Nuclear Time-Reversal Violation and Atomic Electric Dipole Moments

Transcription

1 225 R Nucler Time-Reversl Violtion nd Atomic Electric Dipole Moments J. Engel University of North Crolin October 10, 2005

2 Outline T Symmetry EDM s 199 Hg 225 R 1 T Symmetry T is Different Observed T Violtion 2 EDM s Connection with T Violtion Shielding Hg Problems with Existing Clcultions Our Approch Results R Importnce of Octupole Deformtion Our Clcultion

3 Outline T Symmetry EDM s 199 Hg 225 R T is Different Observed T Violtion 1 T Symmetry T is Different Observed T Violtion 2 EDM s Connection with T Violtion Shielding Hg Problems with Existing Clcultions Our Approch Results R Importnce of Octupole Deformtion Our Clcultion

4 225 R T is Different Observed T Violtion The T Opertor in QM is Different. Not liner: so i is odd under T. T [x, p]t 1 = [x, p] Hs no eigensttes in the conventionl sense: T = T (α ) = α T = α α for α complex Typicl physicl sttes J, M not even close to eigensttes of T As result, T violtion doesn t show up s mixing of sttes with opposite T

5 225 R T is Different Observed T Violtion Is T Violted in the Rel World? Yup! Violtion is seen in decy of K-mesons (direct) nd B-mesons (through CP violtion). And we strongly believe tht T ( CP) violtion plyed n importnt role in the erly universe, cusing excess of mtter over ntimtter.

6 225 R T is Different Observed T Violtion Wht is the Source of T -Violtion? K nd B phenomen lmost certinly due to phse in the 3 3 CKM mtrix, which converts (d, s, b) to wek eigensttes tht couple to W nd Z. But this cn t be responsible for bryogenesis, which must rise outside the stndrd model, e.g. through supersymmetry hevy neutrinos Higgs sector... To confuse things more, there s the strong CP problem. We need to see T -violtion outside mesonic systems to understnd its sources. EDM s re not sensitive to CKM T violtion, but re to other sources. They re lredy putting pressure on supersymmetry.

7 Outline T Symmetry EDM s 199 Hg 225 R Connection with T Violtion Shielding 1 T Symmetry T is Different Observed T Violtion 2 EDM s Connection with T Violtion Shielding Hg Problems with Existing Clcultions Our Approch Results R Importnce of Octupole Deformtion Our Clcultion

8 225 R Connection with T Violtion Shielding Wht Do EDM s Hve to Do With T Consider nondegenerte ground stte g : J, M. Symmetry under rottions R y (π) for vector opertor like d i e i r i, g : J, M d g : J, M = g : J, M d g : J, M. T tkes M to M, like R y (π). But d is odd under R y (π) nd even under T, so for T conserved g : J, M d g : J, M = + g : J, M d g : J, M. Together with the first eqution, this implies d = 0. If T is violted, rgument fils becuse T cn tke g : JM to different stte with J, M.

9 225 R Connection with T Violtion Shielding There re EDM Experiments on Neutrons, Atoms... Bsic principle: B E B E f f H = µ B d E nd there is chnge in precession frequency (liner in E) when E is flipped.

10 N _ g R Connection with T Violtion Shielding How Do Things Get EDM s? Underlying theory genertes T -violting πnn vertex: A neutron gets EDM from digrm like this: N? g q q π γ _ g π g n p n A nucleus cn get one from nucleon EDM or through T -violting nucleon-nucleon interction, e.g. N... N π g... γ W nh i ḡ 0 τ 1 τ 2 ḡ1 2 (τ 1 z + τ1 z ) + ḡ 2 (3τ1 z τ2 z τ 1 τ 2) ḡ1 2 (τ z 1 τ z 2 ) (σ 1 + σ 2) o ( 1 2) (σ 1 σ 2) exp ( mπ r1 r2 ) m π r 1 r 2 Finlly, nucler EDM induces tomic EDM. The gol of the tomic experiments discussed here is to constrin (or determine) the three ḡ s.

11 225 R Connection with T Violtion Shielding Shielding by Electrons Unfortuntely for tomic experiments Theorem (Schiff) The nucler dipole moment cuses the tomic electrons to rerrnge themselves so tht they develop dipole moment opposite tht of the nucleus. In the limit of nonreltivistic electrons nd point nucleus the electrons dipole moment exctly cncels the nucler moment, so tht the net tomic dipole moment vnishes! Skip proof

12 225 R Connection with T Violtion Shielding All is Not Lost, Though... Th nucleus hs finite size. Shielding is not complete, nd nucler T violtion cn still induce tomic EDM d. Post-screening nucleus-electron interction doesn t explicitly involve the nucler EDM D, but rther relted quntity: The nucler Schiff moment ( S e p rp R2 ch ) r p. p If, s you d expect, S R 2 N D, then d is down from D by O ( R 2 N /R2 A) Ughh! Fortuntely the lrge nucler chrge nd reltivistic wve functions offset this fctor by 10Z Overll suppression of D is only bout 10 3.

13 T Symmetry EDM s Compring Limits 199 Hg 225 R Connection with T Violtion Shielding Limit on the neutron EDM: Limit on the 199 Hg EDM: d N < e cm d < e cm So neutron nd Hg mesurements re comprble, ssuming d N nd D re comprble. Actully, experiments re complementry: Neutron EDM depends only on T-odd π NN coupling, while nucler EDMs lso depend on π 0 NN coupling. γ _ g π g n p n N _ g N... N π g... γ Still, uncertinties in nucler-structure physics mke quntittive comprison difficult. Let s get hndle on them!

14 Outline T Symmetry EDM s 199 Hg 225 R Problems with Existing Clcultions Our Approch Results 1 T Symmetry T is Different Observed T Violtion 2 EDM s Connection with T Violtion Shielding Hg Problems with Existing Clcultions Our Approch Results R Importnce of Octupole Deformtion Our Clcultion

15 T Symmetry EDM s Sitution in 199 Hg 199 Hg 225 R Problems with Existing Clcultions Our Approch Results Two clcultions of Schiff moment exist: Single-prticle-model result of Flmbum et l S z Hg = 0.09 gḡ gḡ gḡ 2 (e fm 3 ) Recent RPA result by Dmitriev, Sen kov, Auerbch S z Hg = gḡ gḡ gḡ 2 (e fm 3 ) In the better clcultion Isosclr coefficient in better clcultion unnturlly smll; uthors don t explin why. Schemtic Lndu-Migdl interction used in RPA No estimte of uncertinty. J. H. de Jesus did more comprehensive clcultion for his Ph.D.

16 (iv) (v) (vi) T Symmetry EDM s Joo s clcultion 199 Hg 225 R Problems with Existing Clcultions Our Approch Results 1 Skyrme-HFB in (sphericl) 198 Hg core, with severl Skyrme interctions 2 MBPT for interction between lst qusineutron nd core First order in W since it is very wek QRPA order in Skyrme interction W13 W11 W02 S z 11 S z 20 S z 20 Lowest-order digrms; only iii nd vi contribute (i) (ii) (iii) S z 02 S z 11 S z 02 W11 W20 W31

17 T Symmetry EDM s Building QRPA 199 Hg 225 R Problems with Existing Clcultions Our Approch Results Digrms like these re summed... c yielding digrm-a. We lso include digrms B. W 31 A S z 02 i V 13 W 11 S z 20 B i V 31 W 11 S z 02 These we evlute but find negligible: c c c

18 225 R Problems with Existing Clcultions Our Approch Results Constructing good Skyrme interction W probes spin density. Interction should hve good spin response. M. Bender et l fit some time-odd terms of SkO to Gmow-Teller resonnce energies nd strengths.

19 225 R Problems with Existing Clcultions Our Approch Results Testing SkO nd other Skyrme interctions 36 Digrms involve excittion of core sttes by Schiff opertor. Strength distribution of isosclr nlog of this opertor is mesured in 208 Pb. How do our Skyrme interctions do? 10 3 Strength (fm 6 /MeV) E X1 E X2 SkP SkO SIII Energy (MeV)

20 225 R Problems with Existing Clcultions Our Approch Results Wht we get with SkO S z Hg 0 gḡ gḡ gḡ 2 (e fm 3 ) Flmbum et l Single-prticle zero-rnge limit Digrm A only Full result So ll s, but especilly 0 nd 2 re quenched when collectivity is dded to digrm A... nd 0, 2 shrink even further, while 1 grows, when digrms B re dded. W 31 A S z 02 i V13 W 11 S z 20 B i V31 W 11 S z 02

21 225 R Problems with Existing Clcultions Our Approch Results Why some of this hppens 1 Treting excittions in QRPA pushes Schiff strength up, so ll s re reduced. 2 S p e ( p r 2 p 5 3 R2 ch ) r p First Second Totl 1 Second term smll for g 1, which ffects protons nd neutrons the sme wy, similr in mgnitude with opposite sign for g 0 nd g 2, which ffect them in opposite wys. Integrted mplitudes (e fm 3 ) Energy (MeV) 3 Finlly, digrms B must hve opposite sign for 1, where they dd to digrm A, thn for 0 nd 2, where they cncel it.

22 T Symmetry EDM s Summrizing Hg 225 R Problems with Existing Clcultions Our Approch Results Flmbum et l S z Hg = 0.09 gḡ gḡ gḡ 2 (e fm 3 ) Dmitriev, Sen kov, Auerbch S z Hg = gḡ gḡ gḡ 2 (e fm 3 ) Our best result: SkO S z Hg = gḡ gḡ gḡ 2 (e fm 3 ) Rnge from ll Skyrme interctions (excluding SIII) S z Hg = ( ) gḡ 0 +( ) gḡ 1 +( ) gḡ 2 (e fm 3 )

23 Outline T Symmetry EDM s 199 Hg 225 R Importnce of Octupole Deformtion Our Clcultion 1 T Symmetry T is Different Observed T Violtion 2 EDM s Connection with T Violtion Shielding Hg Problems with Existing Clcultions Our Approch Results R Importnce of Octupole Deformtion Our Clcultion

24 225 R Importnce of Octupole Deformtion Our Clcultion Nucler Deformtion

25 225 R Importnce of Octupole Deformtion Our Clcultion Anlogy: Collective Qudrupole Moments Ψ JM DMK J (θ, φ) χintr. K, where K is the projection of J on the symmetry xis. The intrinsic sttes re deformed. When K = 0, the qudrupole opertor cn be written s Q µ = D 2 µ0q intr. 0 so tht mtrix elements within rottionl bnd look like: Ψ JM Q µ Ψ J M = ( ) three D functions χ intr. Q0 intr. χ intr. So the qudrupole moment nd E 2 trnsition rtes re proportionl to the intrinsic qudrupole moment, which cn be lrge/collective.

26 225 R Importnce of Octupole Deformtion Our Clcultion Now Wht About Schiff Moments? Need T-violting nucler interction W to get one. Treting W s perturbtion: S = m 0 S m m W 0 E 0 E m + c.c. where 0 is the unperturbed nucler ground stte. S will not be enhnced if nucleus is only qudrupole deformed. Need octupole deformtion too. Then, two collective effects help you out: 1 Prity doubling 2 Lrge nd robust intrinsic Schiff moments

27 225 R Importnce of Octupole Deformtion Our Clcultion Point 1: Prity Doublets When the intrinsic stte is symmetric, it breks prity (spontneously) becuse nd re degenerte, with P =. Physicl sttes must hve good prity: χ intr. (±) = 1/ 2 ( ± ) These will be nerly degenerte if the deformtion is rigid. So our expression for the Schiff moment becomes S 0 S 0 0 H T 0 E 0 E 0 + c.c. where 0 nd 0 form prity doublet.

28 T Symmetry EDM s Spectrum of 225 R 199 Hg 225 R Importnce of Octupole Deformtion Our Clcultion

29 225 R Importnce of Octupole Deformtion Our Clcultion Point 2: Lrge Intrinsic Schiff Moment 0 S 0 S intr. S intr. just like in qudrupole trnsitions, so tht nd furthermore S 2/3 S intr. H T E 0 E 0 S intr. > R 2 N D intr.. Dipole moments in these nuclei re collective lso, but subject to cncelltion: they vnish in the limit ρ neutron = ρ proton. Net result: S is enhnced in n octupole-deformed nucleus like 225 R by 2 or 3 orders of mgnitude over 199 Hg, ccording to collective-model estimtes. But these neglect spin polriztion! We need to tke it into ccount. Skip 225 R clcultion

30 T Symmetry EDM s Clcultion in 225 R 199 Hg 225 R Importnce of Octupole Deformtion Our Clcultion P- nd T -Breking Odd-A Hrtree-Fock We brek ll possible symmetries. Core polriztion of ll kinds utomticlly included. Agin use rnge of Skyrme interctions, with SkO preferred. All this is ccomplished with the progrm HFODD (in collbortion with J. Dobczewski, M. Bender, J.H. de Jesus, nd P. Olbrtowski.

31 T Symmetry EDM s Relted Observbles 199 Hg 225 R Importnce of Octupole Deformtion Our Clcultion Density distributions of the Rdium isotopes

32 225 R Importnce of Octupole Deformtion Our Clcultion Binding nd Seprtion Energies Single-Prticle Energies

33 225 R Importnce of Octupole Deformtion Our Clcultion Octupole, Dipole, Schiff Stuff

34 T Symmetry EDM s The Bottom Line 199 Hg 225 R Importnce of Octupole Deformtion Our Clcultion For 225 R, we get S z R = 1.5 gḡ gḡ gḡ 2 (e fm 3 ) For 199 Hg we got S z Hg = gḡ gḡ gḡ 2 (e fm 3 ) If the three ḡ s re comprble, the Schiff moment in R is lrger by over 100, on verge. Dzub et l. [PRA66, (2002)] find further enhncement of the R EDM by fctor of 3 in the tomic physics. Looks good for the R experiment!

35 225 R Importnce of Octupole Deformtion Our Clcultion THE END