enhancements and suppressions of cp violating effect in the … · 2018. 9. 12. · enhancement and...

Enhancements and suppressions of CP violating effect in the nucleons, nuclei, and atoms:

role of the spin

2018/09/12 Spin 2018 Ferrara

Nodoka Yamanaka(IPN Orsay)

© 2016 Japan Society for the Promotion of Science.

2016-2017www.jsps.go.jp

背厚3mm

JSPS16-17_01_表紙（英）.indd 1 2016/12/01 8:36:38

We need new source(s) oflarge CP violation beyond the standard model !

CP violation of Standard model is not sufficient to explain matter/antimatter asymmetry …

Prediction of Standard model:

Real observed data:

ratio photon : matter

1020 : 1

1010 : 1

CP violation of standard model is in great deficit!

Electric dipole moment (EDM)

+

-

→ HEDM is P-oddUnder parity tr.:

Direction:

→ HEDM is CP-odd !Under time reversal:

⇒ This is what will be evaluated!

Electric dipole moment:Permanent polarization of internal charge of a particle.

Interaction:

Transformation properties:

(Spin is the only vector quantity in spin ½ particle )

⇒ Parallel with the spin (angular momentum)

Aim of this talk

This is a disorganized review of mechanisms of enhancement and suppression of hadronic, nuclear and atomic CP violating contributions to the EDM

The EDM can experimentally be measured in many systems

(Neutron, atoms, muon, electron in molecules, etc)

There are also much experimental R & D, with new techniques(Proton, nuclei, heavy hadrons, tau, electrons in other systems,…)

We must know how the elementary level CP violation and the EDM of the above systems are related in theory

Are there enhancements, suppressions, specific sensitivity…?

EDM from physics beyond Standard model

EDM operator in relativistic field theory: dimension five-5 operator

� i2d ̄�µ⌫F

µ⌫�5 �d � ·ENonrela. lim.

Can be calculated using Feynman diagrams:

q,e q,e

BSM particles γ

1-loop diagram (e.g. SUSY)

2-loop diagram (e.g. 2-Higgs models)

BSM particles

3-loop diagram (e.g. Standard model)

W

g

q q

γ, gγγ

q,e q,e

EDM receives very small contribution from SM, whereas BSM new physics may contribute with low loop level :

EDM is a very good probe of BSM new physics!

EDM is generated by CP violating interactions.

CPV int. CPV int.

CPV int.

EDM of composite systems

The EDM is often measured in composite systems

The EDM of composite systems is not only generated by the EDM of the components,

but also by CP violating many-body interactions.

p

n

p

+

-

EDM of constituents CP-odd many-body interaction

Example of QCD level many-body interactions inducing neutron EDM:

quark chromo-EDM P, CP-odd 4-quark interaction

q

q

q

q

g

qq g g

g

Weinberg operator

Effect of CPV many-body interaction may be enhanced/suppressed!

(neutron, atoms, molecules, nuclei)

Elementary level CP violation and its origin

Quark EDM, chromo-EDM:

CP-odd 4-quark interaction:

Weinberg operator:

SUSY: 1-loop 2-Higgs doublet: 2-loop

Tree level: * Left-right sym. * Scalar exchange

2-loop diagram: * 2-Higgs doublet model * Vectorlike quark model

All those processes scale as 1/MNP2

Probe BSM sectors without LO interaction with light quarks

γ,g

qqγ,g

q

γ,g

qH

t

g

g

g

q

q q

q

WL

WR

q

q q

q

EDM from elementary level CP violation

Energy scale

QCDHadron TeVNuclearAtomic

q EDM

q cEDM

e-q int

4-q int

ggg

θ-term

N EDM

e-N int

N-N int

Schiff moment

MQM

Paramagnetic Atom EDM / Molecules

Diamagnetic Atom EDM

Nuclear EDM

Left-Right

Leptoquark

Composite models

Extradimension

observable : Observable available at experiment

: Sizable dependence

: Weak dependence

Standard Model

Supersymmetry

e,µ EDM

: Matching

(RGE)

Higgs doublets

(θ-term)(PQM)

(PQM)

BSM physics:

What we want to find

⇒ Elementary level CPV is unknown and small : can be factorized

⇒ We want to evaluate coefficients and find interesting systems!

Depends on the structure of the system!

Unknown CP violating couplings beyond the standard model

dA = (aπ(0) Gπ(0) + aπ(1) Gπ(1) ) e cm + Ke de +…

⇒ We want to find systems with large enhancement factors

⇒ Linear coefficients depends only on the structure of the system, not in NP

(or understand and avoid suppression)

Atomic EDM and Schiff’s screening

In atoms, EDM of nonrelativistic constituents suffers Schiff’s screening

3 leading P, CP-odd processes in atoms :

EDM of bare constituent Atomic EDM : screening via rearrangement

+ ++

-- -

Ŝ � e2

Z�

p=1

�15r2p �

13�r2�ch

�rp

S =�

i

��0|Ŝ|�i��i|W |�0�E0 � Ei

+ c.c.W: P, CP-odd N-N interaction

Schiff moment operator:

Schiff moment (residual nuclear moment due to nuclear finite size)

Relativistic effect of constituents (electrons in heavy atoms)

CP-odd electron-nucleon interaction

L. I. Schiff, Phys. Rev. 132, 2194 (1963).

Typically, looses sensitivity by αQED2 ~ 10-4

Electron EDM in atoms/molecules : relativistic enhancement

Tl atom

Fr atom

YbF molecule

-585

Ke

-910

ThO molecule

Limit to de

1x10-27e cm

9x10-29e cm

de’s effect is now accurate thanks to the well established atomic level physics

(Relativistic Hartree-Fock, Relativistic coupled-cluster)

Electron EDM is enhanced in heavy paramagnetic atoms/molecules due to the relativistic effect

Paramagnetic polar molecules : enhancement due to parity doubling

P. G. H. Sandars, Phys. Lett. 14, 194 (1965); Phys. Lett. 22, 290 (1966).

dA =X

n

h 0|� ePZ

i zi| nih n|dePZ

j (1� �j)�j ·Ej | 0iEn � E0

= 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

Relativistic effect : Not canceled by Schiff theorem

Limit to de

1.6x10-27e cm

—

Paramagnetic atoms:

Regan et al., PRL 88, 071805 (2002)

Sakemi et al., on-going

Hudson et al., Nature 473 (2011) 493

Baron et al., Science 343 (2014) 269

Ginges et al., Phys. Rep. 397 (2004) 63 B. P. Das et al., Handbook of Relativistic Quantum Chemistry 1-26 (2015)

PQ mechanism

Hadronic CP violation: from QCD to hadron level

Nucleon EDM

N N

γ

P, CP-odd π-N interaction

N N

π

P, CP-odd contact N-N interaction

N

NN

N

Nucleon EDM

N N

γ

quark EDM

quark chromo-EDM

P, CP-odd 4-quark interaction

q

q

q

q

g

qq

γ

qq

θ-term

g g

g g

g

Weinberg operator

quark EDM

quark chromo-EDM


q

q

q

q

g

qq

γ

qq

θ-term

g g

g g

g

Weinberg operator

RGE

QCD calculations

EFT

To nuclear level calculation

CP-odd NN potential

TeV scale CPV QCDGeV scale CPV QCDCPV hadron EFTNuclear level inputs

+ Processes with W, Z, H

Quark-gluon level enhancement/suppression

Relativistic effect : Z graph

Quark scalar density : enhancement

Quark spin (tensor, axial charges) : suppression

NY, S. Imai, T. M. Doi, H. Suganuma, Phys. Rev. D 89, 074017 (2014).NY, T. M. Doi, S. Imai, H. Suganuma, Phys. Rev. D 88, 074036 (2013).

Quark EDM is a superposition of flipping after gluon emissions/absorptions

⇒ Quark EDM is suppressed after QCD corrections!

Scalar density of particles and antiparticles has the same sign ⇒ Becomes large with long worldline⇒ Enhancement by relativistic effect

Renormalization group evolution of CPV QCD operatorsChange of energy scale modifies the coupling constants, mixes operators

Large uncertainty due to nonperturbative effect below µ = 1 GeV

d

d lnµC(µ) = �̂T (↵s)C(µ)

�̂(0) =

0

@8CF 0 08CF 16CF � 4nc 00 2nc nc + 2nf + �0

1

A

Anomalous dimension matrix:

Renormalization group equation:

C : Wilson coefficients of CPV operators

q q

γ

Degrassi et al., JHEP 0511 (2005) 044 Yang et al., Phys. Lett. B 713 (2012) 473 Dekens et al. JHEP1305(2013)149

Renormalization = resummation of perturbative QCD corrections

⇒ We have to stop (perturbative) RG evolution and calculate the hadronic processes with nonperturbative methods

Significant changes for quark/gluon operators due to QCD

Renormalization group evolution of CPV QCD operators

Quark EDM:

µ = 1 TeV

dq

µ = 1 GeV

0.8 dq

Weinberg operator:

µ = 1 TeV µ = 1 GeV

g g

g

g g

g

0.17 + 0.30

g

qq - 0.15

γ

qq

Scalar density:

µ = 1 TeV

qq

µ = 1 GeV

2 qq

Roughly, scalar increases and spin decreases when scale goes down

Well-known nucleon matrix elements

hN |q̄q|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

hN |q̄�µ⌫q|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

Phenomenological extractions (ChPT), lattice QCD

Lattice QCD, phenomenological extractions (pQCD)

JLQCD(2018)ETM(2016)

chiQCD(2016)RQCD(2016)

Ling et al.(2017)BMW(2016)

Lutz et al.(2014)QCDSF-UKQCD(2012)

Ruiz de Elvira et al.(2017)Yao et al.(2016)

Hoferichter et al.(2015)Alarcon et al.(2012)

0 10 20 30 40 50 60 70σπN (MeV)

Nucleon scalar density:

Nucleon tensor charge:

Contribution of the quark EDM to the nucleon EDM

Important input in EDM related ChPT

Input of CP-odd electron-nucleon interaction

Input of CP-odd electron-nucleon interaction

⇒ Visible disagreement

⇒ Birth of a puzzle?

hN |q̄q|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


～ 10 ⇒ enhanced

～ 1 < 5/3 (quark model) ⇒ suppressed Obey the rough rule

PNDME(2018)

JLQCD(2018)

ETM(2017)

RQCD(2016)

Green et al.(2012)

Radici et al.(2018)

Kang et al.(2016)

0 0.2 0.4 0.6 0.8 1 1.2 1.4gT

Obey the rough rule

Pion-nucleon level enhancement/suppression

Count the power of mπ2 (or mq) and match operators between QCD and pion-nucleon physics

A rough rule of ChEFT :

Evidently, if the chiral representations of the CP-odd operators at the QCD and hadron levels do not match, we have a suppression by at least mπ2.

Unfortunately, not all hadron matrix elements are available from lattice QCD

Use chiral EFT to relate unknown ones with known ones

P, CP-odd π-N interaction

N N

π

Nucleon EDM

N N

γ

quark chromo-EDM


q

q

q

q

g

qq

g g

g

Weinberg operator

J. de Vries et al., PRC 84, 065501 (2011)

Less known nucleon matrix elements in ChEFT

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hN |q̄�µ�5q|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Nucleon pseudoscalar density:

Use nucleon axial charge as input (anomalous Ward identity)

⇒ Pion pole dominance

πNN interaction from quark chromo-EDM:

πNN interaction from four-quark interaction:

Vacuum alignment contribution, may be enhanced by scalar density Contact term rather small from high energy QCD input

J. de Vries et al, PLB766, 254 (2017) C.-Y. Seng, arXiv:1809.00307 [hep-ph]

Vacuum alignment, but may cancel by chiral symmetry arguments

Contact interaction is important in factorization model (scalar density)

Chiral EFT plays an important role in the control of errorbars

/ 1m2⇡

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～ 100 !!

h⇡0|OCP|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 ～ O(1-10)

CP-odd electron-nucleon interaction : purely atomic effect

Scalar-pseudoscalar type:

Tensor type:

Pseudoscalar-scalar type:

CT N̄�µ⌫N ēi�µ⌫�5e

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CSP N̄N ēi�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

CPSN̄i�5N ē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

Atomic level : enhanced for paramagnetic atoms, like for de very suppressed by close electron spin shell (diamagnetic)

Hadron level : enhanced by quark scalar density hN |q̄q|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

Nuclear level : enhanced by nucleon number

Hadron level : not enhanced by tensor charge (spin)

Nuclear level : suppressed by configuration mixing (depends on nuclei)


Hadron level : enhanced by pion pole

Nuclear level : suppressed due to nonrelativistic nucleons

hN |q̄i�5q|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

Compensation!

e

NN

eP, CP-odd e-N interaction have specific sensitivity to some NP

Extended Higgs, leptoquark, R-parity violation, etc.

K. Yanase et al., arXiv:1805.00419 [nucl-th]

Nucleon EDM : status

Quark EDM:

Single nucleon EDM has low sensitivity to isovector couplings

Experimental limit : dn < 3 x 10-26e cm

Chiral loop:θ < 10-10 ⇒ Strong CP problem

dq < 10-26cm～

⇒ CP problems for 1-loop level EDM (e.g. SUSY)

nucleon EDM has specific sensitivity to quark EDM generated by some NP

⇒ Constrain Split SUSY, R-parity violation, leptoquarks, …

Not enhanced, dn ～ dq, but

R. J. Crewther et al., PLB88, 123 (1979) J. de Vries et al., PRC92, 045201 (2015)

J. Ellis et al., PLB112, 231 (1982)

N

π γ

J. M. Pendlebury et al., PRD 92,092003 (2015)

Nuclear EDM / Schiff moment from nucleon level CP violation

Two leading contributions to nuclear EDM/Schiff moment:

1) Nucleon’s intrinsic EDM:

2) Polarization of the nucleus:

Contribution from the nucleon EDM (spin)

Polarize the whole system by the parity and CP mixing due to CP-odd nuclear force

Strong pairing force : only unpaired nucleon(s) contribute pn

p

May be enhanced by the many-body effect?

Nucleons are nonrelativisitic in nuclei

⇒ Nucleon EDM is not enhanced in nuclei

s-wave p-wave

+

-+

-

polarized system

+ =

P, CP-odd nuclear force

P, CP-odd nuclear force : pion exchange is dominant

N

N

N

N

π ⇠ 1q2 �m2⇡

N̄N N̄i�5N

P, CP-odd Hamiltonian (3-types):

Isoscalar Isotensor Isovector

4 important properties:• Coherence in nuclear scalar density : enhanced in nucleon number • One-pion exchange : suppress long distance contribution • Spin dependent interaction : closed shell has no EDM • Derivative interaction : contribution from the surface

What is expected:• Polarization effect grows in A for small nuclei ? • May have additional enhancements with cluster structure, deformation, …

HPT = �1

8⇡mN

h�Ḡ(0)⇡ ⌧a · ⌧b + Ḡ

(2)⇡ (⌧a · ⌧b � 3⌧

za ⌧

zb )�(�a � �b) + Ḡ

(1)⇡ (⌧

ab �a � ⌧

zb �b)

i·rabem⇡rab

rab

EDM of light nuclei and counting rule

dA(pol) ～ d(2/3H) + n x 0.005 Gπ(1) e fmα-N polarization (times # α-N combinations)

Isovector coupling obeys a counting rule

α α

pn

n

d11B = 0.02 G(1)π e fm

Example of 11B EDM:

3H cluster

NY, T. Yamada, Y. Funaki, in preparation

EDM of cluster with open shell

Isoscalar and isotensor appears from single valence nucleon and 3H cluster (vanish for α-N polarization)

EDM of light nuclei can be measured using storage rings⇒ No Schiff’s screening⇒ Very high sensitivity to new physics expected

⇒ Explained by the cluster structure

Nuclear EDM / Schiff moment of heavy nuclei: suppression

dA = (A/4) x (α-N polarization) ??

n

α α α …

…

EDM of larger nuclei is larger?

No!Large nuclei have configuration mixing

≒ (Simple shell model picture)

e.g. 129Xe EDM : d129Xe ～ 0.000074 Gπ(1) e fmN. Yoshinaga, K. Higashiyama, R. Arai and E. Teruya, Phys. Rev. C 89, 045501 (2014).

EDM of large nuclei is quenched due to destructive interference of the spin of valence nucleon(s).

Ψ = + + + …

Schiff moment of octuple deformed nuclei: enhancement

Octupole deformation occurs in heavy nuclei (225Ra, 223Rn, 223Fr, etc)

Octupole deformation

225Ra

⇒ enhance nuclear Schiff moment

199Hg

a0(isoscalar) a1(isovector) a2(isotensor)

Octupole deformation enhances by O(1000) times!!

J. Dobaczewski and J. Engel, Phys. Rev. Lett. 94, 232502 (2005) J. Dobaczewski et al., arXiv:1807.09581 [nucl-th].

-1.5 e fm3 6.0 e fm3 -4.0 e fm3

0.02 e fm3 -0.007 e fm3 0.03 e fm3

(Comparison 199Hg result of S. Ban et al., Phys. Rev. C 82, 015501 (2010))

⇒ close opposite parity levels⇒ parity doubling due to axially asymmetric shape

Comparison of Schiff moment with 199Hg:

Weinberg operator : a very unknown contribution

Weinberg operator is generated in many interesting models (2HDM, vectorlike quark, …)

Its contribution to the EDM is however very obscure

Summary of problems in the study of WO:

Hadron level : no reliable calculations

Lattice calculation needs high statistics

WO is gluonic ⇒ low energy constant in chiral EFT not known

Nuclear level : large uncertainty due to the short distance wave function

Possible approach : Lattice QCD calculation of nuclear force? High energy QCD experiments?

t

H

S. Weinberg, Phys. Rev. Lett. 63, 2333 (1990).

At least, an order estimation of the relative size with chromo-EDM is necessary

(recall that WO mixes with quark chromo-EDM in RGE)

Only model calculation of intermediate quantity existsM. Pospelov et al., PRD 67, 015007 ( ︎2003 ︎)

J. Dragos et al., EPJ Web Conf. 175, 06018 (2018)

J. Bsaisou et al., JHEP 1503 (2015) 104

W

g

q q

γ, g

EDM from CKM matrix

EDM in the Standard model starts from * 3-loop diagram for quark ~10-35e cm * 4-loop diagram for electron ~10-40e cm

We consider the complex phase of CKM matrix as the CP violation in the Standard model:

Very small due to GIM cancellation

Leading CP violation from Jarlskog invariant

J = Im[Vts*VtdVusVud*] = -Im[Vcs*VcdVusVud*]C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985).= (3.06 ± 0.21)x10-5 (PDG value)

Long distance processes (hadronic level):

Short distance processes :

* Neutron EDM ~10-32e cm * Deuteron EDM ~10-31e cm

N Λ,Σ

π N

π

Λ,ΣN

N

N

Generated by hadron level |ΔS|=1 interaction

C.-Y. Seng, PRC 91, 025502 (2015) NY et al., JHEP02(2016)067

A. Czarnecki et al., PRL 78, 4339 (1997) M. Pospelov et al., Sov. J. Nucl. Phys. 53 (1991) 638

W

g

q q

γ, g

EDM from CKM matrix

EDM in the Standard model starts from * 3-loop diagram for quark ~10-35e cm * 4-loop diagram for electron ~10-40e cm

We consider the complex phase of CKM matrix as the CP violation in the Standard model:

Very small due to GIM cancellation

Leading CP violation from Jarlskog invariant

J = Im[Vts*VtdVusVud*] = -Im[Vcs*VcdVusVud*]C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985).= (3.06 ± 0.21)x10-5 (PDG value)

Long distance processes (hadronic level):

Short distance processes :

* Neutron EDM ~10-32e cm * Deuteron EDM ~10-31e cm

N Λ,Σ

π N

π

Λ,ΣN

N

N

Generated by hadron level |ΔS|=1 interaction

C.-Y. Seng, PRC 91, 025502 (2015) NY et al., JHEP02(2016)067

A. Czarnecki et al., PRL 78, 4339 (1997) M. Pospelov et al., Sov. J. Nucl. Phys. 53 (1991) 638

Caution : Unknown systematics due to mixing of hypernuclear states for larger nuclei

Nonperturbative effect

• A review of enhancement/suppression in EDM. • Schiff’s screening in atoms damps the leading CPV. • Scalar is enhanced, spin is suppressed, but O(1). • Notable enhancement : relativistic electron in atoms/

molecules, octuple deformation of nuclei, and maybe scalar density.

• Suppression : nuclear configuration mixing • We have to note that experimentally measurable systems

are not numerous : limited # of cases to be studied.

Summary

Summary:

Future subjects:• Still unknown mechanisms : Weinberg operator, but

important for Higgs sector. • We are waiting for new experiments!

Advertisement

N. Yamanaka,Analysis of the Electric Dipole Moment in the R-parity Violating Supersymmetric Standard Model,Springer, 2014.

EDM Physics is reviewed !!

N. Yamanaka, B. K. Sahoo, N. Yoshinaga, T. Sato, K. Asahi and B. P. Das, Probing exotic phenomena at the interface of nuclear and particle physics with the electric dipole moments of diamagnetic atoms ,  European Physical Journal A 53, 54 (2017) arXiv:1703.01570 [nucl-th].

For values and error bars of hadron level CP violation, see

For details of particle physics level calculations, see

N. Yamanaka, Review of the electric dipole moment of light nuclei,  International Journal of Modern Physics E 26, 1730002 (2017) arXiv:1609.04759 [nucl-th].

For details of nuclear EDM calculation, see

enhancements and suppressions of cp violating effect in the … · 2018. 9. 12. · enhancement and...

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