Partial compositeness: From anarchy to symmetry

Within the composite Higgs paradigm, partial compositeness has emerged as an elegant mechanism for generating large flavor hierarchies such as are observed in the quark and lepton masses and mixings. This mechanism exploits the strong renormalization group effects of the compositeness dynamics when these are flavor symmetric. Despite its remarkable properties, at this point it is stringently constrained by the body of flavor- and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>C</a:mi> <a:mi>P</a:mi> </a:mrow> </a:math> -violation tests, so that the compositeness scale must be at least <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>O</c:mi> <c:mo stretchy="false">(</c:mo> <c:mn>100</c:mn> <c:mo stretchy="false">)</c:mo> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:mi>TeV</c:mi> </c:math> , beyond the direct reach of proposed colliders. On the other hand, composite Higgs theories with flavor-symmetric strong dynamics, but with realistic flavor-violating hierarchies introduced in an manner, can extend the Glashow–Iliopoulos–Maiani mechanism of the standard model and thereby be far less constrained, at the edge of LHC reach and well within reach of future colliders. We show how the best features of both of these types of dynamics can be combined if flavor symmetries of the strong composite dynamics are emergent in the IR near the compositeness scale but absent in the far UV. In this case, flavor hierarchies can be generated by the renormalization group flow in the UV, followed by an IR stage in which the dynamics flows towards accidental flavor and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>C</g:mi> <g:mi>P</g:mi> </g:math> symmetries. We point out how the collider and low-energy phenomenology is significantly impacted by the IR stage. Our analysis includes a discussion of the distinctive features of the small neutrino masses and their large mixings.