EWPT Nucleation With MSSM and Electromagnetic Field Creation arXiv:1001.2783v1 [astro-ph.CO] 15 Jan 2010 Ernest M. Henley Department of Physics, University of Washington, Seattle, WA 98195 Mikkel B. Johnson Los Alamos National Laboratory, Los Alamos, NM 87545 Leonard S. Kisslinger Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213 Using EW-MSSM field theory, so the EWPT is first order, we derive the equations of motion for the gauge fields. With an isospin ansatz we derive e.o.m. for the electrically charged W fields uncoupled from all other fields. These and the lepton currents serve as the current for the Maxwell- like e.o.m. for the electromagnetic field. The electromagnetic field arising during EWPT bubble nucleation without leptons is found. We then calculate the electron current contribution, which is seen to be quite large. This provides the basis for determinining the magnetic field created by EWPT bubble collisions, which could seed galactic and extra-galactic magnetic fields. PACS Indices:12.38.Lg,12.38.Mh,98.80.Cq,98.80Hw Keywords: Cosmology; Electroweak Phase Tran- sition; Bubble Nucleation I. INTRODUCTION There have been many attempts to find the origin of the large-scale galactic and extra-galactic mag- netic fields that have been observed (see Ref[1] for a review). One possible seeding of these magnetic fields is via early universe phase transitions: the elec- troweak phase transition (EWPT) and the Quantum Chrodynamics chiral phase transition (QCDPT). Research on the QCDPT has explored not only seeding of the galactic and extra-galactic structure, but also possible effects in Cosmic Microwave Back- ground Radiation (CMBR) correlations[2–11]; and large scale magnetic structure which could produce observable CMBR polarization correlations[12] aris- ing from bubble collisions during the QCDPT[13]. Since the electromagnetic (em) field along with the W ± and Z fields are the gauge fields of the Stan- dard EW model, the EWPT is particularly inter- esting for exploring possible cosmological magnetic seeds . It has been shown that in the Standard EW model there is no first order EWPT[14], no expla- nation of baryogenesis, or any interesting cosmologi- cal magnetic structures created during the crossover transition. However, there has been a great deal of activity in the supersymmetric extension of the standard model[15], and with a MSSM having a Stop with a mass similar to the Higgs there can be a first order phase transition and consistency with baryogenesis[16–18]. Moreover, with a first order phase transitions bub- bles of the new phase nucleate and collide, which is essential for our present research on magnetic field creation. A number of authers have used EW-MSSM models with the Standard EW Model plus a right- handed Stop to explore the EWPT. See, e.g., Refs. [16, 19]. There have been other models for CP vi- olation and baryogenesis, such as two-Higgs models (see Refs.[16–18] for references and discussion) and leptoquarks (see, e.g., Ref.[20] for a discussion and references.) The goal of our present work on the creation of electromagnetic fields via nucleation is both to find the nature of the fields and to derive the bound- ary conditions for our study of magnetic field gen- eration with EWPT bubble collision, which is in progress[21, 22]. For this reason we introduce the complete Lagrangian that is needed to study bubble collisions. In our present calculations we could use a two-Higgs model, as the precise nature of the ex- tension of the Standard EW Model is not needed for creation of electromagnetic fields during nucleation, as we shall show; while in our studies of magnetic field generation with EWPT bubble collision we use the MSSM and treat all the equations of motion, derived below, with a right-handed Stop. In the most detailed previous research on the study of magnetic fields arising from EWPT transitions[8–10] a model was used in which the equations of motion (e.o.m.) for the em field in- volved the chargeless Higgs, and the EWPT bub- bles were empty of the em field until the bubbles collided and overlapped. In the present work we de- rive the e.o.m. directly from the EW Lagrangian, using a MSSM including the right-handed Stop field for consistency with a first order phase transition.