Low-energy T violation

4th Int. Symp. On Lepton Moments Centerville, Cape Cod July 19 - 22, 2010

o  Schiff’s theorem 101 o  T-violation & motivation o  A few words on β-decay (R,D) o  Mostly EDMs, theory thoughts

Rob G. E. Timmermans KVI, University of Groningen

With Cheng-Pang Liu & TRIµP group @ KVI

Prelude: The Schiff theorem

o  What is the crux? (atoms; non-technical) o  The Schiff theorem and its corrections revisited o  Why would experimentalists (or theorists) care?

The EDM: a harbinger* of the New Standard Model?

* One that initiates a major change; one that foreshadows what is to come [M-W].

It may be that the next exciting thing to come along will be the discovery of a neutron or

electron electric dipole moment… these seem to me to offer one of the most promising

possibilities for progress in physics

-  Purcell & Ramsey, 1950 -  Landau, 1957 -  Ramsey, 1958

Ultimately the validity of all such symmetry arguments must rest on experiment

The classics

E.M. Purcell & N.F. Ramsey, PR 87, 807 (1950); L.I. Schiff, PR 132, 2194 (1963).

The crux of the matter Shielding theorem (Schiff, 1963):

EDM of a nonrelativistic atom ≡ 0 i.e. point particles, Coulomb force

Electrostatic force balance, rearrangement of charged constituents to keep atom stationary - electron cloud screens nucleus - zero electric field on nucleus

The measurability of EDMs is severely constrained; one has to exploit the loopholes (Schiff ‘63, Sandars ‘65): -  relativistic effects (electron) -  finite-size effects (nucleus) -  magnetic interactions (electron-nucleus)

Residual interaction: HEDM = -eS•[∇,δ(re)] S = P- & T-odd EM moment, “Schiff moment ” S ~ offset δ〈r2〉 of charge & dipole rms distributions in nucleus.

Electric field in neutral radium atom: -  induced and applied static external -  time-dependent Hartree-Fock (RPA+exchange)

The Schiff theorem at work

Jacinda Ginges, priv. comm. (2008); cf. Dzuba et al., PLA 118, 177 (1986).

Total field at the nucleus: E = E0Zi/Z, Zi = Z-n, charge of ion Note E ≈ -5E0 at r ≈ a0/Z , radius of 1s electron.

Group System Advantages Proj. gain D. Weiss (Penn State) Cs Rb opt. latt. Long coherence 400 D. Heinzen (Texas) Trapped Cs Long coherence 100?

H. Gould (LBL) Cs fountain Long coherence 100? Y. Sakemi (RCNP) Trapped Fr Long coherence 100? L. Hunter (Amherst) GdIG solid Huge S/N 100? S. Lamoreaux (Yale), C.-Y. Liu (Indiana) GGG solid Huge S/N 100-105? E. Hinds, B. Sauer (Imperial) YbF beam/trap Int. E, long T 10-100 D. DeMille (Yale) PbO* cell Int. E, good S/N 2-100? J.M. Doyle, G. Gabrielse (Harvard), D. DeMille (Yale)

ThO cold beam Int. E, good S/N 10-103

E. Cornell (JILA) Trapped HfF+ Int. E, huge T 100? N. Shafer-Ray (Oklahoma) PbF beam/trap Int. E, long T 100? L. Willmann, K. Jungmann (KVI) 213Ra At. enhanc. 103-104? J. Miller, Y. Semertzidis, Y. Kuno (J-PARC)

Muon Dedicated magn. storage ring

105-106

K. Kirch (PSI), G. Onderwater (KVI) Muon Small ring 104

Ongoing lepton EDM searches

Adapted from D. DeMille, no doubt incomplete, please give updates & corrections…

d(atom) ↔ d(

electron) ?

Group System Advantages Proj. gain D. Wark, M. v.d. Grinten, P. Harris (Sussex/RAL, ILL)

UCN Cryogenic 10-100?

O. Naviliat-Cuncic, K. Kirch (PSI), S. Paul (Munich)

UCN Neutron intensity 10-100?

S. Lamoreaux, M. Cooper, J.C. Peng (LANSCE, SNS)

UCN in superfluid 4He

3He comagnetometer 100-103?

N. Fortson (Washington) 199Hg vapor cell ? M. Romalis (Princeton) Liquid 129Xe Density, long T 100-105 P. Fierlinger (Munich) L129Xe on chips ? ? K. Asahi (Tokyo Tech) 129Xe Optical coupling

nuclear spin oscillator ?

T.E. Chupp, C.E. Svensson (TRIUMF)

223Rn cell Nucl. enhanc. 10-100?

Z.-T. Lu, R. Holt (ANL) Trapped 225Ra At. + nucl. enhanc. 104-106? L. Willmann, K. Jungmann (KVI) Trapped 213,225Ra At. + nucl. enhanc. 104-106? Storage Ring EDM Collab., Y. Semertzidis (BNL) et al.

Proton Deuteron

Dedicated magn. storage ring

105-106 > 1014

Ongoing hadronic EDM searches

Adapted from D. DeMille, no doubt incomplete, please give updates & corrections…

d(atom) ↔ Sc

hiff moment

?

Amplification in paramagnetic atoms & polar molecules Enhancement: dpara /de ~ Z3α2 where Z2α2 due to relativity, Z from field of nucleus Eext ~ 101-4 V/cm : Eint ~ Z3α2e/a02 ~ 108-10 V/cm

Atomic calculation for Cs, Tl, Fr, Ra : dpara/de ~ 100, -585, 1150, 40.000

P.G.H. Sandars, PL 14, 194 (1965); PL 22, 290 (1966); PRL 19, 1396 (1968).

Limit on proton EDM: dp ~ d(205Tl) = -1.5(2.5)X10-23 e.cm

Polar molecule: “ion-like” charge separation: Schiff cancelled: shielding/enhancement = 0.67

The EDM landscape

Contributions to the EDM of an atom

The atomic EDM consists of:

o  intrinsic EDMs of electron de and of the nucleus dnuc: dnuc consists of dn,p and the P- & T-odd NN interaction

o  polarization effects by the P- & T-odd electron-nucleus interaction Ve-nuc

- Nuclear excitations are much less effective: ΔEe/ΔEnuc ~ 10-6 - Ve-nuc contains P- & T-odd leptonic,semileptonic, and hadronic sources

P- & T-odd electron-nucleus interaction

Red vertices: P- & T-odd couplings

Nuclear EDM in diagram (b):

Paramagnetic systems

P- & T-odd ingredients: -  de, partially shielded -  P- & T-odd e-N interactions: not shielded -  P- & T-odd nucl. charge moments: S (partially shielded), C3, … -  P- & T-odd nucl. magn. moments: dnuc⊗µnuc , M2, …

Hydrogen-like systems (1s1/2 electron), scaling as Z or A increases:

(1) from the atomic structure (2) from the nuclear charge (3) from the coherent (isoscalar) nucleon contributions (4) from y2y in S, scales roughly as A2/3 (5) from M2 in Smag, scales roughly as A2/3

Q: Is the contribution from de really so dominant?

dA ( de : e-N : S : Smag ) ≈ Z x ( Z : A : A2/3 : A2/3 ) (1) (2) (3) (4) (5)

End of prelude; Lunch?

o  Interpretation of EDMs requires atomic, nuclear, particle theory o  Dominance of de for dpara and Schiff moment for ddia? o  Results for different systems (Hg, Ra, …) in Part II o  This should not take the fun out of it: Once finite EDMs are discovered, all this really starts to matter

Low-energy T violation

4th Int. Symp. On Lepton Moments Centerville, Cape Cod July 19 - 22, 2010

o  Schiff’s theorem 101 o  T-violation & motivation o  A few words on β-decay (R,D) o  Mostly EDMs, theory thoughts

Rob G. E. Timmermans KVI, University of Groningen

With Cheng-Pang Liu & TRIµP group @ KVI

time → ← time

start identical to start

antiparticle particle

P C T

After H. Wilschut

matter antimatter

mirror

A crown jewel: The CPT theorem

Holds on very general grounds: Nature is local, causal & Lorentz invariant. True for all gauge theories!

T (Wigner, 1932) is unlike P or CP (e.g. no quantum number); there are only few high-precision tests of T-invariance.

1.  “S-matrix reciprocity”: Sfi=S-i,-f , compare reaction and its inverse. Example: polarization P and asymmetry A in pp elastic scattering.

2.  Nonzero value of T-odd observable after weak decay: Can also be due to final-state interactions (“T-violation mimicry”) T-invariance + unitarity implies: 〈-f|HW|-i〉 = ∑f’ 〈f|S0|f’〉 〈f’|HW|i〉 = 〈f|HW|i〉 but only when S0 = 1, i.e. only when FSI can be neglected.

3.  Nonzero value of T-odd operator in a nondegenerate state: Best example: the electric dipole moment (EDM).

4. Difference in oscillation time from A to B and from B to A.

5. Energy level fluctuations: GUE vs. GOE.

How to find T violation?

ε KL ~ K2+εK1 ε’

KL → 2π

(dn)SM ~ 10-7.10-7. s12s2s3sδ x e/M ~ 10-32 e.cm

All CP-odd effects involve J ~ s12s2s3sδ In flavor-conserving nonleptonic interactions: no 1st-order T-violation

A nonzero EDM implies new physics!

(de)SM ~ 10-38 e.cm

CP & T violation in the SM

T-violation in the Standard Electroweak Model

1.  In flavor-conserving nonleptonic interactions, there is no T-violation in 1st-order weak in the CKM model

(dn)SM ~ 10－7.10－7 s12s2s3sδ x e/M ~ 10－32 e.cm

2. In semileptonic processes, there is no T-violation in 1st-order weak in the CKM model

(D/a)SM ~ 10－7 s12s2s3sδ ~ 10－11

3. The QCD “vacuum angle” (θ-term) has a stringent bound from the experimental limit on the neutron EDM

|θ| < 3 x 10－10

EDMs and triple correlations (D,R) probe TV beyond the SM

Experiments on nuclear β-decay have recently undergone a renaissance: the small recoil (≈ 100 eV) of the daughter nucleus can be measured with atomic-physics techniques: laser-cooling and trapping in magneto-optical traps: It is easier to measure things that stand still !

β-decay for new physics (non “V-A”) searches

The trap sample: o  isotope selective o  spin manipulation o  point source o  recoil-ion spectrometry

Ideal environment for precision experiments

Triple correlations in nuclear β-decay

Differential decay distribution:

A nonzero D- (or R-) coefficient in nuclear β-decay is evidence for T- (i.e. CP-) violation outside of the Standard Model. To measure the D-correlation in a recoil-experiment in a trap (MOT), a polarized sample of parent nuclei is needed.

Ongoing expt’s: 37K (Behr@TRIUMF) and 21Na (Wilschut@KVI)

In the SM, β-decay is left-handed, or “V-A”; in general, it could also be, partially, right-handed “V+A”, scalar “S”, or tensor “T”:

P. Herczeg & I.B. Khriplovich, PRD 56, 80 (1997).

I.B. Khriplovich, NPB 352, 385 (1991); P. Herczeg, PPNP 46, 413 (2001); J. Res. NIST 110, 453 (2005)

Connecting EDMs and β-decay J

pe pν J

pe σe

D = J(pexpν) P-even, T-odd

R = J(pexσe) P-odd, T-odd

D = a Im (aLR/aLL) R = －(a±b) Im (aLT/aLL) gT/2gA －a Im (aLS/aLL) gS/2gV a ~ MFMGT , b ~ |MGT|2

Limit β-decay Limit other (q e) Potential BSM (q→e)

Im (aLR/aLL) 10−3 n, 19Ne 3×10−7 EDM ++ Im (aLT/aLL) 3×10−3 8Li 10−4 EDM +/− Im (aLS/aLL) 0.1 19Ne+scalar 4×10−4 Γ(π→eν) −

R: strong limits from Tl EDM (P,T-odd e-q forces) and Γ(π→eν) D: limited by n and Hg EDM; can be as large as expt. for leptoquark-like models

H. Wilschut

+

-

A permanent electric dipole moment violates P and T. The experimental signature is a linear Stark effect, or a spin precession in an external electric field.

Ph.D. thesis J. Hudson

Spin-1/2: -  electric dipole moment -  magnetic dipole moment -  “anapole” moment

Spin-1: also electric & magnetic quadrupole moments

Nucleon EM current:

〈n|(JEM)µ|n〉 = un(p’)[f1γµ+…+dnσµνγ5qν]un(p) An atomic-physics quantity of interest to particle physics!

Static EM moments

-  SM EDMs are unmeasurably small: A finite EDM implies new physics! -  In SUSY models, several complex phases occur; in contrast to the SM, EDMs arise already at one-loop level

Pics. from M. Pospelov & A. Ritz, AP 318, 119 (2005).

Neutron EDM (10－23 e.cm): dn ≈ K sinθ [100 GeV]2/M2

The limits for SUSY are becoming uncomfortably tight (“SUSY CP problem”)…

Particle Limit [e.cm] (95% C.L.)

System Prediction SM [e.cm]

New Physics limit [e.cm]

electron 1.9x10－27 205Tl atom 10－38 10−27 muon 1.8x10－19 rest frame E 10－35 10−22 tau 3.1x10－16 e+e－→τ+τ－γ 10－34 10－20 proton 6.5x10－23

[7.9x10－25] 205Tl-F mol.

[199Hg atom] 10－31 5x10－26

neutron 7.5x10－26 (1) 3.2x10－26 (2)

UCN 10－31 5x10－26

Λ hyperon 1.5x10－16 rest frame E 10－30 5x10－25 199Hg 3.1x10－29 199Hg atom 10－33 10－29

- The most precise experiments are done with neutral systems. - The results for charged particles (except µ) are indirectly inferred.

(1)   P.G. Harris et al., PRL 82, 904 (1999). (2)   C.A. Baker et al., PRL 97, 131801 (2006).

Fortson Group, Seattle, Washington; W.C. Griffith et al., PRL 102, 101601 (2009)

d(199Hg) = 0.49(1.29)(0.76)x10－29 e.cm

d(199Hg) < 3.1 x 10－29 e.cm (95% C.L.)

The EDM of the mercury atom

Q1: What are the limits on CP violation? Q2: How does this compare to e.g. neutron?

Scale ~ 1 yeV Scale ~ 1 TeV The EDM landscape

The first nonzero EDM will be a major discovery. Ultimately, we will need the complete picture to address the origin of CP violation.

Questions for theory: - Best candidates? - Observables ⇔ microscopic CPV?

The EDM of the neutron Weak CPV (CKM): dn ~ 10－31 e.cm Strong CPV (QCD): θ vacuum angle

Soft-pion theorem* (mπ→0): dn ~ gπ [g0－g2] ln(M/mπ) e/M

gπ

gi

Exp. limit ⇒ |θ| < 3x10－10

Limit on neutron EDM

Theories ruled out by dn (Ramsey, ‘77)

New expt’s: ILL, PSI, SNS

* R.J. Crewther, P. Di Vecchia, G. Veneziano, E. Witten, PL 88B, 123 (1979).

Contributions to a nuclear EDM

A nuclear EDM consists of:

(a)   EDMs of the nucleons, one-body operator, σ, no coherent effect; (b)   “exchange” contributions (two-body) of order O(v2/c2); (c)   “polarization” contributions -> many-body enhancement.

For (c), we need the P-odd, T-odd NN interaction and the wave function.

The P-odd & T-odd NN interactions

One-pion exchange is dominant (EDM operator, ~ er, is long range) Subleading: short-range, heavy degrees of freedom (model dependent)

CP-violation parameters: g0 = gπ(0), g1 = gπ(1), g2 = gπ(2), ... these are related to quark EDMs, quark- and gluon color-EDMs, ... by nonperturbative QCD.

1. V.V. Flambaum, I.B. Khriplovich, O.P. Sushkov, NPA 449, 750 (1986). 2. V.F. Dmitriev, R.A. Sen’kov, N. Auerbach, PRC 71, 035501 (2005). 3. J.H. de Jesus, J. Engel, PRC 72, 045503 (2005). 4. S. Ban, J. Dobaczewski, J. Engel, A. Shukla, PRC 82, 015501 (2010).

Sensitivity of the mercury EDM

1. 〈Sz〉Hg = 0.09gπg0 +0.09gπg1 -0.18gπg2 e.fm3

2. 〈Sz〉Hg = 0.00gπg0 +0.06gπg1 -0.01gπg2 e.fm3

3. 〈Sz〉Hg = 0.01gπg0 +0.07gπg1 -0.02gπg2 e.fm3

A complicated many-body nuclear calculation is needed. Core polarization is important, and reduces the single-particle result (1); The results from (2) and (3) were in reasonable agreement. The most recent results (4), however, are smaller for the isovector term ~ g1 , and sometimes have opposite sign, compared to 3.

Schiff moment in terms of P-, T-odd NNπ couplings g0, g1 , g2:

-  Big enhancement ~104 from atomic degeneracy. -  Additional factor from octupole deformation in 225Ra?

Amplification in radium atoms

1. 〈Sz〉Hg = 0.01gπg0 +0.07gπg1 -0.02gπg2 e.fm3 2. 〈Sz〉Ra = -1.5 gπg0 +6.0 gπg1 +4.0 gπg2 e.fm3

V.V. Flambaum, PRA 60, R2611 (1999); V.A. Dzuba, V.V. Flambaum, J.S.M. Ginges, PRC 61, 062509 (2000); J. Dobaczewski, J. Engel, PRL 94, 232502 (2005).

EDM measurements for charged particles

Precession: dS/dτ = µxB* + dxE* - Motional E-field, E* = γcβxB, large (GV/m)! - Suitable for muon & for deuteron (proton, 3He?, …)

I.B. Khriplovich, PLB 444, 98, (1998); Hyperfine Interact. 127, 365 (2000); F.J.M. Farley et al., PRL 93, 052001 (2004); Yu.F. Orlov, W.M. Morse, Y.K. Semertzidis, PRL 96, 214802 (2006).

G. Onderwater

- One-body contributions: - Leading chiral-log estimate: dn+dp = 0 (isovector), so dD = 0 - But 3He ≈ 4He + nhole , so d3He ≈ dn

- Two-body contributions, d(pol) + d(ex) ≈ d(pol) , are larger (enhancements!) - EDMs of n, D, and 3He are linearly independent!

The EDMs of the nucleon, deuteron & helion

(1) R.J. Crewther, P. Di Vecchia, G. Veneziano, E. Witten, PL 88B, 123 (1979). (2) C.-P. Liu & RGET, PRC 70, 055501 (2004). (3) I. Stetcu, C.-P. Liu, J.L. Friar, A.C. Hayes, P. Navratil, PLB 665, 168 (2008).

g0 g1 g2 Ref. p －0.09 0.00 0.09 (1)

n 0.09 0.00 －0.09 (1) D 0.00+0.00 0.15+0.00 0.00+0.00 (2)

3He2+ 0.15+0.09 0.23+0.00 0.15－0.09 (3)

gπ

gi Nuclear EDMs assuming OPE dominance and “naturalness”:

The EDM of the deuteron

dDpol = 〈3S1||τz- er||3P1〉/√6

The (nuclear) theory is very well under control. The deuteron and the neutron are always complementary; D could be more sensitive.

dD = -4.67 dcd + 5.22 dcu dn = -0.01 dcd + 0.49 dcu

With QCD sum rules*, express the g’s in quark (color-)EDMs:

I.B. Khriplovich & R.A. Korkin, NPA 665, 365 (2000); C.-P. Liu & RGET, PRC 70, 055501 (2004). * M. Pospelov, PLB 530, 123 (2002).

The simplest case with a P-, T-odd NN interaction: dD = dn+dp+d(“two-body”)

In terms of P-, T-odd pion-nucleon couplings:

dD = 0.23g1 + 0.09g0 + … dn = 0.14 [g0-g2] + …

T violation in polarized-n - polarized-p scattering

C.-P. Liu & RGET, PLB 634, 488 (2006).

(a)   90° spin rotation of x-polarized neutron around y-axis through x-polarized proton target, En = 0.025 eV

(b)   Time reversal of process (a) (c)   180° rotation around y-axis of (b)

results in -90° spin rotation instead

Null test for T violation, constrains the P-, T-odd NN interaction, like EDM!

Proposal for SNS: P-odd (T-even) neutron spin rotation in parahydrogen to 2.7x10-7 rad/m; target density N ~ 0.4x1023/cm3 Assume similar sensitivity (polarized target!), then:

| 7.7g0 + 1.1g1 - 28g2 + … | < 2.7x10-7 Cf. neutron EDM limit: | 14 (g0 - g2) + … | < 6.3x10-11

Exploit resonance in e.g. 139La? → factor 106 enhancement?!

Short-term goal [e.cm]

Final goal [e.cm]

g0 g1 g2 Limit on θ

n 5x10-27 5x10-28 0.14 -0.14 2x10-12

D 10-27 10-29 0.10 0.23 0.00 10-13 129Xe 10-30-10-31 10-33 6x10-5 6x10-5 12x10-5 10-13 199Hg 3x10-29 - 2x10-6 2x10-4 -3x10-5 5x10-10 225Ra ? ? -0.06 -0.12 0.11 ?

The bottom-line: Sensitivity to CP violation

-  The neutron & the deuteron are complementary; -  129Xe is intrinsically ~10 less sensitive than 199Hg; -  D & 129Xe at their final goals are comparable; -  Enhancements in 225Ra overcome the Schiff screening.

Some conclusions

o  EDM experiments are (by far) the best way to probe T violation

o  Theory (atomic, nuclear/hadronic, ultimately QCD) is needed to relate the measured EDMs to microscopic CP violation.

o  We need several experiments to unravel the origin of CP/T violation.

o  Dedicated magnetic storage rings for charged particles (muon, deuteron, proton, …): a new horse in the race!

o  D & 129Xe are complementary to the neutron (or proton), and, at their final goals (10-29 vs. 10-33), comparable in sensitivity.

o  For 225Ra the atomic & nuclear enhancements overcome more-or-less completely the Schiff screening, compared to 199Hg.

It is easier to measure things that stand still…

Thank you for your attention!