Composite quarks and leptons with embedded QCD

We construct a model of quark and lepton compositeness based on an <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>15</a:mn><a:mo stretchy="false">)</a:mo></a:math> gauge interaction that confines chiral preons, which are also charged under the weakly coupled <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>4</e:mn><e:msub><e:mo stretchy="false">)</e:mo><e:mrow><e:mi>PS</e:mi></e:mrow></e:msub><e:mo>×</e:mo><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>2</e:mn><e:msub><e:mo stretchy="false">)</e:mo><e:mi>L</e:mi></e:msub><e:mo>×</e:mo><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>2</e:mn><e:msub><e:mo stretchy="false">)</e:mo><e:mi>R</e:mi></e:msub></e:math> gauge group. The breaking of the latter, down to the Standard Model group, is achieved by scalar <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>15</m:mn><m:mo stretchy="false">)</m:mo></m:math> bound states at a scale in the 30–100 TeV range. The embedding of the QCD gauge group in <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>4</q:mn><q:msub><q:mo stretchy="false">)</q:mo><q:mrow><q:mi>PS</q:mi></q:mrow></q:msub></q:math> slows down the running of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>α</u:mi><u:mi>s</u:mi></u:msub></u:math> in the UV. We estimate the effects of the strongly coupled <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>S</w:mi><w:mi>U</w:mi><w:mo stretchy="false">(</w:mo><w:mn>15</w:mn><w:mo stretchy="false">)</w:mo></w:math> dynamics on the running of the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>S</ab:mi><ab:mi>U</ab:mi><ab:mo stretchy="false">(</ab:mo><ab:mn>4</ab:mn><ab:msub><ab:mo stretchy="false">)</ab:mo><ab:mrow><ab:mi>PS</ab:mi></ab:mrow></ab:msub><ab:mo>×</ab:mo><ab:mi>S</ab:mi><ab:mi>U</ab:mi><ab:mo stretchy="false">(</ab:mo><ab:mn>2</ab:mn><ab:msub><ab:mo stretchy="false">)</ab:mo><ab:mi>L</ab:mi></ab:msub><ab:mo>×</ab:mo><ab:mi>S</ab:mi><ab:mi>U</ab:mi><ab:mo stretchy="false">(</ab:mo><ab:mn>2</ab:mn><ab:msub><ab:mo stretchy="false">)</ab:mo><ab:mi>R</ab:mi></ab:msub></ab:math> gauge couplings, which likely remain perturbative beyond the compositeness scale of about <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mrow><ib:msup><ib:mrow><ib:mn>10</ib:mn></ib:mrow><ib:mrow><ib:mn>3</ib:mn></ib:mrow></ib:msup><ib:mi>–</ib:mi><ib:msup><ib:mrow><ib:mn>10</ib:mn></ib:mrow><ib:mrow><ib:mn>4</ib:mn></ib:mrow></ib:msup><ib:mtext> </ib:mtext><ib:mtext> </ib:mtext><ib:mi>TeV</ib:mi></ib:mrow></ib:math>, and even above a unification scale. A composite vectorlike lepton doublet acquires a mass in the TeV range probed at future colliders, and an extended Higgs sector arises from six-preon bound states.