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Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Nuclear Anapole Moment

Mikhail Kozlov1 and Sidney Cahn2

1Petersburg Nuclear Physics Institute2Yale University

Berkeley, 2006

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Plan of the talk

Weak Interactions in AtomsCharged and Neutral Currents. Effective P-odd Hamiltonian

Nuclear Anapole MomentAnalytical model of Flambaum & Khriplovich

Weak Coupling ConstantsWhat Anapole Moments can Give to the Theory

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Outline

Weak Interactions in AtomsCharged and Neutral Currents. Effective P-odd Hamiltonian

Nuclear Anapole MomentAnalytical model of Flambaum & Khriplovich

Weak Coupling ConstantsWhat Anapole Moments can Give to the Theory

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Weak currents

e

n p

ν−

W-

Charged currents can be seenin nuclear decays and other in-elastic processes.

Neutral currents can be alsoseen in elastic scattering. Inatomic physics they lead toadditional non-Coulomb in-teraction of the electronswith the nucleus and witheach other.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Weak currents

e

n p

ν−

W-

Charged currents can be seenin nuclear decays and other in-elastic processes.

e e

A(Z,N) A(Z,N)

Z

Neutral currents can be alsoseen in elastic scattering. Inatomic physics they lead toadditional non-Coulomb in-teraction of the electronswith the nucleus and witheach other.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Weak neutral currents

• Because of the very large mass of Z -boson, ∼100 GeV,the weak interaction is contact on atomic scale.

• It includes P-even and P-odd (PNC) parts.• P-even part leads to small corrections to isotope shift and

to hyperfine structure.• PNC part leads to the pseudo scalar correlations in atomic

processes.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Weak neutral currents

• Because of the very large mass of Z -boson, ∼100 GeV,the weak interaction is contact on atomic scale.

• It includes P-even and P-odd (PNC) parts.• P-even part leads to small corrections to isotope shift and

to hyperfine structure.• PNC part leads to the pseudo scalar correlations in atomic

processes.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Weak neutral currents

• Because of the very large mass of Z -boson, ∼100 GeV,the weak interaction is contact on atomic scale.

• It includes P-even and P-odd (PNC) parts.• P-even part leads to small corrections to isotope shift and

to hyperfine structure.• PNC part leads to the pseudo scalar correlations in atomic

processes.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Weak neutral currents

• Because of the very large mass of Z -boson, ∼100 GeV,the weak interaction is contact on atomic scale.

• It includes P-even and P-odd (PNC) parts.• P-even part leads to small corrections to isotope shift and

to hyperfine structure.• PNC part leads to the pseudo scalar correlations in atomic

processes.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Effective P-odd electron-nucleus interaction

HP = HnsiP + Hnsd

P

=GF√

2

(−QW

2γ5 +

κ

iγ0~γ~i

)ρ(~r),

where GF ≈ 1.2225× 10−14 a.u. is the Fermi constant,~i isnuclear spin, ~γ are Dirac matrices, and ρ(~r) is nuclear density.Dimensionless constants QW and κ characterize the strength ofthe NSI and NSD parts respectively.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Weak charge

In the lowest order the standard model gives:

QW = −N + Z (1− 4 sin2 θW) ≈ −N,

where N is the number of neutrons and θW is Weinberg angle.Radiative corrections to this expression change QW by fewpercent:

QW = −0.9857 N + 0.0675 Z .

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

NSD coupling constant κ

There are three contributions to the constant κ in HnsdP :

κ =K

i + 1κA + κ2 + κQw ,

K ≡ (−1)i+1/2−l (i + 1/2).

where κA is the anapole moment constant, κ2 corresponds tothe weak neutral currents, and κQw appears as a radiativecorrection to the NSI part; i is nuclear spin and l is orbitalangular momentum of the valence nucleon.

Typically |Qw | ∼ 100|κ|.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

VeAN Weak Neutral Current & Anapole Moment

VN+AN

Ve+Ae

Z0

N

e e

γ

N Z0, W±

σσσσe

I

(a) (b)

33

Weak Neutral Current. Anapole moment.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Hyperfine correction to the Weak Neutral Current(second order radiative correction to the weak amplitude)

e e

A(Z,N) A(Z,N)

Z γ

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

VeAN Weak Coupling Constant

In the nuclear shell model

κ2 =1/2− K

i + 1C2ν ,

where C2ν is coupling constant for the valence nucleon:

C2n ≈ −C2p ≈λ

2(1− 4 sin2 θW ),

and λ ≡ gA/gV ≈ 1.25.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Outline

Weak Interactions in AtomsCharged and Neutral Currents. Effective P-odd Hamiltonian

Nuclear Anapole MomentAnalytical model of Flambaum & Khriplovich

Weak Coupling ConstantsWhat Anapole Moments can Give to the Theory

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Nuclear Toroidal Current

• In the nonrelativistic approximation PNC interaction of thevalence nucleon with the nuclear core has the form:

HP ∼GF gn

2√

2c(~σ~p)

mpcn(r),

where n(r) is core density and gn dimensionless effectiveweak coupling for valence nucleon.

• As a result, the spin ~σ acquires projection on themomentum ~p and forms spin spiral.

• Spin spiral leads to the toroidal current. This current isproportional to the magnetic moment of the nucleon and tothe cross section of the core.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Nuclear Toroidal Current

• In the nonrelativistic approximation PNC interaction of thevalence nucleon with the nuclear core has the form:

HP ∼GF gn

2√

2c(~σ~p)

mpcn(r),

where n(r) is core density and gn dimensionless effectiveweak coupling for valence nucleon.

• As a result, the spin ~σ acquires projection on themomentum ~p and forms spin spiral.

• Spin spiral leads to the toroidal current. This current isproportional to the magnetic moment of the nucleon and tothe cross section of the core.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Nuclear Toroidal Current

• In the nonrelativistic approximation PNC interaction of thevalence nucleon with the nuclear core has the form:

HP ∼GF gn

2√

2c(~σ~p)

mpcn(r),

where n(r) is core density and gn dimensionless effectiveweak coupling for valence nucleon.

• As a result, the spin ~σ acquires projection on themomentum ~p and forms spin spiral.

• Spin spiral leads to the toroidal current. This current isproportional to the magnetic moment of the nucleon and tothe cross section of the core.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Anapole constant κA

In 1980 Flambaum & Khriplovich have shown that in thenuclear shell model

κA ≈ 1.15 · 10−3A2/3µn gn,

where A = Z + N is the number of nucleons; µn and gn aremagnetic moment in nuclear magneton and weak couplingconstant of the unpaired nucleon.For nuclei with unpaired proton and neutron we have:

µp = 2.8µN , gp ≈ 5;

µn = −1.9µN , gn ≈ −1.

⇒ The anapole moment is much bigger for nuclei with unpairedproton.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Estimates of Anapole Moments of Some Nuclei(assumed couplings: gp = 4 and gn = −1; κ′

A= K

i+1 κA )

Nucleus i l 100× κ′A

100× κ2 |κa/κ2|valence neutron

87Sr38 9/2 4 −3.9 5.0 0.8137Ba56 3/2 2 4.6 −3.0 1.5173Yb70 5/2 3 4.5 −3.6 1.3199Hg80 1/2 1 5.0 −1.7 2.9201Hg80 3/2 1 −6.0 5.0 1.2

valence proton27Al13 5/2 2 −10.0 −5.0 2.069Ga31 3/2 1 −17.0 −5.0 3.481Br35 3/2 1 −19.0 −5.0 3.8115In49 9/2 4 −27.0 −5.0 5.2

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Outline

Weak Interactions in AtomsCharged and Neutral Currents. Effective P-odd Hamiltonian

Nuclear Anapole MomentAnalytical model of Flambaum & Khriplovich

Weak Coupling ConstantsWhat Anapole Moments can Give to the Theory

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Weak interactions inside the nucleus(why do we need many weak coupling constants)

q q

q q

Z

N N

N N

Z

q g q

N N

N N

Z

qq_

N N

N N

qq_

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

DDH constants(connection to couplings gp & gn)

There are 7 independent weak couplings for π-, ρ-, andω-mesons known as DDH constants.Proton and neutron couplings can be expressed in terms of 2combinations of these constants:

gp = 8.0× 104[70f̃π − 19.5h̃0

],

gn = 8.0× 104[−47f̃π − 18.9 h̃0

],

where

f̃π ≡ fπ − 0.12h1ρ − 0.18h1

ω,

h̃0 ≡ h0ρ + 0.7h0

ω.

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Experimental data for DDH constants(Haxton & Wieman, 2001)

FIG. 2: Current status of hadronic PNC parameters. This figure, reproduced from3, shows the

ranges of values of a particular linear combination of these parameters for the two anapole ex-

periments on Cs and Tl, pp scattering experiments.42–45, a pα scattering experiment46,47, a γ-ray

circular polarization in 18F experiment48,49, and angular asymmetry for polarized 19F decay50,51.

The size of the plot indicates the DDH “reasonable range” for these particular linear combinations.

Note the poor agreement of the 133Cs and 205Tl bands with the other data. The green dot corre-

sponds to the theoretical “best values”. As indicated by Holstein52, a consistent set of couplings is

not produced. Our measurements could add over a dozen new bands to this plot, similar to those

shown in light pink and blue (approximately equal numbers of each type). (Figure reproduced

from3).

34

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Conclusions

• At present the data for weak nuclear constant isinconsistent. That may indicate the problems both with thetheory and with the experiment.

• AM of the nuclei can give very important information, whichcan help to better understand nuclear weak interactions.

• AM of the nuclei with unpaired neutron are particularlyinteresting, as they depend on the different combination ofDDH constants compared to most other experiments.

• For the nuclei with unpaired neutron κA ≈ −κ2.⇒ PNC effects may be strongly suppressed!

Weak Interactions in Atoms Nuclear Anapole Moment Weak Coupling Constants

Conclusions

• At present the data for weak nuclear constant isinconsistent. That may indicate the problems both with thetheory and with the experiment.

• AM of the nuclei can give very important information, whichcan help to better understand nuclear weak interactions.

• AM of the nuclei with unpaired neutron are particularlyinteresting, as they depend on the different combination ofDDH constants compared to most other experiments.

• For the nuclei with unpaired neutron κA ≈ −κ2.⇒ PNC effects may be strongly suppressed!

逆コンプトンガンマ線によるパリティ非保存実験

1. Beta decay: T.D.Lee and C.N. Yang, Phys. Rev. 104 (1956).2. Exp.: C.S. Wu et al., Phys. Rev. 105 (1957) 1413.3. γ-decay: 181Ta N. Tanner, Phys. Rev. 107, 1203 (1957).4. -6 x10-6: V.M. Lobashov et al., JETP Lett. 5, 59 (1967); Phys. Lett. 25B 104 (1967).5. Anapole moment: Ya. B. Zeldovich, Sov. Phys. JETP 6, 1184 (1958).6. C.S. Wood et al., Science 275, 1759 (1997).

Neutrino oscillation: νe νµ ντ

CMK mixing

Unified Theories for future

Interaction Carriers act on Particle

Gravitation Graviton

LeptonsWeak W+, W−, Z0

Electromagnetic

Strong

Photon

Gluon Quarks) Grand

Unification

Time

181Ta: N. Tanner, Phys. Rev. 107 (1957) 1203.V.M. Lobashov et al., PL 25B (1967) 105,

159Tb: W.P Pratt et al., Phys. Rev. C2 (1970) 1499.

180Hf: K.S. Krane et al., Phys. Rev. Lett. 26 (1971) 1579.

P γ= 2.8 (0.45) 10-3

P γ= -6

(1) x

10-6

∆E

二準位 摂動計算

K.S. Krane et al., PRL 26, 1579 (1971).PRC 4, 1906 (1971).

B. Jenschke and P. Bock, PL 31B, 65 (1970).E.D. Lipson, F. Boehm and J.C. van den Leeden, PL 35B, 307 (1971)

W.V. Yuan et al., Phy. Rev. C44, 2187 (1991).

Parity violation in neutron absorptionThe doorway state for parity violation interaction is spin-dipoleresonances (isovector and isoscalar).Therefore, statistical treatment is essential to analyze the PNC effect.

Nuclear force by meson exchange Parity violation interaction for NN

Parity violation force via electromagnetic interactions

Electric moment : D = α rMagnetic moment: µ = g σAnapole moment: t = κ µ x D = κ σ x r

= κ σp

Weak coupling

Z π, ρ, ωf , h0, h1 , h2 , h0 , h1

ρ ωρ ρ ωπ

C.S. Wood et al., Science 275, 1759 (1997)C.S. Wood, Can. J. Phys. 77, 7-75 (1999)

Also, A. Krasznahorkay, M. Fujiwara, P. van Aarle, H. Akimune, I. Daito, H. Fujimura, Y. Fujita, M.N. Harakeh, T. Inomata, J. Janecke, S. Nakayama, A. Tamii, M. Tanaka, H. Toyokawa, W. Uijen, and M. Yosoi, Phys. Rev. Lett. 82 (1999) 3216--3219.

W.C. Haxton et al., Phys. Rev. Lett. 86, 5247 (2001).W.C. Haxton et al., Phys. Rev. C 65, 045502 (2003).

κAM(133Cs)=0.090(16)

neutron proton deuteron

2.2 MeVγ ray emission

Expected asymmetry -5 x 10-8

Aγ = σL - σR

σL + σR

d

p

n

LANL project

AL = σ (ｐ+ｐ) (ｐ + ｐ)+ σσ (ｐ+ｐ) (ｐ + ｐ)- σ

LANL, SIN, LBL, LAMPF, ANL

10-6 -- 10-7

Circular polarization

Photo emission from polarized nuclei

Pγ, Aγ : 19F(1.081 MeV), 18F(110 keV), 21Ne(2.789 MeV), 180Hf, 181Ta,

Gatchna, Cal Tech/Seattle, Florence, Mainz, Queens, Seattle/Chark River, Grenoble

|γr> =( εx + iεy ) exp(ikz)

|γl> = (εx – iεy) exp(ikz)

E1 excitation M1 excitation

1. Direct counting of NRF yields2. Both E1 and M1 excitations are used.3. Self-corrections for experimental error4. Circular polarized beam with high stability and

High emittance is needed.

Αγ = 2 T(E1)T(M1)

1 eV

10 – 100 keV 10 - 300

Summary1. Brief History of Parity violation Studies:

New physics beyond standard model2. New possibility at SPring-83. NRF experiments with a circular polarized

γ-ray beam4. New formula for Aγ5. Works are now in progress:

FIRL: H. Ohkuma, Y. Arimoto, Tamura, S. Suzuki, et. al., NRF: K. Kawase, M.F. H. Ohkuma, et al.,

Theoretical considerations (A. Titov, M. Fujiwara).

Concept of Far Infra Red Free Electron Laser (FIRFEL) for BCS

7.5-10.5 MeV, 1.5 m (acceleration Length)/5 cells,0.5 kW FIR, wave length 50-100 µm

原研（峰原）案の遠赤外超伝導自由電子レーザー

キロワット級遠赤外レーザー光 1012 photons/sec

0

2 1011

4 1011

6 1011

8 1011

1 1012

1.2 1012

1.4 1012

1.6 1012

1.8 1012

2 1012

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Ee = 8GeV (1/γ = 64µrad)

SCW 10T (εc = hω

c = 0.43MeV)

Photon Flux Density [photons/s/mrad2/0.1%BW/mA]

Degree of Polarization

γψ

ω/ωc = 1

CircularPolarization（→）

LinearPolarization（→）

FluxDensity（←）

Photons from SCW

遠赤外レーザーと8 GeV蓄積電子の衝突による逆コンプトンガンマ線

K.S. Krane et al., PRL 26, 1579 (1971).PRC 4, 1906 (1971).

B. Jenschke and P. Bock, PL 31B, 65 (1970).E.D. Lipson, F. Boehm and J.C. van den Leeden, PL 35B, 307 (1971)W.V. Yuan et al., Phy. Rev. C44, 2187 (1991).

Parity violation in neutron absorption

The doorway state for parity violation interaction is dipoleresonances (isovector and isoscalar).Therefore, statistical treatment is essential to analyze the PNC effect.

原子核のM1励起とE1励起・及びPNC実験

1+1—

In NRF …

PNC transitions in np-system

13 P

13

13 DS +

)0( =IE1 0

3P)1( =I

)0( =I

∆I=1

13

13 DS +

M1(π)11P

01S

)1( =I

)1( =I0

3P∆I=0,2

13

13 DS +

)0( =I

11P)0( =I

∆I=0

M1

E1∆I=0

13

13 DS +

)0( =I

11P

)0( =I

E1

M1

03P

)1( =I

)1( =I0

1S∆I=0,2

∆I=1

13

13 DS +

)0( =I

)0( =I

∆I=0

E1 2,1,03P

)1( =I

M1

M1(π)

E~Ethr

E > Ethr+1 MeV

we found a principle possibility to find constraints for PNC coupling constantsusing only the simplest nuclear object: np-system

0≈− thrEEγ

MeVEE thr 10≈−γπf

vh

一つの実験で全ての強弱結合定数の決定 混迷からの脱出

22 111111112)(

EMMEMEEMEA VVPNC

RL+

∆⊗+∆⊗+∆⊗= π

γ

ZRA|||||)(1| 2,121 ππππ <<+=∆M

(+)

(-)(-)

PNC asymmetry:polarized beam and unpolarized target

核子ー核子間、短距離力に極めて重要な情報

Total cross section of deuteronphoto-disintegration

M. Fujiwara and A.I. Titov, PRC submitted October 2003.