Parity Nonconservation in Cesium: Is the Standard Model in Trouble?

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1 Parity Nonconservation in Cesium: Is the Standard Model in Trouble? Walter Johnson Department of Physics Notre Dame University johnson May 10, 2001 Abstract This is a brief review of the current status of PNC in cesium including a discussion of the reported 2.3 σ disagreement between experiment and the Standard Model N D Atomic Physics TU Dresden Seminar

2 Overview review e q e q e fl q e Z q H (1) eff = G 2 2 Q W γ 5 ρ(r) where the conserved weak charge is Q W = N + Z ( 1 4sin 2 θ W ) For states v and w that have the same parity w ez v = Q W Structure factor Measure: E PNC = w ez v Calculate: Structure factor Ratio gives Q W N D Atomic Physics TU Dresden Seminar 1

3 Some Properties of Cesium review Configuration: [Xe] 6s 55 electrons A=133 (100%) N=78 Z=55 I=7/2 g 7/2 valence proton µ = µ N Q = b Levels of Interest 7s 1/2 H H 6s 1/2 (5395Å) H H ν 43 (6s) =9, 192, 631, 770 Hz defines the second! N D Atomic Physics TU Dresden Seminar 2

4 Z-e Coupling from Standard Model review H (1) = G ( ) [ ( ) ψe γ µ γ 5 ψ e c1p ψpi γ µ ψ pi 2 ( )] + c 1n ψni γ µ ψ ni H (2) = G ( ) [ ( ψe γ µ ψ e c2p ψpi γ µ ) γ 5 ψ pi 2 i i + c 2n ( ψni γ µ γ 5 ψ ni )] where the standard-model coupling constants are c 1p = ( sin 2 ) θ W 0.038, c 1n = 1 2, 1 c 2p = 2 g ( A 1 4sin 2 ) θ W 0.047, c 2n = 1 2 g ( A 1 4sin 2 ) θ W In the above, g A 1.25 is a scale factor for the partially conserved axial current A N. N D Atomic Physics TU Dresden Seminar 3

5 Nonrelativistic Nucleons details H (1) : ( ψp γ µ ψ p ) φ p φ p δ µ0 ( ψn γ µ ψ n ) φ n φ n δ µ0 where φ p and φ n are nonrelativistic field operators. From this we extract an effective Hamiltonian to be used in the electron sector; namely, H (1) eff = G 2 2 γ 5 [2Zc 1p ρ p (r)+2nc 1n ρ n (r)]. Here, ρ p (r) and ρ n (r) proton and neutron density functions normalized to 1. Assuming ρ p (r) =ρ n (r) = ρ(r), we may rewrite the effective Hamiltonian as H (1) eff = G 2 2 γ 5 Q W ρ(r) where Q W =[2Zc 1p +2Nc 1n ]= N +Z ( 1 4sin 2 θ W ) N D Atomic Physics TU Dresden Seminar 4

6 Axial Nuclear Current details H (2) : ( ψp γ µ γ 5 ψ p ) φ p σ i φ p δ µi ( ψn γ µ γ 5 ψ n ) φ n σ i φ n δ µi The corresponding effective Hamiltonian in the electron sector is obtained from H (2) eff = G 2 α [c 2p φ p σφ p + c2n φ n σφ n ] Only unpaired valence nucleons (with polarization corrections) contribute, so the size of H (2) is smaller than that from H (1) by a factor of 1/A. For a single valence proton, this reduces to: H (2) eff = G 2 c 2p κ 1/2 I(I +1) α I ρ p(r) where κ = (I +1/2) for I = L ± 1/2. N D Atomic Physics TU Dresden Seminar 5

7 Anapole Moment PNC in nucleus nuclear anapole: details The anapole is a toroidal electromagnetic current localized to the nucleus. H (a) eff = G 2 K a κ I(I +1) α I ρ p(r) Combining the two spin-dependent interactions: H (a) eff + H(2) eff = G 2 K κ I(I +1) α I ρ p(r) with K = K a κ 1/2 κ c 2p N D Atomic Physics TU Dresden Seminar 6

8 Another Spin-Dependent Term [ ] The action of H hyperfine H (1) eff nuclear spin-dependent correction details gives yet another H (Q W ) eff = G 2 K QW κ I(I +1) α I ρ p(r) with 1 K QW (133 Cs) C. Bouchiat and C. A. Piketty, Z. Phys. C 49, 91 (1991); Phys. Lett. B 269, 195 (1991). N D Atomic Physics TU Dresden Seminar 7

9 Atomic Structure details For the 6s 7s transition in atomic cesium: 7s ez 6s = n { 7s ez np1/2 np 1/2 H (1) 6s E np E 6s + 7s H(1) np 1/2 np 1/2 ez 6s E np E 7s } 1. 9 n=6 with SD wave functions & energies (90%) 2. n=10 weak RPA level (10%) 3. Breit interaction at weak HF level (0.2%) 4. Nucleon structure correction ρ N (r) (<0.1%) 5. H (2 ) contribution at weak RPA level N D Atomic Physics TU Dresden Seminar 8

10 Singles-Doubles Equations digression Ψ v =Ψ DHF + δψ { δψ = ρ ma a ma a am abmn ρ mnab a ma na b a a + ρ mv a ma v + ρ mnvb a ma na b a v Ψ DHF m v bmn E C = E DHF C E v = E DHF v + δe C + δe v (we also include limited triples) N D Atomic Physics TU Dresden Seminar 9

11 Core Excitation Equations digression (ɛ a ɛ m )ρ ma = bn ṽ mban ρ nb + bnr v mbnr ρ nrab bcn v bcan ρ mnbc (ɛ a + ɛ b ɛ m ɛ n )ρ mnab = v mnab + cd v cdab ρ mncd + rs v mnrs ρ rsab [ + v mnrb ρ ra r c + [ a b m n ] δe C = 1 2 abmn v abmn ρ mnab v cnab ρ mc + rc ṽ cnrb ρ mrac ] 15,000,000 ρ mnab coefficients for Cs (l =6). N D Atomic Physics TU Dresden Seminar 10

12 digression m a = m a m b n + a a r b n + m c b n + exchange terms m a n b m a n b = a + m r n s b m + a c b d n m a n b + c + a m r n b + m a c n r b + exchange terms Brueckner-Goldstone Diagrams for the core SD equations. N D Atomic Physics TU Dresden Seminar 11

13 Valence Equations digression (ɛ v ɛ m + δe v )ρ mv = bn ṽ mbvn ρ nb + bnr v mbnr ρ nrvb bcn v bcvn ρ mnbc (ɛ v + ɛ b ɛ m ɛ n + δe v )ρ mnvb = v mnvb + cd v cdvb ρ mncd + rs v mnrs ρ rsvb [ + v mnrb ρ rv r c + [ v b m n ] v cnvb ρ mc + rc ṽ cnrb ρ mrvc ] δe v = ma ṽ vavm ρ ma + mab v abvm ρ mvab + mna v vbmn ρ mnvb 1,000,000 ρ mnvb coefficients for each state (Cs) N D Atomic Physics TU Dresden Seminar 12

14 SD Correlation Energy digression Correlation energy (cm -1 ) Na K Rb Expt. E (2) E (2) +E (3) δe υ Nuclear charge Z Cs Fr Ground-state correlation energies for alkali-metal atoms N D Atomic Physics TU Dresden Seminar 13

15 Calculations of cesium 6s 7s PNC Amplitude PNC Group E PNC Breit Novosibirsk ± Notre Dame ± HF-level units: iea Q W N N D Atomic Physics TU Dresden Seminar 14

16 Status of PNC Experiments PNC (a) Optical rotation: n + n φ = E PNC /M 1 6p 1/2 6p 3/2 transition Element Group 10 8 φ Thallium Oxford -15.7(5) Thallium Seattle -14.7(2) Lead Oxford -9.8(1) Lead Seattle -9.9(1) Bismuth Oxford -10.1(20) (b) Stark interference: Add E(t) =A cos ωt and detect the hetrodyne signal R = E PNC /β 6s 1/2 7s 1/2 (mv/cm) Element Group R 4 3 R 3 4 Cesium Paris (1984) -1.5(2) -1.5(2) Cesium Boulder (1988) -1.64(5) -1.51(5) Cesium Boulder (1997) (8) (8) N D Atomic Physics TU Dresden Seminar 15

17 Bennett & Wieman 2 PNC Measured β = (43) expt (67) theor a 3 0 Updated theory error estimates! Diff 10 3 Expt Tests Novo ND σ expt Stark(6s-7s) 7p ez ns τ 6p1/2 6s ez 6p τ 6p3/2 6s ez 6p α vs ez np β vs ez np A 6s Ψ 6s (0) A 7s Ψ 7s (0) A 6p1/2 1/r 3 6p A 7p1/2 1/r 3 7p S. C. Bennett & C. E. Wieman, Phys. Rev. Letts. 82, 2484 (1999). N D Atomic Physics TU Dresden Seminar 16

18 Cesium: Theory vs. Experiment PNC β = (43) exp (67) th a 3 0 (1999) (eliminating axial vector + anapole contribution) I(E PNC )= (37) exp (21) th e a 0 (dividing by theoretical matrix element) Q W = (29) exp (34) th Marciano & Rosner (with radiative corrections) Q SM W = (03) rad. corr. Expt. - Theory = 2.3 σ This difference has been cited as evidence for new physics beyond the Standard Model! N D Atomic Physics TU Dresden Seminar 17

19 Result for Anapole Moment digression Difference R 3 4 R 4 3 leads to: K = (63) (κ 1/2)/κ K (2) = K (Q W ) = K (a) = (63) Theoretical estimates 3 K (a) = W. C. Haxton and C. E. Wieman, arxiv:nucl-th/ N D Atomic Physics TU Dresden Seminar 18

20 10. Electroweak model and constraints on new physics 19 Table 10.4: (continued) Quantity Value Standard Model Pull m t [GeV] ± ± M W [GeV] ± ± ± M Z [GeV] ± ± Γ Z [GeV] ± ± Γ(had) [GeV] ± ± Γ(inv) [MeV] ± ± 0.15 Γ(l + l )[MeV] ± ± 0.03 σ had [nb] ± ± R e ± ± R µ ± ± R τ ± ± R b ± ± R c ± ± A (0,e) FB ± ± A (0,µ) FB ± A (0,τ) FB ± A (0,b) FB ± ± A (0,c) FB ± ± A (0,s) FB ± ± ) ± ± s 2 l (A(0,q) FB June 14, :38

21 Electroweak model and constraints on new physics Table 10.4: (continued) Quantity Value Standard Model Pull A e ± ± ± ± A µ ± A τ ± ± A b ± ± A c ± ± A s 0.85 ± ± R ± ± ± κ ν ± ± ± R ν ± ± ± ± ± gv νe ± ± ± ga νe ± ± ± Q W (Cs) ± 0.28 ± ± Q W (Tl) ± 1.2 ± ± Γ(b sγ) Γ(b ceν) June 14, :38

22 Possible Explanation of 2.3 σ PNC ' The previous result suggested the possible existence of a Z particle to several authors: 1. R. Casalbuoni, S. De Curtis, D. Dominici, and R. Gatto, Phys. Lett. B460, 135 (1999). 2. J. L. Rosner, Phys. Rev. D61, (2000). $ 3. J. Erler and P. Langacker, Phys. Rev. Lett. 84, 212 (2000). & % N D Atomic Physics TU Dresden Seminar 19

23 Breit Revisited PNC Weak HF level: ( h0 + V HF ɛ HF v ) ψhf v = h PNC ψ HF v E PNC = ψ7s HF HF HF ez ψ 6s + ψ 7s ez ψ6s HF Type 7s ez 6s 7s ez 6s E PNC Coul Breit % -0.29% -0.30% -0.30% This correction was included in ND calculation E PNC = = but not in Novosibirsk calculation. N D Atomic Physics TU Dresden Seminar 20

24 Derevianko s observation Brueckner level: ( h 0 + V HF + ˆΣ ɛ Br v ) ψbr v = h PNC ψ Br v PNC δvpnc HF ψv Br E PNC = ψ7s Br ez + δ RPA (ez) + ψ Br 6s ψ Br 7s ez + δ RPA (ez) ψ Br 6s Type 7s ez 6s 7s ez 6s E PNC Coul Breit % -0.60% -0.59% -0.59% Using this result for the Breit correction, the final theoretical PNC amplitudes become Group Coul Breit E PNC Novosibirsk Notre Dame N D Atomic Physics TU Dresden Seminar 21

25 Summary PNC With Breit corrections: E theor PNC = (4) or (10)? and the deviation of the Q W from the standard model is reduced to 1.5 σ if 0.4% theoretical accuracy is still assumed. However, if a more realistic 1% theoretical uncertainty is assumed, the corresponding value of the weak-charge becomes Q W ( 133 Cs) = (0.28) expt (0.74) theor and shows NO significant deviation from the standard model. 4 HELP! accurate calculations needed HELP! 4 A. Derevianko, Phys. Rev. Lett. 85, 1618 (2000); V. A. Dzuba et al., Phys. Rev. A 63, (2001); M. G. Kozlov et al., arxiv:physics ( ). N D Atomic Physics TU Dresden Seminar 22