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 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  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 Baryogenesis For a review see: hep-ph/ , hep-ph/ 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?

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: 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: 2 nd order phase transition at Tc = 225 GeV  one-loop approx 1 st order phase transition at Tc = 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 2 nd 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 1 st order phase transition arises For Higgs mass = 120 GeV and top mass = 175 GeV  the critical temperature is decreased to 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

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/ , A. Ayala et al. hep-ph/ In general magnetic field in the primordial neutral plasma can be produced by: Local (axial) charge separation  local current  magnetic field Out of equilibrium conditions During EW 1 st order PT  Out 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 EWPT T. Vachaspati, (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., [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: Skalozub + Bordag ( )  Electroweak phase transition in a strong magnetic field  Effective action in one-loop + ring contributions  Higgs massResult: The phase transition is of 1 st order for magnetic field The baryogenesis condition is not satisfied

Strong magnetic fields