Gravitational wave imprints of the doublet left-right symmetric model

We study the stochastic gravitational wave (GW) background resulting from the strong first-order phase transition (SFOPT) associated with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:msub><a:mo stretchy="false">)</a:mo><a:mi>R</a:mi></a:msub><a:mo>×</a:mo><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:msub><a:mo stretchy="false">)</a:mo><a:mrow><a:mi>B</a:mi><a:mo>−</a:mo><a:mi>L</a:mi></a:mrow></a:msub></a:math>-breaking in the doublet left-right symmetric model (DLRSM). For different values of the symmetry-breaking scale <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>v</g:mi><g:mi>R</g:mi></g:msub><g:mo>=</g:mo><g:mn>20</g:mn></g:math>, 30, and 50 TeV, we construct the one-loop finite temperature effective potential to explore the parameter space for regions showing SFOPT. We identify the region where the associated GW background is strong enough to be detected at planned GW observatories. A strong GW signature favors a relatively light <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>C</i:mi><i:mi>P</i:mi></i:math>-even neutral scalar <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>H</k:mi><k:mn>3</k:mn></k:msub></k:math>, arising from the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>S</m:mi><m:mi>U</m:mi><m:mo stretchy="false">(</m:mo><m:mn>2</m:mn><m:msub><m:mo stretchy="false">)</m:mo><m:mi>R</m:mi></m:msub></m:math> doublet. The <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>S</q:mi><q:mi>U</q:mi><q:mo stretchy="false">(</q:mo><q:mn>2</q:mn><q:msub><q:mo stretchy="false">)</q:mo><q:mi>L</q:mi></q:msub></q:math> subgroup of DLRSM is broken by three vacuum expectation values: <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:msub><u:mrow><u:mi>κ</u:mi></u:mrow><u:mrow><u:mn>1</u:mn></u:mrow></u:msub></u:mrow></u:math>, <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mrow><w:msub><w:mrow><w:mi>κ</w:mi></w:mrow><w:mrow><w:mn>2</w:mn></w:mrow></w:msub></w:mrow></w:math>, and <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>v</y:mi><y:mi>L</y:mi></y:msub></y:math>. We observe a preference for <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi mathvariant="script">O</ab:mi><ab:mo stretchy="false">(</ab:mo><ab:mn>1</ab:mn><ab:mo stretchy="false">)</ab:mo></ab:math> values of the ratio <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mi>w</fb:mi><fb:mo>=</fb:mo><fb:msub><fb:mi>v</fb:mi><fb:mi>L</fb:mi></fb:msub><fb:mo>/</fb:mo><fb:msub><fb:mi>κ</fb:mi><fb:mn>1</fb:mn></fb:msub></fb:math>, but no clear preference for the ratio <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mi>r</hb:mi><hb:mo>=</hb:mo><hb:msub><hb:mi>κ</hb:mi><hb:mn>2</hb:mn></hb:msub><hb:mo>/</hb:mo><hb:msub><hb:mi>κ</hb:mi><hb:mn>1</hb:mn></hb:msub></hb:math>. A large number of points with strong GW signal can be ruled out from precise measurement of the trilinear Higgs coupling and searches for <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:msub><jb:mi>H</jb:mi><jb:mn>3</jb:mn></jb:msub></jb:math> at the future colliders.