[Paper Review] Triple Higgs Boson Coupling in Gauge-Higgs Unification

Yuki Adachi, Nobuhito Maru|arXiv (Cornell University)|Sep 8, 2018

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper investigates the triple Higgs boson coupling in a five-dimensional $SU(3)\times U(1)_X$ gauge-Higgs unification (GHU) model, where the Higgs potential arises from quantum corrections and exhibits periodicity due to higher-dimensional gauge symmetry. The authors compute the coupling and find a 70% deviation from the Standard Model prediction, arising from the non-linear, periodic structure of the Higgs potential despite matching the SM Higgs mass and vacuum expectation value.

ABSTRACT

We consider the triple coupling of the Higgs boson in the context of the gauge-Higgs unification scenario. We show that the triple coupling of the Higgs boson in this scenario generically deviates from SM prediction since the Higgs potential in this scenario has a periodicity. We calculate the coupling in the five-dimensional $SU(3)$ x $U(1)_X$ gauge-Higgs unification model and obtain 70% deviation from the SM prediction.

Motivation & Objective

• To investigate the triple Higgs boson coupling $\lambda_{hhh}$ in the gauge-Higgs unification (GHU) scenario, where the Higgs arises as a component of a higher-dimensional gauge field.
• To analyze how the periodic structure of the Higgs potential in GHU—resulting from compactified extra dimensions—leads to deviations from the Standard Model (SM) prediction for $\lambda_{hhh}$.
• To compute the triple coupling in a specific $SU(3)\times U(1)_X$ GHU model with brane-localized third-generation quarks and bulk fermions, including messenger and mirror fermions.
• To determine whether the observed Higgs boson mass and vacuum expectation value (VEV) in the SM can be reproduced while generating a significant deviation in $\lambda_{hhh}$.

Proposed method

• The Higgs potential is derived from one-loop quantum corrections in a five-dimensional $SU(3)\times U(1)_X$ gauge theory compactified on an $S^1/Z_2$ orbifold with radius $R$, leading to a periodic potential $V(H) = -\sum_{n,k} a_k(n) \cos(\pi R n k H)$.
• The Higgs mass and triple coupling are computed as second and third derivatives of the potential at the vacuum: $m_h^2 = \partial^2 V / \partial H^2|_{H=v}$ and $\lambda_{hhh}^{\text{GHU}} = \partial^3 V / \partial H^3|_{H=v}$, respectively.
• The coefficients $a_k(n)$ are calculated from loop contributions of gauge bosons, massless fermions, and bulk fermions with $Z_2$-odd masses, with $a_k(n) \propto 1/n^5$ or $1/n^5 \cdot e^{-\pi R M n}$.
• The vacuum expectation value $v$ is determined by solving the stationary condition $\partial V / \partial H|_{H=v} = 0$, which involves a sum over Kaluza-Klein modes.
• The deviation from the SM prediction is quantified as $\Delta\lambda_3 = \lambda_{hhh}^{\text{GHU}} - 3m_h^2 / v$, with the dominant contribution arising from large representations ($k=4$) in the fermion sector.
• The infinite sum over Kaluza-Klein modes is approximated by the leading terms, yielding $\Delta\lambda_3 \sim -\sum_k (10^{-1} \pi k)^3 (10^{-1} M_{\text{KK}})$, where $M_{\text{KK}} = 1/R$ is the Kaluza-Klein scale.

Experimental results

Research questions

• RQ1 Does the periodic Higgs potential in gauge-Higgs unification lead to a deviation in the triple Higgs boson coupling compared to the Standard Model?
• RQ2 Can a 5D $SU(3)\times U(1)_X$ GHU model reproduce the observed Higgs boson mass and vacuum expectation value while generating a significant deviation in $\lambda_{hhh}$?
• RQ3 What is the magnitude of the deviation in $\lambda_{hhh}$ in this specific GHU model, and what determines its size?
• RQ4 How do the contributions from different Kaluza-Klein modes and fermion representations affect the triple coupling?
• RQ5 Is the deviation robust against accidental cancellations, and what role does the KK scale play in determining the size of $\Delta\lambda_3$?

Key findings

• The triple Higgs boson coupling in the GHU scenario deviates significantly from the SM prediction due to the periodic structure of the Higgs potential, which breaks the SM relation $\lambda_{hhh} = 3m_h^2 / v$.
• In the $SU(3)\times U(1)_X$ GHU model with brane-localized third-generation quarks and bulk messenger/mirror fermions, the triple coupling deviates by 70% from the SM prediction.
• The deviation arises because the Higgs potential is a sum of cosine terms with periodicity $V(H + 2/R) = V(H)$, leading to a non-linear dependence of $\lambda_{hhh}$ on the Higgs VEV, unlike the linear SM Yukawa couplings.
• The dominant contribution to the deviation comes from fermions in the $\overline{\mathbf{15}}$ representation ($k=4$), which enhance the coupling due to their large representation dimension.
• The size of the deviation is estimated as $\mathcal{O}(1)$ times the weak scale, with the KK scale $M_{\text{KK}} \sim \text{TeV}$ playing a key role in the magnitude of $\Delta\lambda_3$.
• The result is consistent with other models where higher-dimensional non-renormalizable terms lead to similar deviations (~60%), suggesting robustness of the effect in GHU frameworks.