Gravitational wave production and baryogenesis in a simple left-right model

The left-right model with the simplest Higgs structure has a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:msub><a:mrow><a:mo stretchy="false">)</a:mo></a:mrow><a:mrow><a:mi>L</a:mi></a:mrow></a:msub></a:mrow></a:math> doublet <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>H</e:mi><e:mi>L</e:mi></e:msub></e:math>, a <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>S</g:mi><g:mi>U</g:mi><g:mo stretchy="false">(</g:mo><g:mn>2</g:mn><g:msub><g:mo stretchy="false">)</g:mo><g:mi>R</g:mi></g:msub></g:math> doublet <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>H</k:mi><k:mi>R</k:mi></k:msub></k:math>, and a singlet <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>σ</m:mi></m:math> that couples to the doublets as <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>σ</o:mi><o:mo stretchy="false">(</o:mo><o:mo stretchy="false">|</o:mo><o:msub><o:mi>H</o:mi><o:mi>L</o:mi></o:msub><o:msup><o:mo stretchy="false">|</o:mo><o:mn>2</o:mn></o:msup><o:mo>−</o:mo><o:mo stretchy="false">|</o:mo><o:msub><o:mi>H</o:mi><o:mi>R</o:mi></o:msub><o:msup><o:mo stretchy="false">|</o:mo><o:mn>2</o:mn></o:msup><o:mo stretchy="false">)</o:mo></o:math>. The left-right symmetry has <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>H</w:mi><w:mi>L</w:mi></w:msub><w:mo stretchy="false">↔</w:mo><w:msub><w:mi>H</w:mi><w:mi>R</w:mi></w:msub></w:math> and <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>σ</z:mi><z:mo stretchy="false">↔</z:mo><z:mo>−</z:mo><z:mi>σ</z:mi></z:math>. We study gravitational wave production and baryogenesis in the electroweak phase transitions in the model. For two benchmark points, <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>σ</cb:mi></cb:math> first gets a vev, followed by <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi>H</eb:mi><eb:mi>R</eb:mi></eb:msub></eb:math> and then <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>H</gb:mi><gb:mi>L</gb:mi></gb:msub></gb:math>. An interesting feature is that the vev of <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi>H</ib:mi><ib:mi>L</ib:mi></ib:msub></ib:math> is initially much higher than its zero temperature value, leading to a more strongly first-order transition and higher frequency gravitational waves. An unusual benchmark point has the <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>σ</kb:mi></kb:math> vev at zero when the electroweak symmetry breaks. This results in both <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msub><mb:mi>H</mb:mi><mb:mi>L</mb:mi></mb:msub></mb:math> and <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msub><ob:mi>H</ob:mi><ob:mi>R</ob:mi></ob:msub></ob:math> vevs being equal and in the multi-TeV range. At a lower temperature, the <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mi>σ</qb:mi></qb:math> vev turns on, breaking the left-right symmetry and <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msub><sb:mi>H</sb:mi><sb:mi>L</sb:mi></sb:msub></sb:math> drops to its standard model value. Since the electroweak symmetry is broken at the multi-TeV scale, the frequency of gravitational waves will be much higher than usual. Baryogenesis is also discussed.