The Electric Dipole Moment of the Neutron revisited

1
The Electric Dipole Moment ofthe Neutron
revisited
Schedar Marchetti
2
Motivations 1

• The electric dipole moment (edm) of particles is
  an important window to CP beyond SM in ?F0
  sector
• In the SM the edms arise from dCKM
  this contribution is much
• smaller than current exp. limits ( 6 order
  of magnitude)
• dN lt 6.3 10-26 e cm
• In Supersymmetric models there are new sources of
  CP from the
• complex phase of the soft SUSY breaking
  parameters and µ term
• The presence of new CP is needed to have an
  efficient baryogenesis
• Unconstrained MSSM 40 phases
• GUT
  4 allowed phases but only 2
• mSUGRA
  are physical fA and fµ
• Flavour Universality
  
• Are this phases costrained using the current
  exp. costraints from neutron edms ?

3
Motivations 2

• Neutron edm SUSY problem
• naive estimation dN 2(100 )
  sin fA,µ 10-23 e cm
• Two regions
• M gt O(TeV) fA,µ O(1)
  Hierarchy Problem
• M lt O(TeV) fA,µ O(10 2)
  Fine tuning? dCKM O(1)?
• To go beyond complete one loop analysis
  of neutron edms
• scan of the parameter space just
  to see what happens varying
• M in this regions
• Alternative picture some cancellations
  mechanism beyond the
• 
  various contributions?

2
GeV
M
Supersymmetric scale
4
Electric Dipole Moment

• The electric dipole moment of a classical
  distribution of charge is
• defined as
• d ?
  d3x x ?(x)
• The presence of an edm violates CP d
  d
• d ? d , J ? J Under
  Time Reversal
• d ? d , J ? J Under
  Parity
• d ? 0 violate T and P and so CP (CPT
  theorem)
• In QFT the classical interaction Hint d E
  corresponds to
• Heff dE ? sµ? ?5 ? Fµ? C7 O7
  (prove that dE d)

spin
J
J
i
2
5
Electric Dipole Moment

• If we consider strong interacting particle, such
  as atoms and hadrons
• (e.g. mercury and neutron), other operators
  must take into account
• Heff C7(µ) O7(µ) C8(µ) O8(µ) CG(µ)
  OG(µ)
• O7 q sµ? ?5 q Fµ?
  Electric dipole
• O8 gs q sµ? ?5 ta q Gµ?
  Chromoelectric dipole
• OG gs fabc Gµ? Gb?? G?s eµ??s
  Gluonic dipole
• The Weinberg operator OG can be neglected at the
  leading order
• only O7 and O8 enter in the game

EDM
i
2
i
a
2
1
3
a
c
6
6
Electric Dipole Moment

• Outline of the calculation Effective
  Theories

Projection of full theory on dipole operators
Matching
MSUSY
Ci Ci(M)
Renormalization group equations
µ
Evolution from matching to hadronic
scale governed by anomalous dimension matrix
Mixing
Operator Matrix Elements
Few informations
?QCD
e.g. naive dimensional analysis, ChPT, QCD Sum
Rules
d
u
1
dN 4C7(µ) C7(µ)
3
µ 2 GeV
7
Electric Dipole Moment
One Loop diagrams
Chargino exchange
Neutralino exchange
Gluino exchange
CP
CP
2
mu

?LR
u
CP
Mass Insertion Approximation
2
L
mu

2
?LR
u

mu

R
8
CP Violation Sources beyond CKM
Quark-Squark sector
Super-CKM




'
'
'
'
uL Vu uL uR Vu uR
uL Vu uL uR Vu uR
L
R
L
R




'
'
'
'
dL Vd dL dR Vd dR
dL Vd dL dR Vd dR
L
R
R
L
Quark mass diagonal

diag
Vu mu Vu mu
L
R
Gauge int. governed by CKM



uL


L2 (uL uR) mu

2

uR
CP F
CP F
CP
2



New source of flavour and CP violation
diag
2
diag
Vu mQ Vu mu ?u ?
(Vu Au Vu - µ cot ß) mu

L
L
L
L
L
2
mu


2
diag
2
mu (Vu Au Vu µ cot ß)
Vu mU Vu mu ?u ?
diag

L
L
R
R
R
CP F
CP F
CP
9
CP Violation Sources beyond CKM
Neutralino sector
Chargino sector






? ( W- , h )
?0 ( B- , W0 , h0 , h0 )
u


d
u
?- ( W-, h- )
d
1
L - (?0)T MN ?0 h.c.
L - (?-)T MC ? h.c.
2
CP
CP
M1 0 -cßswmz sßswmz
0 M2 cßcwmz -sßcwmz
-cßswmz cßcwmz 0 - µ
-cßswmz cßcwmz - µ 0
M2
v2 sß mw
MN
MC
µ
v2 cß mw
CP
CP
diag
diag
MC UT MC V
MN ZT MN Z
10
Electric Dipole Moment
Explicit expression of the supersymmetric
contributions
Gluino exchange
2
as
Im(?LR )
q
Qq A( , )
mg
2
mg


q
q
Qq A ? B
C8
C7
3
2
2

4p
mg
mq

mq

L
R
u
C ? 0, Qd ? 1
C8
Chargino exchange
2
2
2
m?

m?

u
ae
Im(Gi )
(Qu- Qd) C( ) Qd D ( )
u
?
i
i
C7
2
2

m?
2
4p sw
mq

mq

i1
i
L
L
q
C8
Qq ? 1
Neutralino exchange
2
2
2
4
m?

m?

m?

? Im(? j ) D( ) Im(? LR) A( , )
ae
Qq
i
?
q
q
q
i
i
C7 -
2
2
2
2
4p sw
m?

mq

mq

mq

i1
jL,R
i
j
L
R
11
An Exploratory Analysis - 1

• Switch on a single phase fµ

First Scenario mass parameters above
TeV scale
Parameter range Mi (1000,1500), Au Ad
(1000,1500), mq (1000,1500), µ
(1000,1500), (GeV) fA fA (-p,
p), fµ (-p, p)

u
d

• positive sign
• negative sign
• exp. limit

12
An Exploratory Analysis - 2
Second Scenario mass parameters under
TeV scale
Parameter range Mi (100,150), Au Ad
(100,150), mq (100,150), µ (100,150),
(GeV) fA fA (-p, p), fµ (-p, p)

u
d

• positive sign
• negative sign
• exp. limit

13
An Exploratory Analysis - 3

• Two independent phase

fA
fA
fA
fµ
fµ
fµ
neglecting terms suppressed by a factor
O( )
mq
fµ
2
fA , fµ
MW

• Gluino contribution seems to depend mainly on fµ
  this might
• depend strongly on the assumption fA fA

u
d
14
Preliminary Conclusions

• Two observations
• 1 Hierarchies gluino gt chargino gtgt
  neutralino
• 2 Gluino tend to be opposite in sign to chargino
  possibility of a
• systematic negative interference between the
  two contributions ?
• in the previous literature the
  sensitivity to this cancellations was
• limited to more or less limited areas, and
  requiring at least an O(TeV)
• parameter fine tuning ?

Ibrahim et al. hep-ph/9707409 Pokorski et
al. hep-ph/9906206
15
Improved Analysis (work in progress)

• This is only a quick look to go more in details
• The previous choice of parameters is clearly
  inconsistent
• universal soft breaking at the GUT scale and
  running the parameters
• down to EW scale
• Inclusion of the NLO contributions at least for
  the dominant gluino
• exchange
• resummation of the
  terms through RGE
• Possible contribution from Chromoelectric and
  Weinberg operators
• Hadronic matrix elements beyond naive estimation
• Another edm could take into the game (e.g.
  electron, mercury)
• crossing analysis

µ
as
( )
n
as ln
4p
M