Lattice investigations of the chimera baryon spectrum in the Sp(4) gauge theory

We report the results of lattice numerical studies of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>S</a:mi><a:mi>p</a:mi><a:mo stretchy="false">(</a:mo><a:mn>4</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math> gauge theory coupled to fermions (hyperquarks) transforming in the fundamental and two-index antisymmetric representations of the gauge group. This strongly coupled theory is the minimal candidate for the ultraviolet completion of composite Higgs models that facilitate the mechanism of partial compositeness for generating the top-quark mass. We measure the spectrum of the low-lying, half-integer spin, bound states composed of two fundamental and one antisymmetric hyperquarks, dubbed chimera baryons, in the quenched approximation. In this first systematic, nonperturbative study, we focus on the three lightest parity-even chimera-baryon states, in analogy with QCD, denoted as <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi mathvariant="normal">Λ</e:mi><e:mrow><e:mi>CB</e:mi></e:mrow></e:msub></e:math>, <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi mathvariant="normal">Σ</h:mi><h:mrow><h:mi>CB</h:mi></h:mrow></h:msub></h:math> (both with spin <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mn>1</k:mn><k:mo>/</k:mo><k:mn>2</k:mn></k:math>), and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msubsup><m:mrow><m:mi mathvariant="normal">Σ</m:mi></m:mrow><m:mrow><m:mi>CB</m:mi></m:mrow><m:mrow><m:mo>*</m:mo></m:mrow></m:msubsup></m:mrow></m:math> (with spin <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mn>3</p:mn><p:mo>/</p:mo><p:mn>2</p:mn></p:math>). The spin-<r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mn>1</r:mn><r:mo>/</r:mo><r:mn>2</r:mn></r:math> such states are candidates of the top partners. The extrapolation of our results to the continuum and massless-hyperquark limit is performed using formulas inspired by QCD heavy-baryon Wilson chiral perturbation theory. Within the range of hyperquark masses in our simulations, we find that <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msub><t:mi mathvariant="normal">Σ</t:mi><t:mi>CB</t:mi></t:msub></t:math> is not heavier than <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi mathvariant="normal">Λ</w:mi><w:mi>CB</w:mi></w:msub></w:math>.