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
