1. 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

2. 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
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PAVI 2011 Sidney Cahn

3. The primary mechanism for PNC in atomsZ0
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
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PAVI 2011 Sidney Cahn

4. With an energy difference Hz
“This value is, of course, fantastically small.”
-I. B. Khriplovich
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5. 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:
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PAVI 2011 Sidney Cahn

6. VeAN term depends on nuclear spin: NSD-PNCZ0
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
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PAVI 2011 Sidney Cahn

7. 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
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PAVI 2011 Sidney Cahn

8. 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

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

10. 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
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PAVI 2011 Sidney Cahn

11. 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
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PAVI 2011 Sidney Cahn

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

13. 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

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

15. 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

16. Using molecules to get at NSD-PNC
Diatomic molecules systematically have close rotation+hyperfine levels of opposite parity--B-field tuning can give E ~ 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)]
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PAVI 2011 Sidney Cahn

17. 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
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PAVI 2011 Sidney Cahn

18. Free radical rotation + hyperfine Zeeman
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19. Experimental schematicB E0
|B>
|A>
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PAVI 2011 Sidney Cahn

20. Near Crossing Apply Oscillating E Field
|B>
E Field
|A>
Center of Magnet
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PAVI 2011 Sidney Cahn

21. 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: Gh Er Mm Ky Phys. Rev. Lett. 100, (2008)
Weak Term
Odd in E
Stark Term
Even in E
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22. Signal and Asymmetry
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PAVI 2011 Sidney Cahn

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

24. 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)
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PAVI 2011 Sidney Cahn

25. Sensitivity estimates
t ~ 100 ms (6 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
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PAVI 2011 Sidney Cahn

26. 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: Gh Er Mm Ky Phys. Rev. Lett. 100, (2008)
PAVI 2011 Sidney Cahn

27. Near Crossing Apply Single Pulse E Field (step potential)
|B>
E Field
|A>
Center of Magnet
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PAVI 2011 Sidney Cahn

28. Simple Stark mixing at a level crossing
|B> D
|A> dt
Fourier Transform
of Electric Field
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PAVI 2011 Sidney Cahn

29. 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
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PAVI 2011 Sidney Cahn

30. 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
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PAVI 2011 Sidney Cahn

31. 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
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PAVI 2011 Sidney Cahn

32. 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
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33. Rabi-Flopping In 138BaF
Preliminary
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34. 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

35. 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, (2005)
Laser Cooling of a Diatomic Molecule,
E.S. Shuman, J.F. Barry, D. DeMille,
Nature 467, 820–823 (14 October 2010)
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PAVI 2011 Sidney Cahn

36. 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
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PAVI 2011 Sidney Cahn

37. 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 *
Ed Deveney Rich Paolino
Bridgewater State USCG Academy
Non-local ZOMBIEs
Rising ZOMBIE
Corey Adams
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PAVI 2011 Sidney Cahn

38. CAD ZOMBIE-land?
Prod
Prep
Stark
Detect
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39. ZOMBIE-land in the flesh!
PAVI 2011 Sidney Cahn

40. 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

41. 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