Non-equilibrium QFT Applied to Electroweak Baryogenesis

Non-Equilibrium Quantum Field Theory
Applied to Electroweak Baryogenesis
Christopher Lee
Institute for Nuclear Theory,
University of Washington
With
Vincenzo Cirigliano
Michael Ramsey-Musolf
and Sean Tulin
California Institute of Technology

Outline
Closed Time-Path Formalism
Quantum Transport Equations
Solution for Baryon Asymmetry

Goal
Derive transport equations for particle
densities:
Thermal expectation values of currents:
where
Bosons
Fermions

Nonequilibrium QFT
Consider a matrix element:
In equilibrium T=0
field theory:
Non-adiabaticity
Degeneracy

Nonequilibrium QFT
Consider a matrix element:
“path-ordering”
+
–
x 0

Green’s s Functions
Four possible Green’s functions on contour:
x 0

Schwinger-Dyson Equations
Apply to both sides:

Quantum Transport Equations
Subtract resulting equations, take “

Examples of Self-Energies
Fermion and scalar interactions with Higgs vevs, Higgs
particles, and Higgsinos
CP
CP
CP
(In progress!)

Example: The Squark Source
Riotto
CP-violating contribution to source:
“Decoherence”
ε d
Resonant enhancement
when
“Plasma”
ε p

Example: The Squark Source
CP-conserving contribution to source:
Cirigliano,
CL,
Ramsey-
Musolf
Keep chemical potential to first order in
ε µ
ε p
Resonant enhancement
when

Solving the Diffusion Equations
Coupled transport equations for particle densities:
e.g.
In progress:
cf. Huet,
Nelson
(semiclassical)
• CTP calculation of Γ Y
• Including all relevant
linear combs. of densities
• Numerical solution of
coupled equations

Solution for Baryon Density
Insert solution for
into equation for
Baryon density left over inside bubble of broken
EW phase:
(constant)
Resonant enhancements of relaxation terms mitigate
but do not cancel out those of CP-violating sources

The Future of Baryogenesis
More complete, consistent calculation of BAU
with non-equilibrium QFT
Experimental searches for EDMs, new particles
? ?
Where will
the bands
move?
?
CMB BBN
?
d e
BAU
d e
d n
BAU
d Hg
d Hg
d n