Parity Nonconservation in Atoms: The Weak Charge and Anapole Moment of 133 Cs

Transcription

1 Parity Nonconservation in Atoms: The Weak Charge and Anapole Moment of 133 Cs Walter Johnson University of Notre Dame 1) Weak charge Q W of 133 Cs provides a test of the Standard Electroweak Model. 2) First (only) observation of an anapole moment κ a was in 133 Cs. 3) Q exp W and κexp a require accurate calculations together with error estimates! Collaborators: J. Sapirstein, S. Blundell, and M. S. Safronova Coupled-Cluster Symposium July

2 Atomic Parity Nonconservation e q e q γ Z e q e q A consequence of Z exchange is violation of Laporte s rule: Radiative (E 1 ) transitions take place only between states of opposite parity. Coupled-Cluster Symposium July

3 Laporte: Otto Laporte ( ) discovered the law of parity conservation in physics. He divided states of the iron spectrum into two classes, even and odd, and found that no radiative transitions occurred between like states. 1 1 O. Laporte, Z. Physik (1924). Coupled-Cluster Symposium July

4 Z Exchange in the Standard Model 2 H PV = G 2 [ēγ µ γ 5 e where = t, b, s, c ( ) c 1u ūγ µ u + c 1d dγµ d + + ēγ µ e ( )] c 2u ūγ µ γ 5 u + c 2d dγµ γ 5 d + c 1u = sin2 θ W c 2u = 1 2 (1 4 sin 2 θ W ) c 1d = sin2 θ W c 2d = 1 2 (1 4 sin 2 θ W ) 2 W. J. Marciano in Precision Tests of the Standard Electroweak Model, Ed. P. Langacker, (World Scientific, Singapore, 1995), p Coupled-Cluster Symposium July

5 Electron Axial-Vector Nucleon Vector Contribution of coherent vector nucleon current: H (1) = G 2 2 γ 5 Q W ρ(r) where ρ(r) is a nuclear density ( neutron density) and Q W = 2[(2Z + N)c 1u + (Z + 2N)c 1d ] = N + Z (1 4 sin 2 θ W ) N Coupled-Cluster Symposium July

6 Electron Vector Nucleon Axial-Vector Contribution of vector axial-vector nucleon current: H (2) = G 2 α [c 2p φ p σφ p + c2n φ n σφ n ] where designates nuclear matrix elements. c 2p 1.25 c 2u = c 2n 1.25 c 2d = Coupled-Cluster Symposium July

7 A) Nucleon Axial-Vector Contribution H (2) = G 2 κ 2 α I ρ(r) κ 2 from Extreme Shell Model and from Nuclear Calculations. 3 Element A State κ 2 [Sh. Mod.] κ 2 [3] K 39 1d 3/2 (p) Cs 133 1g 7/2 (p) Ba 135 2d 3/2 (n) Tl 205 3s 1/2 (p) Fr 209 1h 9/2 (p) W. C. Haxton, C.-P. Liu, and M. J. Ramsey-Musolf, Phys. Rev. Lett. 86, 5247 (2001). Coupled-Cluster Symposium July

8 B) Nuclear Anapole Moment Contribution PNC in nucleus nuclear anapole: H (a) = e α A G 2 κ a α I ρ(r) Theoretical estimates 4 for 133 Cs gave κ a = Experiment: 5 κ a = 0.09(2) κ a 5κ 2 4 V. V. Flambaum, I. B. Khriplovich, O. P. Sushkov Phys. Letts. B (1984). 5 V. V. Flambaum and D. W. Murray, Phys. Rev. C56, 1641 (1997); W. C. Haxton and C. E. Wieman, Ann. Rev. Nucl. Part. Sci. 51, 261 (2001) Coupled-Cluster Symposium July

9 C) Hyperfine Interference Contrubution Interference between the hyperfine interaction H hf and H (1) gives another nuclear spin-dependent correction of the form H (hf) = G 2 κ hf α I ρ(r) 133 Cs: κ hf = Tl: κ hf = κ hf 1 2 κ 2 Coupled-Cluster Symposium July

10 Summary of Phenomenology H (1) = G 2 2 γ 5 Q W ρ(r) H (2) G 2 κ α I ρ(r) where κ = κ 2 + κ a + κ hf. 1. Measure Q W as a test of Standard Model 2. Measure κ as a test of weak nuclear forces! Coupled-Cluster Symposium July

11 Optical Rotation Experiments Aim is to measure E PNC = f z i Q W : FIGURE 2. A medium possessing circular birefringence causes rotation of the plane of light polarization. The plane of polarization of a linearly polarized laser beam passing through a medium with n + n is rotated. The rotation angle φ R φ = Im (E PNC ) /M 1. On resonance (ω = ω 0 ), this leads to optical rotation ϕ with a dispersively-shaped magnetic field dependence given by ϕ ω 0` Coupled-Cluster = Symposium 2c Re[n +(ω 0 ) July n (ω )] 11 ß ` 2g F µ B B z =γ 0 2`0 1 +(2g F µ B B z =γ 0 ) 2 ; (3) where ` is the path length through the sample, c is the speed of light in vacuum, and

12 Optical Rotation Experiments R φ = Im (E PNC ) /M 1 Measured values of R φ Element Transition Group 10 8 R φ 205 Tl 205 Tl 208 Pb 208 Pb 209 Bi 2 P 1/2 2 P 3/2 Oxford (95) (45) 2 P 1/2 2 P 3/2 Seattle (95) (20) 3 P 0 3 P 1 Oxford (94) -9.80(33) 3 P 0 3 P 1 Seattle (95) -9.86(12) 4 S 3/2 2 D 3/2 Oxford (91) (20) Coupled-Cluster Symposium July

13 Stark-Interference Experiment Boulder PNC apparatus: A beam of cesium atoms is optically pumped by diode laser beams, then passes through a region of perpendicular electric and magnetic fields where a green laser excites the transition from the 6S to the 7S state. The excitations are detected by observing the florescence (induced by another laser beam) with a photo-diode. Coupled-Cluster Symposium July

14 Stark-Interference Experiments Evolving values of R = Im (E PNC ) /β (mv/cm) for 133 Cs Transition Group R 4 3 R 3 4 6s 1/2 7s 1/2 Paris (1984) -1.5(2) -1.5(2) 6s 1/2 7s 1/2 Boulder (1988) -1.64(5) -1.51(5) 6s 1/2 7s 1/2 Boulder (1997) (8) (8) The vector current contribution from the last row is [ Im E exp V R V = ± (6s 7s) 1011] = ± (0.0031) exp ± (0.0021) th Coupled-Cluster Symposium July

15 Other Experiments Element Transition Group Fr 7S 1/2 8S 1/2 Stoney Brook Fr 7S 1/2 [F = 4] 7S 1/2 [F = 5] Maryland, TRIUMF Yb (6s 2 ) 1 S 0 (6s5d) 3 D 1 Berkeley Yb (6s6p) 3 P 0 (6s6p) 3 P 1 Berkeley Ba + 6S 1/2 5D 3/2 Seattle Dy (4f 10 5d6s)[10] (4f 9 5d 2 6s)[10] Berkeley Sm (4f 6 6s 2 ) 7 F J (4f 6 6s 2 ) 5 D J Oxford Coupled-Cluster Symposium July

16 Calculations of the 6s 7s Amplitude in Cs Units: i( Q W /N) ea 0 SD(T) (4) CI+MBPT PTSCI (5) PNC-CI SDCC S. A. Blundell et al., Phys. Rev. D45, 1602 (1992). 7 M. G. Kozlov, S. G. Porsev, and I. I. Tupitsyn, PRL 86, 3260 (2001). 8 V. A. Dzuba, V. V. Flambaum, and J. S. M. Ginges, Phys. Rev. D 66, (2002). 9 V. M. Shabaev et al., Phys. Rev. A 72 (2005) 10 B. P. Das et al., THEOCHEM 768, 141 (2006) Coupled-Cluster Symposium July

17 Example of a PNC Calculation E PNC = n 7s D np np H (1) 6s E 6s E np + n 7s H (1) np np D 6s E 7s E np Weak RPA gives E PNC accurate to about 3%. follows: Therefore, we organize calculation as n = 6 9 valence states: evaluate matrix elements using SD wave functions (98%) n = 1 5 core states and n > 10: evaluate using weak RPA amplitudes (2%) Coupled-Cluster Symposium July

18 Contributions to PNC Amplitude Contributions to E PNC in units iea 0 Q W /N. n 7s D np np H (1) 6s E 6s E np Contrib n 7s H (1) np np D 6s E 7s E np Contrib n = (4) RPA part (1) Total (4) Coupled-Cluster Symposium July

19 Brueckner-Goldstone Diagrams for the SDCC Equations m a = m a m b n + a a r b n + m c b n + exchange terms m a n b m a n b = a + m r n s b m + a c b d n m a n b + c + a m r n b + m a c n r b + exchange terms Coupled-Cluster Symposium July

20 Data Analysis [ ] E exp PNC = QW Eth PNC N + κ ɛ F F E exp 34 E exp 43 β (a 3 0 ) (80) /β (mv/cm) (80) /β (mv/cm) (77) 34 (10 11 ) (49) 43 (10 11 ) (47) V (10 11 ) (37) PNC (10 11 ) (45) Q exp W (46) κ exp 0.117(16) E exp E exp E exp E th Coupled-Cluster Symposium July

21 Analysis of 6s 7s Amplitude in 133 Cs Combining the calculations and the measurements Q exp W (133 Cs) = 71.91(46) 72.73(46) differs with the standard model value Q SM W (133 Cs) = 73.09(3) by 2.5 σ. 0.8 σ Additional Corrections: Breit Interaction -0.6% Vacuum Polarization +0.4% αz Vertex Corrections -0.7% Nuclear Skin Effect -0.2% Coupled-Cluster Symposium July

22 Analysis of 6s 7s Amplitude in 133 Cs Combining the calculations and the measurements Q exp W (133 Cs) = 71.91(46) 72.73(46) differs with the standard model value Q SM W (133 Cs) = 73.09(3) by 2.5 σ. 0.8 σ. Additional Corrections: Breit Interaction -0.6% Vacuum Polarization +0.4% αz Vertex Corrections -0.7% Nuclear Skin Effect -0.2% Coupled-Cluster Symposium July

23 the data currently favor T<0, thus strengthening the exclusion limits. A more detailed analysis is required if the extra neutrino (or the extra down-type quark) is close to its direct mass limit [208]. This can drive S to small or even negative values but at the expense of too-large contributions to T. These results are in agreement with a fit to the number of light neutrinos, N ν =2.986 ± (which favors a larger value for α s (M Z )= ± mainly from R l and τ τ ). However, the S parameter fits are valid even for a very heavy fourth family neutrino. Constraints on New Physics Γ Z, σ had, R l, R q asymmetries M W ν scattering Q W E 158 T all: M H = 117 GeV all: M H = 340 GeV all: M H = 1000 GeV S Figure 10.4: 1 σ constraints (39.35 %) on S and T from various inputs combined with M Z. S and T represent the contributions of new physics only. (Uncertainties from m t are included in the errors.) The contours assume M H = 117 GeV except for the central and upper 90% CL contours allowed by all data, which are for M H = 340 GeV and 1000 GeV, respectively. Data sets not involving M W are insensitive to U. Due to higher order effects, however, U = 0 has to be assumed in all Coupled-Cluster Symposium July

24 Anapole Moment of 133 Cs Group κ κ 2 κ hf κ a Safronova and Johnson 0.117(16) (16) Haxton et al (16) (16) Flambaum and Murray 0.112(16) (16) 7 Bouchiat and Piketty from Haxton et al. 2 from Flambaum and Murray 3 from Bouchiat and Piketty 4 The spin-dependent matrix elements from Kraftmakher are used. 5 Shell-model value with sin 2 θw = This value was obtained by scaling the analytical result from Flambaum and Khriplovich (κhf = ) by a factor Contains a 1.6% correction for finite nuclear size; the raw value is 0.094(16). Coupled-Cluster Symposium July

25 Constraints on Nuclear Weak Coupling Constants (h 0 ρ +0.7h 0 ω) F 133 Cs pp 0 18 F pα f π 0.12h 1 ρ 0.18h 1 ω 11 B. Desplanques, J. F. Donoghue, and B. Holstein, Ann. Phys. (NY) (1980); W. C. Haxton and C. E. Wieman, Ann. Rev. Nucl. Part. Sci. 51, 261 (2001) Coupled-Cluster Symposium July

26 Conclusions Measurements of the weak charge in heavy atoms provide important tests of the validity of the electroweak standard model and provide limits on possible extensions. Measurements of the nuclear anapole moment provide constraints on nucleon-nucleon weak coupling constants that are inconsistent with PNC experiments in light nuclei. New measurements badly needed! Measurements of PNC in atoms depend on precise atomic manybody calculations to provide useful new information concerning weak interaction physics. Error estimates on calculations of PNC amplitudes are mandatory! Coupled-Cluster Symposium July