EDM Implications for BSM Physics

December 8th, 2018 ACFI Workshop

K. Fuyuto, M. Ramsey-Musolf, T. Shen, PLB788(2019)52 J. de Vries, P. Draper, K.Fuyuto, J. Kozaczuk and D. Sutherland, 1809.10143 K. Fuyuto, X-G He, G. Li and M. Ramsey-Musolf, work in Progress

Kaori Fuyuto

University of Massachusetts, Amherst

CPV interactions in New Physics New physics generally contains CP phases.

My talk discusses

-  What kind of CPV interactions are in BSM

-  EDM constraints on CP phases

✔ Leptoquark

✔ 　Dark Photon

- Implication for QCD theta term

Leptoquark

Leptoquark Leptoquark couples to quark and lepton

a, b : Flavor indices �u,e : Complex

X =

✓VY

◆Scalar LQ : (3,2, 7/6)

Epsilon tensor : ✏12 = 1

L � ��abu uaXT ✏Lb � �ab

e eaX†Qb + h.c.=

J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013)J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013)I. Dorsner, S. Fajfer, A. Greljo, J. F. Kamenik and N. Kosnik, Phys. Rept. 641, 1 (2016)

✔ Sources for two CP-violating interactions

Leptoquark Two CP-violating interactions are induced:

Semileptonic 4-fermi interaction Electron EDM

L = � i

2dee�

µ⌫�5eFµ⌫ � 1

⇤2

C(1)

lequLjeR✏jkQ

kuR + h.c.

�

�

ua

V

�u �e

eL eR

J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013)J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013)I. Dorsner, S. Fajfer, A. Greljo, J. F. Kamenik and N. Kosnik, Phys. Rept. 641, 1 (2016)

V

eR uR

�u�e

Q L1-loop Tree-level

Leptoquark Two CP-violating interactions are induced:

L = � i

2dee�

µ⌫�5eFµ⌫

Electron EDM

� 1

⇤2

C(1)

lequLjeR✏jkQ

kuR + h.c.

�

1-loop Tree-level

4-fermi interaction can be larger than electron EDM.

J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013)J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013)I. Dorsner, S. Fajfer, A. Greljo, J. F. Kamenik and N. Kosnik, Phys. Rept. 641, 1 (2016)

Semileptonic 4-fermi interaction

�

ua

V

�u �e

eL eR

V

eR uR

�u�e

Q L

Leptoquark Two CP-violating interactions are induced:

L = � i

2dee�

µ⌫�5eFµ⌫

Electron EDM

� 1

⇤2

C(1)

lequLjeR✏jkQ

kuR + h.c.

�

1-loop Tree-level

J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013)J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013)I. Dorsner, S. Fajfer, A. Greljo, J. F. Kamenik and N. Kosnik, Phys. Rept. 641, 1 (2016)

Semileptonic 4-fermi interaction

�

ua

V

�u �e

eL eR

V

eR uR

�u�e

Q L

� 1

2⇤2Im

⇣C(1)

lequ

⌘ei�5e uu

Leptoquark Two CP-violating interactions are induced:

L = � i

2dee�

µ⌫�5eFµ⌫

Electron EDM Electron-nucleon interaction

�GFp2CS ei�5e NN

Constrained by EDM measurements in paramagnetic systems ✔ Polar molecule systems

J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 88, 035009 (2013)J. M. Arnold, B. Fornal and M. B. Wise, Phys. Rev. D 87, 075004 (2013)I. Dorsner, S. Fajfer, A. Greljo, J. F. Kamenik and N. Kosnik, Phys. Rept. 641, 1 (2016)

�

ua

V

�u �e

eL eR

V

eR uR

�u�e

Q L

Analytic formula

- Electron-nucleon interaction

CS ' gSv2

2m2V

Im��11u �11

e

� gS = 6.3J. Engel, M. J. Ramsey-Musolf andU. van Kolck, Prog. Part. Nucl. Phys. 71, 21 (2013)

e e

�V

u

✔ Up-quark contribution

CS , de / Im��11u �11

e

�

de = �emuaNC

32⇡2m2V

Im��a1�1a

� 23I2

✓m2

ua

m2V

◆+

5

3J2

✓m2

ua

m2V

◆�- Electron EDM

Loop function I2, J2 :

u e

mV : LQ mass

Analytic formula

✔ Up-quark contribution

CS dominates the systems!

de↵jCS

⇠ O(10�2)

de = �emuaNC

32⇡2m2V

Im��a1�1a

� 23I2

✓m2

ua

m2V

◆+

5

3J2

✓m2

ua

m2V

◆�- Electron EDM

Loop function I2, J2 :

u e

mV : LQ mass

- Electron-nucleon interaction

CS ' gSv2

2m2V

Im��11u �11

e

� gS = 6.3J. Engel, M. J. Ramsey-Musolf andU. van Kolck, Prog. Part. Nucl. Phys. 71, 21 (2013)

Current experimental values :

Effective EDM : dj ⌘ de + ↵jCS

↵ThO(HfF+) = 1.5(0.9)⇥ 10�20 e cm

V. Andreev et al. [ACME Collaboration], Nature 562(2018)7727

|de| < 1.1⇥ 10�29 e cm

ThO : dThO = (4.3± 4.0)⇥ 10�30 e cm

Sole source:

W. B. Cairncross et al., PRL. 119, no. 15, 153001 (2017)

|de| < 1.3⇥ 10�28 e cm

HfF+ : dHfF+ = (0.9± 7.9)⇥ 10�29 e cm

Sole source:

Current limit on de and CS

|de| . 10�31 e cm

Current limit

Result Blue region:

Allowed at 90% C.L.

Black lines:

Predictions of de |de| = 10�29,30,31 e cm

Im��11u �11

e

�=

���11u �11

e

�� sin ✓ue

Result Blue region:

Allowed at 90% C.L.

Black lines:

Predictions of de |de| = 10�29,30,31 e cm

LQ Model : de < CS

Im��11u �11

e

�=

���11u �11

e

�� sin ✓ue

Result Up-quark EDM and cEDM

u ue

V � , g

Green : Neutron

Orange : Proton

dp,n ⇠ 10�32 e cm

Nonzero dp,n point to different CPV sources.

* Comparable to SM values

QCD theta term

2. IR Solution R. Peccei and H. R. Quinn, Phys.Rev.Lett. 38 (1977) 1440R. Peccei and H. R. Quinn, Phys.Rev. D16 (1977) 1791{1797.a : Axion ✓ ! a/fa

Ex) Peccei-Quinn Symmetry

QCD theta term

“Strong CP problem”

QCD theta term : L = ✓↵s

8⇡Gµ⌫G

µ⌫

✓ . 10�10From neutron EDM limit :

1. UV Solution A.E. Nelson, PLB136 (1984) 387, S. M. A. Barr, PRD30(1984)1805. S. M. Barr, PRD30(1984)1805

at UV, but at some scale. ✓ = 0

Ex) Nelson-Barr models

(⇡ 10�10)✓ 6= 0

Dimension 6 operators New Physics : Dimension 6 operators

For example, OuB = Q�µ⌫uRHBµ⌫

H

u uOuB

✓ ⇠ �✓ ⇠ 1

16⇡2⇤2CuB⇤

2

Quadratic divergence

� 10�10

They give large threshold corrections to theta term.

If experiments, EDMs r colliders, see any sing of dim 6 operators, it might point to IR solution.

See DM predictions n pure theta scenario

dHg and dRa as a function of dn

�1.0 �0.5 0.0 0.5 1.0dn [10�26 e cm]

�0.75

�0.50

�0.25

0.00

0.25

0.50

0.75

d X[1

0�26

ecm

]

dHg ⇥ 100dRa

dHg x 100

dRa

Inside of color regions is prediction in pure theta scenario. * Theoretical uncertainties give a spread of region.

Predictions of pure theta scenario

Predictions of pure theta scenario dHg and dRa as a function of dn

�1.0 �0.5 0.0 0.5 1.0dn [10�26 e cm]

�0.75

�0.50

�0.25

0.00

0.25

0.50

0.75

d X[1

0�26

ecm

]

dHg ⇥ 100dRa

dHg x 100

dRa

Inside of color regions is prediction in pure theta scenario. Outside of color regions point to other BSM CP sources.

�1.0 �0.5 0.0 0.5 1.0dn [10�26 e cm]

�3

�2

�1

0

1

2

3

d X[1

0�26

ecm

]

dp

dD

dHe

dp , dD and dHe as a function of dn

dHe

dD

dp

EDM measurements would give implication for strong CP problem.

Predictions of pure theta scenario

Conclusion

de ⌧ CS

Leptoquark : Electron EDM and e-N interaction

CS is dominant source.

* Sole-source limit is not available.

Dark Photon : Dimension 5 operators �

⇤Tr [Wµ⌫⌃] Xµ⌫ Examined by EDMs.

* Induced by light degree of freedom

QCD theta term : Unique EDM predictions

Looking for various EDMs is necessary.* Implication for solution to strong CP problem