, 055502 (2009) difficult to calculate exactly in Skyrme HF  T&H: 1) calculate single HF for A-1 nucleus → 2) use proton mean field for proton wf → 3) use neutron mean field for neutron wf →  in agreement with T&H’s Wood-Saxon e.g.: 33 S 34 Cl 34 S different than O&B

20. 20 new calculations  c self consistent RPA build on relativistic Hartree with –DD-ME1, DD-ME2 –NL3, TM1 relativistic Hartree-Fock with –PKO1, PKO2, PKO3 –PKO1 but Coulomb exchange term turned off Conclusions: 1) RHF+RPA (without C-Ex) = RH+RPA  proper treatment of Coulomb field is essential for  c 2) more investigations required (e.g. proper n-p mass difference, isoscaler and isovector pairing, deformation) H. Liang et al., Phys. Rev. C, 064316 (2009)

21. 21 new calculations  c II Perturbation Theory: charge independent Hamiltonian H 0 treat Coulomb force perturbatively details: V C : uniformly charged sphere off diagonal matrix elements  largest elements for giant isovector monopole states (IVMS) wave function for PT: gs (H 0 ) + IVMS N. Auerbach, Phys. Rev. C 79, 035502 (2009) z-comp. of isovector monopole operator isospin impurity num. factor (model dep.) symm. potential strength Model characteristics: includes collectivity pure isospin formulation BUT: equivalent to W-spin uncertainties in model parameters neglects non-Coulomb charge dep. int.