Prospects for Atomic Parity Violation Experiments

Transcription

1 Prospects for Atomic Parity Violation Experiments Konstantin Tsigutkin and Dima Budker socrates.berkeley.edu/~budker/

2 Outline A brief story of parity violation in atoms Mechanisms of APV Summary of measurements of atomic parity violation Prospects for new experiments on APV Berkeley experiment with Yb isotopes: present status and perspectives

3 Atomic PNC: important landmarks 1959 Ya. B. Zel dovich: PNC (Neutr. Current) Opt. Rotation in atoms 1974 M.-A. & C. Bouchiat Z 3 enhancement PNC observable in heavy atoms Novosibirsk, Berkeley discovery of PNC in OR(Bi) and Stark-interf.(Tl) 1995 Boulder, Oxford, Seattle, Paris PNC measured to 1-2% in Cs, Tl, Bi, Pb Prof. Ya. B. Zel dovich 1997 Boulder 0.35% measurement, discovery of anapole moment

4 Sources of parity violation in atoms Z 0 -exchange between e and nucleus P-violating, T-conserving product of axial and vector currents ˆ G h= C e e N N + C e e N N 2 1N γμγ5 γμ 2N γμ γμγ 5 N Z 0 e C 1n, C is by a factor of 10 larger than 1p 2N leading to a dominance of the time-like nuclear spin-independent interaction (A e,v N ) C A contribution to APV due to Z 0 exchange between electrons is suppressed by a factor ~1000 for heavy atoms.

5 Nuclear Spin-Independent (NSI) electron-nucleon nucleon interaction NSI Hamiltonian in non-relativistic limit assuming equal proton and neutron densities ρ(r) in the nucleus: ˆ G h () W = QWγ 5ρ r 2 2 The nuclear weak charge Q W to lowest order in the electroweak interaction is 2 Q = N + Z(1 4sin θ ) N W The nuclear weak charge is protected from strong-interaction effects by conservation of the nuclear vector current. Thus, APV measurements allows for extracting weak couplings of the quarks and for searching for a new physics beyond SM NSI interaction gives the largest PNC effect compared to other mechanisms NSI interaction is scalar mixes only electron states of same angular momentum j W

6 NSI interaction and particle physics implications APV utilizes low-energy system and gives an access to the weak mixing angle, Sin 2 (θ W ), at low-momentum transfer. J.L. Rosner, PRD 1999 V.A. Dzuba, V.V. Flambaum, and O.P. Sushkov, PRA 1997 J. Erler and P. Langacker, Ph.Lett. B 1999 APV experiments are sensitive to new tree-level physics at energies that cannot be currently achieved in colliders. Limits of the mass and mixing angle for Z in E 6 models. The shaded area is excluded by the measurements of APV and from collider experiments Yb APV Collider Exps Qweak: 2.3 TeV Cs APV

7 NSI interaction and particle physics implications (continued) Standard Model extensions, Oblique radiative corrections, Higgs sector. Precision measurements of electroweak quantities constrain linear combinations of S isospin conserving, and T isospin breaking parameters. Constraints of S and T from Γ(Z 0 ) and from value of Sin 2 (θ W ) as determined from forward-backward scattering asymmetries APV experiments are not providing complimentary information to the high-energy experiments M.J. Ramsey-Musolf, PRC 1999 Thus, the impact of the NSI APV is expected in constraining new treelevel physics rather than oblique radiative corrections

8 Isotope ratios and neutron distribution The atomic theory errors can be excluded by taking ratios of APV measurements along an isotopic chain. While the atomic structure cancels in the isotope ratios, there is an enhanced sensitivity to the neutron distribution ρ n (r). nuc A = δ ( Q + Q ) PNC W W Q N q Z q nuc 2 W = ( n 1) + (1 4sin θw)( p 1) q = ρ () r f()d r r, q = ρ () r f()d r r 3 3 n n p p R is sensitive, in particular, to the difference in the neutron distributions. This could be used to determine nuclear structure and test nuclear models complementing parity violating electron scattering measurements f(r) is the variation of the electron wave functions inside the nucleus normalized to f(0)=1. APNC ( N') QW ( N') R 1 +Δ APNC ( N) QW ( N) Δq q q n n n [ q ] n

9 ~Z 3 scaling of APV effects Considering the electron wave functions in nonrelativistic limit and pointlike nucleus the NSI Hamiltonian becomes: Since it is a local and a scalar operator it mixes only s and p 1/2 states. ˆ G hw = σ p (r) + (r) σ p 4 2m e ( 3 3 δ δ ) 2 p1/2 hˆw s Z Q W Z due to scaling of the probability of the valence electron to be at the nucleus Z from the operator p, which near the nucleus (unscreened by electrons) Z. Q W N~Z. Strong enhancement of the APV effects in heavy atoms

10 Sources of NSD interaction Anapole moment ˆ G κ r hnsd = γ 0 γi ρ () r 2 I Weak neutral current Hyperfine correction to the weak neutral current K κ = κ A I + 1 I + 1/ K = ( 1) + κ + κ 2 l 2 ( I Q w ; + 1/ 2) κ κ A / 2 K = C I + 1 A 2α 2/3 μ g α α ; A = N + Z; κ A -Anapole moment κ 2 -Neutral currents κ QW -Radiative corrections

11 Anapole moment In the nonrelativistic approximation PNC interaction of the valence nucleon with the nuclear core has the form: n(r) is core density and g α is dimensionless effective weak coupling constant for valence nucleon. ˆ Gg ( ) h ~ σp A n( r r α ) 2 2 m As a result, the spin σ acquires projection on the momentum p and forms spin helix Spin helix leads to the toroidal current. This current is proportional to the magnetic moment of the nucleon and to the cross section of the core. p Khriplovich & Flambaum 3 2/3 κa A μ α g α neutron: μ n =-1.2; g n =-1 proton: μ p =3.8; g p =5 Anapole moment is bigger for nuclei with unpaired proton

12 Nuclear physics implication: weak meson coupling constants There are 7 independent weak couplings for π-, ρ-, and ω-mesons known as DDH constants. Proton and neutron couplings, g α, can be expressed in terms of 2 combinations of these constants: g g p n = f 19.5h 4 0 π = f 18.9h 4 0 π f f 0.12h 0.18h π π ρ ω h h + 0.7h ρ ω h 0 At present the values of the coupling constants are far from being reliably established. The projected measurement of the anapole moment in 173 Yb should provide an important constraint. Ask E158 SLAC group for an update after Jan. 2007

13 Signature of the weak interaction in atoms h NSI mixes s 1/2 and p 1/2 states of valence electron A PV of dipole-forbidden transition. If A PC is also induced, the amplitudes interfere PC PV PC PC PV PV R A + A A + 2 A A + o( A ) A PC Interference A PC A PC interference E-field Stark-effect E1 PC-amplitude E E1-PNC interference term is odd in E MUST: Reversing E-field changes transition rate Determine A PC with high precision Transition rate A PV A Limit A Stark PC

14 Results of APV measurements Atom Transition Group Year Measurement -Im(A PV /M1) (10-8 ) 209 Bi 4 S 3/2-2 D 3/2 Oxford (20) 2% 208 Pb 3 P 0-3 P 1 Seattle (12) 1.2% 205 Tl 133 Cs 6P 1/2 1/2-6P 3/2 6S 1/2 1/2-7S 1/2 Anapole moment: Unpaired proton 133 Cs Oxford (33) 3% 3/2 Oxford (45) 3% Seattle (17) 1.2% -Im(A PV /β) (mv/cm) 1/2 Boulder (34) 2% Boulder (6) 0.35% Paris (40) 2% Cs I=7/2 205 Tl I=1/2 κ A (6.2) -22(30) * Measurements of APV with precision better than 5%

15 Ongoing experiments on APV Group Atom/Ion Goal Advantages Status Berkeley Yb isotopic chain Nuclear structure, anapole moment A PNC PNC is a factor of 100 bigger than that of Cs. Seven isotopes. Ongoing measurements Seattle Single trapped Ba + (Ra + ) Q W, anapole moment Precise theory, A PNC is a factor of 20 bigger than that of Cs. Nine stable isotopes, ΔN=8 Preliminary exps. on RF spectroscopy of trapped ions Stony Brook, Legnaro,, Yale, TRIUMF (Vancouver) Cold Fr Anapole moment Precise theory, bigger effect than that of Cs, trapped atoms Preliminary exps. on trapping of Fr Yale Diatomic molecules Anapole moment, C 2 A PNC is enhanced due to proximity of the opposite parity levels. Level crossing. Development of theory and exp. techniques

16 Atomic structure of Yb Proposed by D. DeMille, PRL 1995 By observing the 6s 21 S 0 6s6p 3 P nm decay the pumping rate of the 6s 21 S 0 6s5d 3 D nm transition is determined. In addition, the population of 6s6p 3 P 0 metastable level is probed by pumping the 6s6p 3 P 0-6s7s 3 S nm transition.

17 Yb isotopes and abundances Seven stable isotopes, two have non-zero spin C.J. Bowers et al, PRA 1999

18 Rotational invariant and geometry of Rotational invariant to which the PV-Stark interference term is proportional is chosen so that E is along the excitation light axis. This suppresses the interference between M1 and Stark amplitudes emphasizing the PV-Stark contribution. the Yb experiment ρ ρ ρ ρ ρ ( ε B) ( ε ( E B ) r r = i ( ) j m m m j m r A = iξ ( 1) ε j, m,1, m m j, m ; q = m m q q A Stark β ( 1) E ε,,1,, -q q q PNC -q Reversals: B even E odd θ θ±π/2 odd β = 2.24(25) 10-8 e a 0 /(V/cm) Stark transition polarizability (Measured by J.Stalnaker at al, PRA 2006) ξ = 1.08(24) 10-9 (Q W /104) e a 0 /(V/cm) Nuclear spin-independent PV amplitude (Calculations by Porsev et al, JETP Lett 1995; B. Das, PRA 1997 )

19 PV effect on line shapes: even isotopes r E = (E,0,0) r ε = (0,sinθ,cosθ) R = E sin θ + 2E sin θcosθ β βξ 2 2 ± 1 β E 2 R = cos θ E βξ sinθcosθ Yb PV-Stark interference terms Rate modulation under the E-field reversal yields: RE+ RE 2ξ = R + R β E E+ E

20 PV effect on line shapes: odd isotopes r E = (E,0,0) r ε = (0,sinθ,cosθ) β E 6 β E center FF 2 2 R = (4sin θ + cos θ) + E βff ξ sin θcosθ 2 2 side FF 2 R = cos θ E βff ξ sin θcosθ r r ξ = ξ + I J ξ ξ NSD ea 0 for odd Yb isotopes ξ=10-9 ea 0 ξ` must be measured with 0.1% accuracy NSD

21 Experimental setup Light collection efficiency: Interaction region: ~0.2% (556 nm) Detection region: ~25% Yb density in the beam ~10 10 cm -3 Reversible E-field up to 15 kv/cm, spatial homogeneity 99% Reversible B-field up to 100 G, homogeneity 99%

22 Optical system and control electronics Light powers: Ar + : 15W Ti:Sapp (816 nm): 1W Doubler (408 nm): 50 mw PBC: Confocal design, 25 cm; Finesse ~4000 (upgrading to 40000) Locking: Pound-Drever-Hall technique

23 Doppler width and spectral resolution Intensity [V] MHz 173 Yb (5/2-3/2) 176 Yb 17 MHz Frequency shift [MHz] Application of the atomic beam collimator allows to reduce the Doppler broadening by a factor of 10. Spectral lines of closely neighboring isotopes can be clearly resolved. Scanning over 408 nm line, observing 556 nm fluorescence at the interaction region.

24 Line shapes under the B-fieldB 174 Yb Under application of B-field line profiles demonstrate predicted shapes Signal averaged over 100 scans Scan rate = 1 Hz Ready to collect data with E-field reversals

25 Systematic effects E ρ = ρ ( E, de, de y z ) E-field inhomogeneity B = ( dbx, dby, B0 ) B-field inhomogeneity ρ ε = ( 0, e idc (sin θ + dθ cosθ),cosθ dθ sin θ) dk ρ Residual light propagation in the PBC ( ( ) ( ) ) β ξ -q Distortion of linear polarization of the light M1~300ξ r r r r r Σ = i + M dk + i F m m m F m q q A ( 1) E ε 1 ε ε,,1,, -q -q Terms having same dependence on the leading E-field reversal and same polarization angle dependence as the Stark-PNC interference term must be limited dbx de y β B β dc de z << ξ << ξ Required: Non-reversing db x, de z << 1%

26 Summary The program of measurements needed to understand the system is complete It is now possible to proceed with confidence towards a first measurement of APV in Yb The challenge will then be to refine the system to achieve the fractional precision needed to observe NSD effects

27 Timeline Berkeley experiment: ½ yr A PV enhancement, A PV :10% 1 yr Q W in single Yb isotope, A PV :1% 1½ yr Q W in chain of Yb isotopes, A PV :0.1% 2 yr Anapole moment ElectroWeak Workshop