A Higgs-Higgs bound state due to New Physics at a TeV

TL;DR

This work investigates how TeV-scale new physics can modify the Higgs sector via dimension-6 operators, potentially yielding strong Higgs self-interactions even for a relatively light Higgs with $m_h \lesssim 2 m_t$. It constructs both linear and non-linear Higgs effective field theories and a low-energy topless EFT by integrating out the top quark, then develops a non-relativistic Higgs effective theory (NRHET) to study possible bound states of two Higgs bosons (Higgsium). The authors derive how the D=6 operators shift the Higgs self-couplings to $\lambda_3^{eff}$ and $\lambda_4^{eff}$, modify gluon-fusion production and di-Higgs processes, and determine NRHET matching coefficients $C_{NR}$ for linear and non-linear realizations. They show that Higgsium is readily realizable in the non-linear realization for TeV-scale new physics and provide criteria for bound-state formation and formation/decay times, suggesting that a di-Higgs bound state would offer a direct probe of the new physics scale ${\mathcal M}$. The results highlight di-Higgs production and bound-state phenomena as promising avenues to explore beyond-Standard-Model dynamics at the TeV scale.

Abstract

We examine the effects of new physics effecting the Higgs sector of the standard model, focusing on the effects on the Higgs self couplings. We demonstrate that a low mass higgs, m_h < 2 m_t, can have a strong effective self coupling due to the effects of a new interaction at a TeV. We investigate the possibility that the first evidence of such an interaction could be a higgs-higgs bound state. To this end, we construct an effective field theory formalism to examine the physics of such a low mass higgs boson. We explore the possibility of a non relativistic bound state of the higgs field (Higgsium) at LHC and construct a non relativistic effective field theory of the higgs sector that is appropriate for such studies (NRHET).

Figures (10)

• Figure 1: Integrating out the top quark.
• Figure 2: The gluon fusion $g \, g \to h$ production process. The production process through the effective local operators in shown in the second column. The effective local operators come from integrating out the top quark and new physics at $\mathcal{M}$.
• Figure 3: The gluon fusion $g \, g \to h \, h$ production process and the effective local operators.
• Figure 4: The two higgs production process in the effective theory.
• Figure 5: Tree level $h \, h \to h \, h$ scattering in the extended higgs theory. Time flows left to right.