1

SOME NUCLEAR ASPECTS OF THE

SAKHAROV CONDITIONS

U. van Kolck

Supported by CNRS and US DOE

Institut de Physique Nucléaire d’Orsay and University of Arizona

Outline

Matter vs Antimatter

EFT and the Role of Nuclear Physics

T Violation

B Violation

Conclusion

I. B ≠ 0 as an initial condition. Difficulty: washed out by inflation

II. B = 0 as initial condition but B ≠ 0 from “baryogenesis” (after inflation)

Requirements? Sakharov ’67

B violation: ∆B ≠ 0 processes deviation from thermal (and chemical) equilibrium: ∆B > 0 and ∆B < 0 processes not to occur at the same rate C and CP violation: B = 0 (B ≠ 0) state (not) invariant under C and CP

10

1 GeV 3 K 3 K

6 10B BB B B

B B T T T

N N N N NN N N Nγ γ

η −

>

− −≡ ⋅

+

First part

Second part

6

3 K

10B

B T

NN

−<

In Standard Model, all conditions fulfilled but not sufficient: B violation: violated by non-perturbative quantum effects from non-Abelian electroweak gauge group --- sphaleron processes, efficient only at temperatures above MEW ~ 100 GeV.

http://www-cdf.lbl.gov/~jmuelm

en/www/ M

icrophysical_mechanism

s.html

C and CP violation: both violated by weak interaction, but CP too small.

deviation from thermal (and chemical) equilibrium: provided by expansion of the universe, but much too slow above MEW ~ 100 GeV.

( )

( )( )

2 3

2 2 4

3 2

1 21 2

1 1CKM

A iU A

A i A

λ λ λ ρ ηλ λ λ λ

λ ρ η λ

− −

= − − + − − −

2 6 8 5( ) 3 10CPJ A λ η λ −= + ⋅

W ±iu

jd

0.23λ ≅

Wolfenstein ’83

Jarlskog ’85

Kobayashi + Maskawa ‘73

0.8A ≅ 0.1ρ ≅ 0.3η ≅

In Standard Model, all conditions fulfilled but not sufficient: B violation: violated by non-perturbative quantum effects from non-Abelian electroweak gauge group --- sphaleron processes, efficient only at temperatures above MEW ~ 100 GeV.

http://www-cdf.lbl.gov/~jmuelm

en/www/ M

icrophysical_mechanism

s.html

C and CP violation: both violated by weak interaction, but CP too small.

deviation from thermal (and chemical) equilibrium: provided by expansion of the universe, but much too slow above MEW ~ 100 GeV.

( )( )( )( )( )( )2 2 2 2 2 2 2 2 2 2 2 2 12

2010CP t b t u c u b s b d s d EWJ m m m m m m m m m m m m M

η−

− − − − − −

e.g. Canetti, Drewes + Shaposhnikov ‘12

“Every disadvantage has its advantage.” J. Cruijff (b. 1947), Dutch soccer player philosopher

new physics

Issue: once a signal is observed,

how many/which observables do we need to identify the new source(s) of T , B ?

Strategy: use Effective Field Theory

to study various T, B effects

Opportunity: any new signal of T, B

is likely to represent new physics

The Way of EFT

QCD

Chiral EFT

Q

(cPT)

| | 1 | | 2, , , ?T B BM M M// ∆ = ∆ =

unknown physics

, ,100 GeV

EW Z WM m mϕ

Standard Model (incl higher dim ops)

hadr

onic

+

nucl

ear

phys

ics

atom

ic

phys

ics ~3 keV

at eM mα

QED

4, , ,

1GeVQCD NM m m fρ ππ

, , ,10 MeV

10

nuc NNM f r mπ π

quarks, gluons, leptons, photon,

weak bosons, Higgs (+dark matter)

(3,1), (3) (2) (1)c L YSO SU SU U× ×

up + down quarks, gluons, electron, …, photon

(3,1), (3) (1)c emSO SU U×

nucleons, pions, electron, …, photon

(3,1), (1) ,(2) (2)

em

L R

SO USU SU×

nuclei, electron, …, photon

(3,1), (1)emSO U

violate S and transform in specific ways under χ symmetry

Main Idea

Chiral EFT

Q

(cPT)

, ,100 GeV

EW Z WM m mϕ

Standard Model (incl higher dim ops)

hadr

onic

+

nucl

ear

phys

ics , , ,

10 MeV1

0nuc NNM f r mπ π

quarks, gluons, leptons, photon,

weak bosons, Higgs (+dark matter)

(3,1), (3) (2) (1)c L YSO SU SU U× ×

nucleons, pions, electron, …, photon

(3,1), (1) ,(2) (2)

em

L R

SO USU SU×

( ) ( ), ,S S ii

q G q GO= +∑

( ) ( )( ), ,EFT S S ii

N NOχ π π∆

∆

= +∑∑

preserves symmetry S

χ symmetry

give rise to specific relations among

S–violating observables

preserves symmetry S

BSM models

low-energy symmetry (violation)

source of S violation

chiral symmetry

Chiral Nuclear Filter

T VIOLATION

for much more …

following

Electromagnetic Form Factors A

Electric Magnetic Toroidal polarity

0 (charge, mono)

1 (di, ana)

2 (quadru)

etc.

,P T

,P T ,P T

,P T ,P T

,P T

,P T

∅ ∅

1S =

1 2S =

0S =

(Permanent) Electric Dipole Moment (EDM)

( )( )

P

edm

edm Td edm

d S E HH d S E

d S E H

→ − ⋅ − = −= − ⋅ → − − ⋅ = −

inside.hlrs.de/_old/htm/Edition_01_11/article_11.htm

l

S

S

E

E

( )22

3 194 104 fm

(4 )tF

n CPW

mGd fe J eM ππ

π−

≈

Weak interactions:

Experiment:

( ) 13

15

0.2 1.5(stat) 0.7(syst) 10 fm

10 fm (UCN, proposed)nd e

e

−

−

= ± ± ⋅

127.9 10 fmpd e−< ⋅

163.1 10 fm (95% c.l.)Hgd e−< ⋅

1610 fm (storage ring, proposed)dd e−

Baker et al ’06 (ILL)

Bodek et al (ILL+PSI) Budker et al (SNS)

Griffith et al ’09 (UW)

Nuclear Schiff moment from RPA, … Dmitriev + Sen’kov ’03

Orlov et al (BNL? COSY?)

e.g. Donoghue, Golowich + Holstein ‘92

Proton and 3He as well? How about 3H?

The Way of EFT Q?TM /

unknown physics

, ,100 GeV

EW Z WM m mϕ

Standard Model (incl higher dim ops)

~3 keV

at eM mα

4, , ,

1GeVQCD NM m m fρ ππ

, , ,10 MeV

10

nuc NNM f r mπ π

quarks, gluons, leptons, photon,

weak bosons, Higgs (+dark matter)

(3,1), (3) (2) (1)c L YSO SU SU U× ×

neglected here

( )

( ) ( )

( )

3 3

2

2

2

1 82

†2

2

1

H.c.

(4 ) H.c.

(4 ) H.c.

L u u R d d R

Bu Wu u R Bd Wd d R

abc a b c

i j i a j aij L R L R L R L R

R R u d

T

T

T

T

M

M

M

M

q G g u g d

g B g W u g B g W d

w f G G G

i q u q d q u q d

u d iD

µνµν

µν µν µν µν

νρ µµν ρ

µµ

σ ϕ ϕ

τ ϕ τ ϕ

π ε σ σ λ λ

π ξ γ ϕ ϕ

− +

+ + + + +

+

+ + +

+ +

+

i iju djϕ ε ϕ∗=e.g. single Higgs

dim

ensi

on

[ ]

2

2

2H.c. Tr16

L q L

sL u u R d d R

q g W U q

gq f u f d G G

µµ

µνµν

γ τ

θϕ ϕπ

± ± = −

+ + + + +

CKM matrix (dim=4)

q term (dim=4)

53 10CPJ −⋅

1010θ −<

small…

G Gρσµν µνρσε≡

quark EDM (eff dim=6)

quark color-EDM (eff dim=6)

gluon color-EDM (dim=6) four-quark

contact (dim=6)

Jarlskog ’85

‘t Hooft ‘76

LR four-quark contact (dim=6)

Buchmüller + Wyler ’86 Weinberg ’89

de Rujula et al. ’91 …

Ng + Tulin ‘11

, , 100 GeVEW Z WM m mϕ

The Way of EFT

QCD

Q?TM /

, ,100 GeV

EW Z WM m mϕ

~3 keV

at eM mα

4, , ,

1GeVQCD NM m m fρ ππ

, , ,10 MeV

10

nuc NNM f r mπ π

up + down quarks, gluons, electron, …, photon

(3,1), (3) (1)c emSO SU U×

q

q Baluni ‘79 chiral rotation

imaginary mass term

4 MeV2

u dm mm ≈+

≡13

d u

u d

m mm m

ε+

≡−

average quark mass mass splitting

up/down quarks

m fϕ

RG

q

q

q q

+ … very small…

neglected from now on…

RG ( )21

2mm θ ε θ∗ = −m θ∗

W

4, , , 1GeVQCD NM m m fρ ππ

ϕ

G

G

+ …

+ …

+ …

+ …

,Z B A

W

( )2 24 Ti Mπ σ

2Tw M

2Tg M

2Tg M

( )2 24 TMπ ξ

)2

(

T

iq M

gcf

m =

( )iqc

)2

(

T

iq

mM

egdf

=

( )iqd

2T

Gwc

M

=

Gc

2

2

(4 )i

T

i

MC π σ

=

iC

2

2(4 )i

TMD π ξ

=

iD

… Dekens + De Vries ’13

+

+ …

+ RG

generically, RG brings in effects of ( )1

( )

( )

( )

( )

( )

( )

23 5

(0) (1)3

(0) (1)3

15 5

85 5

13 5

8

1 Tr2

12

1212

6

4

4

4

4

QCD s

q q

q q

abc a b cG

a a a a

ij i j

q i g G q G G

qq q q qi q

q c c G q

q d d q F

c f G G G

C qq qi q q q qi q

C q q qi q q q qi q

D q q q

m

q

m

D

m

µνµν

µνµν

µνµν

νρ µµν ρ

µµ

ε τ ε θ γ

τ σ

τ σ

γ γ

λ γ λ λ γ λ

ε τ γ τ γ γ

ε

= ∂/ + / −

− + + −

− +

− +

+

+ − ⋅

+ − ⋅

+

+

τ τ

τ τ

3 5a a

ij i jq q q qµµτ γ λ τ γ γ λ

+

q

CIC

gCEDM

qEDM

qCEDM

uq

d

=

two flavors

)2

(

T

iq

mM

egdf

=

)2

(

T

iq M

gcf

m =

2T

Gwc

M

=

2

2

(4 )i

T

i

MC π σ

=

LRC 2

2(4 )i

TMD π ξ

=

N.B. To this order, T P→

The Way of EFT

Chiral EFT

Q

(cPT)

?TM /

, ,100 GeV

EW Z WM m mϕ

hadr

onic

+

nucl

ear

EDM

s

~3 keV

at eM mα

4, , ,

1GeVQCD NM m m fρ ππ

, , ,10 MeV

10

nuc NNM f r mπ π

nucleons, pions, electron, …, photon

(3,1), (1) ,(2) (2)

em

L R

SO USU SU×

q

RG

A+

qq N

+ …

…

…

…

π

+ …

+ …

+ …

+ …

, , , 10 MeV1 0nuc NNM f r mπ π

short-range isoscalar

and isovector (-> proton

and neutron) EDMs

isoscalar and isovector P, T

pion-nucleon couplings

isoscalar and isovector (derivative) P, T

2-nucleon contacts

three-pion coupling

0,1d

1,2C

0,1gfπ

2 fπ

∆

Mereghetti, Hockings + v.K. ’10 De Vries et al, ‘13

N

( )

( )

( )

( )

( )

( )

23 5

(0) (1)3

(0) (1)3

15 5

85 5

13 5

8

1 Tr2

12

1212

6

4

4

4

4

QCD s

q q

q q

abc a b cG

a a a a

ij i j

q i g G q G G

qq q q qi q

q c c G q

q d d q F

c f G G G

C qq qi q q q qi q

C q q qi q q q qi q

D q q q

m

q

m

D

m

µνµν

µνµν

µνµν

νρ µµν ρ

µµ

ε τ ε θ γ

τ σ

τ σ

γ γ

λ γ λ λ γ λ

ε τ γ τ γ γ

ε

= ∂/ + / −

− + + −

− +

− +

+

+ − ⋅

+ − ⋅

+

+

τ τ

τ τ

3 5a a

ij i jq q q qµµτ γ λ τ γ γ λ

+

q

CIC

gCEDM

qEDM

qCEDM

uq

d

=

two flavors

(2) (2) (4)L RSU SU SO×

chiral symmetry

)2

(

T

iq

mM

egdf

=

)2

(

T

iq M

gcf

m =

2T

Gwc

M

=

2

2

(4 )i

T

i

MC π σ

=

LRC 2

2(4 )i

TMD π ξ

=

N.B. To this order, T P→

Key to disentangle TV sources: each breaks chiral symmetry in a particular way,

and thus produces different hadronic interactions

Mereghetti, Hockings + v.K. ’10 De Vries et al, ‘13

q

qCEDM

qEDM

gCEDM

CIC

LRC

a chiral pseudo-vector: same as quark mass difference

a chiral vector

a rank-2 chiral tensor

another rank-2 chiral tensor

{ }1,8,w wσ →chiral invariants: cannot be separated at low energies, CI

link to P,T-conserving charge symmetry breaking

( )( )

( ) ( )

2†

†0 1 3

†0 1 3

† † † †1 2

23

2

2

12

2

PTN

N Nm

N d d S N F

N g g N

C N N N S N C N N N S N

f

f

χ

µ

π

π

νµ ν

µ µµ µ

τ

π

π

= ⋅ + +

− +

− ⋅ +

+ ∂ + ⋅∂

∆−

+

τ π

τ τ

π

iv

v

Where are the differences?

PV, TV pion-nucleon coupling

short-range EDM contribution

PV, TV two-nucleon contact

terms related by chiral symmetry + higher orders six LO couplings

for EDMs cf. Barton ’61

and nuclear followers

three-pion coupling

( )1,0µ =

v

0,2

S µ σ =

velocity

spin

2

m

0

q( )n p

mm

gm

π

−∆ = only for LRC

[ ]0 1 3,1

2T N N g gDf

Nππ

π= − ⋅ + +τ π

There are differences!

2 2 22

2 20

3

2 2, , , ,QCD QCD QCD QCD

TCD T TQ T

g gg wm m mm M M M M

M f fM M M Mπ π ππ αθ εξ

π// //

=

2 2

2 2

3 2

24

1

3

2, , , ,QCD Q

T

CD QCD QCD

TCD T TQ

g gg wf fM M M M

m Mm MM

mm M Mπ π ππ αθ ε ξπ// //

=

For example,

different orders; two-derivative interactions

important at higher order

pion physics suppressed

comparable to two-derivative

interactions

N.B. 2 3 3g N Nπ τ in high orders for all sources up to dim 6

( )0 qm23 MeV

n pm mg θεθ

−

≈

1)

2) for q, link to CSB, e.g.

using lattice QCD (Beane et al ’06)

Mereghetti, Hockings + v.K. ’10

Crewther et al ’79 Thomas ’95

… Hockings + v.K. ‘05

Narison ‘08 Ottnad et al ’10

De Vries et al ’10’11

Nucleon EDFF (to NLO)

0TJ = + + + …

LO for all sources ensures RG invariance brings in two parameters

provides estimates in terms of pion parameters at “reasonable” renormalization scale

order depends on source short-ranged; long-ranged;

( ) ( )2 ( ( ) 2)1

2( ) ' ( )i i i iEF d S qHq q− = + + −

p

'q p p= −

'1 ( )2

N

p pk

m

= +

− v

'p

( ) ( ) ]( )(0) (1)1

2 21 3, 2 ( ) ( )T E

NE

kq k q q S F

mqFqJ µ µρ µσ ν

ρσ

νσρρη η η τ/

= − − + + − + −

v

EDM + Schiff moment + …

( )( )

(0) (0) 0 12

02

2qm30 1

44 3N Q

n

CD

pAeg gm

gd dMf

m mmg

mm

π π

ππ

ππ

= + + + − +

−

( )( )0

2 2 2em(1) (1) 0 1

20

22

52 ln 144 5

A

N QCD

g g g m m

m Mfd d L

m me

gm mπ ππ π

ππ π

ππ

µ ± = + + + + − +

−

2 ln 44 EL

dγ π≡ − +

−cf. Crewther et al `79

( )2

32

1| | ln 2.0 10 fm2

2

4A N N

ne

fd mg m e

mπππ

δ ε θ θε

−−> ≈ ⋅

( )2

(0) 42

1 3| | 1.4 104

fm2 4

N

N

NA mm mmf m

g ed e π

ππ

ε πθ δ

π

δ θε

− −> − ≈ ⋅

renormalization q

q

Shintani et al. ‘14

Mereghetti + vK ‘15

no sign of chiral loop, but

Example from lattice

consistent with naïve estimate

( )( )0

2 2 2em(1) 0

2 22 2

5' 146 4

A

N QCD

m mg gm Mmf m

eS m mπ π

π

π π

ππππ ±

= − − +

−

( )( ) 2

qm( 022

0)24

' 026 QC

A n p

D

m m mm Mf

egm

gSπ

π

ππ

ππ

= − + +

−

Thomas ’95

6 35.0 10 fmeθ−− ⋅

q

momentum dependence of EDFF from lattice would isolate

5 36.8 10 fmeθ−⋅

q only parameter!

0g

Nuclear EDMs, MQMs, …

TJ

Tψ

TJ

TVTJ

TV

Tψ

TψTψ Tψ

Tψ

= + +

…

… …

…

…

…

… …

…

…

0TJ

…

… = + + …

Analogous for ,T TJ J De Vries, Mereghetti, Liu,

Timmermans + v.K. ‘12

De Vries, Mereghetti, Higa, Liu, Stetcu,

Timmermans + v.K. ’11 0TJ

0TJ

…

… = + + … 0

TJ Park, Min + Rho ’95 …

Maekawa, Mereghetti, De Vries + v.K. ’11 De Vries, Mereghetti, Timmermans + v.K. ‘13

TV = + + + + + + …

…

…

generic LO, but effect vanishes for q when N=Z

+

LO for LRC only

+ …

Tψ

… from solution of the Schrödinger equation

introduces dependence on binding energy AB

Weinberg ’90, ‘91 Ordónez + v.K. ‘92

…

Light-Nuclear EDMs (LO)

nnm d

ep

n

dd

q term qEDM qCEDM 2

2QCD

nuc

MMθ

( )1

2

2T

nuc

MMg

f

( )1

2

2T

nuc

MMg

f

( )1 ( )1

2

2

T

QCDwM

M

gCEDM, CIC

Crewther et al. ’79 Thomas ’95 … De Vries et al. ’10’11

LRC

2

2

T

QCDMM

ξ

( )1

( )1 ( )1 ( )1d

n

dd

2

2nuc

QCDMM

2

2nuc

QCDMM

t

h

dd

h

n

dd

2

2nuc

QCDMM

2

2nuc

QCDMM

2

2nuc

QCDMM

( )1 ( )1

( )1 ( )1 ( )1 ( )1 ( )1

De Vries et al ’11 ’13 Bsaisou et al ’13 ’14 ‘15

[135] De Vries et al ‘11 [147] Khriplovich + Korkin ‘00 [87] Bsaisou et al ‘15 [131] Liu + Timmermans ‘04 [136] De Vries et al ‘11 [137] Bsaisou et al ‘13 [138] Yamanaka + Hiyama ‘15 [132] Stetcu et al ‘08 [134] Song et al ‘13

all agree to 10% or better

Mereghetti + vK ‘15

d n pd d d+ for q term, qEDM, gCEDM, CIC for q term and qEDM ( )0.84h t n pd d d d+ +

3h t dd d d+ for qCEDM for qEDM ( )0.94h t n pd d d d− −

some separation of sources possible

B VIOLATION

in progress, with

Bingwei Long (Sichuan) and

Jan Bakker (Groningen), Rob Timmermans (Groningen),

Jordy de Vries (NIKHEF)

dim=6

Weinberg ’79 Wiczek + Zee ’79 Abbott + Wise ’82 …

Chang + Chang ’80 Kuo + Love ’80 Rao + Shrock ’82 …

Abbott + Wise ’82 …

Özer ’82 Caswell, Milutinović + Senjanović ’83 … Buchoff + Wagman ‘15

( ) [ ]2 5| |

( ) ( )| |

1 |

|

|

2

2

1 |,i iB B T T T

B i iBi iB

q Gc c

qqql q Cq q C q CM

q qM ∆ = ∆

∆ = ∆

=

= = + + + + ∑ ∑

interesting only if

| | 2 | | 1B BM M∆ = ∆ =

B L− not exact (why would it be?)

(true in some models)

| | 1,B L B∆ = ∆ = ∆ | | 2, 0B L∆ = ∆ =dim=9

RG

Conclusion

Stronger conclusions possible with lattice QCD calculations for various B, T sources heavy nuclear EFT formulation.

Chiral symmetry provides a handle to (partially) distinguish B, T sources at low energies

Baryon asymmetry in the universe suggests that new sources of B, T might be important, but they must exist anyway because B, T broken already in SM

Light-nuclear EDM measurements could provide the needed data to isolate T sources

EFT provides a model-independent framework for B, T in the SM and beyond

B in progress