Electric dipole moments

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Electric dipole moments
Stephan Huber, University of Sussex
EPP seminar, June 2008
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Outline

• 1) Computation of EDMs
  Pospelov Ritz, hep-ph/0504231
• classical
• non-relativistic quantum mechanics
• quantum field theory and CP violation
• effective field theories
• 2) Models
• Standard Model
• Two Higgs doublet model
• supersymmetry
• 3) Electroweak baryogenesis and EDMs

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1) How are EDMs computed ?
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1) How are EDMs computed ?
In short EDMs are the zero momentum limit of a
part of the fermion-fermion-photon 3-point
function, of the sort
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Classical, non-relativistic
A particle placed into magnetic and electric
fields B and E is described by
S spin of the particle µ magnetic dipole
moment d electric dipole moment under space
inversion parity S ? - S P (t ? t, x ?
-x) B ? - B T (t ?
- t, x ? x) E ? - E
? EDM violates parity! (and T)
CP violation
CPT
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QM, non-relativistic
Non-relativistically, a spin ½ fermion is
described by a 2-component spinor ?(?1, ?2),
and the Schrödinger equation for the previous
Hamiltonian is (Pauli-type equation)
Where are the
Pauli matrices (h1) The first term of this
equation can be derived from relativistic the
Dirac equation
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Dirac equation
Dirac equation for a spin ½ fermion with charge e
and mass m coupled to an electromagnetic field
(the Dirac spinor has 4 components!)
which can be obtained from the Lagrangian
In the non-relativistic limit, v c, the Dirac
equation reduces to the Pauli equation and fixes
the gyromagnetic ratio of a Dirac fermion to be
g2
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Generalized Dirac equation
To obtain also the EDM-type interaction one has
to generalize the Dirac theory
Because of the ?5 the last term violates P, CP
and T
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Remarks 1) These extra terms are (mass)
dimension-5 operators, i.e. d has dimension of a
length (mass-1) and can therefore not be present
in an renormalizable QFT (effective,
non-renormalizable interaction) it will however
be generated by loops of CP (T) is violated 2)
The EDM-type interaction could also be generated
by a CP conserving, but CPT and Lorentz
violating interaction
Also these operators are constrained by EDM
experiments!
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EDMs in quantum field theory

• Main idea
• Perform the relevant process fermion-fermion-phot
  on interaction
• in the full renormalizable theory (SM, 2HDM,
  MSSM,...)
• in the effective Lagrangian described above
• match the coefficients of the effective
  Lagrangian to reproduce the full
• result in the relevant limit here in the
  limit of very small momentum transfer

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CP violation at various energy scales
1) Above 1 GeV partonic CP violation
straight forward perturbative QFT loop
computations
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2) At the nuclear scale
problems because of QCD strong coupling effects !
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(No Transcript)
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3) At the scale of nuclei, atoms, molecules
a) Paramagnetic atoms (one unpaired electron)
(atomic matrix elements know to 10-20)
b) Diamagnetic atoms (total electron angular
momentum vanishes)
(problems with nuclear matrix elements,
uncertainty factor a few?)
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Neutron EDM
Again difficult because of QCD effects One
approach QCD sum rules Pospelov Ritz 2001
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2) Models
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Standard model
CP violation related to the single phase in the
CKM matrix ? SM CP violation is related to flavor
violation (W exchange) But an EDM is flavor
conserving CP violation ? EDMs in the SM are at
least flavor violation squared and
therefore very suppressed (3 loops!)
EDM measurements have no SM background!
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Supersymmetry
Many new CP-violating phases from SUSY
breaking Leading EDMs at 1-loop
For superpartner masses of a few hundred GeV and
large phases, the neutron EDM is about a 100
times to large! (SUSY CP problem)
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3) Baryogenesis with two Higgs doublets
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The 2HDM

? 4 extra physical Higgs degrees of freedom 2
neutral, 2 charged ? CP violation, phase F ?
there is a phase induced between the 2 Higgs
vevs simplified parameter choice 1 light Higgs
mh ? SM-like, so LEP bound of 114 GeV applies 3
degenerate heavy Higgses mH ? keeps EW
corrections small
early work Turok,
Zadrozny 91 Davies, Froggatt, Jenkins,
Moorhouse 94 Cline, Kainulainen, Vischer 95
Cline, Lemieux 96
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The mechanism
broken phase
symmetric phase
H(z)
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The mechanism
H(z)
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The mechanism
H(z)
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strong PT
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Electric dipole moments
Barr, Zee 90
Experimental bounds delt1.6 10-27 e cm
dnlt3.0 10-26 e cm
de in units of 10-27 e cm, dn in units of 10-26
e cm, f0.2
Fromme, S.H., Seniuch 06
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The baryon asymmetry
The relative phase between the Higgs vevs, ?,
changes along the bubble wall ? phase of the top
mass varies ?t?/(1tan2ß) top
transport generates a baryon asymmetry, but
tanßlt10 (?) ? only one phase, so EDMs
can be predicted here dn0.1 10-26 7
10-26 e cm exp. bound dnlt 3.0 10-26 e cm
?B in units of 10-11, f0.2
Moretti et al. 07 LHC could see a triple Higgs
coupling Hhh?
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The phase transition
Evaluate 1-loop thermal potential loops of
heavy Higgses generate a cubic term ? strong PT
for mHgt300 GeV mh up to 200 GeV ? PT
independent of F ? thin walls only for very
strong PT (agrees with Cline, Lemieux 96)
Fromme, S.H., Senuich 06
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The bubble wall
Solve the field equations with the thermal
potential ? wall profile ?i(z)
kink-shaped with wall thickness Lw
? becomes dynamical
Lw
(numerical algorithm for multi-field profiles, T.
Konstandin, S.H. 06)
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Transitional CP violation
in the general singlet model the broken minimum
can be CP conserving, but the symmetric minimum
violates CP ? CP violating wall profile CP
conservation at T0
Lw3
Lw20, 10, 5, 3
S.H., John, Laine, Schmidt 99
S.H., Schmidt 00
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Baryogenesis in the MSSM
Konstandin, Prokopec, Schmidt, Seco 05
strong PT from stop loops ? right-handed stop
mass below mtop left-handed stop mass
above 1 TeV to obtain mh115 GeV Carena et
al.96 CP violation from varying chargino mixing
vw0.05, M2200 GeV, maximal phase
obs ?0.9 x 10-10
resonant enhancement of ? for M2 µ chargino
mass lt 300 GeV large phases gt 0.2 required ? 1st
and 2nd generation squarks heavy to keep
1-loop EDMs small
similar but somewhat more optimistic results in
Carena, Quiros, Seco, Wagner 02 Cirigliano,
Profumo, Ramsey-Musolf 06 ? scenario is tightly
constrained!
? Split SUSY light stop