Sidney B. Cahn Yale University

Transcription

1 Sidney B. Cahn Yale University Первое сообщение о прогрессе в фтористый барий в Ельском опыте Второе будет о возможных систематических действиях в ловушках с использованием низкотемпературного масла (фомблин) для покрытий стенок ловушки для времени жизни нейтронов.

2 анапольный момент тороидальные токи 1957 Яков борисович зельдович 1957

3 Яков борисович зельдович

4 удержаниe нейтронов в графитовых и бериллиевых сосудах 1959 Яков борисович зельдович 1959

5 Яков борисович зельдович

6 Ya. B. Zeldovich, Sov. Phys. JETP 33,1531 (1957), Electromagnetic Interaction with Parity Violation V.V. Flambaum and I.B. Khriplovich, Sov. Phys. JETP 52(5), Nov. 1980, P-odd nuclear forces a source of parity violation in atoms V.V. Flambaum, I.B. Khriplovich and O.P. Sushkov, Phys. Lett. 146B, 367 (1984), Nuclear Anapole Moments O.P. Sushkov and V.V. Flambaum, Sov. Phys. JETP 48(4), Oct. 1978, Parity breaking effects in diatomic molecules L.N. Labzovskii, Sov. Phys. JETP 48(3), Sept. 1978, L-doubling and parity non-conservation effects in spectra of diatomic molecules V.V. Flambaum and I.B. Khriplovich, Phys. Lett. 110A (3), 15 July 1985, 121, On the Enhancement of Parity Nonconserving Effects in Diatomic Molecules M.G. Kozlov, Sov. Phys. JETP 62(6) December 1985, Semiempirical calculations of P- and P,T-odd effects in diatomic molecules-radicals M.G. Kozlov, V.I. Fomichev, Yu Yu Dmitriev, L.N. Labzovsky and A.V. Titov, J.Phys. B: 20(1987) 4939, Calculation of the P- and T-odd spin-rotational Hamiltonian of the PbF molecule M.G. Kozlov, L.N. Labzovskii, and A.O. Mitrushchenkov, Sov. Phys. JETP 73 (3) Sept. 1991, Parity nonconservation in diatomic molecules in a strong constant magnetic field.

7 The primary mechanism for PNC in atoms e V e + A e e A e V N term leads to term in atomic Hamiltonian Z 0 simplest PNC invariant H G F r ( σ r r p) δ 3 ( ) N V N + A N N 2 1/ mz axial vector associated with electron short-range Yukawa potential

8 s Effect of Z 0 -exchange on atomic structure 1/ 2 H s 1/ 2 r r 3 r G ( σ p) δ ( ) F + s 1/ 2 E H Weak E p ( p1/ 2 s1/ 2 mixes s 1/2 and p 1/2 states: 1/ 2 ) p 1/ 2 = s 1/ 2 + iη (Mixing coefficient η pure imaginary because of T invariance) PNC effects grow rapidly with Z: p r Z; 3 δ ( r ) = ψ(0) 2 Z; p 1/ 2 A V e N : Q W 2 = 2( NC1 n + ZC1 p) = N + Z(1 4sin θ s HWeak p i R( Z Z 1 / 2 1/ 2 ) W 3 ) N Z All atomic PNC observations made in heavy atoms (Z 55)

9 V e A N term depends on nuclear spin: NSD-PNC e V e + A e e V e A N term gives Hamiltonian: r r r r 3 r H G ( I σ)( σ p) δ ( ) F Z 0 Why is it smaller than A e V N? 1. V e /A e = (1-4sin 2 θ W ) ~ Only one unpaired nuclear spin: ~1/Z compared to Q W N V N + A N N V e A N /Q W ~ (1-4sin 2 θ W )/Z ~ 10-3 for heavy atoms

10 Suppression of tree-level NSD-PNC diagram makes radiative corrections non-negligible! e e e V e +A e σ e A e σ e Z 0 I γ Z 0 γ N V N +A N N Z 0, W ± N V N I Tree-level NSD-PNC from suppressed V e A N term PNC weak interactions inside nucleus induce nuclear anapole moment that couples to electron magnetically Coherent sum of weak charge (A e V N ) and electromagnetic hyperfine interaction

11 A closer look at the nuclear anapole moment PNC weak interactions between nucleons perturb nuclear structure: N 1 N 1 π, ρ, ω Z 0, W ± N 2 N 2 Hamiltonian for valence nucleon gives spin-momentum correlation r r r r H ~ G ( σ p) g F(, τ) F eff, i i i 6 terms in principle; only 2 terms important in practice

12 PNC in the nucleus induces a nuclear spin helix = magnetic dipole + anapole = + Simple model for nuclear anapole (valence nucleon + constant-density core): r a ~ G F g eff eμ m r p 0 A 2/3 I

13 NSD-PNC Hamiltonian H NSD NSD-PNC vs. Z ( κ Z + κ r ) ( I κ Zp = -κ Zn = -(1-4sin 2 θ W )g A / a + κ Q r r σ )( σ r p) δ r ( ) 3 r κ a 9 10 αμ A mr 0 2/3 g eff.08g eff A 100 2/3 ( g p 4, g n ~ < 1) κ Q small (<κ a /4), well understood--ignore In heavy atoms, anapole dominates: κ a > κ 2! (Collective enhancement causes radiative correction > tree level!) κ a κ 2 for A 10 (odd proton) A 100 (odd neutron)

14 Status of hadronic PNC measurements & effect of future anapole measurements Odd-p isotopes ( 4) Odd-n isotopes ( 3)

15 Determination of C 2 s (?) Measurements with a few heavy nuclei would determine intranuclear PNC couplings to ~30% (nuclear shell model acc.) Additional measurements could be interpreted as measurements of κ Z with uncertainty δκ Z /κ Z ~ 0.2 (κ a /κ Z ) A 2/3 The goal: 20% measurement of NSD-PNC in nuclei with κ a κ Z i.e., Al (Z=13, A=27); Sr (Z=38, A=87) This requires a technique with greatly improved sensitivity!

16 Determination of C 2 s (?) light odd-n isotope ( 87 Sr) light odd-p isotope ( 27 Al) Bates SAMPLE e-p vs. e-d elastic scattering C2d SLAC e-d deepinelastic scattering ( 79) C 2u

17 Discovery potential for new physics? NuTev (3σ anomaly!) molecule PNC Λ 1 = mass scale (TeV) of 4-Fermi contact operators induced by compositeness of fermions from M. Luo, The Future in Precision Tests of the Standard Electroweak Model, Ed. P. Langacker (World Scientific 1995)

18 Using molecules to get at NSD-PNC Diatomic molecules systematically have close rotation+hyperfine levels of opposite parity-- B-field tuning can give ΔE ~ ev! [Kozlov, Labzowsky, & Mitruschenkov, JETP 73, 415 (1991)] Ground state levels have long lifetimes, narrow lines high sensitivity to PNC energy shifts (from AC Stark) [Fortson] Can use proven technique for nearly-degenerate levels (atomic Dy) [Nguyen, Budker, DeMille, & Zolotorev PRA 56, 3453 (1997)] Versatile, well-characterized beam source for all desired species [widely used; charaterized by Tarbutt et al., {Hinds}, J. Phys. B 35, 5013 (2002).] Wide range of molecular species with required spectroscopic data already known [Hertzberg, etc.] Estimated sensitivity sufficient for desired low-z nuclei (odd p and odd n), plus wide range of heavier nuclei Simple molecules (1 valence e -, 2 S 1/2 state) amenable to interpretation (via calculated valence electron wavefunctions) at ~20% level [Kozlov & Labzowsky, J. Phys B 28, 1933 (1995)]

19 Free radical rotation + hyperfine Zeeman Rotation J P + e - spin 1/2 + nuclear spin (I=1/2) B-field required for crossing of opposite-parity levels is μ B B ~ rotational splitting hfs < rotational splitting (except for heaviest systems) so B decouples hfs 3/2-1/2-1/ B

20 Free radical rotation + hyperfine Zeeman 137 BaF rotation/hfs Zeeman shifts (I=3/2) Energy (MHz) Magnetic field B (Gauss)

21 Strategy to detect PNC in near-degenerate levels B> H = A> A B ( 0 ihw + de ih + de Δ iδt ψ ( t) = c ( t) A + c ( t) B e ; c (0) = 1 A B W A B B ) E = E0 sin( ω t); de0 << ω; Δ < ω A ψ ( T ) = ΔT 2 2 H Δ 2 2 W 2 4sin de ω 0 Weak Term Odd in E + 2 de0 ω Stark Term Even in E

22 Simulated signals for 137 BaF Ideal Asymmetry Broadened Asymmetry 137 BaF; Δ ~ 1/T ~ 1kHz ω = 2π*100 khz de 0 /ω = 0.1 H W = 4 Hz Asymmetry ξ = ξ = H Δ H Δ W W 0 ω de 0 ω de 0 Δ Δ Γ Detuning Δ (khz)

23 Боже мой!

24 YCBM Yale Compact Beam Machine

25 Дейвид *СТАХАНОВ* Рамло

26

27 B-Field homogeneity is key to experiment! We use magnetic field probes based on Nuclear Magnetic Resonance Measuring the proton precessional frequency tells us the magnetic field value An array of these probes will monitor the magnetic volume We need a field which is homogeneous to 0.1 ppm over a cylinder of L=5cm R=0.5cm

28 MRI Primate Magnet

29 Prior Status Previously we had 0.12ppm homogeneity over an L=2cm R=1.25cm cylinder using only superconducting shim coils! Extending this region to 5cm should be straightforward thanks to room temperature shimming coils Next step: array of probes

30 NMR Probe

31 Array of NMR probes

32 Деннис мурфрий

33 Spectrometer Circuit Diagram

34 Homogeneity Before and After Shimming

35 Versatile beam source of free radicals Widely used by physical chemists; characterized for YbF Tarbutt, Hudson, Sauer, Hinds Рыжов, Рябов, Ежов Pulsed supersonic beam for rotational cooling (T~3K) Metal atoms (laser ablated) + reactive carrier gas admixture combine to form free radicals dn/dt ~ 10 4 /s demonstrated for many

36 BaF Spectrum R1 4.5 Q1 5.5 Q1 6.5 Q1 7.5 Q1 8.5 Q1 9.5 Q Q Q Q Q Q1 5 Q1P 6 Q1P 7 Q1P 8 Q1P 9 Q1P 10 Q1P 11 Q1P 12 Q1P 13 Q1P 14 Q1P 15 Q1P 5 Q1M 6 Q1M 7 Q1M 8 Q1M 9 Q1M 10 Q1M 11 Q1M 12 Q1M 13 Q1M 14 Q1M 15 Q1M 16 Q1M 5 Q1P1 6 Q1P1 7 Q1P1 8 Q1P1 9 Q1P1 10 Q1P1 11 Q1P1 12 Q1P1 13 Q1P1 14 Q1P1 15 Q1P1 5 Q1M1 6 Q1M1 7 Q1M1 8 Q1M1 9 Q1M1 10 Q1M1 11 Q1M1 12 Q1M1 13 Q1M1 14 Q1M1 15 Q1M1 16 Q1M1 4.5 QR QR QR QR QR QR QR QR QR QR QR QR QR QR QR QR QR QR QR QR QR QR QR QR12

37 Beam Intensities Molecule BaF YbF BaF Distance from source(m) Beam Size (diam) Solid Angle Det. Eff Pulse rate (Hz) Flux/pulse 8.79 e5 3.18e5 1.58e4 Flux/pulse/str/puls e/rot state 5.27e7 2.55e8 1.39e6

38 Molecule PNC Experimental schematic B E 0 B> A>

39 Sensitivity estimates τ ~ 160 μs (5 typ. Velocity) Γ~ 1 khz 1/(2πτ) (0.1 ppm B-field homogeneity) dn/dt ~ 10 4 /s (Hinds pulsed beam) for time T 1 With δh W τ T dn / dt ( ) δh W ~ 10 Hz/ T(sec) molecule Z k a /k 2 H W (Hz) T (10%) 199 HgF 80 1/ s 137 BaF 56 1/ s 87 SrF 38 1/ m 113 InO 49 3/ s 27 AlS 13 1/ m

40 Can these measurements be interpreted? Semi-empirical method determines wavefunctions from experimental data on hfs & g-factors Broad expectation of ~20% uncertainty Same method used to calculate electron EDM enhancement in YbF EDM enhancement for YbF also calculated by 3 different ab initio methods--agree with each other & semi-empirical within 20% Should be checked explicitly for anapole, other molecules Can cross-check vs. anticipated atomic results for Yb, Ba! 20% accuracy in interpretation seems very likely AND can be checked explicitly!

41 What about systematics? multiple reversals (de/dt, Δ, B, A> B>) systematics require product of two imperfections main residuals from stray dc E-field + B-field gradient BUT effects of stray E strongly suppressed at crossing point (requires spin flip); H W /d ~ 1 mv/cm typical! multiple crossing points with wildly different PNC/Stark ratios because of angular factors can check for systematic deviations in non-trivial way

42 B-field crossing points for 137 BaF Energy (MHz) Magnetic field B (Gauss) B (G) m F <A H W B> (Hz) PNC/d (mv/cm) / / / /

43 Periodic chart of viable nuclei

44 Conclusions & Outlook Molecule PNC experiments look very promising for study of NSD-PNC: excellent S/N & systematics, leverage from developed techniques Multiple nuclei (odd p, odd n) immediately available for anapole moment determination at ~20% level Measurements of fundamental Z 0 couplings (C 2 s) at 20-50% level possible after several iterations Likely extensions with new molecular data, new sources of cold molecules: an anapole factory?!? Lots of work to do:

45 Acknowledgements: Yale University Professor David P DeMille David Rahmlow, Dennis Murphree Graduate Students Professor Richard Paolino, USCG Professor Edward Deveney, BSC Миша Козлов, Виктор Ежов Моя Любимая Жена Лаура The National Science Foundation (NSF)