Funding: Yale University, NSF Molecular Anapole Factory Fabbrica Anapole Molecolare 17:45 siamo afFAMati Sidney Cahn Yale University F Ba Funding: Yale University, NSF 9/6/11 PAVI 2011 Sidney Cahn

The mechanisms for PNC in atoms & molecules Nuclear spin-dependent PNC & the nuclear anapole moment The most sensitive atomic PNC experiment (Berkeley, Dy) The (great) advantages of diatomic molecules A Signal Strategy Sim. Signals Exp. Details: Source, Interaction Region, Detection Region Real Signals for 138Ba F Prospects: “anapole moment table” + better measurements of VeAN couplings C2N, C2P 9/6/11 PAVI 2011 Sidney Cahn

The primary mechanism for PNC in atoms Z0 Ve + Ae VN + AN e C1(N,P): AeVN term leads to term in atomic Hamiltonian simplest PNC invariant short-range Yukawa potential axial vector associated with electron 9/6/11 PAVI 2011 Sidney Cahn

With an energy difference Hz “This value is, of course, fantastically small.” -I. B. Khriplovich 9/6/11 PAVI 2011 Sidney Cahn

Effect of Z0-exchange on atomic structure mixes s1/2 and p1/2 states: (Mixing coefficient i pure imaginary because of T invariance) PNC effects grow rapidly with Z: 9/6/11 PAVI 2011 Sidney Cahn

VeAN term depends on nuclear spin: NSD-PNC Z0 Ve + Ae VN + AN e VeAN term gives Hamiltonian: Why is it smaller than AeVN? 1. Ve/Ae = (1-4sin2W) ~ .08 2. Only one unpaired nuclear spin: ~1/Z compared to QW  VeAN /QW ~ (1-4sin2W)/Z ~ 10-3 for heavy atoms 9/6/11 PAVI 2011 Sidney Cahn

Suppression of tree-level NSD-PNC diagram makes radiative corrections non-negligible! Ve+Ae Ae e e g Z0 Z0  I VN+AN VN I Z0, W± N N N PNC weak interactions inside nucleus induce nuclear “anapole moment” that couples to electron magnetically Tree-level NSD-PNC from suppressed VeAN term Coherent sum of weak charge (AeVN) and electromagnetic hyperfine interaction 9/6/11 PAVI 2011 Sidney Cahn

a  Zfor A  10 (odd proton) Overall Z2 NSD-PNC vs. Z/A NSD-PNC Hamiltonian Differing dependences on Z/A ZP = -ZN = -(1-4sin2W)gA/2  -.05 (indep. of A) Q  A2/3 is both small (< a /4) & well understood--ignore  In heavy atoms, anapole dominates:a > Z! (Collective enhancement causes radiative correction > tree level!) a  Zfor A  10 (odd proton) A  100 (odd neutron) 9/6/11 PAVI 2011 Sidney Cahn

PNC in the nucleus induces a nuclear spin helix = magnetic dipole + anapole Simple model for nuclear anapole (valence nucleon + constant-density core): 9/6/11 PAVI 2011 Sidney Cahn

A closer look at the nuclear anapole moment PNC weak interactions between nucleons perturb nuclear structure: N2 N2’ , ,  Z0, W N1 N1’ “DDH” description of hadronic PNC Hamiltonian for valence nucleon gives spin-momentum correlation 6 terms in principle; only 2 linear combinations of terms important in practice 9/6/11 PAVI 2011 Sidney Cahn

Assuming ~30% uncertainty in nuclear structure calculations Status of hadronic PNC measurements & effect of future anapole measurements Odd-p isotopes (4) Odd-n isotopes (3) Assuming ~30% uncertainty in nuclear structure calculations 9/6/11 PAVI 2011 Sidney Cahn

Determination of C2’s (?) C. Bouchiat and C.A. Piketty, Z. Phys. C. 49, 91 (1991). Y ~  27Al X ~ A2/3 * f(structure) 9/6/11 PAVI 2011 Sidney Cahn

Determination of C2’s (?) Measurements with a few heavy nuclei would determine intranuclear PNC couplings to ~30% (nuclear structure unc.) Additional measurements could be interpreted as measurements of Z with uncertainty Z/Z ~ 0.2  (a/Z)  A2/3    The goal: 20% measurement of NSD-PNC in nuclei with a ~ Z i.e., Al (Z=13, A=27); Sr (Z=38, A=87)  This requires a technique with greatly improved sensitivity! 9/6/11 PAVI 2011 Sidney Cahn

Determination of C2’s (?) PV-DIS (JLAB) projected Bates SAMPLE e-p vs. e-D elastic scattering 2000+2003 anticipated light odd-n isotope (87Sr) (proj.) Current allowed region Standard Model prediction SLAC e-D deep- inelastic scattering (‘79) 9/6/11 PAVI 2011 Sidney Cahn

A Yale Collaboration Named eeman-tuned ptically prepared and detected olecular eams for the nvestigation of lectroweak effects using tark interference. Z O M B I E S PAVI 2011 Sidney Cahn

Using molecules to get at NSD-PNC Diatomic molecules systematically have close rotation+hyperfine levels of opposite parity--B-field tuning can give E ~ 10-11 eV! [Sushkov, Flambaum, Sov. Phys. JETP 48, 608 (1978), Flambaum, Khriplovich, Phys. Lett. A 110, 121 (1985) 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 [Herzberg, 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-, 2S1/2 state) amenable to interpretation (via calculated valence electron wavefunctions) at ~20% level [Kozlov & Labzowsky, J. Phys B 28, 1933 (1995)] 9/6/11 PAVI 2011 Sidney Cahn

The most sensitive atomic PNC experiment: Dy “Close enough” energy levels D = 3.1 MHz + B-field tuning to near degeneracy gives small energy denominator ~10-11 eV(!) and maximal sensitivity c.f. Cs (Boulder) HW ~ 14 Hz 9/6/11 PAVI 2011 Sidney Cahn

Free radical rotation + hyperfine Zeeman 9/6/11 PAVI 2011 Sidney Cahn

Experimental schematic B E0 |B> |A> 9/6/11 PAVI 2011 Sidney Cahn

Near Crossing Apply Oscillating E Field |B> E Field |A> Center of Magnet 9/6/11 PAVI 2011 Sidney Cahn

Strategy to detect PNC in near-degenerate levels |B> |A> D. DeMille, S.B. Cahn, D. Murphree, D.A. Rahmlow, and M.G. Kozlov Using molecules to measure nuclear spin-dependent parity violation PACS: 37.10.Gh 11.30.Er 12.15.Mm 21.10.Ky Phys. Rev. Lett. 100, 023003 (2008) Weak Term Odd in E Stark Term Even in E 9/6/11 PAVI 2011 Sidney Cahn

Signal and Asymmetry 9/6/11 PAVI 2011 Sidney Cahn

Simulated/Calculated signals for 137BaF Dots: Numerical Solid: Calculated 137BaF;  ~ 2*1 kHz  = 2*10 kHz dE0 / = 0.1 HW =2*4 Hz 9/6/11 PAVI 2011 Sidney Cahn

Viable nuclei for anapole measurement Everything OK (one dot/isotope) Only molecular spectral data needed Only isotopically enriched sample needed Maybe possible with cryogenic beam source Radioactive (unnatural e pericoloso) 9/6/11 PAVI 2011 Sidney Cahn

Sensitivity estimates t ~ 100 ms (6 cm @ typ. Velocity) ~ 1 kHz  1/(2pt) (0.1 ppm B-field homogeneity) dN/dt ~ 104/s (Hinds pulsed beam) for time T With dHW ~ 10 Hz/T(sec) molecule Z ka/k2 HW(Hz) T (10%) 199HgF 80 1/1 60 3 s 137BaF 56 0.7/1 10 100 s 87SrF 38 0.5/1 4 20 m 113InO 49 3/1 20 30 s 27AlS 13 1.5 100 m 9/6/11 PAVI 2011 Sidney Cahn

Nucleon “Axe”-ial Weak Couplings INT 08-3 Program “Low Energy Precision Electroweak Physics in the LHC Era” The gmg5 Project Nucleon “Axe”-ial Weak Couplings D. DeMille, S.B. Cahn, D. Murphree, D.A. Rahmlow, and M.G. Kozlov Using molecules to measure nuclear spin-dependent parity violation PACS: 37.10.Gh 11.30.Er 12.15.Mm 21.10.Ky Phys. Rev. Lett. 100, 023003 (2008) PAVI 2011 Sidney Cahn

Near Crossing Apply Single Pulse E Field (step potential) |B> E Field |A> Center of Magnet 9/6/11 PAVI 2011 Sidney Cahn

Simple Stark mixing at a level crossing |B> D |A> dt Fourier Transform of Electric Field 9/6/11 PAVI 2011 Sidney Cahn

Typical level-crossing data Dm = 0 crossings E-field from step potential on cylindrical boundary B-field at crossing from position of peak Interaction time t from width of peak agrees with calc. within 5% D 9/6/11 PAVI 2011 Sidney Cahn

Typical level-crossing data Dm = +/-1 crossings E-field time dependence & lineshape similar to that for PV measurement B-field at crossing from position of central dip Radial E-field D 9/6/11 PAVI 2011 Sidney Cahn

Calculated Level Crossings in 138BaF from spin-rotational Hamiltonian: Energy vs. Magnetic Field |ms, mI, mN> Hamiltonian + E-field map + E-field pulse + signal expression + line data Line width Data table Stats & estimated uncertainty Conclusions page 9/6/11 PAVI 2011 Sidney Cahn

Recently Extracted 138BaF X-ings Type Initial Calc.X Obs. X Calc. d Obs. d Unc.obs. (Gauss) (Gauss) (Hz/V/cm) (Hz/V/cm) (Hz/V/cm) Preliminary 9/6/11 PAVI 2011 Sidney Cahn

Rabi-Flopping In 138BaF Preliminary 9/6/11 PAVI 2011 Sidney Cahn

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 Z0 couplings (C2’s) at 20-50% level possible after several iterations Likely extensions with new molecular data, new sources of cold molecules: an “anapole factory”?!? 9/6/11 PAVI 2011 Sidney Cahn

He at 4K Buffer Gas Cooling High Flux, Beam Source for Cold, Slow Atoms or Molecules, S.E. Maxwell, et al Phys. Rev. Lett. 95, 173201 (2005) Laser Cooling of a Diatomic Molecule, E.S. Shuman, J.F. Barry, D. DeMille, Nature 467, 820–823 (14 October 2010) 9/6/11 PAVI 2011 Sidney Cahn

BRH137 > 87 > 27 > 4 The lowest A nuclei, we may consider next, in a triatomic molecule would give 1,2 < 4 H,D Si = O 9/6/11 PAVI 2011 Sidney Cahn

Yale ZOMBIEs Misha Kozlov PNPI Foreign ZOMBIE ZOMBIE Bokor* Dave DeMille ZOMBIE Patient Zero: Sid Cahn ZOMBIE Grad. Stud. Jeff Ammon ZOMBIE Post-Doc Emil Kirilov Dave Rahmlow Dennis Murphree U Conn. Ven. Financial Former ZOMBIEs *http://en.wikipedia.org/wiki/Zombie Ed Deveney Rich Paolino Bridgewater State USCG Academy Non-local ZOMBIEs Rising ZOMBIE Corey Adams 9/6/11 PAVI 2011 Sidney Cahn

CAD ZOMBIE-land? Prod Prep Stark Detect 9/6/11 PAVI 2011 Sidney Cahn

ZOMBIE-land in the flesh! PAVI 2011 Sidney Cahn

Can these measurements be interpreted? Semi-empirical method determines electron wavefunctions from experimental data on hfs & g-factors Broad expectation of ~20% uncertainty from molecular theory 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 (vs. EDM) & for other molecules (already done for BaF w/20% agreement) Possibility to cross-check vs. anticipated atomic results for Yb, Ba!  ~20% accuracy in interpretation seems very likely AND can be checked explicitly vs. other systems 9/6/11 PAVI 2011 Sidney Cahn

What about systematics? multiple reversals (dE/dt, , B, |A>|B>)  systematics require product of two imperfections main residuals from stray dc E-field + B-field gradient BUT effect of stray E strongly suppressed at crossing point (requires spin flip); HW /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 cross-check vs. atomic experiments (Ba, Yb)? 9/6/11 PAVI 2011 Sidney Cahn