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QED at Finite Temperature and Constant Magnetic Field: 1. The Standard Model of Electroweak Interaction at Finite Temperature and Strong Magnetic Field. Neda Sadooghi Department of Physics Sharif University of Technology Tehran-Iran Prepared for CEP seminar, Tehran, May 2008. Introduction. - PowerPoint PPT Presentation
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QED at Finite Temperature and Constant Magnetic Field:
1. The Standard Model of Electroweak Interaction at Finite Temperature and Strong Magnetic Field
Neda SadooghiNeda SadooghiDepartment of Physics
Sharif University of TechnologyTehran-Iran
Prepared for CEP seminar, Tehran, May 2008
Introduction
The connection between Particle Physics Cosmology
Particle physics tests its predictions about matter genesis in the framework of cosmology
Cosmology can use the predictions of particle physics in order to cure unsolved problems in the theories concerned with the evolution of the universe
The Problem of Baryogenesis
Timeline of Big Bang
1. The very early universe The Planck epoch The grand unification epoch The electroweak epoch The inflationary epoch The inflationary epoch
Reheating Bayogenesis
2. The early universe
3. …
Elementary particle physics
Fermions Quarks and Leptons (elementary particles)
Quarks: Q = u,d,s,b,c,t + antiquarks Leptons: L= electron, muon, tau + neutrinos and antiparticles
Hadrons (composites) Baryons: QQQ
Proton (uud), Neutron (udd), Lambda hyperon (uds) Mesons: QQ-bar
, Kaon, ccbar
Bosons Gauge bosons
The problem of BaryogenesisFor a review see: hep-ph/9707419, hep-ph/0609145
1. Why the density of baryons is much less than the density of photons?
Observation: from CMB data
Theory:
2. Why in the observable part of the universe, the density of baryons is many orders greater than the density of antibaryons?
1910
n
nnBB
1810
n
nnBB
410B
B
n
n
The Problem of Baryogenesis
In a baryo-symmetric universe the number density of baryons would be 9 orders of magnitude smaller than what is observed in reality.
Consequence:Consequence: Then, in the world would not be enough building material
for formation of celestial bodies and life would not be possible.
Sakharov Conditions (1967)
For baryogenesis, 3 conditions are necessary:
C and CP violation
Non-conservation of baryonic charge
Deviation from thermal equilibrium in the early universe
Different Mechanisms for Baryogenesis
Baryogenesis in massive particle decays Electroweak baryogenesis Affleck-Dine scenario of baryogenesis in SUSY Spontaneous baryogenesis Baryogenesis through leptogenesis Baryogenesis in black hole evaporation Baryogenesis by topological defects
Domain walls, cosmic strings, magnetic monopoles, textures
Electroweak baryogenesis in a constant magnetic field
Electroweak Baryogenesis
Checking the Sakharov’s conditions: C and CP violation
In the EWSM there are processes that violated C and CP
Baryon non-conservation: The baryon number is violated via quantum chiral anomalies. C
and CP violation are necessary to induce the overproduction of baryons compared to antibaryons
EWSM at finite temperature: 2nd order phase transition at Tc = 225 GeV one-loop approx 1st order phase transition at Tc = 140.42 GeV ring diagrams
Baryon number non-conservation in EWSM Periodic potential in EW gauge field
Each minima corresponds to a topological winding number Transition from one vacuum to another can proceed
either by tunneling. This is very suppressed at T=0 or over the barrier in a thermal system at high T
The top of the barrier corresponds to an unstable, static solution of the field equations called sphaleron, with E = 8-14 GeV
It can be shown that
Electroweak phase transition at finite T
Theoretically it is possible to determine the effective potential at one-loop order, leading to a Tc = 225 GeV
This is a 2nd order phase
transition
Potentials are calculated
at T = 0, 175, 225, 275 GeV
(from bottom to top)
Electroweak phase transition at finite T
Considering the contribution of ring diagrams to the effective potential, a 1st order phase transition arises
For Higgs mass = 120 GeV
and top mass = 175 GeV
the critical temperature is
decreased to 140.42 GeV
Result
Although the minimal EWSM has all the necessary
ingredients for successful baryogenesis, neither the amount of CP violation whithin the minimal SM,
nor the strength of the EW phase transition
is not enough to generate sizable baryon number
Other methods …
Different Mechanisms for Baryogenesis
Baryogenesis in massive particle decays Electroweak baryogenesis Affleck-Dine scenario of baryogenesis in SUSY Spontaneous baryogenesis Baryogenesis through leptogenesis Baryogenesis in black hole evaporation Baryogenesis by topological defects
Domain walls, cosmic strings, magnetic monopoles, textures
Electroweak baryogenesis in a constant magnetic field
Primordial magnetic fields
Observation:
Large scale magnetic fields observed in a number of galaxies
Note: A homogeneous magnetic field would spoil the universe
isotropy, giving rise to a dipole anisotropy in the background
radiation
COBE: Large scale magnetic field of primordial origin
GB 610
Magnetogenesis
Necessary:
A small seed field which is exponentially amplified by the turbulent fluid motion
Problems:
Find a mechanism to generate a seed field Cosmological (EW or QCD) phase transitions
Find a mechanism for amplifying the amplitude and the coherence scale of the magnetic seed field Magnetohydrodynamics
A possible scenario of magnetogenesis (EWPT)K. Enqvist; astro-ph/9707300, A. Ayala et al. hep-ph/0404033In general magnetic field in the primordial neutral plasma can be produced by:
Local (axial) charge separation local current magnetic field
During EW 1st order PT Out of equilibrium conditionsOut of equilibrium conditions bubble nucleation
Net baryon number gradient charge separation
Instabilities in the fluid flow magnetic seed field production
Turbulent flow near the bubbles walls amplification + freezing of the seed field
The magnetic field produced is of order
Hydrodynamic turbulence magnetic field enhancement by several orders
Inflation large coherence scale
Magnetic field in the aftermath of EWPTT. Vachaspati, 0802.1553 (hep-ph)
Decay of EW sphaleron changes the baryon number and produces helical magnetic field
Use the relationship between the sphaleron, magnetic monopoles and EW strings (Nambu 1977, Vachaspati 1992, 2000)
A possible decay mechanism for two linked loops of EW Z-strings
Decay Mechanism of Sphaleron Decay
Sphaleron may be thought as two linked loops of EW Z-strings
The Z-strings can break by the formation of magnetic monopoles and an electromagnetic magnetic field connects the monopole-anti-monopole pairs
The Z string can shrink and disappear leaving behind two linked loops of electromagnetic magnetic field
Magnetic field production during the preheating at the electroweak scale: A. Gonzalez-Arroyo et al., 0712.4263 [hep-ph] and a series of papers since 2005
To recap:
Decay of EW sphaleron changes the baryon number and produces
helical magnetic field
The helicity of the magnetic field is related to the number of
baryons produced by the sphaleron decay (Cornwall 1997,
Vachaspati 2001)
It is therefore interesting to study EW phase transition and
baryogenesis in the presence of constant magnetic field
Electroweak baryogenesis in strong hypermagnetic field
Series of papers by:Series of papers by: Skalozub + Bordag (1998-2006)
Electroweak phase transition in a strong magnetic field Effective action in one-loop + ring contributions Higgs mass
Result:Result: The phase transition is of 1st order for magnetic field
The baryogenesis condition is not satisfied
Strong magnetic fields