Theoretical Constraints on the Higgs Effective Couplings
Ian Low, Riccardo Rattazzi, Alessandro Vichi
TL;DR
The paper investigates theoretical constraints on Higgs effective couplings within the SILH framework, focusing on four dimension-six operators ${\cal O}_H$, ${\cal O}_y$, ${\cal O}_g$, and ${\cal O}_\gamma$. It analyzes how naturalness, global symmetries, and unitarity constrain the signs of their coefficients $c_H$, $c_y$, $c_g$, and $c_\gamma$ across fundamental and composite Higgs scenarios, including little Higgs and holographic models. A key result is the general positivity of $c_H$ (with certain triplet-scalar exceptions) and the consistent reduction of gluon-fusion Higgs production in composite Higgs models, linked to cancellations of the Higgs quadratic divergence by heavy top partners. The work emphasizes that precision Higgs-coupling measurements at the LHC and future colliders can illuminate the underlying electroweak-breaking dynamics and the naturalness of the Higgs sector.
Abstract
We derive constraints on the sign of couplings in an effective Higgs Lagrangian using prime principles such as the naturalness principle, global symmetries, and unitarity. Specifically, we study four dimension-six operators, O_H, O_y, O_g, and O_gamma, which contribute to the production and decay of the Higgs boson at the Large Hadron Collider (LHC), among other things. Assuming the Higgs is a fundamental scalar, we find: 1) the coefficient of O_H is positive except when there are triplet scalars, resulting in a reduction in the Higgs on-shell coupling from their standard model (SM) expectations if no other operators contribute, 2) the linear combination of O_H and O_y controlling the overall Higgs coupling to fermion is always reduced, 3) the sign of O_g induced by a new colored fermion is such that it interferes destructively with the SM top contribution in the gluon fusion production of the Higgs, if the new fermion cancels the top quadratic divergence in the Higgs mass, and 4) the correlation between naturalness and the sign of O_gamma is similar to that of O_g, when there is a new set of heavy electroweak gauge bosons. Next considering a composite scalar for the Higgs, we find the reduction in the on-shell Higgs couplings persists. If further assuming a collective breaking mechanism as in little Higgs theories, the coefficient of O_H remains positive even in the presence of triplet scalars. In the end, we conclude that the gluon fusion production of the Higgs boson is reduced from the SM rate in all composite Higgs models. Our study suggests a wealth of information could be revealed by precise measurements of the Higgs couplings, providing strong motivations for both improving on measurements at the LHC and building a precision machine such as the linear collider.