1. Parity violation in one single trapped radium ion Lotje Wansbeek Theory Group, KVI University of Groningen, The Netherlands ECT* Workshop “The lead radius experiment” Trento, August 5, 2009

2. August 5, 2009ECT* Workshop "The lead radius experiment", Trento2/26 Low-energy tests of the Standard Model The Standard Model (SM) of particle physics is incomplete  searches for physics “beyond the SM” at two, complementary, fronts: High energy collider experiments: Direct observation of new particles Low energy searches: indirect, but with high precision Requires: High-energy physicsRequires: Atomic and nuclear physics theory + experiment < 1% LHC @ CERNTRI  P @ KVI Radium ion experiment: Weak charge Q W (Ra)  Weinberg angle Mixing angle between the photon and the Z 0 -boson

3. August 5, 2009ECT* Workshop "The lead radius experiment", Trento3/26 Atomic parity violation (APV) Weak charges of quarks in the nucleus add coherently: Q W = –N+(1–4 sin 2 θ W )Z + rad. corr. + “new physics” where θ W is the weak  - Z 0 mixing (or Weinberg) angle. Coulomb interaction: - Mediated by photons, massless, so long-range - Gives the atomic spectrum + selection rules - Nucleus has an electric charge Q EM = Z - Strength scales  Z Weak interaction (violates parity): - Mediated by Z 0 bosons, mass ≈ 91 GeV, so short-range - Atomic states acquire tiny admixture of opposite-parity states - Nucleus also has a weak charge Q W (conserved current!) - Strength scales faster than Z 3 e q q e γ q e q e V A Z0Z0

4. August 5, 2009ECT* Workshop "The lead radius experiment", Trento4/26 ≈ 3 % Experiments on the Weinberg angle High energy (near the Z 0 -pole) 1.SLD @ SLAC (Stanford) 2.LEP @ CERN (Geneva) Medium energy 1.E158 @ SLAC (Stanford) Q w (e) of the electron 2.NuTeV @ Fermilab (Chicago) neutrino scattering 3.Qweak @ J-Lab (Virginia), proposed Q w (p) of the proton Cesium (2004) 1 2 3 4 5 Low energy: atomic parity violation (APV) Cesium atoms: 6S 1/2 –7S 1/2 transition  Experiment: 0.35%, Wieman group, Boulder  Theory: 0.3%, Derevianko et al. Barium ions: 6S 1/2 –5D 3/2 transition  Experiment: Fortson group, UW, Seattle  Theory: 0.5% Francium atoms: 7S 1/2 – 8S 1/2 transition  Experiments: Legnaro, Stony Brook  Theory: ? Radium ions: 7S 1/2 –6D 3/2 transition  Experiment: KVI, University of Groningen  Theory: 3% Radium ion

5. August 5, 2009ECT* Workshop "The lead radius experiment", Trento5/26 APV in one single ion Cs experiment  Single valence system  Atomic beam experiment Ba +, Ra + experiment  Single valence system  Single, trapped ion Experimental advantages of single-ion APV  Tractable systematics  Long coherence times  Only trace quantities required Single trapped Ba + ion

6. August 5, 2009ECT* Workshop "The lead radius experiment", Trento6/26 APV in one single ion The concept  Interference between E2 and E1 APV produces differential shift Δ diff of the two ground state Zeeman levels  Δ diff can be measured with RF spectroscopy (about 10 Hz) q e 7S 1/2 E1 APV E2 6D 3/2 6D 5/2 7P 1/2 7P 3/2 q e V A Z0Z0 Weak interaction (violates parity) Weak charges of quarks in the nucleus add coherently: Q W = –N+(1–4 sin 2 θ W )Z + rad. corr. + “new physics” where θ W is the weak  - Z 0 mixing (or Weinberg) angle. + ε nP 1/2 + ε nP 3/2

7. August 5, 2009ECT* Workshop "The lead radius experiment", Trento7/26 Differential light shift is directly proportional to the parity-violating amplitude E1 APV APV in one single ion Calculate atomic wavefunctions Measure Infer weak charge Parity-violating amplitude E1 APV is connected to the weak charge by Cesium (Wieman et al.) Experiment: 0.35% Theory: 0.27% Q w =  73.16(29) exp (20) th

8. August 5, 2009ECT* Workshop "The lead radius experiment", Trento8/26 The scaling of the APV effect  The Bouchiat & Bouchiat (1974) “faster than Z 3 -law” says: where K r is a relativistic factor, and Q W ~ N ~ Z Z (atomic number) [arb. units] Z3Z3 Z3KrZ3Kr Ra + Ba + Sr + Mg + Ca + Be + x: DF calculation for n = 2,3,4,5,6,7 Ra + Ba + Ra + Z3Z3 Ba + (Cs)Sr + Ca + Ra + Z 3 Kr E1 APV effect in Ra + is 20 times larger than for Ba +, and 50 times larger than for Cs!

9. August 5, 2009ECT* Workshop "The lead radius experiment", Trento9/26 Expected sensitivity Conclusion: for Ra +  Similar sensitivity  Stability much easier to achieve!  Ra + is a superior APV candidate:  In 1 day, a 5-fold improvement over Cs appears feasible! E1 APV N τ T needed Ba + 2.518024 hrs Ra + 46.410.69 hrs  Achieved in Cs atoms (N large): 0.35 %  To reach 0.2 % we need: where: N = number of ions τ = coherence time (lifetime D 3/2  S 1/2 ) T = measurement time Statistical signal-to-noise:* * N. E. Fortson, Phys. Rev. Lett. 70, 2383 (1993).

10. August 5, 2009ECT* Workshop "The lead radius experiment", Trento10/26 Theoretical status Calculation of E1 APV in Ra + using relativistic coupled-cluster (CC) theory 1 : E1 APV = 46.4(1.4) · 10 -11 iea 0 (-Q w /N)  Accuracy (3 %) estimated from hyperfine constants vs. theory  The Delaware 2 group (2009) find 45.9 · 10 -11 iea 0 (-Q w /N)  Dzuba et al. 3 (2001) find 45.9 · 10 -11 iea 0 (-Q w /N) with a 1 % error  Achieved in Cs: 0.3 %  For a SM test, we need sub-1 % accuracy! 1.L.W. Wansbeek et al., Phys. Rev. A 78, 050501(R) (2008). 2.R. Pal et al., Phys. Rev. A 79, 062505 (2009). 3.Dzuba et al., Phys Rev. A 63, 062101 (2001).

11. August 5, 2009ECT* Workshop "The lead radius experiment", Trento11/26 Improving the accuracy Work to be done on the theory side  Improvement of CC theory  Inclusion of small corrections Breit (magnetic) interaction Vacuum polarization + other QED corrections Nuclear structure effects  Study of different isotopes Experimental input is needed!  Last and only spectroscopic data is from Ebbe Rasmussen (1934)  ISOLDE @ CERN (1980s) Isotope shifts of the 7S 1/2 – 7P 1/2 line Hyperfine structure of this line Lifetimes  Isotope shift of the of the 7P 1/2 – 6D 3/2 line for 212-214 Ra + planned @ KVI With new experimental input: sub-1% is a realistic goal!

12. August 5, 2009ECT* Workshop "The lead radius experiment", Trento12/26 What is the uncertainty from nuclear input?  E1 APV in Cs and Fr (S-S transition) is dominated by 3 terms:  These are of comparable size, but signs differ  Strong cancellations, final result is half the size of the largest contribution  E1 APV in Ra + (Ba + ) (S-D transition) is strongly dominated by 1 term:  Largest contribution (around 110 %) comes from the 7P 1/2 (6P 1/2 ) state  No strong cancellations The parity violating amplitude in the sum-over-the-states method:

13. August 5, 2009ECT* Workshop "The lead radius experiment", Trento13/26 Factorizing the SP-matrix element James and Sandars (J. Phys. B 32, 1999) write: With Normalization constant, depends on particular atomic states, not on isotope Normalization constant, independent of particular atomic states Equivalent charge radius Integral over the neutron density and radial wavefunction

14. August 5, 2009ECT* Workshop "The lead radius experiment", Trento14/26 Nuclear structure effects in APV  Assume constant-density nucleus  Solve radial Dirac equations inside nucleus  Match solutions, near the nucleus, to atomic wavefunctions of the form  Look at the effects of small variations of the constant-density nucleus Atomic wavefunctions Measure of the neutron skin Higher moments of the charge distribution

15. August 5, 2009ECT* Workshop "The lead radius experiment", Trento15/26 What data is available for radium?  We take the radius for 214 Ra = R 0 from the data table by Angeli: R 0 = 5.5705 (130) fm  The difference between R 0 and R N can be deduced from the isotope shifts measured by Ahmed et al.  This gives R N a relative and a total error  For the neutron skins, we use the calculation by Brown et al., which has a 25 % error A R p [fm] A Fractional uncertainty

16. August 5, 2009ECT* Workshop "The lead radius experiment", Trento16/26 The resulting uncertainty Uncertainty [%] Total Skin RpRp The uncertainty of H W due to the uncertainty in the neutron skin and the charge radius lies between 0.15 - 0.35 % depending on the isotope. Charge radius Measure of the neutron skin A

17. August 5, 2009ECT* Workshop "The lead radius experiment", Trento17/26 The total uncertainty To summarize the uncertainty: Atomic structure  The calculation of E1 APV in Ra + is currently accurate to about 3 % 1 % accuracy seems feasible, provided there is new experimental input  Even in Cs, the dominant theoretical (0.3 %) error is due to atomic structure Nuclear structure  Neutron skin and charge radius give additional 0.15 % – 0.35 % uncertainty However:  Our aim is sub-1%!  What more can be done?

18. August 5, 2009ECT* Workshop "The lead radius experiment", Trento18/26 An alternative: a ratio measurement?  The idea is (Dzuba et al.) Taking the ratio of two measurements of E1 APV for two isotopes N and N’ will cancel the atomic uncertainty.  A value for the ratio is equally informative on the Weinberg angle  For radium a wide range of isotopes is available  What about the nuclear uncertainties? The uncertainties in the neutron skins and charge radii are correlated  By taking a ratio you can use this fact!

19. August 5, 2009ECT* Workshop "The lead radius experiment", Trento19/26 The ratio defined The intermediate 7P 1/2 state contributes 110% Isotope-independent terms cancel To a good approximation, the ratio is given by The ratio is the ratio of two parity violating amplitudes for two different isotopes. We had

20. August 5, 2009ECT* Workshop "The lead radius experiment", Trento20/26 The ratio rewritten After some rewriting: R 0 : the radius of 214 Ra due to isotope shifts, ratios are known more accurately Neutron skin On the basis of these figures (Brown et al.), we write for the neutron skin in radium

21. August 5, 2009ECT* Workshop "The lead radius experiment", Trento21/26 The uncertainty of the ratio With this expression for the neutron skin, the ratio is written:

22. August 5, 2009ECT* Workshop "The lead radius experiment", Trento22/26 The relevant isotopes of radium Available off-line for EDM experiment Produced on-line Spectroscopy this September LifetimeSpin 2094.6(2) s5/2 21113(2) s1/2 21213.0(2) s 2132.74(6) m1/2 2142.46(3) s 22128.2 s5/2 22311.43(5) d3/2 2243.6319(23) d 22514.9(2) d1/2 2261600 y 22742.2(5) m3/2 2294.0(2) m5/2 {   Comercially available

23. August 5, 2009ECT* Workshop "The lead radius experiment", Trento23/26 Nuclear uncertainty in the ratio For the ratio of the isotope pair 214 and 226 we find:  Total fractional uncertainty 0.14 % Uncertainty due to skin 0.10 % (error taken twice as large) Uncertainty due to radius 0.09 %  The separate errors where 0.15 and 0.30 %! A ratio measurement  Cancels the atomic calculation uncertainty  Reduces the nuclear uncertainty

24. August 5, 2009ECT* Workshop "The lead radius experiment", Trento 24 The TRI  P facility @ KVI Ion Catcher RFQ Cooler MOT Beyond the Standard Model Nuclear Physics Atomic Physics Particle Physics Production Target Magnetic Separator MeV meV keV eV neV AGOR AGOR cyclotron Ion catcher (thermal ioniser or gas-cell) Low-energy beam line RFQ cooler/buncher MOT MOT D D D D Q Q Q Q Q Q Q Q Magnetic separator Production target Trapped Radioactive Isotopes: micro-laboratories for Fundamental Physics

25. August 5, 2009ECT* Workshop "The lead radius experiment", Trento25/26 Experimental status summarized  Ba + & Ra + lasers set up in experimental hall  Construction of collector and precision Paul traps  Radium production with AGOR cyclotron at TRI  P facility: Chain of isotopes: 212 Ra, 213 Ra and 214 Ra produced With low intensity ( 206 Pb) beam: ~ 10 3 particles/sec of each isotope  Successful trapping of Radium isotopes demonstrated in January ’09  First laser spectroscopy of trapped Radium ions expected in September ‘09

26. August 5, 2009ECT* Workshop "The lead radius experiment", Trento26/26 Conclusions & outlook  Ra + is an excellent candidate for a competitive APV experiment The effect in Ra + is very large Easy wavelengths Large range of isotopes available  Experimentally, a fivefold improvement over Cs appears feasible  The uncertainty in E1 APV for Ra + Due to atomic calculation uncertainty is about 3 % Due to nuclear structure uncertainties is at least 0.15 - 0.35 %  A ratio measurement Is equally informative Cancels atomic uncertainty Reduces nuclear uncertainty to 0.14 % for the 214-226 pair  Experiment is being set up

27. August 5, 2009ECT* Workshop "The lead radius experiment", Trento27/26 The crew & the money  Experiment Gouri Giri (PhD) Oscar Versolato (PhD) Lorenz Willmann Klaus Jungmann  Theory Lotje Wansbeek (PhD) Bijaya Sahoo (PostDoc) Lex Dieperink Rob Timmermans  International collaborators B. P. Das (India) N. E. Fortson (USA) www.kvi.nl/~radiumion  Funding FOM open competition NWO Toptalent grant NWO Veni fellowship

28. August 5, 2009ECT* Workshop "The lead radius experiment", Trento28/26 APV and physics beyond the SM Extra Z’ boson in SO(10) GUTs  Additional U(1)’ gauge symmetry  Does not affect ordinary Z and W physics  Assume no Z-Z’ mixing Londen and Rosner (1986) Marciano and Rosner (1990) Altarelli et al. (1991) APV and Supersymmetry (SUSY)  Q w (p) and Q w (e) sensitive to SUSY loop correction  But their shifts are correlated  Q w (Z) is, for heavy atoms, insensitive to SUSY loops  APV can help to distinguish models! Ramsey-Musolf and Su (2008)

29. August 5, 2009ECT* Workshop "The lead radius experiment", Trento29/26 The Boulder Cs experiment 6S 1/2 Weak interaction causes states to acquire tiny admixture of opposite-parity states and similar for 7S 1/2 Cs E1 No dipole transition! Measure Atomic calculation Dipole transition! E1 PN C 7S 1/2 6S 1/2 Cs ~ ~ weak interaction 7S 1/2

30. August 5, 2009ECT* Workshop "The lead radius experiment", Trento30/26 The Cs experiment: Status of theory Improved atomic theory 2000-2005: 1 Q W ( 133 Cs) =  72.74(29) exp (36) th Most recent result (2009): 2 Q W ( 133 Cs) =  73.16(29) exp (20) th SM prediction: Q W ( 133 Cs) =  73.16(3) EffectSizeRel. size Coulomb0.8998(25)101 % Breit (magnetic) interaction 3  0.0054(5)  0.6 % QED (vac.pol.+  Z vertex corr.)  0.0024(3)  0.3 % Neutron skin  0.0017(5)  0.2 % e-e weak interaction0.00030.03 % Total E1 APV in iea B [  Q W /N]x10  11 0.8906(26) 1. Ginges and Flambaum, Phys. Rep. 397, 63 (2004). 2. Porsev, Beloy, and Derevianko, Phys. Rev. Lett. 102, 181601 (2009). 3. Derevianko, Phys. Rev. Lett. 85, 1618 (2000). 2009 Bounds on M Z’ from Cesium APV (68% confidence level, ξ= 52°) Old calculation 0.75 < M Z’ < 2 TeV/c 2 New calculation M Z’ > 1.2 TeV/c 2 Main uncertainty still from electron correlations!

31. August 5, 2009ECT* Workshop "The lead radius experiment", Trento31/26 A bit more detail 6D 3/2 6D 5/2 7P 1/2 Off-resonant laser λ= 828 nm Cooling & detection λ=468 nm 7P 3/2 6D 3/2 6D 5/2 7P 1/2 Off-resonant laser λ= 828 nm Cooling & detection λ=468 nm 7P 3/2 6D 3/2 Ra + 6D 5/2 7P 1/2 Off-resonant laser λ= 828 nm Cooling & detection λ=468 nm 7P 3/2 E1 PNC E2 7S 1/2 +εn P 1/2 m=-1/2 ω0ω0 m=+1/2 m=-1/2 Zeeman shift ω0ω0 quadrupole shift 0 Δ+ω diff + differential PNC shift Two laser fields: 1. Antinode at ion  drives E1 PNC 2. Node at ion, maximum gradient  drives E2