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