Transcript Electric Dipole Moments and the Origin of Baryonic Matter

Electric Dipole Moments and
the Origin of Baryonic Matter
M.J. Ramsey-Musolf
V. Cirigliano
C. Lee
S. Tulin
S. Profumo
Caltech
INT
Caltech
Caltech
PRD 71: 075010 (2005)
Caltech MAP-312 (in prep)
What is the origin of baryonic matter ?
Cosmic Energy Budget
Dark Matter
Baryons
Dark Energy
Explaining non-zero rB requires CP-violation
beyond that of the Standard Model (assuming
inflation set rB=0)
What is the origin of baryonic matter ?
Cosmic Energy Budget
E
d  dS
Dark Matter


Baryons
 EDM
Dark Energy

dS E

h
T-odd , CP-odd
by CPT theorem
What are the
Searches
for permanent
quantitativeelectric
implications
dipoleof new
moments
EDM
experiments
(EDMs) of
forthe
explaining
neutron,the
electron,
origin of
andbaryonic
the
neutral atoms
component
probe of
new
theCP-violation
Universe ?
Baryogenesis and EDMs: Theoretical Tasks
• Attaining reliable computations that relate particle
physics models of new CP-violation to EDMs of
complex systems (neutron, atoms, nuclei)
Nonperturbative QCD, atomic & nuclear structure
• Attaining reliable computations of the baryon asymmetry
from fundamental particle physics theories with
new CP-violation
• Non-equilibrium quantum transport
• Non-zero T and m
• Spacetime dynamics of cosmic phase transitions
Equally difficult but less studied
This talk
Outline
1. Overview
2. Theory: Non-equilibrium QFT
& quantum transport
How to compute rB
systematically from Lnew
3. Phenomenology: SUSY
4. Outlook & Open Issues
Baryon Asymmetry of the Universe (BAU)
b
 0.024  0.001
(7.3  2.5) 1011
YB 

  1.1) 1011
s
(9.2
rB
BBN
WMAP
Baryogenesis: Ingredients
Present universe
Early universe
Sakharov Criteria
• B violation
• C & CP violation
 Y1

• Nonequilibrium
dynamics
Sakharov, 1967
 1
L

 1
S

log 10 (m / m0 )
Weak scale
Planck scale
Baryogenesis: Ingredients
Hˆ , Cˆ  0 , Hˆ , Cˆ Pˆ  0
Sakharov Criteria
  
ˆ Hˆ ,t Bˆ  0
Tr r
• B violation
• C & CP violation


• Nonequilibrium
dynamics
Sakharov, 1967


Hˆ , Cˆ Pˆ Tˆ  0


Tr e

  Hˆ

Bˆ  0
Baryogenesis: Ingredients
Present universe
Early universe
Sakharov Criteria
• B violation
• C & CP violation
 Y1

• Nonequilibrium
dynamics
Sakharov, 1967
 1
L


Weak scale
baryogenesis can be
tested experimentally
 1
S
?
?
log 10 (m / m0 )
Weak scale
Planck scale
Leptogenesis
Early universe
Key Ingredients
Present universe
• Heavy R
 Y1
• mspectrum
• CP violation
Leptogenesis

• L violation
-decay, 0decay, q13
 1
S

Weak scale
log 10 (m / m0 )
Planck scale
EW Baryogenesis: Standard Model
Weak Scale Baryogenesis
Anomalous Processes
• B violation
• C & CP violation
J mB
• Nonequilibrium
dynamics
A
qL

Sakharov, 1967
W

W
Different vacua: D(B+L)= DNCS

Kuzmin, Rubakov, Shaposhnikov
McLerran,…


Sphaleron Transitions
EW Baryogenesis: Standard Model
Shaposhnikov
2
J  s12 s13 s23 c12 c13
c 23 sin 13
 (2.88  0.33) 105
Weak Scale Baryogenesis
mt4 mb4 mc2 ms2
13

3
10
MW4 MW4 MW2 MW2
• B violation
• C & CP violation
• Nonequilibrium
dynamics


F
F
1st order
2nd order
Sakharov, 1967



• CP-violation too weak
• EW PT too weak
Increasing mh



Baryogenesis: New Electroweak Physics
Weak Scale Baryogenesis
• B violation
Unbroken phase
Topological transitions
new
• C & CP violation
• Nonequilibrium
dynamics
(x)
Broken phase

1st order phase transition

CP Violation
Sakharov, 1967
new
• Is it viable?
• Can experiment constrain it?
• How reliably can we compute it?

new


new
e



EDM Probes of New CP Violation
CKM
f
dSM
dexp
dfuture
e
 1040
 1.6 1027
 1031
n
 1030
 6.3 1026
 1029
Hg
 1033
 2.11028
 1032
m
 1028
 1.11018
 1024
199
Also 225Ra, 129Xe, d
If new EWK CP violation is responsible for abundance
of matter, will these experiments see an EDM?
Present n-EDM limit
Proposed n-EDM limit
?
Matter-Antimatter
Asymmetry in
the Universe
Better theory
M. Pendlebury
B. Filippone
“n-EDM has killed more theories than any other single experiment”
Baryogenesis and EDMs: Better Theory ?
Non-equilibrium quantum transport
RHIC
Violent departure
from equilibrium
Electroweak Baryogenesis
new
(x)
“Gentle” departure from
equilibrium
Systematic treatment of
transport dynamics w/
controlled approximations
Systematic Baryogenesis
Goal: Derive dependence of YB on parameters
Lnew systematically (controlled approximations)
Parameters in Lnew
CPV phases
Bubble & PT
dynamics
Departure from equilibrium
• Earliest work: QM scattering & stat mech
• New developments: non-equilibrium QFT
Systematic Baryogenesis: MSSM
F
F
1st order

2nd order
LEP EWWG


Increasing mh



1st order PT in MSSM:
mh < 120 GeV
mh>114.4 GeV
Constraint on mh relaxed for
larger gauge/Higgs sector
(NMSSM, etc.)
See, e.g., Kang
et al for U(1)’
or ~ 90 GeV
(SUSY)
Systematic Baryogenesis
Unbroken phase
(x)
Topological transitions
“snow”
Broken phase
1st order phase transition
Cohen, Kaplan,
Nelson
Joyce, Prokopec,
Turok
nL produced in wall
& diffuses in front
rB
 D 2 rB  W S FW S (x)nL (x)  RrB 
t
FWS (x) !0 deep inside bubble
J mB
qL

W

W
Systematic Baryogenesis
Riotto
Carena et al
Lee, Cirigliano,
Tulin, R-M
Unbroken phase
(x)
Topological transitions
Compute from first
principles given Lnew
Broken phase

1st order phase transition
ni
˜
 D 2 ni  Sn j ,T,, M
t
Quantum Transport Equation
G˜ 0


G˜


=
˜

G˜ 0

G˜ 0
+
+
+…
Schwinger-Dyson Equations
Systematic Baryogenesis
Departure from equilibrium
• Non-adiabatic evolution of states
& degeneracies
G˜
G˜ 0



=
˜

G˜ 0

G˜ 0
+
+
…
+

Generalized Green’s Functions: Closed Time Path
• Non-thermal distributions
Exploit scale hierarchy: expand in scale ratios e
Scale Hierarchy
T > 0: Degeneracies
g
q
q
Time Scales
M(T)
P(T)
tP ~ 1/P


Plasma time:
vW > 0: Non-adiabaticity

t˜L
vW
Decoherence time:
td ~ 1/vW k)
e.g., particle in an
expanding box
Quantum Decoherence
L DL
L
 (x)  An sin kn x
0
n

n
kn 
L
 n
0
n
k = kEFF(,Lw)
2
n=1
n=2

n=3
L  DL
L
Scale Hierarchy
Time scales:
tint ~ 1/w
P ~3Cf T/ 8
k / w1
tP ~ 1/P
td ~ 1/(vwk)
w2~m2 +2Cf T2 + k2
vw ~ 0.1
ep = tint / tP ~ P / w
<< 1
ed = tint / td ~ vwk / w
<< 1
Energy scales:
em  m/T
<< 1
Quantum Transport Equations
G˜

=

G˜ 0

+

G˜ 0

˜

G˜ 0
+
+…
Expand
in ed,p,m
Chiral
From
S-D Equations:
Producing
nL = 0
Relaxation
CPV
•• S
SCPV
Riotto, Carena et
al, Lee et al
Strong
sphalerons
•• M
, H ,, YY , SS
M, H
Lee et al
Currents
Numerical work:
CP violating
• SS sources
Links CP violation in Higgs
and baryon sectors
EDM constraints & SUSY CPV
Lee et al
Near degeneracies
resonances
BBN
WMAP
(x)
new

de
A

de
199Hg
A
199Hg
BAU
BAU


m
new
m
new
Different choices for SUSY parameters






new
e



EDM constraints & SUSY CPV
Future: EDMs & LHC
Dark Matter Constraints
A
de
BBN
WMAP
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
dn
Cirigliano,
 m Profumo, MR-M

m
in preparation
Disfavored
Large Hadron Collider
Large Hadron Collider

Lee et al
II. Theory: Non-equilibrium QFT
& Quantum Transport
Non-equilibrium Quantum Field Theory
Closed Time Path (CTP) Formulation
Oˆ (x)   rnn' n SI TOˆ (x) SI n'
n

SI  T exp i  d 4 x LI


Conventional, T=0 equilibrium field theory:

rnn'  n0 n'0
Oˆ (x)  0 SI TOˆ (x) SI 0

Non-equilibrium Quantum Field Theory
Two assumptions:
0
• Non-degenerate spectrum
• Adiabatic switch-on of LI
0
IN
LI
Oˆ (x)  

0 SI n n TOˆ (x) SI 0
n

ˆ (x) S 0 
 0 SI 0 0 TO
I
ˆ (x) S 0
0 TO
I
0 SI 0
OUT
Non-equilibrium T>0 Evolution
T > 0: Degeneracies
g
q
q
Time Scales
M(T)
P(T)
tP ~ 1/P


Plasma time:
vW > 0: Non-adiabaticity

t˜L
vW
Decoherence time:
td ~ 1/vW k)
Non-equilibrium T>0 Evolution
Oˆ (x)   rnn' n SI [ ]TOˆ (x) SI [ ]n'
+
-
n
Path ordering
operator
  rnn' n POˆ (x) SI [  ] SI [ ] n'

n



4
4
ˆ

r
n
P
O
(x)
exp
i
d
x
L
(

)

i
d
x LI ( ) n'



P  (x1)   (x n )nn' (y1)  (y m ) 
I

n
T 
 (y1 )  (y m )T  (x1)   (x n )



i  d x  dt LI (  )   dt LI ( )


 

3
i
CTP
d 4 x LI ( )




Non-equilibrium T>0 Evolution
Generalized Green’s Functions
G˜ (x, y)  P a (x) *b (y) t ab
G t (x, y) G (x, y)
  

t
G (x, y) G (x, y)
G (x, y)   (x)  * (y)

G (x, y)  * (y)   (x)
G t (x, y)  q (x 0  y 0 )G (x, y)  q (y 0  x 0 )G (x, y)
G t (x, y)  q (x 0  y 0 )G (x, y)  q (y 0  x 0 )G (x, y)

Non-equilibrium T>0 Evolution
Schwinger-Dyson Equations
G˜
G˜ 0
=
G˜ 0
G˜ 0
+
+ …
+
˜





G˜ (x, y)  G˜ 0 (x, y) 

0
˜
˜
G(x, y)  G (x, y) 
˜ (w,z) G˜ (z, y)
 d w  d z G˜ (x,w) 
˜ (w,z) G˜ (z, y)
 d w  d z G˜ (x,w) 
4
4
4
4

A few formal manipulations
0
0
Quantum Transport
quantum memory
m
X j m (X) 
causality
d z
3
X0

Source
dz0  (X,z) G (z, X)  G (X,z)  (z, X)
 G (X,z)  (z, X)   (X,z) G (z, X)
Dirac fermions
X j m (X)    d z  dz0  (X,z) S  (z, X)  S  (X,z)  (z, X)
m
3
X0

Dirac & Majorana fermions
m



X j m 5 (X) 
 d z
3
 S (X,z)  (z, X)   (X,z) S (z, X)
X0

dz0  (X,z) S  (z, X)  S  (X,z)  (z, X)
 X)   (X,z) S (z, X)  2i m (x)  5  (x)
 S (X,z)  (z,
G>,< & >,< : CPV, CPCrelaxation…
Scale Hierarchy
Time scales:
tint ~ 1/w
P ~3Cf T/ 8
k / w1
tP ~ 1/P
td ~ 1/(vwk)
w2~m2 +2Cf T2 + k2
vw ~ 0.1
ep = tint / tP ~ P / w
<< 1
ed = tint / td ~ vwk / w
<< 1
Energy scales:
em  m/T
<< 1
Systematic Expansion
Distribution functions
d k
 (x) 
3

(2 ) 3 (2w k )1 aˆ k eik x  bˆk e ik x

G (x, y)   (x)   (y) 

 d k d q (2 ) (4w w )
3
3
1
6
k
q

aˆ k aˆ q eikx iqy  bˆkbˆq e ikxiqy
 
(2 ) 3 (2w k )  k  q 1 f p (w k )

f
 f 0  f
O(ed)


 
(2 ) 3 (2w k )  k  q f p (w k )
f p (w )  n B (w  m)  O(ed )
f p (w )  n B (w  m)  O(ed )
Systematic Expansion
Small eexpansion
f  f 0  f
Approximations
• neglect O(e3) terms
Source
terms

S(x)CPV ~ ed ep
S(x)CP ~ em ep
f contributions: higher order in ed
Supersymmetric Sources (mSUGRA)
q , W˜ , B˜ , H˜ u,d
q˜
LI yt t˜L t˜R* At u  m* d  h.c.

CPV phases: A , m

Supersymmetric Sources (mSUGRA)
q , W˜ , B˜ , H˜ u,d

q˜

LI  g2 ̃H   d (x) PL   u (x)e



iq m

PR W˜ 
1
iq
̃H   d (x) PL   u (x)e m PR
2
g 
2
CPV phase: m
W˜ 0
 g1B˜  h.c.
Supersymmetric Sources (mSUGRA)
Approximations
• neglect O(e3) terms
• supergauge equilibrium:
q , W˜ , B˜ , H˜ u,d

mV˜  0 , m f  m f˜
q˜
• Higgs vev expansion
(end of talk)

Xm j m 5 (X)   d 3 z  dz0  (X,z) S  (z, X)  S  (X,z)  (z, X)
Neutral gauginos =

Majorana fermions
X0
 S (X,z)  (z,X)   (X,z) S (z,X) 2i m ( x)  5  (x)



Supersymmetric Sources (mSUGRA)
q , W˜ , B˜ , H˜ u,d
SCPV ~  w P  sin m

S


CP
q˜
O (ed ep)

~  m2  m1  () m2  m1 O (em ep)
()
Supersymmetric Sources (mSUGRA)
q , W˜ , B˜ , H˜ u,d
q˜
SCPV ~  w P  ( m sin m   A sin A ) O (ed ep)

S


CP

~  mL  mR   () mL  mR 
()
O (em ep)
Supersymmetric Sources (mSUGRA)
Approximations
Previous work:
• neglect O(e3) terms
(-,+)

>>

Y
• supergauge
equilibrium:
Effect
m decouples:
0, m m
V˜
f
f˜
mL  mR  m H ~ O 1 Y 
• Higgs vev expansion
S
CPV
0

Links rB to Higgsinos
SCP ~ Y mL  mR  mH  


• Yukawa decoupling
O (em ep)

Supersymmetric Sources (mSUGRA)
W ,Approximations
B
• neglect O(e3) terms
q˜ , H
• supergauge equilibrium:

mV˜  0 , m f  m f˜

q , H˜
W˜ , B˜
(Super) gauge interactions


• Higgs vev expansion
• Yukawa decoupling
• Fast supergauge int
Supersymmetric Sources (mSUGRA)
()
()
SCP
~

m

m


m  mH˜  




H˜
H˜  W˜
H˜ 
H˜   W˜ 
MW˜  M2 ,
M H˜  m




e f  w f  if
O (emep) tan (x)   u  d
w f  w (M f , k, T, m f )
f   (M f , k, T, m f )
ex T
hF (x) 
(1 e x T ) 2
Analogous expression for SCPV: 
O (edep) ~ vW

Supersymmetric Sources (mSUGRA)
Resonance Effects
M2 ~ m  eW˜ ~ e H˜

Supersymmetric Transport Equations
Coupled Transport Equations:
m
m J i  S
CP
i
S
CPV
i
S
SS
i
Strong Sphalerons
nL (x)
Baryon number production:
t rB (x)  Dq 2rB (x)  WS
FWS(x)nL (x)  RrB (x)
Profile function
Relaxation coeff
Baryon Number
CPV
2 

S CPV

S


D
˜
˜
t
WS
w
H
rB   n F
r1 W S  r2
 2
SS D  w  R(D  Dq )


YB 

rB
s
 F1 sin  m  F2 sin(  m   A )
Fi = Fi (T ,vw , Mi ,…)
Baryon Number
W S  6  w5 T
 s4 T
SS  16 
CPV
2 

S CPV

S


D
˜
˜
t
WS
w
H
rB   n F
r1 W S  r2
 2
SS D  w  R(D  Dq )



Linear comb of the i
ri  ri (kQ ,kT ,k B ,k H )
O(ws/Y) corrections omitted

Baryon Number & Y
CPV
2 

S CPV

S


D
˜
˜
t
WS
w
H
rB   n F
r1 W S  r2
 2
SS D  w  R(D our
Dq)Y


previous Y
m
tR
H
Cirigliano, Lee, R-M, Tulin
tL
tL
g
Joyce, Prokopec, Turok
Baryon Number & Y
CPV
2 

S CPV

S


D
˜
˜
t
WS
w
H
rB   n F
r1 W S  r2
 2
SS D  w  R(D  Dq )


Previous work
Res
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Non-Res
tR
H
tL
tL
g
III. Phenomenology
SUSY Inputs
1. Strong 1st order PT: light stop
2. rparameter: heavy LH stop
3. mh < 120 GeV:
100 GeV  mt˜  mt
At  m cot   0.6 mt˜L
4. Bubble wall parameters:

Lw  25/T ,  w  0.05
5. Illustrative choice:

M 2  At  200 GeV , mt˜L 1 TeV , tan  0  0.015
Sˆ H˜
Sources & Relaxation
M W˜
R
Huet &
Nelson


m (GeV)
m (GeV)
M W˜

2Ý

Sˆ H˜  SCPV

sin m
H˜


R   
H.N.
Baryon Number
F1 YBW MAP
F2 YBW MAP
Mt˜R

M W˜
Precision
electroweak
m (GeV)
YB 
rB
s

 F1 sin  m  F2 sin(  m   A )

mt˜L (GeV)

F2 F1 ~ 103

CP Violating Phases
WMAP
sin  m
BBN
m (GeV)

EDM Constraints
BBN
WMAP
de
de
A
199Hg
A
199Hg
BAU
BAU


m

M H˜  MW˜
m
˜  50 GeV
D
M

Summary & Outlook
• EWB remains a viable option for explaining the cosmic
baryon asymmetry that can be tested and constrained
using EDMs, precision electroweak, and collider input
• New developments using non-equilibrium QFT are putting
YB computations on a more systematic footing that will
allow for detailed confrontations with lab experiments
• Considerable (hard) work remains to be completed
Complete set of transport coefficients, refined studies of bubble
dynamics, applications to various scenarios for new CP-violation,
phenomenology (EDM, B physics, precision electroweak, collider)
• Exciting field involving an interplay between cosmology and
particle/nuclear physics in both theory and experiment
Non-equilibrium Quantum Transport


1.
2
x
˜ ( x,z) G˜ (z, y)
 m 2 G˜ (x, y)  i (x  y)  i  d 4 z 
2
y
˜ (z, y)
 m 2 G˜ (x, y)  i (x  y)  i  d 4 z G˜ (x,z) 
2.
lim xy x2  y2 G˜ (x, y)12  lim xy mX xm  ym G˜ (x, y)12
3.
lim xy xm  ym G˜ (x, y)12  i jm (X)


m

j m (X) 
X

Source

 d 3z 
X0

dz0  (X,z) G (z, X)  G (X,z)  (z, X)
 G (X,z)  (z, X)   (X,z) G (z, X)
Supersymmetric Sources (mSUGRA)
Approximations
• neglect O(e3) terms
• supergauge equilibrium:
q , W˜ , B˜ , H˜ u,d

mV˜  0 , m f  m f˜
q˜
• Higgs vev expansion
 (x)

Use un-broken phase basis
 to O(2)
for G0(x,y) & expand

x
WS  0
WS  0
Supersymmetric Sources (mSUGRA)
CP Violating Source
 w
O (edep)
e f  w f  if

Supersymmetric Sources (mSUGRA)
Approximations
• neglect O(e3) terms
• supergauge equilibrium:
q , W˜ , B˜ , H˜ u,d
q˜
mV˜  0 , m f  m f˜
Majorana masses M1,2


W˜ 

W˜  
W˜ 3 
B˜ 

  ˜  , W˜ 0   ˜ 3  , B˜    
B˜ 
W 
W 
Supersymmetric Sources (mSUGRA)
q , W˜ , B˜ , H˜ u,d
q˜
Dirac mass |m|

 H˜ d0,
H
  iq m 0,
H
 e H˜ u
0.
d
0.
u
 ˜
H
H˜ u 
H˜ u0 
    , H˜ 0   0 
H˜ d 
H˜ d 
n H˜   n H˜   n H˜  ,
u


d
n H˜ 0  n H˜ 0  n H˜ 0
u
d